consilience our bodies our souls

CONSILIENCE OUR BODIES OUR SOULS Janina Marciak-Kozlowska Institute of Electron Technology, Warsaw, Poland Mirosław Kozłowski Warsaw University, Warsaw, Poland

Contents 1.On the Evolution of the Universe Towards Consciousness………3 2.On Psychon in Quantum of Consciousness……………… ……. 19 3.Exploration on Plausible Tumor Conscious Waves………………26 4. Consciousness of a Moving Human with Velocity Approaching Speed of Light………………………………………………………………….37 5. Quantum Model of Consciousness…………………………………45 6. Human Brain and Cosmos………………………………………….62 7.On the Interaction of the Schumann Waves with Human Brain……68 8. New Schrodinger Equation with Consciousness Term……………76 9.Binding Energy of the Human Brain……………………………….86 10.Consciousness and Biological Dark Matter……………………….95 11. Human Consciousness: Fifth Force…………………………… .103 12. On the Aeons and Consciousness………………………………..111 13.Klein-Gordom Equation for Consciousness Schumann Fields…..121 14.Homo divinus and the Moon……………………………………..127 15.Human Consciousness and Bohm`s Pilot Wave……………… .137 16. Explorations on the Released of Human Brain Energy at the End of Human Earth Life……………………………………………………143 17.Consciousness,Alpha and Omega Points……… ………………147 18. Ethanol Treatment of Cancer and Model of Cancer Growth Wave ( ‘Consciousness”)…………………………………………………..165 19. Gestalt Principle in the Design of Human Brain………… ……177

20. Human Radiance………………………………………………..186 21.Hidden Order…………………………………………………….190 22.How Nonlocal is Consciousness………………………………..199 23.The Quantum Process of Consciousness………………………..202 24.The Seeds of Quantum Mechanics………………………………222 25. On Cancer Tumor Consciousness waves…………… …………232 26 Sacred Number and Consciousness……………………………..245 27.Feynman Approach to Brain Wave Emission Process………….250 28. Ultra High Energy Psychons……………………………………… 253.

Overview of the research

Our monograph is devoted to the study on new paradigm in science Consilience. Consilience refers to the principle that evidence from unrelated sources, especially science and the humanities, can converge and produce unified conclusions. Among the topics contributing to this consilience:      

Nonlocality across space and time (e.g., action at a distance; resonant bonding, retrocausation, precognition) Extended consciousness Survival of consciousness Synchronicity and teleological effects The role of information and meaning Mind interacting with matter

All those problems are discussed in the book. In the light of consilience the consciousness can be investigated only by the inspecting its physics, philosophy and biological aspects In the book the mathematical framework for consilience study of consciousness is presented. The new partial differential equation is developed and solved. It is schown how to quantise information field absorbed and emitted by human mind

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Journal of Consciousness Exploration & Research | October 2016 | Volume 7 | Issue 9 | pp. 723-738 Kozlowski, M., On the Evolution of the Universe towards Consciousness

Exploration

On the Evolution of the Universe towards Consciousness Miroslaw Kozlowski

*

Warsaw University, Warsaw, Poland

Abstract The continuing evolution of observational consciousness is the greatest single fact of our time. In this paper, we develop the model for evolution of Universe towards full consciousness. We assume that excess temperature of the brain emitted waves is the temperature of Consciousness towards which the Universe is tending, T= 10-15eV. From the different scenario of the Universe lifetime, we take as granted the evolving Universe according to which the last state of the Universe is the Consciousness alone with temperature T=10-15 eV. Keywords: Observational consciousness, Universe, evolution, brain temperature.

1. Introduction All possible computations mathematically exist (or will exist) as mathematical systems. What can a “physical existence” of a world where a computation “happens”, bring to it above other computations? All their elementary steps anyway repeatedly happen many times in any “physically existing” or “non-existing” universe. A specific universe has a specific series of operations “happening together at a place” with the mathematical property of representing a specific global computation, but then what? How could a melody exist, not just as a succession of sounds but indeed as a melody, without somebody to hear it? How can a thought exist, not just as a mathematical property of brain computation but as feeling something, without the fundamental addition of an immaterial soul inside the brain to actually feel what the brain is computing? No concept of “physical existence” given to a universe “on a fundamental level”, can add anything to its emergent (non-fundamental) mathematical structures of brain computation to make them “exist” any more than similar structures “happening” in physically non-existing (but mathematically existing) universes. As we shall see, the conscious perception of mathematical structures can explain and constitute their “physical 2 existence”, instead of the other way round. Consciousness can explore mathematics, but mathematics cannot describe consciousness. While mathematical reality is analytic (systems are divisible into parts, down to mute elements), consciousness is fundamentally synthetic (its divisions can only be approximations). Conscious events are subject to time order, which is their order of relative existence: an event A “coming before” an event B is an event that exists inside B (in memory, even if it may be hard to retrieve). In other words, past events exist but future events are not determined yet. * Correspondence: Miroslaw Kozlowski, Prof. Emeritus, Warsaw University, Poland. Email: [email protected] ISSN: 2153-8212

Journal of Consciousness Exploration & Research Published by QuantumDream, Inc.

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Consciousness happens to be approximately split as a multitude of individual minds that coexist “somewhere deeply inside” each other, in a common Matrix (God), like individual physical objects may be said to coexist in a common physical space from which they cannot be dissociated.

2. General Considerations Observational Consciousness Everything we have discussed to this point takes place in a single perceptual consciousness: yours or mine. There is only one. Your consciousness is not in mine, nor mine in yours. We have removed consciousness from a dimensional context, and thereby removed the possibility for relating one consciousness to another. If it does not exist in space and time, where would another consciousness be? But if there is no more than one, whose consciousness do we mean by "perceptual," yours or mine? One answer is to declare that if there can be only one consciousness, it must be mine. I have no way of knowing that "you" really exist at all. You move around and talk and jump back when you touch a hot iron, the same sorts of things I do, but this does not mean that you see and hear and feel; it only means that he Observational Realm To begin with, we will have to show that there is a distinct physical difference between observation and perception. Perception is what I see myself, while observation is what I hear you telling me about what you see. (You may be the "I," and I the "you," from your standpoint.) Socially, morally, culturally, these two are equal; we have been trained since early childhood to accept the experience of others as equivalent to our own. But physically, they are different. What I see consists of photons, while what you are telling me you see consists of words. Perceptions and observations are entirely different physical phenomena, even if they concern the same object. My experience and yours become physically equivalent only when I translate my perceptual experience into observational experience, through the use of words or other symbols. Perception is experienced in the sensory realms, while observation is experienced in its own separate realm, even though the information of which it consists is experienced in the sensory realms. In other words, I hear what you are telling me through the auditory realm, or see what you have written in the visual realm, but what I am experiencing is more than sound or light. I am experiencing your experience through a medium based in sensory perception. Observational experience is something entirely distinct from perception, but it is at the same time reducible to perception. All I am actually perceiving are visions and sounds, even though I am experiencing much more. The sensory reduction of observational experience to sound or light (or even touch) is similar to the tactile reduction of sound and light themselves. This has important consequences for the manner in which the observational realm, and observers, are experienced. Observational experience is coordinated with perceptual experience in the same way that the perceptual realms ISSN: 2153-8212


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are coordinated with each other: through dimensional potentials. In perceptual consciousness, actual experience in any realm is accompanied by potential perception in every other realm. Where I see an object is where 1 may hear or touch it. Observational consciousness works the same way; your description of an object's location is exactly the same as my potential perception of the same object. Even if I am in the next room and you are looking at the object and describing it to me, I can perceive it (whether I actually do or not) at the location you describe. There is, therefore, a dimensional coordination of observational with the whole of perceptual consciousness. Observation is potential perception. The dimensional coordination of observation with perception is a manifestation of the same structure of consciousness as we have already found among the five sensory realms. This explains why the concept of matter tends to be reinforced by observational experience. In the same way that matter is assumed to cause seeing, hearing, and touching, matter simultaneously "causes" you and me to see the same thing at the same place and time. Matter serves to explain potential perception among observers in the same way that it explains it among the senses. But, as we have shown matter to be a limited and unnecessary assumption for perceptual experience, it is likewise unnecessary for observational experience. In the process of eliminating matter we have discovered a structure of consciousness that explains both perception and observation without having to introduce separate metaphysical assumptions for each. In fact, we are able to do away with the troublesome assumption that consciousness has to exist inside of observers. If observation can be shown to be another realm of consciousness similar in structure to the perceptual realms, it does not need to exist inside of me or of you or of anything else. It just is. Observers are manifest in space-time not because they have consciousness "in" them, but because observational information is reducible to sensory experience, of which space-time-mass is the context. What is perceived in the form of observers in space-time-mass is the projection of a six-dimensional pattern onto five dimensions. The sixth dimension (that which corresponds to the observational realm) appears foreshortened in five dimensions the way the fifth dimension appears foreshortened in four. Random non-uniform acceleration is the potential for observational experience. The increase of entropy throughout the universe with the passage of time as implied in the second law of thermodynamics provides the background for experiencing observational information. Orderly non-uniform acceleration is actual observational experience. Orderly motion and communication from observers is discernible only because there is a tendency toward disorder everywhere else. Actual observational experience is science; science, therefore, consists of patterns in six dimensions. As we will see, it is the perspective of the observer himself, as he describes five dimensional patterns that he perceives, that is the dimensional factor added to space-time-mass. But if non-uniform acceleration really indicates a dimension, how do we measure it? We can measure time, space, and mass; how about measuring "order?" What units shall we use? Here we may have run into trouble; non-uniform acceleration is by nature indeterminate. It cannot be measured, and an observer's behavior within it cannot be predicted. You can measure an observer's length, width, velocity, acceleration, and mass, but you cannot say how he, she, or it, will change acceleration. You can measure the energy he uses to accelerate, but you cannot ISSN: 2153-8212


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determine the "curvature" he gives it. (The "curvature" of energy may be either in the form of "work" or of "information.") Measurement is limited to the five perceptual dimensions. Even within these, complete measurement is limited to the macroscopic level, according to the Heisenberg uncertainty principle. Is there a connection, then, between quantum indeterminacy in five dimensions and macroscopic indeterminacy in six? Quantum indeterminacy, we have seen, is due to the tactile reduction of light. Might not macroscopic indeterminacy be due to the sensory reduction of observational experience? On the quantum level, the perceptual realms and their corresponding dimensions are indistinguishable; on the macroscopic level, words are experienced both as sound and symbol, or in two separate realms at once. Therefore the dimensions corresponding to each are neither qualitatively distinct nor quantitatively measurable. The indeterminate behavior of macroscopic observers is in many ways similar to that of subatomic particles. Each reveals the dimensional structure of consciousness at a different level. Another similarity between subatomic particles and observers is that the behavior of each becomes increasingly determinate in the aggregate. We can know very little about where an electron will go from one moment to the next, but if we have several trillion of them in a copper wire, we can predict with great accuracy how many will move how far. We cannot know which ones will move and which not, only their average behavior. Similarly, we can say next to nothing about where one man on the street might be going, but we can predict with considerable accuracy how many people will go to the druggist or to the pet store on a given day. We have no way of knowing who they will be, but they will show up without fail, nevertheless. Marketing analysts bet good money on it every day. As with subatomic particles, the greater the number of observers, the higher the predictability of aggregate behavior there is. A major difference between subatomic particles and observers is that all observers are different while all electrons, protons, etc. are identical. You can tell one man on the street from the next by his looks, his dress, and how he walks, but you cannot tell one pi meson from another; they all "look" and "tend to act" alike. But in making this statement, we should realize where we are looking from. We are looking at both the man on the street and the pi meson from the standpoint of macroscopic sensory experience. All pi mesons may look alike due to the structural limitations of the space, time, and mass dimensions with which we attempt to view and measure them, that is, due to the structural limitations of the quantum screen. If we were to view them from the standpoint of their fellows (don't ask me how), rather than "from above," they might each display a unique personality. (There is certainly room for inherent uniqueness within the uncertainty relation.) If we view observers "from above," or from the standpoint of observational consciousness rather than from perceptual consciousness, they would all look alike! We would know nothing of their faces or clothing, only what they said they were perceiving. If they were good observers, they would say they were all seeing the same thing from different perspectives. (We would have to dismiss the liars, bigots, and charlatans, of course, but that is just what science is supposed to do.) Real observers, as observers, are all identical, even if some of them wear pink socks and some green. From the standpoint of observational consciousness, we can even predict the behavior of individual observers in terms of probability relations the same way we do for a subatomic ISSN: 2153-8212


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particle from the standpoint of perceptual consciousness. We cannot say for sure what a certain man on the street will do today, but our marketing people can tell us how many people buy red ties in New York City on a given day, and as there are 7,628,406 consumers in that market, the particular man we are concerned with has one chance in 5334.55 of buying a red tie today. That is his "wave function." The limitations of a physical definition of life are in physics, not in life. We have already seen that the dimensional structure of consciousness is limited to macroscopic dimensions. It works well in everyday life, in the middle latitudes of space-time-mass. Reality also exists at dimensional extremes, but appears on the screen only in distorted form. Similarly, the quantum screen presents only a limited view of life. The dimension of life is not a space dimension, and appears on the screen only in foreshortened form, the way a third space dimension appears on a flat surface, or motion appears on a still picture. The identity of non- living objects is easy to establish through perception because three dimensions appear at the same time. (Only mass and time must be established by more than one space-time perception.) The identity of living objects, however, requires a more complex and tenuous association of informational patterns. Observational consciousness, or the life that appears to be "in" observers, is a separate and distinct realm of consciousness and cannot ultimately be understood within perceptual consciousness. It appears on the quantum screen only in "flattened" form. Trying to see or hear life is very much like a single cell trying to "feel" sound or light. Life in observers can be experienced only when experience is not limited to perception.

Evolution of Observational Consciousness We are aware of observational information through the senses, but how do we add yet another dimension to the quantum screen? Observation encompasses all perceptual realms in potential form. At every point on the screen where there is an observer there is a "potential screen." When an observer says he sees an object, he is at the point on the quantum screen where we see him and hear the sound of his voice. When another observer tells us about the same object from his perspective, he is on the screen also. Each observer (reports that he) sees the same thing; the only difference between any two observers is perspective. Observational consciousness arises when the location of the object is revealed to be the same for each observer once his perspective is factored out. You or I can, of course, see for ourselves if the object is there in actual perception (itself on the screen where the observers say it is), but we rarely do. For the most part, we rely on the honesty of observers, especially if there are a large number of them. It is difficult to lie in the aggregate. Perspective is essential to the meaning of observational information and constitutes the dimensional factor between perception and observation. The same physical object is observed from any point in space-time-mass but appears different from different perspectives. When perspective is factored out, an additional dimension is imposed on perception and it becomes observation. It is only with this additional dimension that the object is the same for all observers, and only by this means that five-dimensional objects become science.

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But what is the relationship between observational consciousness and the quantum screen, our model for perceptual consciousness? Every observer appears on the quantum screen as a point (or range of points), much as do other physical objects. But where physical objects are fivedimensional, observers are six-dimensional; they are capable of orderly non-uniform acceleration in the form of information or motion. They move on the screen as if they perceived objects around them, and we consider them to be "alive." They are alive, but they do not have actual perceptual consciousness "in" them—that is the screen itself, and there is only one screen. As an observer describes what he perceives, he becomes a "potential screen." He is himself perceived directly on the actual quantum screen, but what he tells us becomes a potential quantum screen at the point he occupies in space-time-mass. A case could be made for a sort of six-dimensional super screen based on an extrapolation of the five-dimensional quantum screen analogous to the quantum screen's own basis on an extrapolation of the four-dimensional photon screen. All of observational experience - all of scientific knowledge—could be said to exist at locations on such a screen. But I think this stretches the screen model too far. Where objects directly perceived in space are experienced much the way they are seen on a television or computer screen, objects and experiences described by others are not so easily experienced in the same manner. We tend to "think" of places and events that we are told about, even if we know they are (or were) potentially perceptible. We do not picture them as clearly. There is no model for observational consciousness as powerful as that for perceptual consciousness because observational consciousness is not as powerful a part of our lives. This, however, is changing. There may well come a time when collective experience is more important than individual experience. A question remains. If observation corresponds to an additional dimension, why is it that some physical phenomena manifest this dimension and others do not? Why do six-dimensional observers exist alongside five-dimensional objects in the same physical world? As we suggested earlier, the application of the structure of light to other realms of perceptual consciousness is most likely due to the fact that vision developed relatively late in evolutionary terms and because "bits" of visual information (photons) are much smaller than the bits of which other sensory information is composed. We can, therefore, understand hearing in terms of potential photons, rather than the other way around. But what if both of these conditions did not apply? What if a new realm of consciousness were to develop whose "bits" were larger than those of existing realms? As the new bits would not be able to constitute a new universal medium, they would have to be projected, in a higher dimensional form, onto the old universal medium. This, I believe, is what is happening with the observational realm. Bits of observational information are the letters and sounds and symbols by which observers communicate; they are all considerably larger than photons. As an example, the tiny lights on a television screen are each composed of many millions of photons. We experience observational information, therefore, as foreshortened six-dimensional forms projected onto the quantum screen along with five-dimensional perceptual objects.

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As human civilization evolves, direct perceptual experience becomes less a part of consciousness as a whole. We learn more about the world through other people, and observational experience becomes increasingly important. We talk, read books, watch movies, and gain information through electronic technology. We use the telephone, listen to radio, and watch the world on television. Observers become more important than objects. Experience through others becomes less distant; potential perception becomes a form of actual experience. You or I do not have to be there to experience what is happening in the world. We experience Asia, Africa, and the far side of the moon without ever perceiving it. Individual experience becomes more and more absorbed in collective experience: the perspective of actual perception is factored out along with that of potential perception. The quantum screen appears more and more like a point on a sixdimensional matrix. We each see ourselves individually as small parts of a greater collective whole. Media such as books, magazines, newspapers, telephones, television, and radio promote the evolution of observational consciousness. Particularly interesting among these is television. I am thinking here not of television programming, but of television as a medium. What we experience on a television screen is what we would see if our eyes were where the camera is. But television is different from other observational media in that it utilizes light, the universal medium of perceptual consciousness. This means that we experience directly what is happening on the screen; there is no need to "envision" a situation on the quantum screen, as is necessary with the print or radio media. Points of light constitute images on a television screen in the same way that photons constitute images on the retina; observation becomes perception. Every other communications medium requires a conceptual operation for factoring out perspective; we have to think of a human writer or radio announcer in a space-time setting in order to appreciate what he or she observes. But television images need not be factored at all. Television information is not processed by an observer: in fact, there is no observer. Observation is experienced directly; everyone watching a live television broadcast experiences the same images, from the same perspective, at the same time. There is among televiewers, therefore, not only common experience, but common perspective. The advent of television brings more "wholeness" to observational consciousness than any other medium. The continuing evolution of observational consciousness is the greatest single fact of our time. Scientists are so close to the work they are doing that they rarely appreciate the immense picture they are unveiling little by little. Most remain comfortable with metaphysical assumptions that keep their work going. If they question them at all, they do not question them often. An independently existing material world remains strong among them, however cracked and contorted by new discoveries, because it has for centuries provided them with a durable metaphysical foundation upon which to build their world. To undermine that foundation now may seem meddlesome and potentially destructive to the work going on above. But I do not mean to undermine their work. I hope merely to redo a foundation that has been undermined already and can no longer withstand the weight above it. This can be done, for the most part, without damage to the superstructure. Those working above may feel an occasional tremor, but they need not be disturbed overall. Their immediate surroundings will change very

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little. They may look up one day, though, and find that the entire building no longer stands where it once stood. If there are people standing on the ground wondering what force and acceleration "really" are, they do not impede progress. Science uses operational definitions to keep the job going, even when nobody knows what it is that is going. The building, if well-constructed, will span small gaps in the foundation. It is only with fear of general collapse that workers look down and wonder just what it is that holds them up. If it is new foundation work they need, they will say yes, that it is science, go ahead with it. But to work on the foundation, we must dig away the soil and rock that lies in the way, and examine it, too. We must know more about the ground in order to support the building. Some scientists will say no, that is not part of the building. The work we do and the materials we use are the building; rock and soil are something else. Keep it away from us. We cannot insist, therefore, that the idea presented here is science. It is an interface between science and that part of life that is not science. It behaves like a scientific theory in some ways, but not in others. It is logical, and its scope is wide: it explains a number of diverse physical phenomena that have not been encompassed before by a single, consistent concept. But I am not sure that it is provable, nor that it will lead to new research in the traditional sense. I hope that predictions based on it will one day be proven or disproven, but this may not happen. Scientists will eventually agree that it is right, but they may never be able to "touch" it, the way they can other theories. The scientist working high on the superstructure may never be able to look down and understand the Earth beneath him in terms of the bricks and two-by-fours that he is used to; all I can hope is that he will know where they come from. He may say that philosophy never gets off the ground. I will agree and point out that his building is the ground, in specially structured form. He will say that my insistence that the building does not exist is absurd. I will say that it exists only because he made it. He will say that by lumping science in with thought, imagination, and opinion, I have ruined its unique properties, as if mixing jewels and dirt. I will say that jewels are dirt. His interest is in what he can see and be sure of, in what will get him through the day; he understands life in terms of science. My interest is understanding science in terms of life. Western civilization has built an expanding universe within the human mind. The world of science is human imagination, carefully contained in an explosion of space and time, balanced by mass. Science creates what it discovers. At a small corner and to the side is the life process, a cross section of life itself. The great weakness of science is that it is contained at all and cannot see itself as such. It cannot go outside without getting cold.

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3. The Model A hypothetical neutrino that does not interact through the weak force could be the source of a recently detected x-ray emission line coming from galaxy clusters. However, previous models using this so-called “sterile” neutrino as a form of dark matter were not able to satisfy constraints from cosmological observations. Now, writing in Physical Review Letters, Kevork Abazajian of the University of California ( Kevork N Abazijan,2014), Irvine, shows that a sterile neutrino with a mass of 7 keV could be a viable dark matter candidate that both explains the new x-ray data and solves some long-standing problems in galaxy structure formation. Cosmologists have long considered neutrinos as possible dark matter particles. However, because of their small mass (less than about 1 eV), conventional neutrinos are too fast, or “hot,” to form the dense dark matter structures needed to hold galaxies and galaxy clusters together. By contrast, sterile neutrinos, which result from certain neutrino theories, can have larger masses and could have been naturally produced in the big bang by neutrino flavor mixing. The problem has been that sterile neutrinos should decay, producing an x-ray signal that no one has observed—until maybe now. Earlier in 2014, an analysis of galaxy cluster data revealed an x-ray emission line, which is consistent with the decay of a 7-keV sterile neutrino. Normally, dark matter with this mass would be too “warm” to match galaxy data. Generations of physicists and chemists have studied what happens when you group together vast numbers of atoms, finding that their collective behavior depends on the pattern in which they are arranged: the key difference between a solid, a liquid and a gas lies not in the types of atoms, but in their arrangement. In this paper, we conjecture that consciousness can be understood as yet another state of matter. Just as there are many types of liquids, there are many types of consciousness. However, this should not preclude us from identifying, quantifying, modeling and ultimately understanding the characteristic properties that all liquid forms of matter (or all conscious forms of matter) share. To classify the traditionally studied states of matter, we need to measure only a small number of physical parameters: viscosity, compressibility, electrical conductivity and (optionally) diffusivity. We call a substance a solid if its viscosity is effectively infinite (producing structural stiffness), and call it a fluid otherwise. We call a fluid a liquid if its compressibility and diffusivity are small and otherwise call it either a gas or a plasma, depending on its electrical conductivity. What are the corresponding physical parameters that can help us identify conscious matter, and what are the key physical features that characterize it? If such parameters can be identified, understood and measured, this will help us identify (or at least rule out) consciousness “from the outside”, without access to subjective introspection. This could be important for reaching consensus on many currently controversial topics, ranging from the future of artificial intelligence to determining when an animal, fetus or unresponsive patient can feel pain. If would also be important for fundamental theoretical physics, by allowing us to identify conscious observers in our universe by using the equations of physics and thereby answer thorny observation-related questions ISSN: 2153-8212


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What is the relation between the internal reality of your mind and the external reality described by the equations of physics? The fact that no consensus answer to this question has emerged in the physics community lies at the heart of many of the most hotly debated issues in physics today. For example, how does quantum field theory with weak-field gravity explain the appearance of an approximately classical spacetime where experiments appear to have definite outcomes? Out of all of the possible factorizations of Hilbert space, why is the particular factorization corresponding to classical space so special? Does the quantum wavefunction undergo a non-unitary collapse when an observation is made, or are there Everettian parallel universes? Does the non-observability of spacetime regions beyond horizons imply that they in some sense do not exist independently of the regions that we can observe? If we understood consciousness as a physical phenomenon, we could in principle answer all of these questions by studying the equations of physics: we could identify all conscious entities in any physical system, and calculate what they would perceive. However, this approach is typically not pursued by physicists, with the argument that we do not understand consciousness well enough. We argue that recent progress in neuroscience has fundamentally changed this situation, and that we physicists can no longer blame neuroscientists for our own lack of progress. However, quantum theory does not say anything specific about the nature oi consciousness — the whole issue is clouded by basic uncertainty over even how to define consciousness. A firm grasp of human mental processes still remain very elusive. We believe that this indicates a deeper problem which scientist in general are reluctant to address: Objective science is based on the dichotomy between subject and object; it rests on the implicit assumption that Nature can be studied ad infinitum as an external objective reality. The role of the observer is at best, secondary, if not entirely irrelevant.

4. Consciousness and Quantum Theory The issue of observation in QM is central, in the sense that objective reality cannot be disentangled from the act of observation, as the Copenhagen Interpretation (CI) nearly states. In the words of John A. Wheeler 1981, we live in an observer-participatory Universe. The vast majority of today's practicing physicists follow CI's practical prescriptions for quantum phenomena, while still clinging to classical beliefs in observer-independent local, external reality). There is a critical gap between practice and underlying theory. In his Nobel Prize speech of 1932, Werner Heisenberg concluded that the atom "has no immediate and direct physical properties at all." If the universe's basic building block isn't physical, then the same must hold true in some way for the whole. The universe was doing a vanishing act in Heisenberg's day, and it certainly hasn't become more solid since. (R. Schild, 2012) This discrepancy between practice and theory must be confronted, because the consequences for the nature of reality are far-reaching An impressive body of evidence has been building to suggest that reality is non-local and undivided. Non-locality is already a basic fact of nature, first implied by the Einstein-Podolsky-Rosen thought experiment despite the original intent to refute it, and later explicitly formulated in Bell's Theorem.

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Moreover, this is a reality where the mindful acts of observation play a crucial role at every level. Heisenberg again: "The atoms or elementary particles themselves . . . form a world of potentialities or possibilities rather than one of things or facts." He was led to a radical conclusion that underlies our own view in this paper: "What we observe is not nature itself, but nature exposed to our method of questioning." Reality, it seems, shifts according to the observer's conscious intent. There is no doubt that the original CI was subjective. Quantum theory is not about the nature of reality, even though quantum physicists act as if that is the case. To escape philosophical complications, the original CI was pragmatic: it concerned itself with the epistemology of quantum world (how we experience quantum phenomena), leaving aside ontological questions about the ultimate nature of reality. The practical bent of CI should be kept in mind, particularly as there is a tendency on the part of many good physicists to slip back into issues that cannot be tested and therefore run counter to the basic tenets of scientific methodology. In order to put forward the classical theory of the brain waves we quantize the brain wave field. In the model (Marciak-Kozlowska, Kozlowski, 2013), we assume: (i) (ii)

The brain is the thermal source in local equilibrium with temperature T. The spectrum of the brain waves is quantized according to formula

E  where E is the photon energy in eV ,

(1)

=Planck constant,   2 , -is the frequency in Hz.

(iii). The number of photons emitted by brain is proportional to the (amplitude)2 as for classical waves. The energies of the photons are the maximum values of energies of waves. For the emission of black body brain waves, we propose the well know formula for the black body radiation. In thermodynamics, we consider Planck type formula for probability P (E) dE for the emission of the particle (photons as well as particles with m≠0) with energy (E, E+dE ) by the source with temperature T is equal to: P(E)dE= BE2 e (-E/kT) dE

(2)

where B= normalization constant, E=total energy of the particle, k = Boltzmann constant=1.3 x 10-23 J K-1. K is for Kelvin degree. However in many applications in nuclear and elementary particles physics kT is recalculated in units of energy. To that aim we note that for 1K, kT is equal k1K = K x 1. 3 10-23 J x K-1= 1.3 10-23 Joule or kT for 1K is equivalent to 1.3 10-23 Joule= 1.3 10-23 /(1.6 10-19) eV = 0.8 10-4 eV. Eventually we obtain 1K= 0.8 10-4 eV, and 1eV= 1.2 104 K (  Emax ) dN 2  BEmax e T dE

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where , B is the normalization constant ,T is the temperature of the brain thermal source in eV. The function dN describes the energy spectrum of the emitted brain photons. dE

Until 2014 no one has find the experimental evidence of the cold source of the new brain photons. But recently the new sort of neutrino with the mass of the order 7 keV was experimentally evidenced. The neutrino  decays according to the scheme: (3)   2 where  denotes x ray photons with energy 3.5 keV . In the paper ( Marciak-Kozlowska, Kozlowski, 2013) the comparison of the photon spectra of CBM and the spectra of brain electromagnetic emission was performed. It occurs that both spectra can be described with formula (2), but with different temperatures. The ratio of the temperatures is

Tbrain  1010 TCBM

(4)

Following formula (4), we argue that, in brain spectra, the photons with energy of the order of

1010 3.7103 eV  3.710 7 eV  3.710 3 K

(5)

can be observed. In Fig.1 the calculated energy spectrum, formula (2) is presented. We present the result of the comparison of the calculated and observed spectra of the brain waves. The calculated spectra are normalized to the maximum of the measured spectra. The calculated spectrum is for temperature of brain source T= 0.8 10-14 eV. The obtained temperature is the temperature for the brain source in the thermal equilibrium. The source is thermally isolated (adiabatic well). However in very exceptional cases the spectrum is changed – by the tunneling to the quantum potential well . The temperature 1 eV ≅ 10 4 K then brain wave thermal spectra T=0.8 10-14 eV= 0.8 10-10 K. It must be stressed that in a paper we abandon the idea that every physical object is either a wave or a particle. Neither it is possible to say that particles “become” waves in the quantum domain and conversely that waves are “transformed “into particles. It is therefore necessary to acknowledge that we have here a different kind of an entity , one that is specifically quantum. For this reason Levy-Leblond and Balibar developed the name quanton. Following that idea the human brain emits quantons with energies E   .The brain quantons are the quantum objects that follows all quantum laws: tunneling,, the superposition and Heisenberg uncertainty rule. For the wave length of the quantons is of the order of Earth radius the quantum nature of the brain will be manifested in the Earth scale. In Fig.3, we present the full theoretical spectrum (in the logarithmic scale) of the brain waves with “ new” photon with energy of the order of 10-7 eV, angular frequency   108 Hz and wave length   1m . From Fig.3 we conclude that the strength of the spectrum of the new photons is millionth times smaller that the spectrum of the  ,  ,  ,  brain waves. We will call them  waves. In Table 1 the calculated energy and wave length according to formulae are presented

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E[eV ]  1015 [ Hz ] (6) And

 [m ] 

107 (7) E[eV ]

Table 1 Maximum Frequency Energy [  1015 eV] [Hz] 3.9 3.9 7.9 7.9 13.9 13.9 30 30

Wave

  

 

108

Wave length [m]

108

108 108 108 108 1

ENERGYDENSITY SPECTRUM

Red Schumann, Blue BRAIN

10 9

10 10

10 11

0

1.

10 14

2. 10 14

3. 10 14

4. 10 14

5.

10 14

ENERGY eV

Fig.1. Theoretical and experimental Brain and Schumann wave spectra { MarciakKozlowska, Kozlowski ,2009] Consciousness can explore mathematics, but mathematics cannot describe consciousness. While mathematical reality is analytic (systems are divisible into parts, down to mute elements), consciousness is fundamentally synthetic (its divisions can only be approximations). Conscious

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events are subject to time order, which is their order of relative existence: An event A “coming before” an event B is an event that exists inside B (in memory, even if it may be hard to retrieve). In other words, past events exist but future events are not determined yet. Consciousness happens to be approximately split as a multitude of individual minds, that coexist “somewhere deeply inside” each other, in a common Matrix (God), like individual physical objects may be said to coexist in a common physical space from which they cannot be dissociated. In Fig.2, the dimensional structures of Universe and Consciousness are presented. Average temperature of consciousness is 10-15eV. Precisely we can say, a measurement and calculated excess temperature of EEG of human mind is 10-15 eV. In that formulation, we follow the paper of A. Penzias and R Wilson [Penzias, Wilson, 1965]. A measurement of Excess Antenna Temperature at 4080 Mc/s”= 10-5 eV. Thanks to Penzias and Wilson, Weinberg and others, the study of the beginning of the universe is now respectable. Professional physicists who investigate the first three minutes or the first microsecond no longer need to feel shy when they talk about their work. But the end of the universe is another matter. The study of the remote future still seems to be as disreputable today as the study of the remote past was thirty years ago. Weinberg himself is not immune to the prejudices that I am trying to dispel. In the following we assume that excess temperature of the brain emitted waves is the temperature of Consciousness towards which the Universe is tending, T= 10-15eV. From the different scenario of the Universe lifetime we take as a granted the evolving Universe according to which the last state of the Universe is the Consciousness alone with temperature T=10-15 eV. The Energy (temperature) of the Universe changes according to formula [ Perkins ,2000 ]

E

106 eV t 0.5

(8)

In formula (8) t is in sec. From formula (8) we obtain T= 1061015   1042 s 2

(9)

At that time dimension of Consciousness and Universe overlaps with radius of the Universe R= 1040 s x c=10 40 s x 3 10 5 Km/s= 10 45 Km. It is 1020 times more then present radius Universe=10 24 Km. It is very interesting that numbers 10 20 and 10 40 are so called Dirac numbers! In paper [Kozlowski, Marciak-Kozlowska, 2009] the model of the Universe evolution was evaluated. In the model the Univers radius is described by formula 1 1 3 R( M , N )   2 M 2 ( N  ) LP , M , N  0,1, 2,3.. (10) 4 in formula (10) LP is the Planck Length. Considering formula (10), the Universe radius can be visualized as in Fig2. ISSN: 2153-8212


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Fig 2 a & b. Evolution of Universe is described by parabola in time (Dark blue). Consciousness (Light blue) is described as the plate. From Special relativity theory, we know the velocity of massive particle with mass m is described by formula v2 1  (1  ) 2 Ek 2 c (1  2 ) mc

(11)

In 1964 the beautiful experiment was performed by Bertozzi [1964]. In that experiment the velocity of electrons and its energies were measured simultaneously. For the first time the maximum velocity of the massive particles were measured. The result of the measurement is presented in Fig 3. The velocity of particles in our Universe cannot be greater than c, the velocity of light, velocity of massive particles tends to c. Above we shown that Universe tends to Consciousness which traces we found in brain waves which propagate with velocity of light. Is the light the attribute of Consciousness to which Universe is attracted?

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Fig .3 b , POINCARE FORMULA 1

v c ^2

0.8 0.6 0.4 0.2 0 0

2

4 6 8 10 Ek mc^2 Fig 3. Poincare formula and experimental points of Bertozzi [11]

5. Concluding Remarks The continuing evolution of observational consciousness is the greatest single fact of our time. In this paper, we developed the model for evolution of Universe towards full consciousness. We assume that excess temperature of the brain emitted waves is the temperature of Consciousness towards which the Universe is tending, T= 10-15eV. From the different scenario of the Universe lifetime, we take as granted the evolving Universe according to which the last state of the Universe is the Consciousness alone with temperature T=10-15 eV. Consciousness is the Spirit of the Universe. It invites and directs Universe to the End/ New Beginning for next 10 40 years.

References Bertozzi American Journal of Physics, vol 32, p 551 (1964). Kozlowski M. & Marciak-Kozlowska J, Dark Energy as the source of the time-dependent Einstein Cosmological Constant, Interational journal of Theoretical Physics, Vol. 14, 1-16, Nova Science Publishers 2009 Weinberg, The first three minutes, , Fontana Paperbacks, 1978 Perkins D, Introduction to to high energy physics, Cambridge Press,,2000 Dyson F , Time without end, Rev. Mod. Phys. 51, 447 ,1979

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Journal of Consciousness Exploration & Research | November 2016 | Volume 7 | Issue 10 | pp. 794-800 Marciak-Kozłowska, J. & Kozlowski, M., On Psychon in Quantum of Consciousness

Research Essay

On Psychon in Quantum of Consciousness Janina Marciak-Kozłowska1 & Miroslaw Kozlowski 1 2

*2

Institute of Electro Technology, Warsaw, Poland Warsaw University, Warsaw, Poland

Abstract In this paper, we formulate the hypothesis that brain waves and Schumann waves are quantum fields with elementary excitation energy, Psychon with EPsychon=10-15eV. With the Psychon entity, we formulate the model for calculation of normalized energy spectra for brain and Schuman waves. The model calculations are in very good agreement with measured energy spectra for both Schuman and Brain waves. Keywords: Brain wave frequencies, Schumann Resonances, Psychon, quantum consciousness. Psychon: A hypothetical unit of thought, mental activity, or nervouse energy Oxford Living Dictionaries

1. Overview of the research Considering human consciousness as the physical phenomenon, we assume that: 1. Consciousness is manifested by activity of brain in the form of electromagnetic brain waves with frequencies 3-40 Hz. 2. On the Earth exists the second mode of electromagnetic waves – Schumann waves with the same frequencies as the human brain waves. For the “antenna” with arm length R the characteristic frequency ω of electromagnetic wave can be calculated as: c  R (1) where c is the light velocity. For Earth radius R = 6.4 108 m we obtain from formula (1)

 = 50 Hz (2) i.e., in the ranges of Schumann waves. The frequency 50 Hz can be calculated in the energy units as 1015 eV  (3) * Correspondence: Miroslaw Kozlowski, Prof. Emeritus, Warsaw University, Poland. Email: [email protected] ISSN: 2153-8212


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where is famous reduced Planck constant. Multiplying both sides of formula (3) one obtains from formula (3)   1015 eV (4) Formula (4) is valid for both modes of electromagnetic waves observed on Earth Surface. Considering formula (4) we conclude that energy quantum for both type of waves is equal   1015 eV . This is elementary value of quantum energy for brain and Schuman waves and according to Oxford Dictionary can be named psychon.

2. Consciousness and Quantum Theory In the following we accept well established experimental data that the Earth atmosphere is fulfilled with two electromagnetic fields with nearly the same frequencies , but different amplitudes Brain waves and Schuman waves. As early as in 2012 we pursued quantum theory (QT) of the Brain and Schumann waves. The issue of observation in QT is central, in the sense that objective reality cannot be disentangled from the act of observation, as the Copenhagen Interpretation (CI) nearly states In the words of John A. Wheeler 1981, we live in an observer-participatory Universe.has vast majority of today's practicing physicists follow CI's practical prescriptions for quantum phenomena, while still clinging to classical beliefs in observer-independent local, external reality). There is a critical gap between practice and underlying theory. In his Nobel Prize speech of 1932, Werner Heisenberg concluded that the atom "has no immediate and direct physical properties at all." If the universe's basic building block isn't physical, then the same must hold true in some way for the whole. The universe was doing a vanishing act in Heisenberg's day, and it certainly hasn't become more solid since. This discrepancy between practice and theory must be confronted, because the consequences for the nature of reality are far-reaching An impressive body of evidence has been building to suggest that reality is non-local and undivided. Non-locality is already a basic fact of nature, first implied by the Einstein-Podolsky-Rosen thought experiment despite the original intent to refute it, and later explicitly formulated in Bell's Theorem. Moreover, this is a reality where the mindful acts of observation play a crucial role at every level. Heisenberg again: "The atoms or elementary particles themselves . . . form a world of potentialities or possibilities rather than one of things or facts." He was led to a radical conclusion that underlies our own view in this paper: "What we observe is not nature itself, but nature exposed to our method of questioning." Reality, it seems, shifts according to the observer's conscious intent. Quantum theory is not about the nature of reality, even though quantum physicists act as if that is the case. To escape philosophical complications, the original quantum mechanics was pragmatic: it concerned itself with the epistemology of quantum world (how we experience quantum phenomena), leaving aside ontological questions about the ultimate nature of reality. The ISSN: 2153-8212


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practical bent of QM should be kept in mind, particularly as there is a tendency on the part of many good physicists to slip back into issues that cannot be tested and therefore run counter to the basic tenets of scientific methodology. In order to put forward the classical theory of the brain waves we quantize the Brain and Schumann wave field. In the model (Marciak-Kozlowska,Kozlowski, 2013) we assume (i) the brain is the thermal source in local equilibrium with temperature T.(ii) The spectrum of the brain waves is quantized according to formula

  E (5)

where E is the photon energy in eV , =Planck constant,   2 , -is the frequency in Hz. (iii). The number of photons emitted by brain is proportional to the ( amplitude)2 as for classical waves. The energies of the photons are the maximum values of energies of waves For the emission of black body brain waves we propose the well know formula for the black body radiation. In thermodynamics we consider Planck type formula for probability dN/dE for the emission of the particle ( photons as well as particles with m≠0) with energy (E,E+dE )by the source with temperature T is equal to[1] : E

dN  BE 2 e(  E max ) max dE (6) psychon

where B= normalization constant, E=total energy of the particle, k = Boltzmann constant=1.3 x 10-23 J K-1. K is for Kelvin degree. However in many applications in nuclear and elementary particles physics kT is recalculated in units of energy. To that aim we note that for 1K, kT is equal k1K = K x 1. 3 10-23 J x K-1= 1.3 10-23 Joule or kT for 1K is equivalent to 1.3 10-23 Joule= 1.3 10-23 /( 1.6 10-19) eV = 0.8 10-4 eV. Eventually we obtain 1K= 0.8 10-4 eV, and 1eV= 1.2 104 K. In formula ( 5) “ temperature “ T (eV) is the energy parameter which describes the shape of the energy spectra. In the following we chose E(eV)psychon as the energy parameter and formula ( 5) can be written as E

dN  BE 2 e(  E max ) max dE (6) psychon

In Fig. 1, we present the experimental data for brain waves[2]:

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BRAIN

dN dE Arbitrary Units

10 9

10 10

10 11

10 12

10 13 2.

10 144.

10 146.

10 148.

10 141.

10 131.2

10 13 1.4

10 13

ENERGY eV

FiG.1. Energy spectra of the brain waves [3]

and in Fig 2. the same for Schumann waves:


SCHUM ANN

5.0

10 9

3.0

10 9

1.

10 14

1.5

10 14

2.

10 14 2.5

10 14

3.

10 14

ENERGY eV

Fig.2 Experimental Energy spectra of the Schumann waves [3]

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In Fig 3., theoretical energy spectra for brain waves with Epsychon=10-15eV is presented [1,2]:

Brain 10 9


10 10 10 11 10 12 10 13 10 14 0

2.

10 144.

10 14 6.

10 148.

10 141.

10 13 1.2

10 13 1.4

10 13

ENERGY eV

Fig.3. Theoretical energy spectra of brain waves , E psychon=10-15 eV [1,2]


Schumann

10 9

10 10

10 11

0

1.

10 14

2.

10 14

3.

10 14

4.

10 14

5.

10 14

ENERGY eV

Fig.4 Theoretical energy spectra of Schuman waves, Epsychon=10-15eV [1,2]

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Comparison of theoretical and experimental data are presented in Fig.5 and Fig.6:

Brain 10 9


10 10 10 11 10 12 10 13 10 14 0

2.

10 144.

10 14 6.

10 148.

10 141.

10 13 1.2

10 13 1.4

10 13

ENERGY eV

Fig.5 Comparison theoretical and experimental Energy spectra of brain waves


Schumann

10 9

10 10

10 11

0

1.

10 14

2.

10 14

3.

10 14

4.

10 14

5.

10 14

ENERGY eV

Fig.6 Comparison of theoretical and experimental energy spectra of Schuman waves

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3. Conclusions In this paper, we argue that the consciousness phenomenon can be described with the help of psychon quantum particle with mass, m=0 and energy Epsychon=10-15eV. The psychon is a boson with spin S=1. As for boson we applied the Planck formula for energy spectra of the brain and Schumann waves. The agreement with measured data is very good.

References [1] M.Kozlowski, J. Marciak-Kozlowska Brain Photons as the Quanta of the Quantum String, Neuroquantology vol 10 No3, (2012) [2]M.Kozłowski, J. Marciak-Kozłowska, Schumann Resonance and Brain Waves: A Quantum Description, Neuroquantology Vol 13, No 2 (2015) [3] A. Nikolaenko, M. Hayakawa, Schumann Resonance for Tyros , Springer Geophysics, 2014.

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Journal of Consciousness Exploration & Research | November 2016 | Volume 7 | Issue 10 | pp. 823-833 Kozlowski, M. & Marciak-Kozłowska, J., Exploration on Plausible Tumor Conscious Waves

Exploration

Exploration on Plausible Tumor Conscious Waves *

Miroslaw Kozlowski 1 & Janina Marciak-Kozłowska2 1 2

Warsaw University, Warsaw, Poland Institute of Electro Technology, Warsaw, Poland

Abstract In this paper, the mathematical model for tumor growth, based on Boltzmann type equation is formulated. The tumor growth factor is defined. The tumor cells density is calculated. It is shown that the tumor evolution strongly depends on the growth factor k. For k0.5 tumor lost the oscillatory character and grows abruptly and emits cells to the host body. We argue that the oscillation of the density of tumor creates the tumor waves which can be coined as the tumor conscious waves. The tumor waves “inform” host consciousness. Keywords: Tumor, conscious, tumor waves, growth factor, density.

1. Introduction Since 2002, cancer has become the leading cause of death for Americans between the ages of 40 and 74 (Jemal, 2005). But the overall effectiveness of cancer therapeutic treatments is only 50%. Understanding the tumor biology and developing a prognostic tool could therefore have immediate impact on the lives of millions of people diagnosed with cancer. There is growing recognition that achieving an integrative understanding of molecules, cells, tissues and organs is the next major frontier of biomedical science. Because of the inherent complexity of real biological systems, the development and analysis of computational models based directly on experimental data is necessary to achieve this understanding. Tumor development is very complex and dynamic. Primary malignant tumors arise from small nodes of cells that have lost, or ceased to respond to, normal growth regulatory mechanisms, through mutations and/or altered gene expression (Sutherland,1988). This genetic instability causes continued malignant alterations, resulting in a biologically complex tumor. However, all tumors start from a relatively simpler, avascular stage of growth, with nutrient supply by diffusion from the surrounding tissue. The restricted supply of critical nutrients, such as oxygen and glucose, results in marked gradients within the cell mass. The tumor cells respond both through induced alterations in physiology and metabolism, and through altered gene and protein expression ( Marusic,1994) leading to the secretion of a wide variety of angiogenic factors. Angiogenesis, formation of new blood vessels from existing blood vessels, is necessary for subsequent tumor expansion. Angiogenic growth factors generated by tumor cells diffuse into the * Correspondence: Miroslaw Kozlowski, Prof. Emeritus, Warsaw University, Poland. Email: [email protected] ISSN: 2153-8212


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nearby tissue and bind to specific receptors on the endothelial cells of nearby pre-existing blood vessels. The endothelial cells become activated; they proliferate and migrate towards the tumor, generating blood vessel tubes that connect to form blood vessel loops that can circulate blood. With the new supply system, the tumor will renew growth at a much faster rate. Cells can invade the surrounding tissue and use their new blood supply as highways to travel to other parts of the body. Members of the vascular endothelial growth factor (VEGF) family are known to have a predominant role in angiogenesis. Physicists have long been at the forefront of cancer diagnosis and treatment, having pioneered the use of X rays and radiation therapy. In the contemporary initiative, the US National Cancer Institute the conviction that physicists bring unique conceptual insights that could augment the more traditional approaches to cancer research is very appealing. In this paper we present the first attempt to consider the tumor cancer as the physical medium with some sort of memory.

2. Conscious of the cancer cells Cancer is pervasive among all organisms in which adult cells proliferate. There is Darwinian explanation of cancer insidiousness which is based on the fact that all life on Earth was originally single-celled. Each cell had a basic imperative: replicate, replicate, replicate. However, the emergence of multicellular organisms about 550 million years ago required individual cells to co-operate by subordinating their own selfish genetic agenda to that of the organism as a whole. So when an embryo develops, identical stern cells progressively differentiate into specialized cells that differ from organ to organ. If a cell does not respond properly to the regulatory signals of the organism it may go reproducing in an uncontrolled way, forming a tumor specific to the organ in which it arises. A key hallmark of cancer is that it can also grow in an organ where it does not belong: for example a prostate cancer cell may grow in a lymph mode. This spreading and invasion processes is called “metastasis”. Metastatic cells may lie dormant for many years in foreign organs evading the body’s immune system while retaining their potency. Healthy cells, in contrast, soon die if they are transported beyond their rightful organ. In some respect, the self-centered nature of cancer cells is a reversion to an ancient premulticellular lifestyle. Nevertheless cancer cells do co-operate to a certain extent. For example tumors create their own new bloody supply, a phenomenon called “angiogenesis” by co-opting the body’s normal wound healing functions. Cancer cells are therefore neither rogue “selfish cells”, nor do they display the collective discipline of organism with fully differentiated organs. They fall somewhere in between perhaps resembling an early form of loosely organized cell colonies. In other words the cancer tumor remember the early state of existence, it has a memory which have been erased in healthy cells. The proliferation of the tumor cells is described by the diffusion processes ( Jamal,,2005) The standard diffusion equation is based on the Fourier law in which as we know all memory of the ISSN: 2153-8212


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initial state is erased. Simply speaking diffusion equation has not time reversal symmetry, i.e. if the function f(x,t) is the solution of Fourier equation, f(x,-t) is not. Let us consider the one-dimensional transport “particles”, e. g., cancer cells. These cells however may move only to the right or to the left on the rod. Moving cells may interact with the fixed host body cells the probabilities of such collisions and their expected results being specified. All particles will be of the same kind, with the same energy and other physical specifications distinguishable only by their direction. Let us define: u(z,t) = expected density of cells at z and at time t moving to the right, v(z,t) = expected density of cells at z and at time t moving to the left. Furthermore, let

 (z ) = probability of collision occurring between a fixed scattering centrum and a cell moving between z and z  . Suppose that a collision might result in the disappearance of the moving cell without new particle appearing. Such a phenomenon is called absorption. Or the moving particle may be reversed in direction or back-scattered. We shall agreeing that in each collision at z an expected total of F(z) cells arises moving in the direction of the original cell, B(z) arise going in the opposite direction. The expected total number of right-moving cells z1  z  z 2 at time t is z2

 u( z, t )dz z1

,

while the total number of cell passing z to the right in the time interval t1  t  t 2 is

(2.6)

t2

w u ( z, t )dt t1

,

(2.7)

where w is the particles speed.

t  Consider the cell moving to the right and passing z   in the time interval 1 t2   / w t2   w  u ( z  , t ' )dt'  w u z  , t ' dt'. w t1   / w t1 

 w

 t  t 2  w

:

(2.8)

These can arise from cells which passed z in the time interval t1  t  t2 and came through ( z, z   ) without collision t2

w (1  δ ( z, t ' ))u ( z, t ' )dt' t1

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plus contributions from collisions in the interval ( z, z   ). The right-moving cells interacting in ( z, z   ) produce in the time t to t , 1

2

t2

w  ( z, t ' ) F ( z, t ' )u ( z, t ' )dt' t1

(2.10)

cells to the right, while the left moving ones give: t2

w ( z, t ' ) B( z, t ' )v( z, t ' )dt' t1

.

(2.11)

Thus t2

2 2    w u z  , t ' dt'  w u ( z , t ' )dt'  w  δ ( z , t ' )(F ( z , t ' )  1)u ( z , t ' )dt' w   t1 t1

t

t

t1

t2

 w  δ ( z , t ' ) B( z , t ' )v( z , t ' )dt'. t1

(2.12)

Now, we can write:  1 u   u  u z  , t '   u( z, t ' )   ( z, t ' )  ( z , t ' )  w w t   z  to get t2

(2.13)

2   u  1 u     z , t '  z , t ' dt '     z t δ( z, t ' )((F ( z, t ' )  1)u( z, t ' )  B( z, t ' )v( z, t ' ))dt'.   w t 1

t

t1

On letting   0 and differentiating with respect to t2 we find u 1 u   ( z , t )(F ( z , t )  1)u ( z , t )  ( z , t ) B( z , t )v( z , t ). z w t

(2.14)

(2.15)

In a like manner

v 1 v    ( z , t ) B ( z , t )u ( z , t )   ( z , t )(F ( z , t )  1)v( z , t ). z w t (2.16) The system of partial differential equations of hyperbolic type (2.15, 2.16) is the Boltzmann equation for one dimensional transport phenomena (Kozlowski, Marciak-Kozlowska,2009) Let us define the total density for cells, ρ( z , t ) 

and density of cells current

ρ( z , t )  u ( z , t )  v( z , t )

(2.17)

j ( z, t )  w(u ( z, t )  v( z , t )).

(2.18)

Considering equations (2.15 – 2.18) one obtains  1 j   ( z , t )u ( z , t )(F ( z , t )  B( z , t )  1)  ( z , t )v( z , t )(B( z , t )  F ( z , t )  1). z w2 t ISSN: 2153-8212


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(2.19)

827


Equation (2.19) can be written as ρ 1 j δ ( z , t )( F ( z , t )  B ( z , t )  1) j   z w 2 t w

or j

(2.20)

w ρ 1 j  . δ ( z , t )(F ( z , t )  B( z, t )  1) z wδ ( z, t )(F ( z, t )  B( z, t )  1) t

(2.21)

Denoting, D, diffusion coefficient D

w ( z, t )(F ( z, t )  B( z, t )  1)

and τ, relaxation time τ

1 wδ ( z , t )(1  F ( z , t )  B( z , t ))

(2.22)

equation (2.21) takes the form

ρ j τ . z t (2.23) Equation (2.23) is the Cattaneo’s type equation and is the generalization of the Fourier equation (Kozlowski,Marciak-Kozlowska,2009). Now in a like manner we obtain from equation (2.15 – 2.18) 1 j 1 ρ   δ ( z, t )u ( z , t )(F ( z, t )  1  B( z, t )) w z w t δ ( z , t )v( z , t )(B( z , t )  F ( z , t )  1)) (2.24) or j ρ   0. z t (2.25) Equation (2.25) describes the conservation of cells in the transport processes. Considering equations (2.23) and (2.25) for the constant D and τ the hyperbolic Heaviside equation is obtained:  2 ρ ρ 2 ρ τ 2  D 2. t t z (2.26) where τ is the relaxation time In the stationary state transport phenomena dF ( z, t ) / dt  dB( z, t )dt  0 and d( z, t ) / dt  0. In j  D

that case we denote F ( z , t )  F ( z )  B( z , t )  B( z )  k ( z ) and equation (2.10) and (2.11) can be written as du  δ ( z )(k  1)u ( z )  δ ( z )kv( z ), dz dv   δ ( z )k ( z )u ( z )  δ ( z )(k ( z )  1)v( z ) dz (2.27) with diffusion coefficient

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D

w δ (z )

(2.28)

and relaxation time τ ( z) 

1 . wδ ( z )(1  2k ( z ))

(2.29)

The system of equations (2.27) can be written as d ( δk ) 2 d u dz du dδ δ (k  1) d (δk )     u δ 2 (2k  1)  (1  k )   0, 2 δk dz dz δk dz  dz 

(2.30)

du  δ (k  1)u  δkv( z ). dz Equation (2.30) after differentiation has the form d 2u du  f ( z)  g ( z )u ( z )  0 2 dz dz , where 1  δ dk dδ  f ( z)     , δ  k dz dz  δ dk g ( z )  δ 2 ( z )(2k  1)  . k dz For the constant absorption rate we put 1 k ( z )  k  constant  . 2 In that case 1 dδ f ( z)   , δ dz g ( z )  δ 2 ( z )( zk  1).

(2.31)

(2.32)

(2.33)

(2.34)

With functions f(z) and g(z) the general solution of the equation (2.30) has the form

u ( z )  C1e



(1 2 k )1 / 2 δdz

 C2 e



 (1 2 k )1 / 2 δdz

. (2.35) In the subsequent we will consider the solution of the equation (2.32) with f(z) and g(z) described by (2.34) for Cauchy condition: u (0)  q, v(a)  0 . (2.36) Boundary condition (2.36) describes the generation of the heat carriers (by illuminating the left end of the strand with laser pulses) with velocity q heat carrier per second. The solution has the form:

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Journal of Consciousness Exploration & Research | November 2016 | Volume 7 | Issue 10 | pp. 823-833 Kozlowski, M. & Marciak-Kozłowska, J., Exploration on Plausible Tumor Conscious Waves 1   2qe f ( 0 )  f ( a )   (1  2k ) 2  cosh f ( x)  f (a) u( z)  1  1  βe 2  f ( 0 )  f ( a )    (1  2k ) 2  (k  1)  k 1  sinh f ( x)  f (a), 1

(1  2k ) 2  (k  1) u( z) 

( f ( 0 )  f ( a ))

2qe 1  βe 2  f ( 0 )  f ( a ) 

1   2  (1  2k )  (k  1) sinh f ( x)  f (a),   k  

(2.37)

where

f ( z )  (1  2k )

1 2 1

 δdz,

   δdz ,

f (0)  (1  2k ) 2  δdz , 0

f (a)  (1  2k ) β

1 2

a

1 2

(1  2k )  (k  1) 1 2

.

(1  2k )  (k  1)

(2.38)

Considering formulae (2.17), (2.18) and (2.37) we obtain for the density, ρ(z ) and current density j(z).

j( z) 

2qwe  f ( 0)  f ( a )  1  βe 2 f ( 0)  f ( a ) 

1   2 ( 1  2 k )  cosh f ( z )  f (a)  1    (1  2k ) 2  (k  1)    1  2k  sinh f ( z )  f (a) 1   2  (1  2k )  (k  1) 

(2.39)

and 1   (1  2k ) 2  cosh f ( z )  f (a)  1   2qe f ( 0) f ( a )   (1  2k ) 2  (k  1) . q  1  βe 2 f ( 0) f ( a )   1     sinh f ( z )  f ( a ) 1    (1  2k ) 2  (k  1)  Equations (2.39) and (2.40) fulfill the generalized Fourier relation w ρ W j , D , δ ( z ) z δ( z)

(2.40)

(2.41)

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Analogously we define the generalized diffusion velocity υD(z) 1 1   2 w(1  2k ) cosh f ( z )  f (a)  (1  2k ) 2 sinh f ( x)  f (a) j( z)  . υD ( z)   1 n( z ) (1  2k ) 2 cosh f ( x)  f (a)  sinh f ( x)  f (a) Assuming constant cross section for heat carriers scattering formula (2.38)

δ ( z )  δo

(2.42)

we obtain from

1

f ( z )  (1  2k ) 2 z , f (0)  0, 1

f (a )  (1  2k ) 2 a

(2.43)

and for density ρ (z ) and current density j(z) 1 1  1  (1 2 k ) 2 aδ   2qwe (1  2k ) 2  2 j( z)  cosh ( 2 k  1 ) ( x  a ) δ   1 1   (1 2 k ) 2 aδ   2 1  βe  (1  2k )  (k  1)  1    sinh (2k  1) 2 ( x  a )δ  , 1    (1  2k ) 2  (k  1)  (1  2k )

(2.44)

 1 δ   (1  2k )  2 ρ( z )  cosh ( 2 k  1 ) ( x  a )   1 1   (1 2 k ) 2 aδ   2 1  βe  (1  2k )  (k  1)  1   1  sinh (2k  1) 2 ( x  a )δ  . 1    (1  2k ) 2  (k  1)  2qe

1  (1 2 k ) 2

aδ

1 2

(2.45)

Formulae (2.44) and (2.45) describe the kinetic of the growth of the cell aggregation- tumor. The development of the tumor strongly depends on the coefficient k. In the following we will call kthe growth coefficient. For k0.5 the cell density grows exponentially, Fig. 2 a, 2 b. For k Mp, μ = Mp

From formula (19 we conclude that  ( x  ct ) is independent of mass mi. In the case mi < Mp from formulae (19) and (20) one obtains

  

  mi 1 

mi Mp

  

 m  2m c 2m c 2    2imi c   ( x  ct )  exp  ( x  ct )  exp  i i  i x  i t    M      p  In formula (21) we put

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Journal of Consciousness Exploration & Research | January 2017 | Volume 8 | Issue 1 | pp. 01-17 Kozlowski, M., & Marciak-Kozłowska, J., Quantum Model of Consciousness

13

2mi c  2mi c 2   k

(22)

and obtain

( x  ct )  e

i ( kx t )

i

e

mi ( kx t ) Mp

(22)

As can concluded from formula (22) the second term depends on the gravity   m 2G  2   m  exp i i (kx  t )  exp i i  (kx  t )   c    M p  1

(23)

where G is the Newton gravity constant. Formula (22) fescribes the influence of the gravity on stte of the consciousness It is interesting to observe that the new constant,  G ,

G 

mi2 G c

(24)

is the gravitational constant. For mi = mN nucleon mass

 G  5.90421039

(25)

5. The Particle in a Box In paper (to be published)) the quantum model of the consciousness waves was proposed. It was shown that instead of waves alpha, beta, theta,delta, gamma we can say about quantons alpha, beta, gamma ,delta, theta.In this paragraph we consider the simplest model for the emission of quantons We consider quantum mechanical system for a particle of mass mi confined in a one-dimensional box of length L and infinite walls. For the particle to be confined within region II, the potential energy outside (regions I and III) is assumed to be infinite. In order to understand further this system, we need to formulate and solve the Schrödinger equations (26). 2 2 2  2  1 2  2 2 i    V         2 2 . t 2mi 2M p 2M p  c t 

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Considering the pilot wave equation 1 2 0 c 2 t 2

(27)

2    2   V , t 2

(28)

2 

one obtains i

where

 In region II, V ( x)  0   

2

2 2

2  V   E

2

2

mi  M p

.

In regions I and III, V ( x)   

   0  E



2  E



2

2

mi M p

2

2 2

2 2

2

 2  V   E

(28)

 2     E  2   E    

For regions I and III (outside the box), the solution is straightforward, the wavefunction  is zero. For region II (inside the box), we need to find a function that regenerates itself after taking its second derivative. 

2

2

2  E

2 

2 E 2

  k 2 ,

where we define k 

2 E 2

(29) .

Perfect candidates would be the trigonometric sine and cosine functions.  ( x)  A cos( kx)  B sin( kx).

To further refine the wave function, we need to At x=0, the wave function should be zero.

(30) impose

boundary conditions:

 (0)  A cos(k 0)  B sin(k 0)  A 1  B  0.

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Equation can only be true if A = 0:  ( x)  B sin(kx). In addition, at x=L, the wave function should also be zero.

 (0)  0  B sin(kL).

True when kL  n or k 

n  ( x)  B sin( x), n  1, 2,3,... L

n : L

(32)

Going back to the Schrödinger's equation, we can then formulate the energies

kL  n 2 E 2

En 

and n  L

k 

2 E 2

2 E 2

n 2 2 2 n 2 h 2  2  L2 8 L2

n 2 2  2 L

since 

(34)

h . 2

Thus, the application of the Schrödinger equation to this problem results in the well-known expressions for the wave functions and energies, namely:

n2h2 2  n x  n  sin   and En  8 L2 . L  L 

(35)

From formula (60) we conclude that for “heavy” classical particles, i.e. for mi >> Mp energy spectrum of the particle in the box is independent of the mass of particle En 

n2 h2 . 8M p L2

(36)

In paper (Marciak-Kozłowska, Kozłowski, 2010) we argue that formula (36) describes the quantum states of the consciousness. The energy of the quanta of the consciousness is of the order of 10-15 eV .Substituting 10-15 eV for En to formula ( 16) and considering the mass of Mp =1031 eV we obtain for the characteristic length, L , the value 10-6 nm., i.e. lower that the nanotubule.. With L=10-6 nm we obtain from formula (36) the following spectrum for brain waves En  E0  7 x1015 , 2.8x1015 ,6.3x1014 ,1.1x1013 ,1.7 x1013 eV

(37)

for n=1,2,3,3,5 respectively.

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The brain photons are emitted as quantum deexcitation in the quantum well, i.e. n  where

 n is the angular frequency of the brain photons with quantum number n and

En  E0

En .E0

are the n-excited state for n=1,2,3,4,5 respectively, and E0 is ground state of the quantum well with energy equals zero. . In Table 1 the comparison of the measured ( EEG) and calculated spectra are presented . The agreement is rather good Table 1 Comparison of the measured (EEG) and calculated brain photons spectra Measured enegies , EEG( eV)

Model calculation EEG(eV)

7 x 10-15 1.7 x10-14 3.4x 10-14 7.0 x10-14 1.4 x10-13

7x 10-15 2.8x 10-14 6.3x 10-14 1.1 x10-13 1.7 x10-13

5. Conclusions In this paper, we put forward the quantization of the brain waves. We propose the theoretical model: the well with infinite walls for the calculations of the brain photons (quantons) spectra. The model is free of additional parameters. By comparison to the measured EEG spectra we obtain the width (dimension of the well,) L=10-6 nm. With value of L we can calculate the whole spectrum of the brain pulsation. It is well known that frequencies  (energies  ) of the brain photons are nearly equal to the frequencies of the Tesla-Schumann waves. The TeslaSchumann waves are the resonances in Earth- ionosphere cavity) . In the paper we investigate the influence of the gravitation on the brain pulsations and obtain the wave functions for gravity dependent brain waves. The connections of the lighting , the Tesla-Schumann resonances and brain waves can be supported by the observation that the primordial charge channel for lighting has the thickness of the order of 10-6 nm is of the order of the radius of atomic nucleus. The calculations of the brain waves frequencies are based on the existence of the strand of the medium –the strand of the 1019 protons with width of the order of 10-15 m and length of the 104km- the string of the consciousness. The vibration of this string produces the brain waves. The energies of the brain waves are the energies of the standing waves of the consciousness string.

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References Schuman W O, Uber die strahlunglosen Eingenschwingumgen einer leitenden Kugel, die von einer Luftschicht und einer Ionospharenhulle umgeben ist.Z Naturforschung 7a , 149-154,1952 Chand N Israil M , Rai J Schuman resonance frequency variations observed in magnetotelluric data recorded from Garhwal Himalayan region India, Ann. Geophys., 23,3497-3507,2009 Kozlowski M, Marciak-Kozlowska J. Modified Schrodinger equation for particles with mass of the order of human neuron mass, J Neuroquantology, 8,1-8,2010

Fig.1 Energy 10-15 eV= Energy of the brain quantons

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Journal of Consciousness Exploration & Research | January 2017 | Volume 8 | Issue 1 | pp. 74-79 Marciak-Kozłowska, J. & Kozlowski, M., Human Brain & Cosmos

74

Exploration

Human Brain & Cosmos Janina Marciak-Kozłowska1 & Miroslaw Kozlowski 1 2

*2


Abstract In this paper, we consider the possible source of human brain waves and Cosmic Background Radiation. We formulate the model which describes the energy spectra of both radiations. Keywords: Cosmic Background Radiation, human brain waves

1. Introduction Quantum theory does not say anything specific about the nature of consciousness - the whole issue is clouded by basic uncertainty over even how to define consciousness. A firm grasp of human mental processes still remain; very elusive. We believe that this indicates a deeper problem which scientist; in general are reluctant to address: objective science is based on the dichotomy; between subject and object; it rests on the implicit assumption that Nature can be studied ad infinitum as an external objective reality. The role of the observer is at best, secondary, if not entirely irrelevant

2. Consciousness & Quantum Theory The issue of observation in QM is central, in the sense that objective reality cannot be disentangled from the act of observation, as the Copenhagen Interpretation (CI) nearly states in the words of John A. Wheeler 1981, we live in an observer-participatory Universe. The vast majority of today's practicing physicists follow CI's practical prescriptions for quantum phenomena, while still clinging to classical beliefs in observer-independent local, external reality). There is a critical gap between practice and underlying theory. In his Nobel Prize speech of 1932, Werner Heisenberg concluded that the atom “has no immediate and direct physical properties at all.” If the universe's basic building block isn't physical, then the same must hold true in some way for the whole. The universe was doing a vanishing act in Heisenberg's day, and it certainly hasn't become more solid since (Schild, 2012).

*

Correspondence: Miroslaw Kozlowski, Prof. Emeritus, Warsaw University, Poland. Email: [email protected]

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This discrepancy between practice and theory must be confronted; because the consequences for the nature of reality are far-reaching an impressive body of evidence has been building to suggest that reality is non-local and undivided. Non-locality is already a basic fact of nature, first implied by the Einstein-Podolsky-Rosen thought experiment despite the original intent to refute it, and later explicitly formulated in Bell's Theorem Moreover, this is a reality where the mindful acts of observation play a crucial role at every level. Heisenberg again: “The atoms or elementary particles themselves . . . form a world of potentialities or possibilities rather than one of things or facts.” He was led to a radical conclusion that underlies our own view in this paper: “What we observe is not nature itself, but nature exposed to our method of questioning.” Reality, it seems, shifts according to the observer's conscious intent. There is no doubt that the original CI was subjective (Schild, 2012). Quantum theory is not about the nature of reality, even though quantum physicists act as if that is the case. To escape philosophical complications, the original CI was pragmatic: it concerned itself with the epistemology of quantum world (how we experience quantum phenomena), leaving aside ontological questions about the ultimate nature of reality. The practical bent of CI should be kept in mind, particularly as there is a tendency on the part of many good physicists to slip back into issues that cannot be tested and therefore run counter to the basic tenets of scientific methodology.

3. The Model In order to put forward the classical theory of the brain waves we quantize the brain wave field. In the model (Marciak-Kozlowska and Kozlowski, 2012) we assume that; (i) (ii) (iii)

The brain is the thermal source in local equilibrium with temperature T. The spectrum of the brain waves is quantized according to formula E  h where E is the photon energy in eV, =Planck constant,  -is the frequency in Hz. The number of photons emitted by brain is proportional to the (amplitude)2 as for classical waves. The energies of the photons are the maximum values of energies of waves for the emission of black body brain waves we propose the well know formula for the black body radiation (Baierlein, 1998).

The energy density within a blackbody is independent of the material from which the blackbody is made. We will assume that this thermodynamic law holds as well for neutrino emitters as for photon emitters. This thermodynamic relation greatly simplifies the task of calculating the energy density. The standard technique is to make the blackbody out of nothing. Enclosure walls at a temperature T are used to surround a vacuum. Emission from the walls fills the vacuum to the energy density required of a black-body at the wall temperature. The energy density per unit volume and per unit frequency range is then calculated. The number of modes per unit volume and frequency is most easily obtained by assuming a rectangular enclosure of

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smooth, almost perfectly reflecting walls. A minute amount of absorption is necessary to insure that the walls and radiation are in thermal contact. This situation is easy to achieve experimentally for photons. A spatial mode of the field is simply a particular space pattern that satisfies a particular boundary condition, for example, for our case the field is zero at the wall. In the standard technique, an integral number of half wavelengths must fit between opposite walls in one direction. Counting the number of spatial three2 3 dimensional modes per unit volume and frequency is then standard and gives 4 c for any wave field satisfying the boundary conditions. The actual modes present for a particular wavefield will be larger than the space count because each space mode may harbor a number of internally different fields. Since photons come in two circular polarizations (left and right handed 2 3 we have N=2 ( 4 c ) for photons. In thermodynamics we consider Planck type formula for probability  for the emission of the particle (photons as well as particles with m≠0) with energy (E, E+dE)) by unit energy by the source with temperature T is equal to  (

8 2 ) c3

1  h  Exp   1  kT 

(1)

For very low temperature, i.e., for hv kT

1

(2)

From formula (1) we obtain for probability emission   8 2 3  c

 

  h   Exp    kT  

( 3)

Formula (3) is black body emission formula (Planck formula) for the vacuum emission. For the emission into surrounding matter we modify formula (3) as P(E)dE= BE2 e (-E/kT) dE

(4)

where we introduce the normalization constant B. The new constant describes interaction of the photons with surrounding matter. With formula (4) we can calculate the normalized to the experimental data the photon energy distribution. In formula (4) E=total energy=(hv)2, k = Boltzmann constant=1.3x10-23 JK-1. K is for Kelvin degree. However in many applications in nuclear and elementary particles physics kT is recalculated in units of energy. To that aim we note that for 1K, kT is equal kx1K = K x 1.3x10-23 J x K-1= 1.3 10-23 Joule or kT for 1K is equivalent to 1.3x10-23 Joule= 1.3x10-23 /(1.6x10-19) eV = 0.8x10-4 eV. Eventually we obtain 1K= 0.8x10-4 eV, and 1eV= 1.2x104 K ( dN 2  BEmax e dE

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The function dN/dE describes the energy spectrum of the emitted brain photons. In Figure 1 the calculated energy spectrum, formula (2) is presented. We present the result of the comparison of the calculated and observed spectra of the brain waves. The calculated spectra are normalized to the maximum of the measured spectra. The calculated spectrum is for temperature of brain source T= 0.8x10-14 eV. The obtained temperature is the temperature for the brain source in the thermal equilibrium. The source is thermally isolated (adiabatic well). However in very exceptional cases the spectrum is changed – by the tunneling to the quantum potential well. The temperature 1 eV ≅ 104 K then brain wave thermal spectra T=0.8x10-14 eV= 0.8x10-10 K. In Figure 2 we present the calculation of the energy spectrum for the Cosmic Background Radiation (CBR) (Durrer, 2008). The formula (5) was used for the model calculation. The normalized theoretical spectrum describes very well the observed CBR.

ENERGY DENSITY SPECTRUM Wat m^2 Hz

The calculated temperature T=2.53 K, which is in excellent agreement with experimentally verified values. It must be stressed that in a paper we abandon the idea that every physical object is either a wave or a particle. Neither it is possible to say that particles “become” waves in the quantum domain and conversely that waves are “transformed “into particles. It is therefore necessary to acknowledge that we have here a different kind of an entity, one that is specifically quantum. For this reason Levy-Leblond and Balibar developed the name quanton, (LevyLeblond, Balibar, 1990). Following that idea the human brain emits quantons with energies E   formula (5). The brain quantons are the quantum objects that follows all quantum laws: tunneling, the superposition and Heisenberg uncertainty rule. For the wave length of the quantons is of the order of Earth radius the quantum nature of the brain will be manifested in the Earth scale.

1.2

10 9

1.

10 9

8.

10 10

6.

10 10

4.

10 10

2.

10 10 0 0

2.

10 144.

10 14 6.

10 148. 10 141.

10 13 1.2

10 13 1.4

10 13

ENERGY eV

Figure 1. Model calculations for energy spectra of brain photons. The temperature of the source, T= 7.8 10-11 K. ISSN: 2153-8212


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Figure 2. Model calculations for energy spectra of Cosmic Background Radiation Temperature of the source T= 2.35 K

4. Conclusions In this paper for the first time the CB photons spectra and human brain photons spectra were calculate on the same footing. It is obvious that consciousness is not located in space. According to special relativity theory all physically observed phenomena are located in 4D space-time. In conclusion the consciousness not exist in time also, is timeless. The brain photons are the effect of the interaction of the timeless consciousness with human brain. The final results of this interaction are the: alpha, beta, delta and theta waves. In the paper we calculated the temperature of the source of the photons located in human brain. It is well known that our space time is filled with Cosmic Background Radiation. It was interesting to calculate the temperature of the CBR source with the same model as for brain photons. As the result the shape of temperature was calculated, temperature was obtained T=2.53 K, which is in very good agreement with observed value. One can conclude by analogy that our space with background radiation was created in the interaction of the timeless conscious with void

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References Schild R. Cosmology of Consciousness, Quantum Physics & Neuroscience of Mind, Cosmology Science Publishers, Cambridge, 2012. Baierlein R. Thermal Physics, Cambridge University Press, 1999. Marciak-Kozlowska J, Kozlowski M. Heisenberg’s Uncertainty Principle and Human Brain. NeuroQuantology 2013; 11(1): 47-51. Kozlowski M, Marciak-Kozlowska J. Brain Photons as the Quanta of the Quantum String. NeuroQuantology 2012; 10(3): 453-461. Durrer R. The Cosmic Background. Cambridge University Press, 2008. Levy-Leblond J, Balibar F. Quantics. Elsevier Publisher, 1990.

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Journal of Consciousness Exploration & Research | February 2017 | Volume 8 | Issue 2 | pp. 160-167 Marciak-Kozłowska, J. & Kozlowski, M., On the Interaction of the Schumann Waves with Human Brain

Article

On the Interaction of the Schumann Waves with Human Brain Janina Marciak-Kozłowska1 & Miroslaw Kozlowski 1 2

*2


Abstract In this paper we developed new hypothesis on the nature of human brain waves and Schumann waves. To that aim we formulated Klein-Gordon equation for Schumann waves and simultaneously for brain waves We show that two new parameters high of potential barrier and relaxation time describe the interaction of Schumann waves with human brain. The interaction is governed by the Heisenberg type inequality. Assuming relaxation of brain of the order of 1 sec we obtain the high of human brain potential barrier of the order of 10-15 eV. The same value was obtained in our ealier papers for the temperature of the brain and Schuman waves. Keywords: Brain , Schumann waves, relaxation time , potential barrier , Heisenberg inequality.

1. Introduction Human consciousness has gone through several distinct permutations throughout history. These structural changes have been documented and supported by a wealth of anthropological, mythological, linguistic, artistic, philosophical, and scientific data. The human brain has not changed in over 200,000 years; yet human beings have developed in language, art, technology, and culture. These developments have stamped humans with a unique identity that is far different than any other species on the planet. Currently, there is a disagreement in theory as to how or why consciousness has shifted over time; however, there is overwhelming evidence that it is shifting again. In the book, The Ever Present Origin, Jean Gebster[ Gebster, 1983] puts forth a theory, which follows the progression and subsequent "mutation" of consciousness from the early hominid, to present day man, and into the future. These developments in consciousness, according to Gebser, occur because of the ever-changing relationship of human beings to space and time. Gebser argues that human consciousness is in transition; therefore, if consciousness mutated in the past, then it will, by simple logic, mutate again. Gebser's book effectively chronicles these changes in consciousness. Through his research into the past eras of human history, Gebser identifies four previous structures of consciousness: Archaic, Magic, Mythic, and Mental. He also states that *


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human beings are in the process of mutating into a new structure that he termed Integral consciousness. There is a direct link between these “structures” of consciousness and specific correlative brainwave states. This interconnection suggests that the human brain adapts to the new structure by adding a corresponding brainwave that aids in explicating and interpreting the new world coming into view. This suggests that the higher brainwaves in the known spectrum were yet dormant and inaccessible to early humans, and, as mutation occurred, there was a reciprocal unfolding of ever-higher frequency waves. This determination also reveals a profound relationship between the developmental growth of a human being, and the development of the species at large, shedding new light on the symmetrical recapitulation of ontogeny and phylogeny. Based on data from Jean Gebser’s model, the Archaic structure of consciousness is directly associated with Delta brainwaves. Furthermore, the Magic structure is associated with Theta brainwaves, the Mythic structure with Alpha brainwaves, and the Mental with Beta brainwaves. This suggests that the new structure on the horizon, which is deemed Integral consciousness, will be accompanied by its’ very own set of brainwave patterns, those of the Gamma wave band. Human beings have acquired brainwave frequencies well up into the Beta range. These brainwaves have been proven to predominate at various stages of development. Human beings will also gain access to Gamma oscillations as their dominant frequency, which allow for higher mental cognition and neuronal synchronization. This will “integrate” the other brainwave states together; creating what philosopher Sri Aurobindo has termed the Supermind. Once this system comes fully online, it will enable a transparent vision of human history, sear the divisive lines of past and future, and bring complete clarity to the development of consciousness. This in turn, will unfold for each and every human being the very meaning of life. The Archaic structure, which there is very little evidence of, can be thought of as a totally nondifferentiated state where humans and nature are in a fused identity. Gebser states that this structure of consciousness was identical to biblical paradise and original wholeness. Keep in mind however, that this paradisiacal state was not a conscious heaven, but rather an unconscious hell. Gebser ties this structure to the early hominid, and to the unconscious, deep-sleep state. The emergence of the Magic structure was, above all, a transition from zero-dimensional undifferentiated identity, to one-dimensional fused unity. In this stage of early development, the identity with Archaic consciousness began to wane. Men and women began to separate themselves from the grip of nature, and saw themselves instead, juxtaposed against an organic backdrop. There was an instinctual banding together during this period of pre-history. The people of this period began to form close knit communities that would mate, hunt, and protect one another from the ravages of nature. This period is best known for its' cave paintings. In part, these paintings tell a great deal about the consciousness during that time. One famous painting ISSN: 2153-8212


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shows a buffalo-hunting scene, where the arrows are all pointing intently towards a fleeing buffalo. According to Gebser, this scene represents magical unity, for in fact, the hunters, buffalo, and arrows, are all part of a unified field, which has the dimly lit consciousness spread out over the world into a group ego. Just as the Archaic structure was an expression of zero-dimensional identity and original wholeness, and the Magic structure, an expression of one-dimensional unity and merging with nature, so is the Mythic structure the expression of two-dimensional polarity. Once human beings extracted themselves more fully from nature, and consciousness began to dwell in the individual, a huge shift came about in the way they operated in the world. The emphasis for them changed from being in the world to having a world. This period is best known for the birth of the Myth. These cosmogonical stories tell of mankind's origins, ancestors, parents, as well as, eternal parent figures that came in the form of Gods and Goddesses. With the advent of this new world-view, mankind is so effectively removed from the grip of nature that for the first time they were able to see it, study it, and in a certain sense, measure it, utilizing it to their advantage. This period is synonymous with the birth of agriculture in Egypt, the rise of the calendric system in the Mayan civilization, and the birth of contemplative religions around the world. It is interesting to note that Gebser also equates this structure with the beginning of recorded history, and so the beginning of time in consciousness. While, according to Gebser, the liberating struggle against nature in the Magic structure brought about a disengagement from nature, and an elementary awareness of the external world, the Mythic structure lead to the emergent awareness of the internal world of the soul, and bore the stamp of the imagination. Scarcely five hundred years ago, during the Renaissance, another unmistakable reorganization of consciousness occurred; the discovery of perspective in painting, which opened up the threedimensionality of space. This period, which Gebser deemed the Mental structure, marked the birth of the Ego, which has been symbolized by a narcissistic and materialistic attitude that has indeed, become synonymous with modern culture and society. The discovery of perspective also brought time into its contemporary maturity. Before the Mental structure appeared, the cyclic nature of the universe had been observed meticulously. The seasons had been mapped and agriculture was flourishing. However, there was another distinct yet surreptitious segregation of time as the polar days and nights, and the cyclical calendar, was broken into a further ratio of hours, minutes, and even seconds. This division of time, this quantifiable measuring of moments, brought with it a host of other methods of measuring, namely the sciences of the world. Once time was instituted and mastered, mankind proceeded to measure and label the world until everything and everyone in it was segregated. This severing of original Archaic wholeness, one-dimensional Magical unity, and ISSN: 2153-8212


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even two-dimensional Mythic polarity, gave rise to three-dimensional Mental duality. This duality effectively took polar compliments and rendered them as diametric opposites. So the cycle of day/night gave way to the dialectic adage, “different as night and day.” Time was also sequestered and spatialized into a past, a present, and a future...the three familiar dimensions of every day life. Presently, according to Gebser, mankind is coming to the deficient phase of the Mental structure. When a structure of consciousness is no longer fit for survival, a new “mutation” with more complexity and organization will enter to take its place. Gebser stresses the word mutation in lieu of evolution. In Gebser’s model, consciousness is not a biological process bound by the laws of natural selection and progress, but rather a spiritual phenomenon that is always existing and ever-present. What is to come next Gebser terms the Integral structure of consciousness. This structure will be beyond space, beyond time, and beyond the purely mental conceptions of our present day modern/post modern world. This unique structure, according to Gebser, will have the ability to make the other structures transparent, thereby integrating them and rendering them available to consciousness. The evolution of a large, complex brain has been the defining feature of the human lineage although human brain size has not changed over the past 200,000 years.i So, what is it that has evolved? Looking carefully again at Gebser's model of consciousness, there are distinct correlations between the description of the structures of consciousness and the description of brainwave states. For example, if the Archaic structure of consciousness and the Delta brainwave state are viewed as amalgams of one another, it begins to shed light on the possible inner workings of consciousness and evolution. The most important defining characteristic of this thesis is that during the Archaic structure, the dominant brain wave state available/accessible to early humans was the Delta wave. And, as mutation through the other structures of consciousness occurred as a result of deficiency, the human brain evolved by accessing other mutually supporting brainwaves. These new brainwaves would allow humans to not only be able to adapt and survive, but also to create a mental map of each new world into which he or she mutated. Now, taking into account the previous subsequent brainwave additions up until the Mental structure, then by simple logic, it can be postulated that a new brainwave will become dominant in the newly emerging Integral structure. Based on the evidence, the new brainwave will be the recently discovered Gamma brainwave.

2. Brainwaves and Consciousness This theory is in part, based on the comparative analysis of the ontogenetic and phylogenetic development of brain structures and functions, the evolution of different brainwave spectrums, and their correlations with different structures of consciousness. ISSN: 2153-8212


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It is well known that the brain is an electrochemical organ; researchers calculate that if all 10 billion interconnected nerve cells discharged at one time that a single electrode placed on the human scalp would record something like 5 millionths to 50 millionths of a volt.Even though this electrical power is very limited, it does occur in very specific ways that are characteristic of the human brain. Electrical activity emanating from the brain is displayed in the form of brainwaves. These brainwaves are measured using a process called electroencephalography, or simply EEG, which is the recording of electrical activity along the scalp produced by the firing of neurons within the brain. It has been documented that the EEG dimensions in humans steadily increase with age. Simply stated, experiences accumulated in the brain over time, form into cortical cell assemblies. These cell assemblies cause more organizational complexity throughout the brain, which require higher frequency brainwaves to operate. Thus, the "wisdom of old age” may find its neurophysiological basis in greater complexity of brain dynamics compared to younger ages. It has also been shown that certain brainwaves predominate at certain developmental stages. These waves slowly increase over time to accommodate for various learned behaviors, as well as genetic development. Through this development unfolds a corresponding “world view”, or picture of reality. It is this picture of reality that Jean Gebser equated directly to his structures of consciousness. Taken one step further, it would be completely plausible to assume that if the ontogeny forms through the successive addition of brainwaves, then too should the corresponding phylogeny develop in the same manner.

3. The model Schuman and Brain waves The measured frequencies of Schuman and brainwaves are nearly the same. [Persinger].In Fig 1. we present our calculations of the spectra . It is worth to underline that both calculated curves give a rather good description of the measured frequencies of Schuman and brain waves [ Marciak-Kozlowska 2013, 2015] In this paper we developed hypothesis that the human brain waves and Schuman waves are the same electromagnetic waves with different amplitudes only. Moreover the ratio of the amplitudes are independent of frequencies , Fig.1

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ENERGY Density SPECTRUM W M^2 Hz

SCHUM AN and BRAIN WAVES

10 9 10 10 10 11 10 12 10 13

0

2.

10 144.

10 14 6.

10 148.

10 14 1.

10 13 1.2

10 13 1.4

10 13

ENERGY eV

Fig.1 The energetic spectra of the Schumann and brain waves [Marciak-Kozlowska, 2015]

3. Our hypothesis 1 Brain waves and Schumann waves are the same waves with Schumann waves of a greater amplitude. 2. Brain waves are result of interaction of the Schumann waves with neurons In the following, we consider one-dimensional Schumann wavet transfer phenomena (Marciak-Kozlowska, 2011). In this monograph the hiperbolic master equation for Schuman wave phenomena was formulated

1  2 m  2Vm 2   )   . 2  2 t 2 t x 2

(

(1)

In this equation m is the mass of the neuron, - is the Planck constant, V is potential and v is the velocity propagation of the Schumann wave in thebrain.We seek a solution in the form

( x, t )  e 2 u( x, t ) for the quantum equation (1).After substitution of Eq. (2) into Eq. (1), one obtains t

1  2u  2u  2  q 2 u ( x, t )  0, 2 2 υ t x

(3)

where

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(2)

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Journal of Consciousness Exploration & Research | February 2017 | Volume 8 | Issue 2 | pp. 160-167 Marciak-Kozłowska, J. & Kozlowski, M., On the Interaction of the Schumann Waves with Human Brain 2

2Vm  mυ   .  2  2  The structure of Eq. (3) depends on the sign of the parameter q2. q2 

For the initial Cauchy condition

u ( x,0)  g ( x), t and the solution of the Eq. (3) has the form [Marciak-Kozlowska, 2013] u ( x,0)  f ( x),

u ( x, t ) 

f ( x  υt )  f ( x  υt ) 2 x  υt 1  g (ς ) I 0  q 2 (υ 2 t 2  ( x  ς ) 2 ) dς  2υ x υt



υ  q2 t  2

x  υt



f (ς )

(4)





I 1  q 2 (υ 2 t 2  ( x  ς ) 2 ) υ t  (x  ς) 2 2

x υt

2

(5)

dς.

When q2 > 0 Eq. (3) is the Klein – Gordon equation (K-G), which is well known from applications in elementary particle and nuclear physics. For q2< 0 Eq,3 is the modified Klein –Gordon Equation with the solution

u ( x, t ) 

f ( x  υt )  f ( x  υt ) 2 x υt 1  g (ς ) J 0 q 2 (υ 2 t 2  ( x  ς ) 2 ) dς  2υ xυt







(6)



υ q 2 t xυt J 0' q 2 (υ 2 t 2  ( x  ς ) 2 )  f (ς ) dς. 2 x υt υ 2t 2  ( x  ς ) 2 In formulae (5) and (6 ) Functions J n(x) and In(x) are Bessel functions [ Zauderer, 1989] Both solutions (5) and (6) exhibit the domains of dependence and influence of the modified Klein-Gordon and Klein-Gordon equation. These domains, which characterize the maximum speed at which a disturbance can travel are determined by the principal terms o f the given equation (i.e., the second derivative terms) and do not depend on the lower order terms. It can be concluded that these equations and the wave equation (for m =0) have identical domains of dependence and influence. The special case is the q 2=0. In that case we obtain the relations between the relaxation time tau and potential ISSN: 2153-8212


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V 

(7)



(8)

mv 2

a nd  is the relaxation time for nergy of the Schumann waves in neuron. Equation (7) is the Heisenberg iformula for Schumann- Brain waves in human brain Potential V is the barrier for the „intruders” to neuron brain It can be calculated following the values of relaxation time for biological structures  is of the order of 1 sec.From formula ( 7) we obtain V



 1015 eV

(9)

and that potential Energy we obtained as the temperature of the brain wave source[ Marciak Kozłowska, 2013, 2015]

3. Conclusions The human being is immersed in electromagnetic field of Schuman waves which influence the contemporary human evolution . It seems to me that Schumann wave are the carriers of the reach information , which for the moment are not know. One hint of existence of this information is the influence of the Schumann field on the psychics of the humans In the light of our study these psychics phenomena are correlated with Schumann wave due to possible interfernce of the Schumann and brain waves – both waves have the same frequencies and velocities= light velocities

References Gebser J, The Ever Present Origin, Ohio University Press, Athens, Ohio. (1985) p 120-121 Persinger M, Schumann resonances frequencies found within quantitative electroencephalographic activity implications for Earth- Brain Interactions Int. Letters of Chemistry , Physics, Astronomy, vol 30,2014 Zauderer E, Partial Differential Equations of Applied Mathematics,, John Wiley & Sons, 1989 Kozlowski M Marciak-Kozlowska J,Heisenberg Uncertainty Principle and Human Brain, Neuroquantology .vol 11 ,2013 Kozlowski M, Marciak-Kozlowska J, Schumann Resonance and Brain Waves: A quantum description Neuroquantology, vol13, 2015

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Journal of Consciousness Exploration & Research | March 2017 | Volume 8 | Issue 3 | pp. 179-188 Kozlowski, M., & Marciak-Kozłowska, J., New Schrodinger Equation with Consciousness Term

179

Research Essay

New Schrodinger Equation with Consciousness Term *


Warsaw University, Warsaw, Poland Institute of Electron Technology, Warsaw, Poland

Abstract In this paper, we developed the new Schrodinger equation with elementary memory term. With the equation we describe Bohm pilot wave which is responsible for the memory (consciousness) of elementary particles. It is the first step in the quest for describing consciousness on the quantum level. Keyword: Quantum mechanics, Schrodinger equation , consciousness, memory.

1. Introduction I am opposing not a few special statements of quantum mechanics held today. I am opposing as it were whole of it, I am opposing its basics views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody. E. Schrodinger- July 1952 Colloqium, in E. Schrodinger The interpretation of Quantum Mechanics, edited by Michel Bitbol, Ox Bow Press,1995.

One of the fundamental aspect of human consciousness is memory. Within contemporary science possibilities, the memory as well as consciousness is far from being explained. The basic problem with consciousness is that we have not the master equation for describe the consciousness in mathematically precise way. For that we must reconsider ab ovo the basic equation of physics–Schrodinger equation and generalize it for inclusion the memory (consciousness) term. In this paper we will followed the D. Bohm hypothesis on existence consciousness on the quantum level. To that aim started with classical diffusion theory we will obtain Schrodinger hyperbolic equation (with second time derivative) which will describe elementary consciousness ( memory)

* Correspondence: Miroslaw Kozlowski, Prof. Emeritus, Warsaw University, Poland. Email: [email protected] ISSN: 2153-8212


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1. Mathematical introduction to classical thermodynamics In classical thermodynamics the energy flux is defined as ( J.Marciak-Kozłowska, M.Kozłowski,2017} t

q(t )    K (t  t ' ) T (t ' )dt'.      thermal history

(1)

diffusion

In Eq. (1) q(t) is the density of the energy flux, T is the temperature of the system and K(t – t') is the thermal memory of the system

K (t  t ' ) 

K  (t  t ' )  exp , τ τ  

(2)

where K is constant, and τ denotes the relaxation time. As was shown in (J. Marciak-Kozlowska, M.Kozłowski,2017)   Kδ (t  t ' )  K (t  t ' )   K  constant K (t  t ' )   exp   τ τ  

diffusion wave damped wave or hyperbolic diffusion.

The damped wave or hyperbolic diffusion equation can be written as (J.Marciak -Kozlowska, M.Kozlowski,2017):

 2T 1 T DT 2    T. t 2 τ t τ

(3)

For τ  0 , Eq. (3) is the Fourier thermal equation T  DT  2T t

(4)

and DT is the thermal diffusion coefficient. The systems with very short relaxation time have very short memory. On the other hand for τ   Eq. (3) has the form of the thermal wave (undamped) equation, or ballistic thermal equation (5).

 2T DT 2   T. t 2 τ

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(5)

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In the solid state physics the ballistic phonons or electrons are those for which τ   . The experiments with ballistic phonons or electrons demonstrate the existence of the wave motion on the lattice scale or on the electron gas scale. For the systems with very long memory Eq. (3) is time symmetric equation with no arrow of time, for the Eq. (5) does not change the shape when t  t . In Eq. (3) we define:

D  υ   T ,  τ 

(6)

λ  υτ ,

(7)

velocity of thermal wave propagation and

where λ is the mean free path of the heat carriers. With formula (6) equation (3) can be written as

1  2T 1 T  2   2T . 2 2 υ t τυ t

(8)

From the mathematical point of view equation:

1  2T 1 T    2T 2 2 υ t D t is the hyperbolic partial differential equation (PDE). On the other hand Fourier equation 1 T   2T D t

(9)

and Schrödinger equation

i

 2 2    t 2m

(10)

are the parabolic equations.

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2. Hyperbolic Schrodinger equation Formally with substitutions

t  it ,   T

(11)

Fourier equation (9) can be written as i

   D 2  t

(12)

and by comparison with Schrödinger equation one obtains

DT  

2 2m

(13)

 . 2m

(14)

and DT 

Considering that DT  τυ 2 (6) we obtain from (14)

τ

 . 2mυh2

(15)

Formula (15) describes the relaxation time for quantum thermal processes. Starting with Schrödinger equation for particle with mass m in potential V:

i

 2 2     V t 2m

(16)

and performing the substitution (11) one obtains

T  2 2   T  VT t 2m

(17)

T  2 V   T  T. t 2m 

(18)



Equation (18) is Fourier equation (parabolic PDE) for τ = 0. For τ  0 we obtain

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τ

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 2T T V  2   T  T, 2 t t  2m τ

(19)

 2 mυ 2

(20)

or

1  2T 2m T 2Vm   2 T   2T . 2 2 υ t  t  With the substitution (11) equation (19) can be written as

i

 2 2  2  V      2 . t 2m t

(21)

 2 t 2

(22)

The new term, relaxation term



describes the memory term for particle with mass m. The relaxation time τ can be calculated as: 1 ,  1   e1p  ...   Planck

(23)

where, for example τe-p denotes the scattering of the particle m on the electron-positron pair (  e p ~ 1017 s) and the shortest relaxation time τPlanck is the Planck time ( τ Planck ~ 1043 s). From equation (23) we conclude that τ  τ Planck and equation (21) can be written as

i

 2 2  2  V     τ Planck  2 , t 2m t

(24)

where 1

τ Planck

1  G  2    5   . 2 c  2M p c 2

(25)

In formula (25) Mp is the mass Planck. Considering Eq. (25), Eq. (24) can be written as

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i

184

 2 2 2 2 2  2     V  2  2  . t 2m 2M p 2M p 2M p c 2 t 2

(26)

The last two terms in Eq. (26) can be defined as the Schrodinger Bohmian ( D. Bohm) pilot wave equation 2  2  2 2   0, 2M p 2M p c 2 t 2

(27)

i.e.

2 

1  2  0. c 2 t 2

(28)

It is interesting to observe that pilot wave  does not depend on the mass of the particle. The pilot wave holds the memory ( consciousness) of the particle With postulate (28) we obtain from equation (26) i

 2 2 2     V  2 t 2m 2M p

(29)

2  2  2 2    0. 2M p 2M p c 2 t 2

(30)

and simultaneously

In the operator form Eq. (21) can be written as pˆ 2 1 Eˆ   Eˆ 2 , 2 2m 2 M p c

(31)

where Eˆ and pˆ denote the operators for energy and momentum of the particle with mass m. Equation (31) is the new dispersion relation for quantum particle with mass m. From Eq. (21) one can concludes that Schrödinger quantum mechanics is valid for particles with mass m « MP. But pilot wave exists independent of the mass of the particles. For particles with mass m « MP Eq. (29) has the form of the Schrodinger equation

i

 2 2     V. t 2m

(32)

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 2   2   V, t 2M p

(33)

but considering Eq. (30) one obtains   2  2   V t 2M p c 2 t 2

(34)

 2  2   i  V  0. 2 2 2M p c t t

(35)

i

or

We look for the solution of Eq. (35) in the form  ( x, t )  eiωt u ( x).

(36)

After substitution formula (36) to Eq. (35) we obtain 2 ω2  ω  V ( x)  0 2 2M p c

(37)

with the solution  M pc2  M pc2 1  ω1 

  M pc  M pc 2

ω2 

2V M pc2

(38) 2

2V 1 M pc2



2 for M p c  V

2

and  M p c 2  iM p c 2 ω1 

  M p c 2  iM p c 2

ω2  ISSN: 2153-8212

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(39) 2V 1 M pc2




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M pc2 2

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 V.

Both formulae (38) and (39) describe the string oscillation, formula (27) damped oscillation and formula (28) over damped string oscillation.

3. The time evolution of the memory Schrodinger -Bohmian pilot wave D. Bohm presented the pilot wave theory in 1952 (Bohm D,1979) and de Broglie had presented a similar theory in the mid 1920’s. It was rejected in 1950’s and the rejection had nothing to do with de Broglie and Bohm later works. There is always the possibility that the pilot wave has mind like property. That’s how Bohm described it. We can say that all the particles in the Universe end even Universe have their own pilot waves, their own information. Then the consciousness is the very complicated receiver of the surrounding pilot wave fields. In our monograph we study of the Schrödinger-Bohm (SB) equation for the pilot wave

i

 2 2 2 2  2 1  2      2 2  .     V  2  t 2m 2M p 2M p  c t 

(40)

In Eq. (40) m is the mass of the quantum particle and MP is the Planck mass ( M P  10-5 g). For elementary particles with mass m > MP equation (40) has the form:

i

 2 2  2  t 2M p 2M p

 2 1  2      2   V c t 2  

(42)

or   2  2 i   V t 2M p c 2 t 2

and is independent of m.

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In the following we will discuss the pilot wave time evolution for the macroscopic particles, i.e. for particles with m >> MP . For V = const. we seek the solution of Eq. (3.42) in the form:

  e γt .

(43)

After substitution formula (.43) to Eq. (42) one’s obtains

2M P2 c 2 2M P2 c 2 M Pγ  γ V 0  2 2

(44)

with the solution

γ1, 2  

iM P c 2 M P c 2   

1

2V . M Pc2

(45)

For a free particle, V = 0 we obtain:

γ1, 2

0,    2M P c 2 i.   

(46)

According to formulae (43) and (46) equation (42) has the solution

 (t )  A  Be



2 M P c 2i t 

.

(47)

For t = 0 we put  (0)  0 , then 2 it     (t )  A1  e τ P ,    

(48)

where τP = Planck time

τP 

 M pc2

.

(49)

From formula (48) we conclude that the free particle in reality is jittering with frequency

   1 and quantum energy E   = 1019 GeV and period T = 10 – 43 s.

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4. Conclusions In this paper we show, that the generalization of the parabolic Schrodinger equation to hyperbolic partial differential equations leads to possibility of the study of consciousness on the quantum level. The consciousness is operated by wave equation (hyperbolic equation) which do not dependent on the mass of particle, even for humans. This the first time when new quantum equation can describe consciousness as a pure quantum phenomenon.

References Kozlowski M, Marciak-Kozlowska J, Introduction to Attoscience, Lambert Academic Publishing, 2017. Bohm D, Quantum theory, Dover Publication, 1980.

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Journal of Consciousness Exploration & Research | March 2017 | Volume 8 | Issue 3 | pp. 189-197 Kozlowski, M., & Marciak-Kozłowska, J., Binding Energy of the Human Brain

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Research Essay

Binding Energy of the Human Brain *



Abstract In this paper, we calculated the binding energy of the human brain and volume occupied by matter in the brain. It turns out that the binding energy - 1030GeV- is the first and fundamental quantum property of the brain. The structure of the brain is rather strange. The matter is from macroscopic point of view absent! Human brain is empty of the matter. We argue that considering mass contents human brain is the sphere of the radius of 0.1m with nucleus of the radius of ( 10-15 m3)1/3= 10-5m. Keyword: Brain, binding energy, neurons.

1. Introduction Good design is created when awareness brings the subconscious to the forefront. When we consider all the information contained within your perceptional context, it is really quite complex: background, foreground, specific objects, relationships between those objects, the parts those objects are made up of, their order—well, you get the idea. That we are able to make sense of any of this is really quite a feat. Most of it is far too detailed to register at the conscious level, but when involved in the process of intentional design, the principles must be taken into consideration and can be realized with a little effort. Our investment of effort to make the viewer's experience effortless is well worth the response to your design (Marciak-Kozlowska, J., Kozlowski, M., 2016) The word gestalt is derived of a German word meaning "shape, form, figure, configuration, or appearance" and is also tied to the more obsolete term stellen, which means "to place or arrange." Most simply put, gestalt is the arrangement of form in various patterns. Gestalt theory has traditionally been used by psychologists as a way to assemble an entire picture of a personality. But it has evolved into becoming relevant to anything that uses the context of basic principles to define highly detailed or complex relationships and how they are expressed as a "whole" composite.

* Correspondence: Miroslaw Kozlowski, Prof. Emeritus, Warsaw University, Poland. Email: [email protected] ISSN: 2153-8212


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2. Historical perspective In the preface to the first (German) Edition of the book “Collected Papers on the Quantum Mechanics” , Zurich 1926 E Schrodinger wrote: a young lady friend recently remarked to the Author (Schrodinger) “When you began this work you have no idea that anything so clever would come out of it , had you.” This unorthodox comparison between scientific and purely aesthetic communication is able to provide a first clue towards criteria distinguishing good fantasy in science from bad. Science as a crowning intellectual achievement is essentially disciplined; but it is not always easy to realize the need for an equally severe discipline in the domain of the imaginative arts. Imagination and intellect, however, are not always in antithesis to one another. Reason implies not only a capacity for logical sequence of argument, but also a sensitivity to balance and contrast a trained intuition without untrained intuition s arrogant claims to shortcircuit the discipline of the intellect When the imagination thus becomes disciplined, and undertakes the severest obligations inherent in perfecting the pattern of an art-form, it has taken the essential step towards security against the weaknesses of fantasy. Structure as disciplined as that of a mathematical argument is capable of transfiguring the merest nonsense into divine nonsense. Modern physics might well be regarded as study of the structure of matter and of the behavior of radiation. A criterion for success pursuit of the former study demands that analysis of material structures into atoms and molecules, and of these into nuclei with groups of associated electrons, must be capable of giving rise to verifiable prediction of the bulk properties of matter, mechanical, thermal, chemical, and electrical. Criteria for theories as to the behaviour of radiation are that the phenomena of light, colour, radio, X-rays, heat radiation, must become explainable by some single mechanism; the only mechanism so far successful has been the propagation of electric and magnetic quantities with a unique and universal speed which is accurately measurable. This speed exceeds that of the fastest material particles, as a limit towards which the latter can only approach. Within the scope of these two most general schemes, the structure of matter has been a prime example of pattern since D Mendeleyev in XIX century arranged all the then known chemical species or elements into a two- dimensional framework. Written down in a table of horizontal rows and vertical columns, the chemical elements were found to repeat certain properties periodically, much as the harmonic properties of the notes on a piano keyboard repeat themselves at intervals of octaves. To form the gross substances which we distinguish by touch, smell, taste, etc., the affinities for chemical combining of atomic species ISSN: 2153-8212


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are found to wax and wane with precise regularity throughout the periods of this table. The whole assemblage of empirically periodic patterns is now understood as manifesting the way in which successive electrons can become associated with atomic nuclei of definite mass: these additions proceed until one after another their possible federations into electrically and mechanically stable groups or sub-patterns are. There have been eras in which an educated man could only live up to his standard if he were at the same time a poet and a philosopher and an experimental or mathematical researcher. E. Schrodinger is a good example. He attended a gymnasium, which emphasized the study of Greek and Latin classics. His book Nature and the Greeks published in 1948 is an elegant exposition of ancient physical theories and their relevance. Schrodinger wrote in 1925 an intensely account of his beliefs, Seek for the Road. The book was influenced by Hinduism and is an argument for the essential oneness of human consciousness.

3. The beautiful mathematics/physics During my work as a lecturer in Physics Department, Warsaw University, I like very much the Kepler – Copernicus ( Kopernik in Polish) - Newton panorama of the planet moving. I started as usual with historical facts and write the basic equations. Considering the FQXI community, I left of all steps and start from the equation:

d 2u m 1 1  u   2 2 F  , 2 d L u u 1 u . r (1) Equation 1 is the master equation which describes the movement of the body with mass m in the field of central forces F(1/u). We can imagine the following functions F(1/u) 1 F    K1u π , K 2u 3 , K 3u 2 , K 4u 0.64 , K 5u  4.62 . u (2) We can imagine the “other” universes for which the central forces have the different F(1/u). But can life be originated and developed in all these universes? This question is answered by the anthropic principle and will be discussed later on. For the moment we can say the following: Macroscopic structure of the Universe we live in can be understood with just two forces: Newton and Coulomb. For both forces 1 F    Ku 2 . u (3) ISSN: 2153-8212


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Why? With the forces described by formula (3) we obtain for equation (1) d 2u Km u   2 . 2 d L

(4) with constant on the right hand side of the equation- only for quadratic in u forces Only for that force! Can you imagine! This is miracle, is not? This beautiful equation describes the classical motion of the planets, and electrons round the source of the force F = Ku2. Moreover, the equation (4) in fact is the harmonic oscillator equation, which can be solved at once the solution to the eq. (4) can be written as u  A cos   0  

mK , L2

(5)

or

r

1 mK A cos   0   2 L

. (6)

Equation (6) describes the conic curves: ellipse, parabola and hyperbola depending on constants A, Θ0, m, K and L. We can choose our coordinate axes so that Θ0= 0 to simplify things just a little: 1 r . mK A cos  2 L (7) This is a conic sections. From plane geometry, any conic section can be written as 1 e r  r0 , 1  e cos  (8) where e is called the eccentricity of the orbit.

4. Other dimensions In any higher organism, a large number of cells must be inter-counted by nerve fibers. If space had only two dimensions, an organ-ism could be only a two-dimensional configuration and its nerve paths would cross. At the intersections, the nerves would have to penetrate each other, for absence of a third dimension would not permit a fiber to be led above or below another one. As a consequence nerve impulses would mutually interfere. The existence of a highly developed organism having many non-intersecting nerve paths in thus possible only in a space having at least three dimensions.

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As we know both the Newtonian gravitational force and electrostatic force can be described in the three dimensional space (formula (9)) K F 2, n  3, r (9) where n is the number of dimension of space. For n  3 the natural generalization of formula (1.180) is F  n  2

K r n 1

,

n  2.

(10) The impossibility of stable planet orbit for n > 3 can be seen in an elementary way. Let m be the mass of planet and L angular momentum (which is constant for the central force (1.181))  L  mr 2  = const. (11) The gravitation potential for the conservative force will be K V   n 2 . r

(12)

At the extreme distances from the central body for a planet with mass m, we have dr  0. dt

(13)

The kinetic energy T at such points is T

p2 1 2  2  mr  , 2m 2

(14)

L2 T . 2mr 2

(15)

then

By conservation of mechanical energy T + V = constant, or

L2 K L2 K    n 2 , 2 n 2 2 2mr1 r1 2mr2 r2

(16) where r1 is the minimum distance from the central body and r2 is the maximum distance, perihelion and aphelion respectively. The equation (16) shows that for n = 4 there can be a finite, positive solution only if r2 > r1. For n > 4 it can be shown that an orbit in which r oscillates between two extremes is likewise ruled out. In general the centripetal force in a circular orbit is

 2. Fc  mr 2  ISSN: 2153-8212


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Using Eq. (15) this becomes L2 Fc  . mr 3

(18) In the actual eccentric orbit, the attractive force must be less than this centripetal force at perihelion, for then the planet is about to move outward. At aphelion, it is just the other way around. These conditions can be expressed respectively by the following inequalities F  Fc ( n  2) K L  n 1 r1 mr13 2

K

or

r1n 2



L2 , (n  2)mr12

(19)

F  Fc (n  2) K L  n 1 r2 mr23 2

or

K r2n 2



L2 . (n  2)mr22

(21)

L2 L2 L2 L2    . 2mr12 (n  2)mr12 2mr22 (n  2)mr22

(22)

and

L2 mr12

L2 1 1    (n  2)   2 2  2mr2

1 1    (n  2) . 2 

(23) This relation obviously cannot be true for n = 4, for then each of the brackets becomes zero. Remembering that r2 > r1 it also cannot be true for any n > 4, which makes the values of the brackets less than ½. Thus, the existence of an elliptic orbit for n  4 is ruled out. The results for planetary orbits are collected in Table 1. 1. Planetary orbits Phenomena

Cases thus excluded

Bio-topology (existence of a highly developed n 3 orbits n=4 n >4 n Mp, μ = Mp

From formula (19 we conclude that Ψ ( x − ct ) is independent of mass mi. In the case mi < Mp from formulae (19) and (20) one obtains

 m µ = mi 1 − i  Mp 

  

(21)

 m  2m c 2m c 2    2imi c  Ψ ( x − ct ) = exp  ( x − ct )  exp  −i i  i x − i t    Mp  h h  h     In formula (21) we put 2m i c η 2mi c 2 ω= η k=

(22)

and obtain

Ψ( x − ct ) = e

i ( kx −ωt )

−i

e

mi ( kx −ωt ) Mp

(22)

As can concluded from formula (22) the second term depends on the gravity   m 2G  2   m  exp − i i ( kx − ω t ) = exp − i  i  ( kx − ω t )    ηc    M p  1

(23)

where G is the Newton gravity constant. Formula (22) describes the Schumann wave

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Journal of Consciousness Exploration & Research| January 2018 | Volume 9 | Issue 1 | pp. 20-39 Marciak-Kozłowska, J. & Kozlowski, M., The Quantum Process of Consciousness

It is interesting to observe that the new constant, α G ,

αG =

mi2G ηc

(24)

is the gravitational constant. For mi = mN nucleon mass

α G = 5.9042⋅10−39

(25)

4. The Particle in a Box In paper ( to be published)) the quantum model of the consciousness waves was proposed. It was showh that instead of waves alpha, beta , theta,delta, gamma we can say about quantons alpha, beta, gamma ,delta, theta.In this paragraph we consider the simplest model for the emission of quantons We consider quantum mechanical system for a particle of mass mi confined in a one-dimensional box of length L and infinite walls. For the particle to be confined within region II, the potential energy outside (regions I and III) is assumed to be infinite. In order to understand further this system, we need to formulate and solve the Schrödinger equations (26). ih

h2 2 h2 h2 ∂Ψ =− ∇ Ψ +V Ψ − ∇2 Ψ + ∂t 2mi 2M p 2M p

 2 1 ∂ 2Ψ  ∇ Ψ −  . c 2 ∂t 2  

(26)

Considering the pilot wave equation ∇2Ψ −

1 ∂ 2Ψ =0 c 2 ∂t 2

(27)

one obtains ih

∂Ψ h2 2 =− ∇ Ψ + V Ψ, ∂t 2µ

(28)

where µ=

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In region II, V ( x) = 0 −

h2 2 ∇ Ψ + V Ψ = EΨ 2µ

h2 2 − ∇ Ψ + 0 = EΨ 2µ −

h2 2 ∇ Ψ = EΨ 2µ

In regions I and III, V ( x) = ∞ −

h2 2 ∇ Ψ + V Ψ = EΨ 2µ

(28)

h2 2 − ∇ Ψ + ∞Ψ = E Ψ 2µ −

h2 2 ∇ Ψ = ( E − ∞) Ψ 2µ

For regions I and III (outside the box), the solution is straightforward, the wavefunction Ψ is zero.

For region II (inside the box), we need to find a function that regenerates itself after taking its second derivative. h2 2 − ∇ Ψ = EΨ 2µ 2µ E ∇ 2 Ψ = 2 Ψ = −k 2 Ψ , h

(29) 2µ E where we define k = . h2

Perfect candidates would be the trigonometric sine and cosine functions. (30)

Ψ ( x ) = A cos( kx ) + B sin( kx).

To further refine the wave function, we need to impose boundary At x=0, the wave function should be zero.

conditions:

(31)

Ψ (0) = A cos( k 0) + B sin( k 0) = A ⋅1 + B ⋅ 0.

Equation can only be true if A = 0: Ψ ( x ) = B sin( kx ). In addition, at x=L, the wave function should also be zero. Ψ (0) = 0 = B sin(kL).

True when kL = nπ or k =

nπ : L

(32)

nπ Ψ ( x ) = B sin( x ), n = 1, 2,3,... L

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Going back to the Schrödinger's equation, we can then formulate the energies

kL = nπ

and

k=

2µ E h2

2µ E nπ 2µ E n 2π 2 = ⇒ = 2 h2 L h2 L 2 2 2 2 2 nπ h nh h En = = since h = . 2 2 2µ L 8µ L 2π

(34)

Thus, the application of the Schrödinger equation to this problem results in the well known expressions for the wave functions and energies, namely: Ψn =

n2 h2 2  nπ x  E = and . sin  n  8µ L2 L  L 

(35)

From formula (60) we conclude that for “heavy” classical particles, i.e. for mi >> Mp energy spectrum of the particle in the box is independent of the mass of particle En =

n2h2 . 8M p L2

(36)

In paper (Marciak-Kozłowska, Kozłowski,2010) we argue that formula (36) describes the quantum states of the consciousness. The energy of the quanta of the consciousness is of the order of 10-15 eV .Substituting 10-15 eV for En to formula ( 16) and considering the mass of Mp =1031 eV we obtain for the characteristic length, L , the value 10-6 nm., i.e. lower that the nanotubule.. With L=10-6 nm we obtain from formula (36) the following spectrum for brain waves En − E0 = 7 x10−15 , 2.8 x10−15 , 6.3x10−14 ,1.1x10−13 ,1.7 x10−13 eV

(37)

for n=1,2,3,3,5 respectively. E n − E0 h En .E0 are

The brain photons are emitted as quantum deexcitation in the quantum well, i.e. ω n = where ω n is the angular frequency of the brain photons with quantum number n and

the n-excited state for n=1,2,3,4,5 respectively, and E0 is ground state of the quantum well with energy equals zero. . In Table 1 the comparison of the measured ( EEG) and calculated spectra are presented . The agreement is rather good

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Table 1. Comparison of the measured (EEG) and calculated brain photons spectra

Measured enegies , EEG( eV)

Model calculation EEG(eV)

7 x 10-15

7x 10-15

1.7 x10-14

2.8x 10-14

3.4x 10-14

6.3x 10-14

7.0 x10-14

1.1 x10-13

1.4 x10-13

1.7 x10-13

4. Conclusions In this paper, we put forward the quantization of the brain waves. We propose the theoretical model: The well with infinite walls for the calculations of the brain photons ( quantons) spectra. The model is free of additional parameters. By comparison to the measured EEG spectra we obtain the width (dimension of the well,) L=10-6 nm. With value of L we can calculate the whole spectrum of the brain pulsation It is well known that frequencies ν (energies hω ) of the brain photons are nearly equal to the frequencies of the Tesla-Schumann waves. The Tesla-Schumann waves are the resonances in Earth- ionosphere cavity). In the paper, we have also investigated the influence of the gravitation on the brain pulsations and obtain the wave functions for gravity dependent brain waves. The connections of the lighting, the Tesla-Schumann resonances and brain waves can be supported by the observation that the primordial charge channel for lighting has the thickness of the order of 10-6 nm is of the order of the radius of atomic nucleus.

The calculations of the brain waves frequencies are based on the existence of the strand of the medium – the strand of the 1019 protons with width of the order of 10-15 m and length of the 104km- the string of the consciousness. The vibration of this string produce the brain waves. The energies of the brain waves are the energies of the standing waves of the consciousness string

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References Schuman W O, Uber die strahlunglosen Eingenschwingumgen einer leitenden Kugel, die von einer Luftschicht und einer Ionospharenhulle umgeben ist.Z Naturforschung 7a , 149-154,1952. Chand N Israil M , Rai J Schuman resonance frequency variations observed in magnetotelluric data recorded from Garhwal Himalayan region India, Ann. Geophys., 23,3497-3507,2009. Kozlowski M, Marciak-Kozlowska J. Modified Schrodinger equation for particles with mass of the order of human neuron mass, J Neuroquantology, 8,1-8,2010.

Fig1. Energy 10-15 eV= Energy of the the brain quantons

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Journal of Consciousness Exploration & Research| April 2018 | Volume 9 | Issue 4 | pp. 323-327 Kozlowski, M., & Marciak-Kozłowska, J. , The Seeds of Quantum Mechanics (I)

323

Essay

The Seeds of Quantum Mechanics (I) Miroslaw Kozlowski*1 & Janina Marciak-Kozłowska2 1 2


Abstract In this essay, I want to point out that sometimes lack of rational explanation can be attributed to the enormous success of great scientists when they make decisive progress in theory construction in spite of very serious personal objections. Such objections may be of a conceptual or a mathematical nature. Keyword: Seed, quantum mechanics, Balmer formula, rational explanation.

One might call this number (h) the fundamental number of hydrogen; and if one should succeed in finding the corresponding fundamental numbers for other chemical elements as well, then one could speculate that there exist between these fundamental numbers and the atomic weights [of the substances] in question certain relations, which could be expressed as some function. J.J. Balmer, Basel 1885 The process of theory development in physics is a very complex one. The best scientists sometimes proceed on the basis of their mystical intuition, ignoring serious conceptual or mathematical objections well known to them at the time. The results soon justify their actions, but the removal of these objections is often not possible for a very long time. An example is presented with J.J. Balmer. In 1960 Eugene Wigner published his “Richard Courant Lecture in Mathematical Sciences”, which he delivered the previous year at New York University. It bore the often-quoted title “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” [1]. He claimed that there is no rational explanation for the enormous usefulness of mathematics in the natural sciences, and that this borders on the mysterious. In this essay, I want to point out that sometimes lack of rational explanation can be attributed to the enormous success of great scientists when they make decisive progress in theory construction in spite of very serious personal objections. Such objections may be of a conceptual or a mathematical nature. Of course, they very often make seminal progress when there are no such objections or when they are not aware of them, but we are concerned here with those cases where they proceed despite objections, urged on by their intuition.

*


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As the following example will show, the greatness of these people lay exactly in that fact: that they were not deterred by objections no matter how serious they seemed to be. Lesser scientists may not have dared to proceed in this way. While it is true that most physicists are pragmatists concerned primarily with what works, they are often prevented to pursue an idea by the objections raised against it. The greatness of a scientist lies in these cases exactly in their ability to recognize when such objections should be ignored. Soon, history bears them out. It is important to distinguish the objections considered here from those that occur after a new theory is proposed. Such objections often become a matter of general and sometimes very intensive scientific debate. Examples of the latter include the two famous objections raised against Boltzmann’s statistical definition of entropy and its increase as a system approaches equilibrium: the Loschmidt reversibility argument and the Zermelo argument of Poincare recurrence. These difficulties were raised after the theory was proposed, and they were far from the tacit objections known to the originator of the theory at the time. The present paper is not meant as a historical study (though such a study should be made). Nor is it a philosophical study on scientific discovery. It is rather an attempt at pointing to the seemingly unreasonable way in which great scientists propose new theories despite their knowledge of serious objections, and to the fact that their judgment is borne out by their success. The examples below are just a few of the many that could be cited.

The Balmer Formula: 1885

Johann Jacob Balmer (1835-1808) On June 25, 1884, Johann Jacob Balmer took a fairly large step forward when he delivered a lecture to the Naturforschende Gesellschaft in Basel. He first represented the wavelengths of the four visible lines of the hydrogen spectrum in terms of a "basic number" h:

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Balmer recognized the numerators as the sequence 32, 42, 52, 62 and the denominators as the sequence 32 - 22, 42 - 22, 52 - 22, 62 - 22. He wound up with a simple formula that expressed the known wavelengths (λ) of the hydrogen spectrum in terms of two integers m and n:

For hydrogen, n = 2. Now allow m to take on the values 3, 4, 5, … Each calculation in turn will yield a wavelength of the visible hydrogen spectrum. He predicted the existence of a fifth line at 3969.65 x 10-7 mm. He was soon informed that this line, as well as additional lines, had already been discovered. At the time, Balmer was nearly 60 years old and taught mathematics and calligraphy at a high school for girls as well as classes at the University of Basle. Balmer was very interested in mathematical and physical ratios and was probably thrilled that he could express the wavelengths of the hydrogen spectrum using integers. Balmer was devoted to numerology and was interested in questions like how many sheep were in a flock or the number of steps of a pyramid. He had reconstructed the design of the temple given in chapters 40-43 of the Book of Ezekiel in the Bible. How then, you may ask, did he come to select the hydrogen spectrum as a problem to solve? One day, as it happened, Balmer complained to a friend he had "run out of things to do." The friend replied: "Well, you are interested in numbers, why don't you see what you can make of this set of numbers that come from the spectrum of hydrogen?" (In 1871 Ångström had measured the wavelengths of the four lines in the visible spectrum of the hydrogen atom.) Balmer published his work in two papers, both published in 1885. The first, titled 'Notiz über die Spektrallinien des Wasserstoff,' is the source of the equation above. He also gives the value of the constant (3645.6 x 10-7 mm) and discusses its significance: "One might call this number the fundamental number of hydrogen; and if one should succeed in finding the corresponding fundamental numbers for other chemical elements as well, then one could speculate that there exist between these fundamental numbers and the atomic weights [of the substances] in question certain relations, which could be expressed as some function." ISSN: 2153-8212


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He goes on to discuss how the constant determined the limiting wavelength of the lines described by the Balmer formula: "If the formula for n = 2 is correct for all the main lines of the hydrogen spectrum, then it implies that towards the ultraviolet end these spectral lines approach the wavelength 3645.6 in closer and closer sequence, but cannot cross this limit; while at the red end [of the spectrum] the C-line [today called H2] represents the line of longest possible [wavelength]. Only if in addition lines of higher order existed, would further lines arise in the infrared region." In this second paper, Balmer shows that his formula applies to all 12 of the known lines in the hydrogen spectrum. Many of the experimentally measured values were very, very close to Balmer's values, within 0.1 Å or less. There was at least one line, however, that was about 4 Å off. Balmer expressed doubt about the experimentally measured value, NOT his formula! He also correctly predicted that no lines longer than the 6562 x 10¯ 7 mm line would be discovered in this series and that the lines converge at 3645.6 x 10¯7 mm with m = 2, 3, 4, . . . and n = 1, 2, 3, . . . ; but the two constants change in a particular pattern. By higher order, he means to allow n to take on higher values, such as 3, 4, 5, and so on in this manner: nm 3 4, 5, 6, 7, . . . 4 5, 6, 7, 8, . . . 5 6, 7, 8, 9, . . . At first Balmer's formula produced nothing but puzzlement, since no theoretical explanation seemed possible. In 1890 Johannes Robert Rydberg generalized Balmer's formula and showed that it had a wider applicability. He introduced the concept of the wave number v, the reciprocal of the wavelength, and wrote his formula as v = R (1/n12 - 1/n22) where n1 and n2 are integers and R is now known as the Rydberg constant (value = 10973731.534 m¯1). Later, many other atomic spectral lines were found to be consistent with this formula. In 1885, Balmer wrote these prophetic words: It appeared to me that hydrogen . . . more than any other substance is destined to open new paths to the knowledge of the structure of matter and its properties. In this respect the numerical relations among the wavelengths of the first four hydrogen spectral lines should attract our attention particularly.

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What one can learn from this is the following: It is today’s common wisdom that the most important thing to know about the scientific method is that it does not exist. There is no general procedure which, when used, will lead to the solution of a given scientific problem. Every field of science uses different tools of research, different techniques, different methods. And when one tries to find the common denominator of all of these, precious little of it is left for the pronouncement of a general “scientific method.” This view, however, comes about by looking at the scientific method as prescriptive. From a descriptive view point, there is a lot to be learned from the way the best scientists work. As the above anecdotal reports indicate, intuition, the “feeling of what’s right,” provides the incentive for a scientist’s creativity. And, as is evident, he or she does so even in the face of serious misgivings about the project. That tremendous progress is made in this way is exactly what makes intuition so unreasonably effective. However, one can go one step further and ask post facto just exactly what was the nature of the problems that were knowingly ignored. Newton published his theory despite his serious misgivings that his gravitational force acted at a distance; it took general relativity to clear that up. Schrödinger ignored that the relativistic theory is in worse agreement than the nonrelativistic one; it took the discovery of spin to clear that up. Dirac did without quantum mechanics in the point limit (he argued that it should not be needed); a quantum mechanical treatment of a point charge was not available until forty years later, and even then, only on the nonrelativistic level. Dyson ignored the lack of a rigorous mathematical foundation of QED; such a foundation is today still not available in its entirety. In all these cases, the problems that were ignored turned out to be considerably more difficult than the problems that were actually solved; typically, their solutions required a much deeper level of theory than the level on which progress was made. Thus, looking back, one finds that it was utterly reasonable to ignore those problems at the time. The genius of these scientists consisted not only of their ability to solve the problems they did solve, but also of their ability to distinguish those problems that cannot be solved yet because they belong to a deeper level than those that can be solved now. Their progress depended crucially on this ability. This insight raises an interesting question: are there problems in present-day physics that should be ignored until we have a deeper-level theory? For instance, one wonders whether the measurement problem of quantum mechanics (sometimes called “the collapse of the wave function problem”) is of this nature. Seventy years of effort involving a very large number of attempts since the founding of nonrelativistic quantum mechanics has not resulted in a definitive solution. Nor has this problem been resolved by going to the relativistic level. Apparently, it is not yet accessible to solutions even at that level, and a still deeper level of theory will be necessary.

References 1. E. P. Wigner "The unreasonable effectiveness of mathematics in the natural sciences,” Commun. Pure Appl. Math. XIII. 1-14 (I960). ISSN: 2153-8212


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Essay

The Seeds of Quantum Mechanics (I) Miroslaw Kozlowski*1 & Janina Marciak-Kozłowska2 1 2


Abstract In this essay, I want to point out that sometimes lack of rational explanation can be attributed to the enormous success of great scientists when they make decisive progress in theory construction in spite of very serious personal objections. Such objections may be of a conceptual or a mathematical nature. Keyword: Seed, quantum mechanics, Balmer formula, rational explanation.

One might call this number (h) the fundamental number of hydrogen; and if one should succeed in finding the corresponding fundamental numbers for other chemical elements as well, then one could speculate that there exist between these fundamental numbers and the atomic weights [of the substances] in question certain relations, which could be expressed as some function. J.J. Balmer, Basel 1885 The process of theory development in physics is a very complex one. The best scientists sometimes proceed on the basis of their mystical intuition, ignoring serious conceptual or mathematical objections well known to them at the time. The results soon justify their actions, but the removal of these objections is often not possible for a very long time. An example is presented with J.J. Balmer. In 1960 Eugene Wigner published his “Richard Courant Lecture in Mathematical Sciences”, which he delivered the previous year at New York University. It bore the often-quoted title “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” [1]. He claimed that there is no rational explanation for the enormous usefulness of mathematics in the natural sciences, and that this borders on the mysterious. In this essay, I want to point out that sometimes lack of rational explanation can be attributed to the enormous success of great scientists when they make decisive progress in theory construction in spite of very serious personal objections. Such objections may be of a conceptual or a mathematical nature. Of course, they very often make seminal progress when there are no such objections or when they are not aware of them, but we are concerned here with those cases where they proceed despite objections, urged on by their intuition.

*


ISSN: 2153-8212


227

www.JCER.com


324

As the following example will show, the greatness of these people lay exactly in that fact: that they were not deterred by objections no matter how serious they seemed to be. Lesser scientists may not have dared to proceed in this way. While it is true that most physicists are pragmatists concerned primarily with what works, they are often prevented to pursue an idea by the objections raised against it. The greatness of a scientist lies in these cases exactly in their ability to recognize when such objections should be ignored. Soon, history bears them out. It is important to distinguish the objections considered here from those that occur after a new theory is proposed. Such objections often become a matter of general and sometimes very intensive scientific debate. Examples of the latter include the two famous objections raised against Boltzmann’s statistical definition of entropy and its increase as a system approaches equilibrium: the Loschmidt reversibility argument and the Zermelo argument of Poincare recurrence. These difficulties were raised after the theory was proposed, and they were far from the tacit objections known to the originator of the theory at the time. The present paper is not meant as a historical study (though such a study should be made). Nor is it a philosophical study on scientific discovery. It is rather an attempt at pointing to the seemingly unreasonable way in which great scientists propose new theories despite their knowledge of serious objections, and to the fact that their judgment is borne out by their success. The examples below are just a few of the many that could be cited.

The Balmer Formula: 1885

Johann Jacob Balmer (1835-1808) On June 25, 1884, Johann Jacob Balmer took a fairly large step forward when he delivered a lecture to the Naturforschende Gesellschaft in Basel. He first represented the wavelengths of the four visible lines of the hydrogen spectrum in terms of a "basic number" h:

ISSN: 2153-8212


228

www.JCER.com


325

Balmer recognized the numerators as the sequence 32, 42, 52, 62 and the denominators as the sequence 32 - 22, 42 - 22, 52 - 22, 62 - 22. He wound up with a simple formula that expressed the known wavelengths (λ) of the hydrogen spectrum in terms of two integers m and n:

For hydrogen, n = 2. Now allow m to take on the values 3, 4, 5, … Each calculation in turn will yield a wavelength of the visible hydrogen spectrum. He predicted the existence of a fifth line at 3969.65 x 10-7 mm. He was soon informed that this line, as well as additional lines, had already been discovered. At the time, Balmer was nearly 60 years old and taught mathematics and calligraphy at a high school for girls as well as classes at the University of Basle. Balmer was very interested in mathematical and physical ratios and was probably thrilled that he could express the wavelengths of the hydrogen spectrum using integers. Balmer was devoted to numerology and was interested in questions like how many sheep were in a flock or the number of steps of a pyramid. He had reconstructed the design of the temple given in chapters 40-43 of the Book of Ezekiel in the Bible. How then, you may ask, did he come to select the hydrogen spectrum as a problem to solve? One day, as it happened, Balmer complained to a friend he had "run out of things to do." The friend replied: "Well, you are interested in numbers, why don't you see what you can make of this set of numbers that come from the spectrum of hydrogen?" (In 1871 Ångström had measured the wavelengths of the four lines in the visible spectrum of the hydrogen atom.) Balmer published his work in two papers, both published in 1885. The first, titled 'Notiz über die Spektrallinien des Wasserstoff,' is the source of the equation above. He also gives the value of the constant (3645.6 x 10-7 mm) and discusses its significance: "One might call this number the fundamental number of hydrogen; and if one should succeed in finding the corresponding fundamental numbers for other chemical elements as well, then one could speculate that there exist between these fundamental numbers and the atomic weights [of the substances] in question certain relations, which could be expressed as some function." ISSN: 2153-8212


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He goes on to discuss how the constant determined the limiting wavelength of the lines described by the Balmer formula: "If the formula for n = 2 is correct for all the main lines of the hydrogen spectrum, then it implies that towards the ultraviolet end these spectral lines approach the wavelength 3645.6 in closer and closer sequence, but cannot cross this limit; while at the red end [of the spectrum] the C-line [today called H2] represents the line of longest possible [wavelength]. Only if in addition lines of higher order existed, would further lines arise in the infrared region." In this second paper, Balmer shows that his formula applies to all 12 of the known lines in the hydrogen spectrum. Many of the experimentally measured values were very, very close to Balmer's values, within 0.1 Å or less. There was at least one line, however, that was about 4 Å off. Balmer expressed doubt about the experimentally measured value, NOT his formula! He also correctly predicted that no lines longer than the 6562 x 10¯ 7 mm line would be discovered in this series and that the lines converge at 3645.6 x 10¯7 mm with m = 2, 3, 4, . . . and n = 1, 2, 3, . . . ; but the two constants change in a particular pattern. By higher order, he means to allow n to take on higher values, such as 3, 4, 5, and so on in this manner: nm 3 4, 5, 6, 7, . . . 4 5, 6, 7, 8, . . . 5 6, 7, 8, 9, . . . At first Balmer's formula produced nothing but puzzlement, since no theoretical explanation seemed possible. In 1890 Johannes Robert Rydberg generalized Balmer's formula and showed that it had a wider applicability. He introduced the concept of the wave number v, the reciprocal of the wavelength, and wrote his formula as v = R (1/n12 - 1/n22) where n1 and n2 are integers and R is now known as the Rydberg constant (value = 10973731.534 m¯1). Later, many other atomic spectral lines were found to be consistent with this formula. In 1885, Balmer wrote these prophetic words: It appeared to me that hydrogen . . . more than any other substance is destined to open new paths to the knowledge of the structure of matter and its properties. In this respect the numerical relations among the wavelengths of the first four hydrogen spectral lines should attract our attention particularly.

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What one can learn from this is the following: It is today’s common wisdom that the most important thing to know about the scientific method is that it does not exist. There is no general procedure which, when used, will lead to the solution of a given scientific problem. Every field of science uses different tools of research, different techniques, different methods. And when one tries to find the common denominator of all of these, precious little of it is left for the pronouncement of a general “scientific method.” This view, however, comes about by looking at the scientific method as prescriptive. From a descriptive view point, there is a lot to be learned from the way the best scientists work. As the above anecdotal reports indicate, intuition, the “feeling of what’s right,” provides the incentive for a scientist’s creativity. And, as is evident, he or she does so even in the face of serious misgivings about the project. That tremendous progress is made in this way is exactly what makes intuition so unreasonably effective. However, one can go one step further and ask post facto just exactly what was the nature of the problems that were knowingly ignored. Newton published his theory despite his serious misgivings that his gravitational force acted at a distance; it took general relativity to clear that up. Schrödinger ignored that the relativistic theory is in worse agreement than the nonrelativistic one; it took the discovery of spin to clear that up. Dirac did without quantum mechanics in the point limit (he argued that it should not be needed); a quantum mechanical treatment of a point charge was not available until forty years later, and even then, only on the nonrelativistic level. Dyson ignored the lack of a rigorous mathematical foundation of QED; such a foundation is today still not available in its entirety. In all these cases, the problems that were ignored turned out to be considerably more difficult than the problems that were actually solved; typically, their solutions required a much deeper level of theory than the level on which progress was made. Thus, looking back, one finds that it was utterly reasonable to ignore those problems at the time. The genius of these scientists consisted not only of their ability to solve the problems they did solve, but also of their ability to distinguish those problems that cannot be solved yet because they belong to a deeper level than those that can be solved now. Their progress depended crucially on this ability. This insight raises an interesting question: are there problems in present-day physics that should be ignored until we have a deeper-level theory? For instance, one wonders whether the measurement problem of quantum mechanics (sometimes called “the collapse of the wave function problem”) is of this nature. Seventy years of effort involving a very large number of attempts since the founding of nonrelativistic quantum mechanics has not resulted in a definitive solution. Nor has this problem been resolved by going to the relativistic level. Apparently, it is not yet accessible to solutions even at that level, and a still deeper level of theory will be necessary.

References 1. E. P. Wigner "The unreasonable effectiveness of mathematics in the natural sciences,” Commun. Pure Appl. Math. XIII. 1-14 (I960). ISSN: 2153-8212


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www.JCER.com

Journal of Consciousness Exploration & Research| June 2018 | Volume 9 | Issue 6 | pp. 562-574 Marciak-Kozłowska, J., & Kozlowski, M., On Cancer Tumor Consciousness Waves

562

Exploration

On Cancer Tumor Consciousness Waves Janina Marciak-Kozłowska1 & Miroslaw Kozlowski*2 1 2

Institute of Electron Technology, Warsaw, Poland Warsaw University, Warsaw, Poland

Abstract Recently, a paper concerning wave emission by cancer cell was published (Murugan et. al.). It interesting to observe that, as early as in 2011, tumor wave emission was predicted for the first time by the herein authors. Keyword: Consciousness, cancer, tumor, wave.

Introduction Recently, Murugan et. al. published a paper in which they reported the finding cancer tumor waves As early as in 2011 M. Kozlowski and J. Marciak-Kozlowska published paper devoted to the study of cancer tumor growth. It was shown that at very first stage cancer tumor emits the specific waves, In this paper we developed model for the emission of the tumor waves. Since 2002, cancer has become the leading cause of death for Americans between the ages of 40 and 74 (Jemal, 2005). But the overall effectiveness of therapeutic cancer treatments is only 50%. Understanding tumor biology and developing an effective prognostic tool could, therefore, have immediate impact on the lives of millions of people diagnosed with cancer. There is growing recognition that achieving an integrative understanding of molecules, cells, tissues, and organs is the next major frontier of biomedical science. Because of the inherent complexity of real biological systems, the development and analysis of computational models based directly on experimental data is necessary to achieve this understanding. Tumor development is very complex and dynamic. Primary malignant tumors arise from small nodes of cells that have lost, or ceased to respond to, normal growth-regulating mechanisms, through mutations and/or altered gene expression (Sutherland, 1988). This genetic instability causes continued malignant alterations, resulting in a biologically complex tumor. However, all tumors start from a relatively simpler, avascular stage of growth, with nutrient supply by diffusion from the surrounding tissue. The restricted supply of critical nutrients, such as oxygen and glucose, results in marked gradients within the cell mass. The tumor cells respond both through induced alterations in physiology and metabolism, and through altered gene and protein expression (Marusic, 1994), leading to the secretion of a wide variety of angiogenic factors. *


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Angiogenesis – formation of new blood vessels from existing blood vessels – is necessary for subsequent tumor expansion. Angiogenic growth factors generated by tumor cells diffuse into the nearby tissues and bind to specific receptors on the endothelial cells of nearby pre-existing blood vessels. The endothelial cells become activated, after which they proliferate and migrate towards the tumor, generating blood vessel tubes that connect to form blood vessel loops that can circulate blood. With the new supply system, the tumor will renew growth at a much faster rate. Cells can invade the surrounding tissues and use their new blood supply as highways to travel to other parts of the body. Members of the vascular endothelial growth factor (VEGF) family are known to have a predominant role in angiogenesis. Physicists have long been at the forefront of cancer diagnosis and treatment, having pioneered the use of X-rays and radiation therapy. In the contemporary initiative, the US National Cancer Institute’s conviction that physicists bring unique conceptual insights that could augment the more traditional approaches to cancer research is very appealing. In this paper, we present the first attempt to consider the tumor cancer as a physical medium with some sort of memory.

2. The Consciousness of Cancer Cells Cancer is pervasive among all organisms in which adult cells proliferate. There is a Darwinian explanation of cancer insidiousness which is based on the fact that all life on Earth was originally single-celled. Each cell had a basic imperative: replicate, replicate, replicate. However, the emergence of multicellular organisms about 550 million years ago required individual cells to co-operate by subordinating their own selfish genetic agenda to that of the organism as a whole. So when an embryo develops, identical stern cells progressively-differentiate into specialized cells that differ from organ to organ. If a cell does not respond properly to the regulatory signals of the organism, it may continue reproducing in an uncontrolled way, forming a tumor specific to the organ in which it arises. A key hallmark of cancer is that it can also grow in an organ where it does not belong: for example, a prostate cancer cell may grow in a lymph mode. This spreading and invasion processes is called “metastasis.” Metastatic cells may lie dormant for many years in foreign organs, evading the body’s immune system while retaining their potency. Healthy cells, in contrast, soon die if they are transported beyond their rightful organ. In some respect, the self-centered nature of cancer cells is a reversion to an ancient premulticellular lifestyle. Nevertheless, cancer cells do co-operate to a certain extent. For example, tumors create their own new bloody supply, a phenomenon called “angiogenesis,” by co-opting the body’s normal wound-healing functions. Cancer cells are therefore neither rogue “selfish cells” nor do they display the collective discipline of an organism with fully-differentiated ISSN: 2153-8212


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organs. They fall somewhere in between, perhaps resembling an early form of loosely-organized cell colonies. In other words, the cancer tumor remembers the early state of existence – it has a memory which has been erased in healthy cells. The proliferation of the tumor cells is described by the diffusion processes (Jamal, 2005). The standard diffusion equation is based on the Fourier law in which, as we know, all memory of the initial state is erased. Simply speaking, the diffusion equation does not have time reversal symmetry, i.e. if the function f(x, t) is the solution of Fourier equation, f(x, -t) is not. Let us consider the one-dimensional transport “particles”, e.g. cancer cells. These cells, however, may move only to the right or to the left. Moving cells may interact with the fixed host body cells, the probabilities of such collisions and their expected results being specified. All particles will be of the same kind, with the same energy and other physical specifications distinguishable only by their direction. Let us define: u(z, t) = expected density of cells at z and at time t moving to the right, v(z, t) = expected density of cells at z and at time t moving to the left. Furthermore, let

 (z ) = probability of collision occurring between a fixed scattering centrum and a cell moving between z and z  . Suppose that a collision might result in the disappearance of the moving cell without new particle appearing. Such a phenomenon is called absorption. Or the moving particle may be reversed in direction or back-scattered. We shall agree that in each collision at z, an expected total of F(z) cells arises moving in the direction of the original cell, while B(z) arise going in the opposite direction. The expected total number of right-moving cells z1  z  z 2 at time t is z2

 u ( z, t )dz

z1

,

(1)

while the total number of cell passing z to the right in the time interval t1  t  t 2 is t2

w  u ( z , t ) dt t1

ISSN: 2153-8212

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(2) Journal of Consciousness Exploration & Research Published by QuantumDream, Inc.

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where w is the particles speed. Consider the cell moving to the right and passing z   in the time interval t1  t2  / w

w

 w

 t  t 2  w :

t2

  u ( z   , t ' ) dt '  w  u z  , t ' dt '.  w t1   / w t1 

(3)

These can arise from cells which passed z in the time interval t1  t  t2 and came through ( z, z   ) without collision t2

w  (1  δ ( z , t ' ))u ( z , t ' ) dt ' t1

(4)

in addition to contributions from collisions in the interval ( z, z   ). The right-moving cells interacting in ( z, z   ) produce in the time t1 to t2, t2

w   ( z , t ' ) F ( z , t ' )u ( z , t ' ) dt ' t1

(5)

cells to the right, while the left moving ones give: t2

w  ( z , t ' ) B ( z , t ' )v ( z , t ' ) dt ' t1

.

(6)

Thus, t2

t

t

2 2    w u  z  , t ' dt '  w  u ( z, t ' )dt '  w  δ ( z, t ' )( F ( z , t ' )  1)u ( z , t ' )dt ' w   t1 t1

t1

t2

 w  δ ( z, t ' ) B( z, t ' )v( z , t ' ) dt '. t1

(7)

Now, we can write:  1 u   u  u  z  , t '   u ( z , t ' )   ( z , t ' )  ( z, t ' )  w w t   z  ISSN: 2153-8212


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to get t2

t

2   u  1 u   z , t '   z , t '  dt '     z t δ ( z, t ' )(( F ( z, t ' )  1)u( z, t ' )  B( z, t ' )v( z, t ' ))dt '.   w t 1

t1

(9)

On letting   0 and differentiating with respect to t2 we find u 1 u   ( z , t )( F ( z , t )  1)u ( z , t )  ( z , t ) B( z , t )v( z , t ). z w t

(10)

In a like manner, 

v 1 v    ( z , t ) B ( z , t )u ( z , t )   ( z , t )( F ( z , t )  1)v( z , t ). z w t

(11)

The system of partial differential equations of hyperbolic type (10,11) is the Boltzmann equation for one dimensional transport phenomena (Kozlowski, Marciak-Kozlowska, 2009). Let us define the total density for cells, ρ ( z , t ) ρ( z, t )  u ( z, t )  v ( z, t )

(12)

and density of cells current j ( z , t )  w(u ( z , t )  v( z , t )).

(13)

Considering equations (12,13), one obtains  1 j   ( z, t )u ( z, t )( F ( z , t )  B ( z , t )  1)  ( z , t )v ( z , t )( B ( z, t )  F ( z , t )  1). z w2 t

(14)

Equation (14) can be written as ρ 1 j δ ( z , t )( F ( z , t )  B ( z , t )  1) j   z w 2 t w

(15)

or

j

w ρ 1 j  . δ ( z, t )( F ( z, t )  B( z, t )  1) z wδ ( z, t )( F ( z , t )  B( z, t )  1) t

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(16) www.JCER.com


567

Denoting D, diffusion coefficient

D

w ( z, t )( F ( z, t )  B( z, t )  1)

and τ, relaxation time

τ

1 wδ ( z, t )(1  F ( z, t )  B( z, t ))

(17)

Equation (16) takes the form ρ j j  D τ . z t

(18)

Equation (18) is the Cattaneo’s type equation and is the generalization of the Fourier equation (Kozlowski, Marciak-Kozlowska, 2009). Now, in a like manner, we obtain from equation (15,18)

1 j 1 ρ   δ ( z , t )u ( z , t )( F ( z , t )  1  B( z , t )) w z w t  δ ( z , t )v ( z , t )( B( z , t )  F ( z , t )  1))

(19)

j ρ   0. z t

(20)

or

Equation (20) describes the conservation of cells in the transport processes. Considering equations (19) and (20) for the constant D and τ, the hyperbolic Heaviside equation is obtained:

τ

 2 ρ ρ 2 ρ   D . t 2 t z 2

(21)

where τ is the relaxation time. In the stationary state, transport phenomena dF ( z , t ) / dt  dB ( z , t ) dt  0 and d( z , t ) / dt  0. In that case, we denote F ( z , t )  F ( z )  B ( z , t )  B ( z )  k ( z ) and equation (10) and (11) can be written as ISSN: 2153-8212


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du  δ ( z )(k  1)u ( z )  δ ( z )kv( z ), dz dv   δ ( z )k ( z )u ( z )  δ ( z )( k ( z )  1)v( z ) dz

568

(22)

with diffusion coefficient

D

w δ (z )

(23)

and relaxation time 1 τ ( z)  . wδ ( z )(1  2k ( z ))

(24)

The system of equations (22) can be written as

d (δ k ) d u dz du dδ δ (k  1) d (δk )     u δ 2 (2k  1)  (1  k )   0, 2 δk dz dz δk dz  dz 

(25)

du  δ (k  1)u  δkv( z ). dz

(26)

2

Equation (25) after differentiation has the form

d 2u du  f ( z)  g ( z )u ( z )  0 2 dz dz ,

(27)

where 1  δ dk dδ  f (z)     , δ  k dz dz  δ dk g ( z )  δ 2 ( z )( 2k  1)  . k dz

(28)

For the constant absorption rate we put 1 k ( z )  k  constant  . 2 ISSN: 2153-8212


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In that case,

1 dδ , δ dz g ( z )  δ 2 ( z )( zk  1). f ( z)  

(29)

With functions f(z) and g(z), the general solution of the equation (27) has the form

u ( z )  C1e



(1 2 k )1 / 2 δdz

 C2e



 (1 2 k )1 / 2 δdz

. (30) Subsequently, we will consider the solution of the equation (2.32) with f(z) and g(z) described by (2.34) for Cauchy condition: u (0)  q, v ( a )  0 .

(31)

Boundary condition (27) describes the generation of the heat carriers (by illuminating the left end of the strand with laser pulses) with velocity q heat carrier per second. The solution has the form: 1   2qe  f (0 ) f ( a )  (1  2k ) 2  cosh f ( x )  f (a) u( z)  2 f ( 0 )  f ( a )   1  1  βe  (1  2k ) 2  (k  1)  k 1  sinh  f ( x)  f (a ), 1

(1  2k ) 2  (k  1) 1   2qe ( f ( 0) f ( a ))  (1  2k ) 2  (k  1) u( z)  sinh f ( x)  f (a ) ,  k 1  βe 2 f (0)  f ( a )    

(32)

where

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f ( z )  (1  2k ) f (0)  (1  2k ) f (a)  (1  2k ) β

1 2 1 2

570

 δdz,

 δdz ,  δdz , 0

1 2

a

1 2

(1  2k )  (k  1) 1 2

.

(1  2k )  (k  1)

(33)

Considering formulae (31,32), we obtain for the density ρ (z ) and current density j(z).

j( z) 

2qwe  f ( 0)  f ( a )  1  βe 2  f ( 0 )  f ( a ) 

1   (1  2k ) 2  cosh f ( z )  f (a )  1    (1  2k ) 2  (k  1)    1  2k  sinh f ( z )  f (a ) 1    (1  2k ) 2  (k  1) 

(34)

and

q

2qe  f ( 0) f ( a )  1  βe 2  f ( 0 )  f ( a ) 

1   (1  2k ) 2  cosh f ( z )  f (a )  1    (1  2k ) 2  (k  1) .   1  sinh f ( z )  f (a ) 1    (1  2k ) 2  (k  1) 

(35)

Equations (34) and (35) fulfill the generalized Fourier relation

j

w ρ , δ ( z ) z

D

W , δ( z)

(36)

where D denotes the diffusion coefficient. Analogously, we define the generalized diffusion velocity υD(z)

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Journal of Consciousness Exploration & Research| June 2018 | Volume 9 | Issue 6 | pp. 562-574 Marciak-Kozłowska, J., & Kozlowski, M., On Cancer Tumor Consciousness Waves 1   w(1  2k ) cosh f ( z )  f (a)  (1  2k ) 2 sinh f ( x)  f (a) j(z)  . υD ( z)   1 n( z ) (1  2k ) 2 cosh f ( x)  f ( a)  sinh f ( x)  f (a)

571

1 2

(37)

Assuming constant cross section for heat carriers scattering δ ( z )  δo we obtain from formula (36) 1 2

f ( z )  (1  2k ) z , f ( 0)  0, 1

f (a )  (1  2k ) 2 a

(38)

and for density ρ (z ) and current density j(z) 1

j( z) 

2qwe

 (1 2 k ) 2 aδ 1

1  βe

 (1 2 k ) 2 aδ

1  1   (1  2k ) 2  2 cosh ( 2 k  1 ) ( x  a )δ   1     (1  2k ) 2  (k  1)

 1   2  sinh (2k  1) ( x  a )δ  , 1    (1  2k ) 2  (k  1)  (1  2k )

1

ρ( z ) 

2qe

 (1 2 k ) 2 aδ

1  βe  (1 2k )

1 2

aδ

(39)

1  1 2 δ   ( 1  2 k )  cosh (2k  1) 2 ( x  a ) 1     (1  2k ) 2  (k  1)

 1   2  sinh (2k  1) ( x  a)δ  . 1    2 (1  2k )  (k  1)  1

(40)

Formulae (39) and (40) describe the kinetic of the growth of the cell aggregation-tumor. The development of the tumor strongly depends on the coefficient k. In the following, we will call k the growth coefficient. For k0.5 the cell density grows exponentially, Figure 2a, 2b. For k0.5

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Figure 2a. Cells density, formula (2.45) as the function of x and growth factor k, for k0.5, del=1/um

We will call the first stage k 3 can be seen in an elementary way. Let m be the mass of planet and L angular momentum (which is constant for the central force (1.181))

& = const. L  mr 2 

(11)

The gravitation potential for the conservative force will be

V 

K r n 2

. (12)

At the extreme distances from the central body for a planet with mass m, we have

dr  0. dt

(13)

The kinetic energy T at such points is

T

p2 1 2 & 2  mr  , 2m 2

(14)

then

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Journal of Consciousness Exploration & Research| June 2018 | Volume 9 | Issue 6 | pp. 575-579 Marciak-Kozłowska, J., & Kozlowski, M., Sacred Number & Consciousness

L2 T . 2mr 2

578

(15)

By conservation of mechanical energy T + V = constant, or L2 K L2 K ,   2 n 2 2  n2 2mr1 r1 2 mr2 r2

(16)

where r1 is the minimum distance from the central body and r2 is the maximum distance, perihelion and aphelion respectively. The equation (16) shows that for n = 4 there can be a finite, positive solution only if r2 > r1 For n > 4 it can be shown that an orbit in which r oscillates between two extremes is likewise ruled out. In general the centripetal force in a circular orbit is

& 2. Fc  mr 2

(17)

Using Eq. (15) this becomes

Fc 

L2 . mr 3

(18)

In the actual eccentric orbit, the attractive force must be less than this centripetal force at perihelion, for then the planet is about to move outward. At aphelion, it is just the other way around. These conditions can be expressed respectively by the following inequalities

F  Fc L ( n  2) K  n 1 r1 mr13 2

K

or

r1n  2



L2 , ( n  2) mr12

(19)

F  Fc ( n  2) K L2  r2n 1 mr23

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or

K r2n  2



L2 . ( n  2) mr22


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(20)

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Journal of Consciousness Exploration & Research| June 2018 | Volume 9 | Issue 6 | pp. 575-579 Marciak-Kozłowska, J., & Kozlowski, M., Sacred Number & Consciousness

L2 L2 L2 L2 .    2mr12 ( n  2) mr12 2mr22 ( n  2) mr22

579

(21)

and L2 mr12

2

L 1 1    ( n  2)   2 2  2mr2

1 1    ( n  2) . 2 

(22)

This relation obviously cannot be true for n = 4, for then each of the brackets becomes zero. Remembering that r2 > r1 it also cannot be true for any n > 4, which makes the values of the brackets less than ½ . Thus, the existence of an elliptic orbit for n  4 is ruled out. The results for planetary orbits are collected in Table 1. Table1. Planetary orbits

Phenomena

Cases thus excluded

Bio-topology (existence of a highly developed n 3 orbits n=4

Possible only for circular orbit

n >4

Excluded if the potential is too vanish at 

n