GRZEGORZ BUGAJAK DEPARTMENT OF METHODOLOGY OF SYSTEM AND INFORMATION SCIENCES CARDINAL STEFAN WYSZYŃSKI UNIVERSITY, WARSAW

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Causality and Determinism in Modern Physics Key words: causality, determinism, indeterminism, quantum mechanics – interpretations.

1. Introductory remarks Many philosophers share the view that the objects of examination in physics are phenomena and relations between them, rather than the deepest ‘structure’ of the objectively existing reality [cf. Rutowski 1984, 53], the research of which is the domain of metaphysics and the philosophy of nature. In other words, physics deals with the phenomenal aspect of reality. Whether one shares this standpoint or not, the standard way of arriving at theorems in physics and the method of falsiﬁcation of hypotheses are, indeed, empirical in character. The starting point is usually an observation of some phenomenon1. The term “observation” 1

What is meant here is the standard research practice in physics. However, nowadays some attempts of another approach are known. According to this approach the starting point is not the observation but rather some theoretical speculation. What is more, even the justiﬁcation of proposed theories is supposed to be independent of empirical data. This approach is represented, for example, in the string theory: „After its successful transition to metaphysics and its selﬁmmunization against empirical control, it is not even clear, if there are any empirical means by which we could ﬁnd out if string theory does describe nature in any adequate way, or not. Even a wrong theory will not necessarily be defeated by nature, if it is able to avoid any contact to nature” [Hedrich 2007, 274]. Therefore, the epistemological status of such attempts is unclear, and they will be ignored in this analysis.

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is used here in its broader sense, i.e. rarely, some direct observation is meant. Most often an observation is performed with the use of special measuring devices. It is practically impossible to think of an observation in physics, from which all measurements would be eliminated. Moreover, the phenomenon under examination is, frequently, brought about artiﬁcially, as an experiment, for the purposes of this examination. And ﬁnally, already at this early stage of research, a scientist has some theory, which, for more or less intuitional reasons, seems to be adequate to describe the examined phenomena. The observed phenomenon undergoes certain theoretical ‘symbolization’ in order for it to be described within a given theory. From this point onwards, a researcher uses mathematical objects and not real events; and logical and mathematical inference applies to mathematical objects. This inference, in turn, provides certain ‘symbolic events’, which are, subsequently, veriﬁed, i.e. confronted with real events observed empirically. If the veriﬁcation is positive, we say that a given theory describes a given phenomenon adequately. Otherwise, another theory is searched for; a theory, whose predictions (those ‘symbolic events’ arrived at through logical inference), will be consistent with empirical experience. We should note that within the practice described above two special assumptions are made: (1) The assumption that in the process of observation and the subsequent ‘theoretical symbolization’, we can, without a danger of severe inadequacy making the whole research miss its point, ignore the “negligibly small” quantities, i.e.: – errors in measurement2, which as it has been already said, is practically inseparable from the process of observation in physics, do not affect the validity of ﬁnal conclusions; – equally insigniﬁcant are simpliﬁcations made during theoretical preparations, when some empirical parameters are ignored in order for a given phenomenon to be, without excessive difﬁculties, placed within the framework of a mathematical theory. This assumption can 2

What is meant here is the random error (leading to measurement uncertainty), unavoidable in every measurement.

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be called the assumption of the mathematicality and ‘idealizability’ of nature [Heller 1986, 14-16]. (2) The assumption that in such research, the enumerative induction is sufﬁcient to acknowledge the validity of the theorems. If an experiment repeated many times (an observation made many times) always proceeds in the same way, we assume that the regularity acknowledged will always occur, whenever the situation happens. The second assumption is not a problem for a physicist, as it is sufﬁcient that some regularity actually occurs in the cases acknowledged so far and that it has practical signiﬁcance. The ﬁrst assumption is possible to maintain only, because physics doesn’t deal with individual cases, but rather with regularities applicable to all (virtually countless) events of the same kind [Gawecki 1969, 70]. In this case, what matters is practical utility of a given theory and not the fact that it can describe particular events a bit imprecisely. Given this background, how can we understand the principle of causality in physics? Its main formula, i.e. “Each event has its cause” seems to be acceptable, or at least attainable within physics. For it involves events – precisely this aspect of reality which is examined by physics. However, the principle of causality, as formulated above, cannot be accepted in physics, because physics, as it has been already said, doesn’t deal with individual cases. Hence, in physics, we cannot ask whether a given single event has its cause, or not. On the other hand, even in some ideal world, where physics would be able to assert a cause for each and every event examined so far, the use of the enumerative induction does not allow for a general statement that every event has its cause. The thesis of causality, as formulated above, has to be, therefore, regarded as external to the system; it can only be valuable for a natural scientist in that it encourages to search for causes, since (according to this thesis) they exist [cf. Rutowski 1984, 54]. Ignoring this heuristic aspect, a natural scientist can agree with Reichenbach, who writes: “If we seek for a particular cause, we need not assume that there is one. We can leave this question open, like the question of what is the cause. Only if we knew that there is no cause would it be unreasonable to seek for a particular cause. But if nothing

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is known about there being a cause, we can search at the same time for the particular cause and for the answer to the question whether there is one” [Reichenbach 1951, 112-113]. Hence, on the one hand, a physicist does not have to take the principle of causality into consideration, e.g. by accepting it tacitly as a precondition of their research, as some maintain [Kiczuk 1977, 129]; on the other hand, there are no reasons, either, for which they would have to reject it, either in a single case or in general. In natural sciences, the idea of causality can be considered in so far as it expresses the principle of determinism [Mazierski 1955-1957, 155]: the same cause (under the same circumstances) brings about the same results [Krajewski 1967, 242], or, to put it in a more precise way: if the state of a certain material system is known in the present, then, its past and future states are known, too [Mazierski 1958, 27-29]. This is the very formula of the principle of determinism, which we will take into account during our discussion. However, we should note here that, sometimes, it is postulated that the principle of determinism should be extended to cover the conviction that “individual representatives of a certain species always act in the same way under the same circumstances” [van Melsen 1953, 208], or more generally, that determinism equals the following conviction: „a thing, of necessity, behaves as it does in accordance with its given nature” [van Melsen 1953, 231]. Even if such views are correct, they are philosophical in nature and hence cannot be considered within the scope of physics. Other attempts of extending the principle of determinism involve introducing the notion of general determinism. Then, this principle would include unambiguous (strict) determinism, as deﬁned above, and ambiguous (or statistical) determinism [e.g. Krajewski 1964, 141-143; cf. Hacking 1983; Walton 1973], namely, the cases where the state of the system S at the moment t0 would determine the whole group of possible states S1, S2, ..., Sn at the moment t, each with some probability P1, P2, ..., Pn in the way that the sum P1 + P2 + .... + Pn would equal 1 [Mazierski 1972, 346-347]. Yet, introducing the notion of general determinism seems to be a misleading attempt, because it attributes the term “deterministic” to cases commonly associated with indeterminism

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[cf. Amsterdamski 1964, 85-92]. Therefore, we will conﬁne ourselves to the approach, which associates the notion of determinism with unequivocal prediction (or retrodiction): the state S0 at the moment t0 determines the state S at the moment t. With the above formula in mind it can be judged whether a given theory is deterministic or not. It is important to note that such a judgment concerns a theory understood here as a mathematical apparatus with some accompanying physical interpretation. The question of the determination of phenomena (whatever a ‘determination of a phenomenon’ may mean) as certain manifestations of reality is an entirely different one. The notion of “the state of a system”, used in the principle of determinism, deserves particular attention. What does it mean? The physical state of a system is the set of empirical data, which “fully describe the properties of a given system and of its surroundings, affecting it” [Mazierski 1958, 27-29]. However, the phrase “fully describe the properties…” raises important problems. We should note that: (1) As a result of the assumption of ‘idealizability’ of nature, mentioned above, and hence applying the procedure of ignoring the “negligibly small quantities”, the properties of a system are never fully described. The state of a system, described with taking into account all its properties known in physics could be called the “absolute state” [cf. Sławianowski 1969, 44-46]. (Yet, we should remember that such a term may be misleading. This is because the cognitive capacities of physics develop constantly and at no stage of this development we can say that they are truly “absolute”). (2) In practice, we obviously use a relative notion of state. This is a set of empirical data, determining important properties of a system; important properties are those which, when taken into account, are sufﬁcient for the theory in question to be applicable. The properties, which should be taken into account are those, which, within a given theory are subject to theoretical symbolization. Thus, the relative state of a system is a notion relative to our purposes (needs) and our

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cognitive capabilities3. Therefore it may be that a system, for some of its relative states, is described by a deterministic theory, while for another relative states there is no determination. As we see from the above discussion, the way a relative state of a system is perceived depends on the theory under consideration. A relative state is relative to our needs. The ﬁrst need determining a description of the state of a system is the use of this notion within a given theory. So, the properties taken into account while describing the state of the system are those required by the theory [cf. Augustynek 1962, 11; Mazierski 1972, 283-284]. If for some phenomenon it is impossible to ﬁnd a relative state of the system, appropriate for the theory by means of which we are trying to describe this phenomenon, it means only that this particular theory is not applicable to this phenomenon. What follows is that it is possible for the same system to be described both by a deterministic and an indeterministic theory, depending on how the state of this system is deﬁned. If the deﬁnition of this state is possible to use within certain deterministic theory, then the system will be regarded as capable of being described within this theory. But if, for some reasons, we do not have the notion of state, which this particular theory requires, it means that this theory is inapplicable. The question of reasons, for which the required state of a system cannot be found, doesn’t have to worry natural scientists. It is sufﬁcient that they, after deciding on such impossibility, attempt to describe the state of the system in question in the way which could be analyzed within some other practically useful theory. This problem is different in philosophy, though. In philosophy, the reasons, for which scientists rejected some particular way of describing 3

Cf. J. J. Sławianowski [1969, 50] and the example presented there. In case of vapours, most frequently we are not interested in their microscopic structure, but rather in their properties exhibited on the macroscopic level. Hence, we use the notions of pressure, temperature, etc., to describe the state of the vapour, which is one of possible relative states, presenting the properties important from practical point of view, while ignoring others. The state described in this way will not be sufﬁcient for the atomistic theory because, for this theory, the pressure and temperature are not essential properties of the system.

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the properties of the system may appear very important. There are, basically, three possibilities: (1) The research methods used, inadequate measurements or measuring devices did not allow for capturing the properties required. (2) These properties are, by deﬁnition, impossible to consider within a given theory, because they comprise a relative state of a system different from a relative state required by the theory in question. (3) These properties are impossible to be captured for some “fundamental reasons”, resulting in the necessity of resigning (not only for practical reasons but for ever) from describing the system by means of this theory, within which the capturing of these properties was necessary to build up the notion of state it requires. If the third possibility is the case, then a philosopher faces the problem concerning philosophical implications of the fact of “fundamental impossibility” of capturing some properties of the system, and hence the equally fundamental inapplicability of a given theory to the description of phenomena in question. All the conclusions, which can be drawn from such a situation have to respect two restrictions: A. The impossibility of applying a deterministic theory doesn’t mean the lack of determination in reality. The view that even all the events in the universe are determined is not the same as the conviction that precise prediction (or retrodiction) is always possible [cf. Majewski 1970, 204-205]. If a phenomenon is possible to be described in a deterministic way, we can conclude that it actually is determined. However, the lack of such description – the lack of a deterministic theory for a certain type of phenomena – doesn’t exclude a possibility of actual determination, since a deterministic relationship may occur independently of our knowledge. In other words, determinism would be excluded here on the epistemological, and not on the ontological level. B. This “fundamental” impossibility of capturing required properties of a system involves a given concrete theory and not the type of theories. For instance, if the theory inapplicable to a certain case was of the deterministic type, it doesn’t imply that no deterministic theory at all can be applied to this case. Thus, ultimately neither

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ontological nor epistemological determinism may be excluded, even in the case of the fundamental impossibility of capturing certain properties of the system.

2. Classical physics It seems that in many discussions of causality in classical physics, what gets overlooked is that, strictly speaking, the notion of causality – unlike the notion of determinism – has virtually no application in physics. Questions expressing the issues of classical physics are of this sort: “I’m moving an object, what is the cause of its movement?” [Gawecki 1969, 163] or „An object is falling down. What is the cause of it?” [Gawecki 1969, 162]. Questions of this sort, about the cause of some phenomenon, are also asked in everyday life – “Something happened, why?” Yet, in the ﬁeld of physics, it doesn’t lead to explicit conclusions. Considering, for example, the problem: “What is the cause of falling down of an object?” may lead to various true, but not necessarily unambiguous answers, e.g. the cause of falling down is: (1) the Earth; (2) the gravitational force; (3) the preceding process of taking an object up to the point from which it has fallen [Gawecki 1969, 164]; (4) some external factor causing an object to lose its balance (if it has kept it before, despite the (1) – (3) factors). Each of the above answers is correct, although each expresses the cause of the same phenomenon in a different way. We can quote numerous arguments for each of the above reasons, yet a physicist wouldn’t be able to decide which of them is ultimately correct, because answers to the above questions cannot be unambiguous. It is not surprising, though. As we already said, physics doesn’t deal with answering the question of the cause of a given individual phenomenon. And if physicists ask such question, they treat it as an auxiliary one, as it can lead to revealing and describing some general regularities (as in the above example – to the analysis of gravitation). The more appropriate question is, therefore, not the one about causality, but about determinism. One may ask if classical physics is

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deterministic or not? Or, more strictly, are the theories of classical physics of the deterministic type or not? The basic theory of classical physics is classical mechanics. Let us brieﬂy remind why this theory is deterministic. Obviously, classical mechanics uses some notion of the state of a physical system. Historically speaking, the ﬁrst deﬁnition of a state was the position of a body in space. Adding the momentum to such a description, we have the classical pair of quantities, sufﬁcient for a certain physical system to capture the behaviour of this system within classical mechanics [cf. van Name 1962, 166]. This theory, for a given state of a material system at a random initial time t0, determines one and only one state of this system at every other time. Capturing the state of the system (determining the momentum and the position), constitutes the basis of describing this system within the theory. The theory, in turn, enables the theoretical determination (prediction) of the state of the system at any other moment of time. This prediction is obviously expressed by means of providing the same pair of quantities, i.e. momentum and position at a desired time. The notion of the state of a system used here, refers to the relative state, since it includes only those of physical features of the system which are essential from the viewpoint of classical mechanics, and ignores many others [cf. Majewski 1988, 19-23]. However, this notion turns out to be sufﬁcient for practical purposes, as it, together with the whole theory of classical mechanics, leads to the results consistent with empirical knowledge. The fact that predictions of the future (or past) ‘state of a system’ are possible and that they are consistent with empirical knowledge decides that the classical mechanics is a theory of a deterministic type.

3. Quantum physics Classical physics, together with its fundamental theory, i.e. Newton’s mechanics, had such great achievements that, at the end of the 19th century, it was regarded as the perfect and extremely important theory in all the ﬁelds which ever were, or would be, examined within physics.

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Some minor problems, as physicists thought, remained unresolved, but they were supposed to be resolved later on within classical mechanics. Yet, the very attempts to solve these problems led to the fundamental turn in physics, namely to the rise of quantum theory4. As we can notice, while reading the history of theories in physics, the development of physics, most frequently, imposes some restrictions on the application of previously established theorems [cf. Piersa 1983, 155-164], e.g. when physicists noticed that the classical description of motion fails for the range of speed approximating the velocity of light, although it is correct for “ordinary” range of speed. Quantum physics, however, seemed to cause something more: total rejection of laws regarded as irrefutable till then. The problems the quantum theory posed are not conﬁned to strictly physical issues. For instance, some attempts are made to build up a new system of logic for the purposes of quantum mechanics, other than the classical binary one [e.g. Dickson 2001; Kiczuk 1978, 53-64]. Moreover, some maintain that a kind of a theory of “discontinuous existence” is necessary, because the notion of motion is called into doubt in quantum mechanics [Whitehead 1925, 53], or even they go so far as to negate the existence of the objects of microphysics [Semczuk 1987, 33-40]. The most frequently considered problem, though, is the fact that as soon as the quantum theory had emerged, deﬁning the notion of causality and reaching some agreement concerning the views on causality became more and more troublesome. The problem of causality, or determinism, in the micro-world became one of the fundamental problems considered by both scientists and philosophers [cf. Schabowski 1966, 221].

3.1. Heisenberg’s uncertainty principle Philosophical discussions of causality and determinism in the micro-world most often focus on Heisenberg’s uncertainty principle, which follows from quantum mechanics. This principle expresses the fact that it is impossible to capture, at the same time, the position and 4

An excellent account of this fascinating history can be found in Kumar [2008].

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momentum for a given particle with unrestricted accuracy5. This principle has its strict mathematical expression, allowing to formulate it in a more precise way, namely, to say that the product of measurement error for momentum and for position cannot be lesser than the so-called Planck constant6. As these very quantities, connected by the uncertainty principle, served for deﬁning the state of a system within classical mechanics, the consequences of this principle seem to be very important for considering the problem of determinism. The understanding of the uncertainty principle is not unambiguous, though. It can be captured in three ways: (1) Uncertainty as an effect of measuring disruption. The principle of uncertainty is often explained as follows: The act of measuring disrupts the system under examination, for there occurs an inevitable interference between the system and the measuring device. Hence, if we try to determine the position of a particle very precisely, its state is so disrupted as the momentum becomes totally indeterminate. And the other way round, if we try to determine the momentum of a particle accurately, its position becomes indeterminate. Shortly speaking, the cause of uncertainty lies in the interference between the measured object and measuring device [Gołębiewski 1982, 37]. Such an approach would suggest that the uncertainty principle is a result of the imperfection of measuring devices. (2) Uncertainty as a consequence of the structure of measuring act. This interpretation, referring also to the measuring process, shows that the disruption of the state of a particle, caused by measuring, doesn’t depend on the quality of measuring devices but rather it is a result of the very act of measurement and hence is more fundamental in character [Svechnikov 1971]. It is impossible to imagine a measurement which wouldn’t disrupt the state of the particle under examination. It follows 5

This principle applies also to other pairs of the so-called canonically coupled quantities, yet, for our present purposes, it is sufﬁcient to formulate this principle for the position and momentum. 6 More strictly, this product cannot be lesser than certain quantity depending on Planck constant; yet, what is important here is that it is a quantity of a positive value, and hence that the position and momentum cannot be measured with unrestricted accuracy

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from the fact that each measurement in physics involves some exchange of energy between the measuring device and the object being measured. Imagine a microscope by which one looks at the world of micro particles7. The light itself (a necessary ‘observational device’), which carries certain energy, would disrupt the state of the particle being observed. If, instead of a microscope, any other device was used, it would always require some “mediator” (like light in a microscope), which would enable the observation of a given particle, disrupting, at the same time, its state and causing the uncertainty. The reason for the disruption lies, therefore, not in the imperfection of measuring devices but in the very structure of the act of observation (measurement). This interpretation usually leads to the conviction that the uncertainty principle is universal, absolutely unavoidable. As far as it well may be, such a point of view is based on two additional assumptions (both may seem plainly trivial, nonetheless they are assumptions): – it is impossible to imagine any knowledge about a physical object, gained in other than experimental way (i.e. beyond any measurement); – it is impossible to ﬁnd an “empirical mediator”, which would enable the observation of an object without disrupting its state signiﬁcantly and hence without causing the uncertainty. It is noteworthy that the fact of disruption of an object state in the process of measuring is not necessarily connected with microphysics and remains true in the macroscopic cases. This problem did not surface in the classical mechanics, because the inﬂuence of the interference between an object and a measuring device is “negligibly small” there. (3) Uncertainty as an effect of the properties of micro-objects. According to this interpretation, the uncertainty principle would express a certain objective feature of nature, namely the fact that such characteristics like position and momentum are not applicable to the objects of the micro-world, considered within quantum mechanics [Wichmann 1971, 34]. Thus, there is no point in talking about position 7

This is an imaginary (and actually impossible) example, but what is meant here is to illustrate problems connected with the act of measurement.

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and momentum of a quantum particle, because such particle simply doesn’t have these properties. The uncertainty principle would therefore express a fundamental restriction, immanently rooted in the very nature of the objects under examination [cf. Romanow-Broniarek 1978, 229], and it would indicate the boundary, beyond which classical ideas and notions of classical physics cannot be extrapolated. Among various approaches to the uncertainty principle, we can ﬁnd opinions, which signiﬁcantly limit too far-reaching conclusions drawn from it. Heisenberg’s uncertainty principle follows from quantum mechanics, and hence it is valid only on the ground of this theory. It is enclosed “within the description of nature provided by quantum mechanics” [van Name 1962]. Hence, if we accept this theory, we, indeed, will arrive at the conclusion that the position and momentum of a particle cannot be known, at the same time, with unlimited accuracy. The reverse implication doesn’t hold, though: the conclusions concerning the correctness of this or that theory of the quantum world do not follow from Heisenberg’s uncertainty principle. Thus, it is illogical to maintain that this principle forces us to accept a given form of the theory of quantum mechanics as absolutely valid. If the uncertainty principle seems to impose no restrictions on the possible theories of micro-world, it cannot impose such restrictions on the way of the existence of things, either8. It concerns something more than just our knowledge but still nothing more than real physical processes [Feyerabend 1960, 27]. The strong expression that the uncertainty “is rooted in the things themselves” may, if at all, be used in the sense physicists attribute to it, namely: “Physical reality is all that may be captured with the use of means available in physics” [Blanché 1969, 56-57].

8

The question whether uncertainty is epistemological or ontological is the matter of discussion [e.g. Tanona 2004]. It seems that any particular ontological engagement of the uncertainty principle may be rightly called to doubt [see for example: Fraley 1994; Morikawa 2007].

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3.2. Interpretations of quantum mechanics Quantum mechanics is, in its fundamental form, like any other theory in physics, a set of mathematical formulas. This mathematical formalism becomes physics through some interpretation of mathematical formulas it contains [cf. Weizsäcker 1980]. Hence, the discussion of the deterministic or indeterministic character of quantum mechanics arises only in connection with an interpretation of this theory [cf. Hajduk 1965, 57; Mazierski 1972, 314]. Before such an interpretation is chosen, such general judgments as: “Wave mechanics is indeterministic in nature” cannot be justiﬁed [Mazierski 1979, 76]. Interpretations of quantum mechanics can roughly be divided into two groups. The ﬁrst group includes those which claim that quantum mechanics is a theory of individual processes [Aleksandrow 1953, 135-136; Głódź 1979, 40], while the second one includes those regarding quantum mechanics as a theory of large sets of micro-objects. In the second case, the term “quantum statistics” used to be suggested. An interpretation of quantum mechanics involves attributing some physical meaning to the mathematical formulas of this theory. The most often considered problems are: the question what the so-called wave function (the solution of the Schrödinger’s equation, a fundamental one in quantum mechanics) represents, and the sense of Heisenberg’s uncertainty principle9. 3.2.1. Schrödinger’s interpretation This approach, coming from the author of the wave mechanics10, takes into account the squared amplitude of a wave function (|Ψ|2), 9

The list of interpretations of quantum mechanics provided below is not complete. We do not take into account the non-standard (although often discussed) interpretations, e.g. the ones by David Bohm and Hugh Everett [see for example Birman 2009, 209-211]. New interpretations still appear too [e.g. Ghose 2009; Lombardi, Castiliano 2008]. 10 Historically, the ﬁrst approach to the quantum world was the so-called “matrix mechanics”, yet it is much more mathematically complicated than the wave scheme; and as these descriptions are equivalent, the one by Schrödinger soon became the standard approach.

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interpreting this quantity as the density of electron’s charge11. Thus, this conception goes towards a kind of a “substantialist” direction. For what it suggests is that an electron exists in a form of “blur”, the so-called “electron cloud”. This interpretation was supported by the famous wave-particle dualism, according to which an electron, exhibiting both corpuscular and wave properties, is actually neither a particle nor a wave; rather, it is something completely different, something which appears as a wave in one type of experiments and as a particle in another. Then, if an electron doesn’t have to be a particle, we can describe it as the “electron cloud”, and we can interpret |Ψ|2 as the density of the electric charge within this cloud. Although this interpretation had to be rejected as inconsistent with some experimental ﬁndings [Feynman et al. 1963, 21-26], it is worth to note that such an interpretation would make quantum mechanics a deterministic theory. If we know the wave function of a given electron at the moment t0, we can also calculate it for any other moment t. And since this function determines the space where an electron is (in the blur form of the cloud of charge), then the theory itself fulﬁls the requirements of a deterministic theory [cf. Sławianowski 1969, 142-143]. 3.2.2. Probabilistic interpretation In our present discussion we need to introduce the distinction between the probabilistic and the statistical interpretation. The probabilistic one belongs to the ﬁrst group of interpretations, i.e. to those, which regard quantum mechanics as a theory of individual phenomena or single objects, while the statistical interpretation belongs to the second group, regarding quantum mechanics as a theory of large sets of objects. This distinction allows to avoid numerous misunderstandings connected with common intuitions about the term “statistical”. However, there are authors who call the interpretation discussed here a “statistical interpretation” [e.g. Szczęsny, Urbaniec 1988, 231]. According to the probabilistic interpretation, the wave function represents a real quantum state of micro-object and the square of the 11

Here and in further analyses, we refer only to the most straightforward example, i.e. to the description of a free electron.

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wave function modulus determines certain probability concerning a particle, e.g. the probability of ﬁnding it within a given space. This very interpretation made many accept indeterminism in quantum physics. The wave function expresses the state of a single microobject, on the one hand, but on the other, it only allows for calculating the probabilities of given states in the future. 3.2.3. The interpretation of quantum ensembles According to this conception, the wave function is also a characteristics of an individual particle, but not “in itself”, but in the sense of its belonging to the so-called statistical ensemble [Błochincew 1953, 62; Błochincew 1954, 66]. Yet, the vicious circle error seems unavoidable here, as the statistical ensemble, in turn, is understood as a set of particles being in the same state described by a given wave function. 3.2.4. Statistical interpretation Unlike the previous interpretations, this one treats quantum mechanics as a theory describing not single micro-particles but rather the behaviour of large amounts of them. “Quantum mechanics is not the theory of a real process, which a particular micro-object is subject to; rather, it illustrates adequately only the behaviour of a set of microobjects” [Terlecki 1953, 21; cf. Pechenkin 2002]. We should note that, within this interpretation, Heisenberg’s uncertainty principle determines only the relation between the dispersion of some quantities within large sets of particles. Thus, one cannot deduce from it any restrictions concerning single events, because nothing prevents single values of the pairs of quantities, the uncertainty principle connects, from being strictly determined [Fayerabend 1960, 30-31]. Within such framework, quantum mechanics would be nothing more than a statistical method of calculating some values. Statistical character of such theory may be underlain by the individually determined phenomena. Such a statistical theory provides then a kind of an average of individual effects [Sławianowski 1965, 40]. And the other way round: there is no contradiction between applying a deterministic theory and using statistical

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methods, which the “proper” statistical mechanics is an example of: the behaviour of some system is basically possible to describe within the theory of the deterministic type, yet, for practical reasons, using the statistical description is sufﬁcient and more convenient. The properties of the system, found for the purposes of such conception, can be insufﬁcient to apply a deterministic prediction; yet, this doesn’t exclude the possibility of describing this system within a deterministic theory. 3.2.5. Copenhagen interpretation This, probably the most popular interpretation, opposes the views that quantum mechanics is a theory of objective phenomena. Within this interpretation, the state of a system is not an objective property, but only a relation to the measuring devices [Feyerabend 1960, 45]. Here, the wave function has a kind of a double meaning: it describes a certain fact and expresses our knowledge about this fact. The probabilities, which the theory uses, do not result from the properties of the electron itself but from our imprecise knowledge about it [Heisenberg 1999]. This probability turns into certainty as a result of our observation when our knowledge of the system changes suddenly. The act of observation “chooses” a concrete case out of numerous ones, which have been only probable so far. A special consequence of such approach is the claim that we can talk only about what happens in the act of measurement. What happens between measurements is unknown. For example, it is impossible even to think of a position that an electron has in between measurements. As a comment to this approach, de Broglie wrote that quantum mechanics theory describes adequately only stationary states but it fails to describe the transitions between them. By declaring that these transitions surpass the space-time frame, quantum mechanics just hides its inadequacy [Blanché 1969, 50]. Heisenberg’s uncertainty principle is interpreted in a special way, too. Referring to the relationship between this principle and measurement disruptions, these disruptions are given a kind of ultimate character. The uncertainty of position and momentum is supposed to be the objective characteristics of nature. What matters here is not the fact that, because of some more or less objective reasons, we are unable to determine

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position and momentum, but the fact that these quantities do not exist, in the case of electron, or rather they do not exist simultaneously [Wichmann 1971]. Thus, the uncertainty principle is formulated as an objective law of nature; and it is often understood that way, by both supporters and opponents of the Copenhagen interpretation. Yet, we should strongly emphasize that no claim within the subjectivist Copenhagen interpretation, can be attributed the characteristics of objectivity, as the whole interpretation goes in the anti-realistic direction. It seems implausible to maintain that there is an objective regularity connecting some properties of an object, if these properties, being the relation to the measuring devices, are not objective in themselves12.

4. Conclusion It is a widespread view that while the classical mechanics is the ﬂagship of deterministic theories, the quantum mechanics is an icon of indeterministic ones. However, it appears that indeterminism of quantum mechanics is limited, at least in the sense that it depends on the interpretation of this theory (with its crucial elements like the wave function and Heisenberg’s uncertainty principle) one accepts. The developments in the research of the micro-world made some interpretations more credible than others, while some of them were totally rejected. Nonetheless, even the claim that indeterminism is irremovable from the description of the micro-world doesn’t imply the negation of the most general formula of the philosophical causality principle, namely, that each event has its cause. For judging the presence or lack of causes is raising an ontological thesis concerning real world. And theses of this kind do not directly follow from the characteristics of the scientiﬁc description of this world, regardless of how accurately they are captured. In other words, there is no direct implication between theses of the epistemology of scientiﬁc knowledge and those of the ontology of the real world. 12

It is worth noting that the authors of the Copenhagen interpretation didn’t agree with one another as far as its proper meaning is concerned [Camilleri 2006; 2007]. According to some authors, there are good reasons for rejecting this interpretation in general [Norris 2001; Putnam 2005].

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References: Aleksandrow A., 1953, O znaczeniu funkcji falowej, transl. S. Czarnecki, in: Zagadnienia ﬁlozoﬁczne ﬁzyki, vol. 1: Zagadnienia ﬁlozoﬁczne mechaniki kwantowej, ed. B. Buras, K. Majewski, Warszawa, 128-137. Amsterdamski S., 1964, Różne pojęcia determinizmu, Studia Filozoﬁczne, no. 2, 85-95. Birman F., 2009, Quantum Mechanics and the Plight of Physicalism, Journal for the General Philosophy of Science 40, 207-225. Blanché R., 1969, Wiedza współczesna a racjonalizm, transl. A. Zabłudowski, Wiedza Powszechna, Warszawa. Błochincew D., 1953, Krytyka idealistycznego ujęcia teorii kwantów, transl. Z. Kopeć, in: Zagadnienia ﬁlozoﬁczne ﬁzyki, vol. 1: Zagadnienia ﬁlozoﬁczne mechaniki kwantowej, eds. B. Buras, K. Majewski, PWN, Warszawa, 34-92. Błochincew D., 1954, Odpowiedź akademikowi W. Fockowi, transl. S. Czarnecki, in: Zagadnienia ﬁlozoﬁczne ﬁzyki, vol. 2: Zagadnienia ﬁlozoﬁczne mechaniki kwantowej i teorii względności, eds. B. Buras, K. Majewski, PWN, Warszawa, 52-66. Camilleri K., 2006, Heisenberg and the Wave-Particle Duality, Studies in History and Philosophy of Modern Physics 37, no. 2, 298-315. Camilleri K., 2007, Bohr, Heisenberg and the Divergent Views of Complementarity, Studies in History and Philosophy of Modern Physics 38, no. 3, 514-528. Dickson M., 2001, Quantum Logic Is Alive ∧ (It Is True ∨ It Is False), Philosophy of Science (Supplement) 68, no. 3, S274-S287. Feyerabend P., 1960, On the Interpretation of the Uncertainty Relations [Eng. Summ.], Studia Filozoﬁczne, no. 4, 21-78. Feynman R. P., Leighton R. B., Sands M., 1963, The Feynman Lectures on Physics. III: Quantum mechanics, Pearson–Addison–Wesley. Fraley L. E., 1994, Uncertainty About Determinism: A Critical Review of Challenges to the Determinism of Modern Science, Behavior and Philosophy 22, no. 2, 71-83.

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Gawecki B. J., 1969, Zagadnienie przyczynowości w ﬁzyce, PAX, Warszawa. Ghose P., 2009, The Central Mystery of Quantum Mechanics, NeuroQuantology 7, no. 4, 623-634. Głódź M., 1979, Determinizm w ﬁzyce współczesnej – według Miakiszewa, in: Z zagadnienień ﬁlozoﬁi przyrodoznawstwa i ﬁlozoﬁi przyrody, vol. 3, ed. K. Kłósak, ATK, Warszawa, 37-47. Gołębiewski A., 1982, Elementy mechaniki i chemii kwantowej, PWN, Warszawa. Hacking I., 1983, Nineteenth-century Cracks in the Concept of Determinism, Journal of the History of Ideas 44, 455-476. Hajduk Z., 1965, Współczesne interpretacje mechaniki kwantowej, Roczniki Filozoﬁczne 13, no. 3, 55-74. Hedrich R., 2007, The Internal and External Problems of String Theory: A Philosophical View, Journal for General Philosophy of Science 38, no. 2, 261-278. Heisenberg W., 1999, Physics and Philosophy: the Revolution in Modern Science, Prometheus Books. Heller M., 1986, Jak możliwa jest „ﬁlozoﬁa w nauce”?, Studia Philosophiae Christianae 22, no. 1, 7-19. Kiczuk S., 1977, Związek przyczynowy w ﬁzyce współczesnej a logika przyczynowości, Roczniki Filozoﬁczne 25, no. 3, 119-134. Kiczuk S., 1978, O pewnej próbie przezwyciężenia kauzalnych anomalii w mechanice kwantowej, Roczniki Filozoﬁczne 26, no. 3, 53-64. Krajewski W., 1964, W sprawie pojęcia determinizmu, Studia Filozoﬁczne, no. 4, 141-146. Krajewski W., 1967, Związek przyczynowy, PWN, Warszawa. Kumar M., 2008, Quantum. Einstein, Bohr, and the Great Debate About the Nature of Reality, Icon Books, Cambridge. Lombardi O., Castagnino M., 2008, A modal-Hamiltonian Interpretation of Quantum Mechanics, Studies in History and Philosophy of Modern Physics 39, no. 2, 380-443.

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Majewski Z., 1970, Z kręgu niemarksistowskich interpretacji ﬁlozoﬁcznych mechaniki kwantowej, Studia Filozoﬁczne, no. 1, 201-205. Majewski Z., 1988, Mechanika klasyczna a zasada determinizmu, Studia Filozoﬁczne, no. 11, 15-24. Mazierski S., 1955-1957, Uogólnienie pojęcia przyczynowości, Roczniki Filozoﬁczne 5, no. 4, 153-171. Mazierski S., 1958, Zasada przyczynowości w aspekcie ﬁzykalnym i metaﬁzycznym, Zeszyty Naukowe KUL 1, no. 4, 27-42. Mazierski S., 1972, Elementy kosmologii ﬁlozoﬁcznej i przyrodniczej, Księgarnia Św. Wojciecha, Poznań–Warszawa–Lublin. Mazierski S., 1979, Geneza i rozwój pojęcia praw statystycznych, Studia Philosophiae Christianae 15, no. 1, 61-80. Morikawa R., 2007, The Limits of Atomism, the Bohm Way of a New Ontology, Electronic Journal of Theoretical Physics 4, no. 16, 1-9. Van Name F. W., 1962, Modern Physics, Prentice-Hall, Englewood Cliffs, New Jersey. Norris C., 2001, Putnam on Realism, Reference and Truth: the Problem with Quantum Mechanics, International Studies in the Philosophy of Science 15, no. 1, 65-91. Pechenkin A., 2002, Mandelstam’s Interpretation of Quantum Mechanics in Comparative Perspective, International Studies in the Philosophy of Science 16, no. 3, 265-284. Piersa H., 1983, Uznawanie twierdzeń ﬁzyki, Roczniki Filozoﬁczne 31, no. 3, 155-164. Putnam H., 2005, A Philosopher Looks at Quantum Mechanics (Again), British Journal for the Philosophy of Science 56, 615-634. Reichenbach H., 1951, The Rise of Scientiﬁc Philosophy, University of California Press, Berkeley–Los Angeles–London. Romanow-Broniarek M., 1978, Ignorabimus Heisenberga, Znak, no. 30, 227-231. Rutowski T., 1984, Przyczynowość na terenie ﬁzyki, ﬁlozoﬁi przyrody, metaﬁzyki i teorii informacji, Roczniki Filozoﬁczne 32, no. 3, 49-71.

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Schabowski Z., 1966, Przyczynek do marksistowskiej teorii przyczynowości, Studia Filozoﬁczne, no. 2, 221-225. Semczuk S., 1987, Status ontologiczny przedmiotów teoretycznych ﬁzyki, Studia Filozoﬁczne, no. 2, 33-40. Sławianowski J. J., 1965, Atomy, przyczynowość, skoki kwantowe, Studia Filozoﬁczne, no. 3, 201-206. Sławianowski J. J., 1969, Przyczynowość w mechanice kwantowej, Wiedza Powszechna, Warszawa. Svechnikov G. A., 1971, Causality and the Relation of States in Physics, Progress Publ., Moscov. Szczęsny J., Urbaniec J., Mechanika kwantowa a upadek mechanicyzmu, in: Wszechświat – maszyna czy myśl? Filozoﬁa mechanicyzmu: powstanie – rozwój – upadek, eds. M. Heller, J. Życiński, Polskie Towarzystwo Teologiczne, Kraków 1988, 224-232. Tanona S., 2004, Uncertainty in Bohr’s Response to the Heisenberg Microscope, Studies in History and Philosophy of Modern Physics 35, no. 3, 483-507. Terlecki J., 1953, Zagadnienia rozwoju teorii kwantowej, transl. Z. Kopeć, in: Zagadnienia ﬁlozoﬁczne ﬁzyki, vol. 1: Zagadnienia ﬁlozoﬁczne mechaniki kwantowej, eds. B. Buras, K. Majewski, PWN, Warszawa, 9-33. Van Melsen A. G. M., 1953, The Philosophy of Nature, Duquesne University Press, Pittsburgh. Walton D., 1973, Hume Exhumed: A Polemic Against Determinism, Journal of Critical Analysis 4, 159-164. Weizsäcker C. F. von, 1980, The Unity of Nature, transl. F. J. Zucker, Farrar Straus Giroux, New York. Whitehead A. N., 1925, Science and the Modern World, The Macmillan Company, New York. Wichmann E. H., 1971, Quantum Physics, McGraw-Hill College, New York.

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Causality and Determinism in Modern Physics Key words: causality, determinism, indeterminism, quantum mechanics – interpretations.

1. Introductory remarks Many philosophers share the view that the objects of examination in physics are phenomena and relations between them, rather than the deepest ‘structure’ of the objectively existing reality [cf. Rutowski 1984, 53], the research of which is the domain of metaphysics and the philosophy of nature. In other words, physics deals with the phenomenal aspect of reality. Whether one shares this standpoint or not, the standard way of arriving at theorems in physics and the method of falsiﬁcation of hypotheses are, indeed, empirical in character. The starting point is usually an observation of some phenomenon1. The term “observation” 1

What is meant here is the standard research practice in physics. However, nowadays some attempts of another approach are known. According to this approach the starting point is not the observation but rather some theoretical speculation. What is more, even the justiﬁcation of proposed theories is supposed to be independent of empirical data. This approach is represented, for example, in the string theory: „After its successful transition to metaphysics and its selﬁmmunization against empirical control, it is not even clear, if there are any empirical means by which we could ﬁnd out if string theory does describe nature in any adequate way, or not. Even a wrong theory will not necessarily be defeated by nature, if it is able to avoid any contact to nature” [Hedrich 2007, 274]. Therefore, the epistemological status of such attempts is unclear, and they will be ignored in this analysis.

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is used here in its broader sense, i.e. rarely, some direct observation is meant. Most often an observation is performed with the use of special measuring devices. It is practically impossible to think of an observation in physics, from which all measurements would be eliminated. Moreover, the phenomenon under examination is, frequently, brought about artiﬁcially, as an experiment, for the purposes of this examination. And ﬁnally, already at this early stage of research, a scientist has some theory, which, for more or less intuitional reasons, seems to be adequate to describe the examined phenomena. The observed phenomenon undergoes certain theoretical ‘symbolization’ in order for it to be described within a given theory. From this point onwards, a researcher uses mathematical objects and not real events; and logical and mathematical inference applies to mathematical objects. This inference, in turn, provides certain ‘symbolic events’, which are, subsequently, veriﬁed, i.e. confronted with real events observed empirically. If the veriﬁcation is positive, we say that a given theory describes a given phenomenon adequately. Otherwise, another theory is searched for; a theory, whose predictions (those ‘symbolic events’ arrived at through logical inference), will be consistent with empirical experience. We should note that within the practice described above two special assumptions are made: (1) The assumption that in the process of observation and the subsequent ‘theoretical symbolization’, we can, without a danger of severe inadequacy making the whole research miss its point, ignore the “negligibly small” quantities, i.e.: – errors in measurement2, which as it has been already said, is practically inseparable from the process of observation in physics, do not affect the validity of ﬁnal conclusions; – equally insigniﬁcant are simpliﬁcations made during theoretical preparations, when some empirical parameters are ignored in order for a given phenomenon to be, without excessive difﬁculties, placed within the framework of a mathematical theory. This assumption can 2

What is meant here is the random error (leading to measurement uncertainty), unavoidable in every measurement.

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be called the assumption of the mathematicality and ‘idealizability’ of nature [Heller 1986, 14-16]. (2) The assumption that in such research, the enumerative induction is sufﬁcient to acknowledge the validity of the theorems. If an experiment repeated many times (an observation made many times) always proceeds in the same way, we assume that the regularity acknowledged will always occur, whenever the situation happens. The second assumption is not a problem for a physicist, as it is sufﬁcient that some regularity actually occurs in the cases acknowledged so far and that it has practical signiﬁcance. The ﬁrst assumption is possible to maintain only, because physics doesn’t deal with individual cases, but rather with regularities applicable to all (virtually countless) events of the same kind [Gawecki 1969, 70]. In this case, what matters is practical utility of a given theory and not the fact that it can describe particular events a bit imprecisely. Given this background, how can we understand the principle of causality in physics? Its main formula, i.e. “Each event has its cause” seems to be acceptable, or at least attainable within physics. For it involves events – precisely this aspect of reality which is examined by physics. However, the principle of causality, as formulated above, cannot be accepted in physics, because physics, as it has been already said, doesn’t deal with individual cases. Hence, in physics, we cannot ask whether a given single event has its cause, or not. On the other hand, even in some ideal world, where physics would be able to assert a cause for each and every event examined so far, the use of the enumerative induction does not allow for a general statement that every event has its cause. The thesis of causality, as formulated above, has to be, therefore, regarded as external to the system; it can only be valuable for a natural scientist in that it encourages to search for causes, since (according to this thesis) they exist [cf. Rutowski 1984, 54]. Ignoring this heuristic aspect, a natural scientist can agree with Reichenbach, who writes: “If we seek for a particular cause, we need not assume that there is one. We can leave this question open, like the question of what is the cause. Only if we knew that there is no cause would it be unreasonable to seek for a particular cause. But if nothing

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is known about there being a cause, we can search at the same time for the particular cause and for the answer to the question whether there is one” [Reichenbach 1951, 112-113]. Hence, on the one hand, a physicist does not have to take the principle of causality into consideration, e.g. by accepting it tacitly as a precondition of their research, as some maintain [Kiczuk 1977, 129]; on the other hand, there are no reasons, either, for which they would have to reject it, either in a single case or in general. In natural sciences, the idea of causality can be considered in so far as it expresses the principle of determinism [Mazierski 1955-1957, 155]: the same cause (under the same circumstances) brings about the same results [Krajewski 1967, 242], or, to put it in a more precise way: if the state of a certain material system is known in the present, then, its past and future states are known, too [Mazierski 1958, 27-29]. This is the very formula of the principle of determinism, which we will take into account during our discussion. However, we should note here that, sometimes, it is postulated that the principle of determinism should be extended to cover the conviction that “individual representatives of a certain species always act in the same way under the same circumstances” [van Melsen 1953, 208], or more generally, that determinism equals the following conviction: „a thing, of necessity, behaves as it does in accordance with its given nature” [van Melsen 1953, 231]. Even if such views are correct, they are philosophical in nature and hence cannot be considered within the scope of physics. Other attempts of extending the principle of determinism involve introducing the notion of general determinism. Then, this principle would include unambiguous (strict) determinism, as deﬁned above, and ambiguous (or statistical) determinism [e.g. Krajewski 1964, 141-143; cf. Hacking 1983; Walton 1973], namely, the cases where the state of the system S at the moment t0 would determine the whole group of possible states S1, S2, ..., Sn at the moment t, each with some probability P1, P2, ..., Pn in the way that the sum P1 + P2 + .... + Pn would equal 1 [Mazierski 1972, 346-347]. Yet, introducing the notion of general determinism seems to be a misleading attempt, because it attributes the term “deterministic” to cases commonly associated with indeterminism

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[cf. Amsterdamski 1964, 85-92]. Therefore, we will conﬁne ourselves to the approach, which associates the notion of determinism with unequivocal prediction (or retrodiction): the state S0 at the moment t0 determines the state S at the moment t. With the above formula in mind it can be judged whether a given theory is deterministic or not. It is important to note that such a judgment concerns a theory understood here as a mathematical apparatus with some accompanying physical interpretation. The question of the determination of phenomena (whatever a ‘determination of a phenomenon’ may mean) as certain manifestations of reality is an entirely different one. The notion of “the state of a system”, used in the principle of determinism, deserves particular attention. What does it mean? The physical state of a system is the set of empirical data, which “fully describe the properties of a given system and of its surroundings, affecting it” [Mazierski 1958, 27-29]. However, the phrase “fully describe the properties…” raises important problems. We should note that: (1) As a result of the assumption of ‘idealizability’ of nature, mentioned above, and hence applying the procedure of ignoring the “negligibly small quantities”, the properties of a system are never fully described. The state of a system, described with taking into account all its properties known in physics could be called the “absolute state” [cf. Sławianowski 1969, 44-46]. (Yet, we should remember that such a term may be misleading. This is because the cognitive capacities of physics develop constantly and at no stage of this development we can say that they are truly “absolute”). (2) In practice, we obviously use a relative notion of state. This is a set of empirical data, determining important properties of a system; important properties are those which, when taken into account, are sufﬁcient for the theory in question to be applicable. The properties, which should be taken into account are those, which, within a given theory are subject to theoretical symbolization. Thus, the relative state of a system is a notion relative to our purposes (needs) and our

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cognitive capabilities3. Therefore it may be that a system, for some of its relative states, is described by a deterministic theory, while for another relative states there is no determination. As we see from the above discussion, the way a relative state of a system is perceived depends on the theory under consideration. A relative state is relative to our needs. The ﬁrst need determining a description of the state of a system is the use of this notion within a given theory. So, the properties taken into account while describing the state of the system are those required by the theory [cf. Augustynek 1962, 11; Mazierski 1972, 283-284]. If for some phenomenon it is impossible to ﬁnd a relative state of the system, appropriate for the theory by means of which we are trying to describe this phenomenon, it means only that this particular theory is not applicable to this phenomenon. What follows is that it is possible for the same system to be described both by a deterministic and an indeterministic theory, depending on how the state of this system is deﬁned. If the deﬁnition of this state is possible to use within certain deterministic theory, then the system will be regarded as capable of being described within this theory. But if, for some reasons, we do not have the notion of state, which this particular theory requires, it means that this theory is inapplicable. The question of reasons, for which the required state of a system cannot be found, doesn’t have to worry natural scientists. It is sufﬁcient that they, after deciding on such impossibility, attempt to describe the state of the system in question in the way which could be analyzed within some other practically useful theory. This problem is different in philosophy, though. In philosophy, the reasons, for which scientists rejected some particular way of describing 3

Cf. J. J. Sławianowski [1969, 50] and the example presented there. In case of vapours, most frequently we are not interested in their microscopic structure, but rather in their properties exhibited on the macroscopic level. Hence, we use the notions of pressure, temperature, etc., to describe the state of the vapour, which is one of possible relative states, presenting the properties important from practical point of view, while ignoring others. The state described in this way will not be sufﬁcient for the atomistic theory because, for this theory, the pressure and temperature are not essential properties of the system.

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the properties of the system may appear very important. There are, basically, three possibilities: (1) The research methods used, inadequate measurements or measuring devices did not allow for capturing the properties required. (2) These properties are, by deﬁnition, impossible to consider within a given theory, because they comprise a relative state of a system different from a relative state required by the theory in question. (3) These properties are impossible to be captured for some “fundamental reasons”, resulting in the necessity of resigning (not only for practical reasons but for ever) from describing the system by means of this theory, within which the capturing of these properties was necessary to build up the notion of state it requires. If the third possibility is the case, then a philosopher faces the problem concerning philosophical implications of the fact of “fundamental impossibility” of capturing some properties of the system, and hence the equally fundamental inapplicability of a given theory to the description of phenomena in question. All the conclusions, which can be drawn from such a situation have to respect two restrictions: A. The impossibility of applying a deterministic theory doesn’t mean the lack of determination in reality. The view that even all the events in the universe are determined is not the same as the conviction that precise prediction (or retrodiction) is always possible [cf. Majewski 1970, 204-205]. If a phenomenon is possible to be described in a deterministic way, we can conclude that it actually is determined. However, the lack of such description – the lack of a deterministic theory for a certain type of phenomena – doesn’t exclude a possibility of actual determination, since a deterministic relationship may occur independently of our knowledge. In other words, determinism would be excluded here on the epistemological, and not on the ontological level. B. This “fundamental” impossibility of capturing required properties of a system involves a given concrete theory and not the type of theories. For instance, if the theory inapplicable to a certain case was of the deterministic type, it doesn’t imply that no deterministic theory at all can be applied to this case. Thus, ultimately neither

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ontological nor epistemological determinism may be excluded, even in the case of the fundamental impossibility of capturing certain properties of the system.

2. Classical physics It seems that in many discussions of causality in classical physics, what gets overlooked is that, strictly speaking, the notion of causality – unlike the notion of determinism – has virtually no application in physics. Questions expressing the issues of classical physics are of this sort: “I’m moving an object, what is the cause of its movement?” [Gawecki 1969, 163] or „An object is falling down. What is the cause of it?” [Gawecki 1969, 162]. Questions of this sort, about the cause of some phenomenon, are also asked in everyday life – “Something happened, why?” Yet, in the ﬁeld of physics, it doesn’t lead to explicit conclusions. Considering, for example, the problem: “What is the cause of falling down of an object?” may lead to various true, but not necessarily unambiguous answers, e.g. the cause of falling down is: (1) the Earth; (2) the gravitational force; (3) the preceding process of taking an object up to the point from which it has fallen [Gawecki 1969, 164]; (4) some external factor causing an object to lose its balance (if it has kept it before, despite the (1) – (3) factors). Each of the above answers is correct, although each expresses the cause of the same phenomenon in a different way. We can quote numerous arguments for each of the above reasons, yet a physicist wouldn’t be able to decide which of them is ultimately correct, because answers to the above questions cannot be unambiguous. It is not surprising, though. As we already said, physics doesn’t deal with answering the question of the cause of a given individual phenomenon. And if physicists ask such question, they treat it as an auxiliary one, as it can lead to revealing and describing some general regularities (as in the above example – to the analysis of gravitation). The more appropriate question is, therefore, not the one about causality, but about determinism. One may ask if classical physics is

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deterministic or not? Or, more strictly, are the theories of classical physics of the deterministic type or not? The basic theory of classical physics is classical mechanics. Let us brieﬂy remind why this theory is deterministic. Obviously, classical mechanics uses some notion of the state of a physical system. Historically speaking, the ﬁrst deﬁnition of a state was the position of a body in space. Adding the momentum to such a description, we have the classical pair of quantities, sufﬁcient for a certain physical system to capture the behaviour of this system within classical mechanics [cf. van Name 1962, 166]. This theory, for a given state of a material system at a random initial time t0, determines one and only one state of this system at every other time. Capturing the state of the system (determining the momentum and the position), constitutes the basis of describing this system within the theory. The theory, in turn, enables the theoretical determination (prediction) of the state of the system at any other moment of time. This prediction is obviously expressed by means of providing the same pair of quantities, i.e. momentum and position at a desired time. The notion of the state of a system used here, refers to the relative state, since it includes only those of physical features of the system which are essential from the viewpoint of classical mechanics, and ignores many others [cf. Majewski 1988, 19-23]. However, this notion turns out to be sufﬁcient for practical purposes, as it, together with the whole theory of classical mechanics, leads to the results consistent with empirical knowledge. The fact that predictions of the future (or past) ‘state of a system’ are possible and that they are consistent with empirical knowledge decides that the classical mechanics is a theory of a deterministic type.

3. Quantum physics Classical physics, together with its fundamental theory, i.e. Newton’s mechanics, had such great achievements that, at the end of the 19th century, it was regarded as the perfect and extremely important theory in all the ﬁelds which ever were, or would be, examined within physics.

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Some minor problems, as physicists thought, remained unresolved, but they were supposed to be resolved later on within classical mechanics. Yet, the very attempts to solve these problems led to the fundamental turn in physics, namely to the rise of quantum theory4. As we can notice, while reading the history of theories in physics, the development of physics, most frequently, imposes some restrictions on the application of previously established theorems [cf. Piersa 1983, 155-164], e.g. when physicists noticed that the classical description of motion fails for the range of speed approximating the velocity of light, although it is correct for “ordinary” range of speed. Quantum physics, however, seemed to cause something more: total rejection of laws regarded as irrefutable till then. The problems the quantum theory posed are not conﬁned to strictly physical issues. For instance, some attempts are made to build up a new system of logic for the purposes of quantum mechanics, other than the classical binary one [e.g. Dickson 2001; Kiczuk 1978, 53-64]. Moreover, some maintain that a kind of a theory of “discontinuous existence” is necessary, because the notion of motion is called into doubt in quantum mechanics [Whitehead 1925, 53], or even they go so far as to negate the existence of the objects of microphysics [Semczuk 1987, 33-40]. The most frequently considered problem, though, is the fact that as soon as the quantum theory had emerged, deﬁning the notion of causality and reaching some agreement concerning the views on causality became more and more troublesome. The problem of causality, or determinism, in the micro-world became one of the fundamental problems considered by both scientists and philosophers [cf. Schabowski 1966, 221].

3.1. Heisenberg’s uncertainty principle Philosophical discussions of causality and determinism in the micro-world most often focus on Heisenberg’s uncertainty principle, which follows from quantum mechanics. This principle expresses the fact that it is impossible to capture, at the same time, the position and 4

An excellent account of this fascinating history can be found in Kumar [2008].

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momentum for a given particle with unrestricted accuracy5. This principle has its strict mathematical expression, allowing to formulate it in a more precise way, namely, to say that the product of measurement error for momentum and for position cannot be lesser than the so-called Planck constant6. As these very quantities, connected by the uncertainty principle, served for deﬁning the state of a system within classical mechanics, the consequences of this principle seem to be very important for considering the problem of determinism. The understanding of the uncertainty principle is not unambiguous, though. It can be captured in three ways: (1) Uncertainty as an effect of measuring disruption. The principle of uncertainty is often explained as follows: The act of measuring disrupts the system under examination, for there occurs an inevitable interference between the system and the measuring device. Hence, if we try to determine the position of a particle very precisely, its state is so disrupted as the momentum becomes totally indeterminate. And the other way round, if we try to determine the momentum of a particle accurately, its position becomes indeterminate. Shortly speaking, the cause of uncertainty lies in the interference between the measured object and measuring device [Gołębiewski 1982, 37]. Such an approach would suggest that the uncertainty principle is a result of the imperfection of measuring devices. (2) Uncertainty as a consequence of the structure of measuring act. This interpretation, referring also to the measuring process, shows that the disruption of the state of a particle, caused by measuring, doesn’t depend on the quality of measuring devices but rather it is a result of the very act of measurement and hence is more fundamental in character [Svechnikov 1971]. It is impossible to imagine a measurement which wouldn’t disrupt the state of the particle under examination. It follows 5

This principle applies also to other pairs of the so-called canonically coupled quantities, yet, for our present purposes, it is sufﬁcient to formulate this principle for the position and momentum. 6 More strictly, this product cannot be lesser than certain quantity depending on Planck constant; yet, what is important here is that it is a quantity of a positive value, and hence that the position and momentum cannot be measured with unrestricted accuracy

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from the fact that each measurement in physics involves some exchange of energy between the measuring device and the object being measured. Imagine a microscope by which one looks at the world of micro particles7. The light itself (a necessary ‘observational device’), which carries certain energy, would disrupt the state of the particle being observed. If, instead of a microscope, any other device was used, it would always require some “mediator” (like light in a microscope), which would enable the observation of a given particle, disrupting, at the same time, its state and causing the uncertainty. The reason for the disruption lies, therefore, not in the imperfection of measuring devices but in the very structure of the act of observation (measurement). This interpretation usually leads to the conviction that the uncertainty principle is universal, absolutely unavoidable. As far as it well may be, such a point of view is based on two additional assumptions (both may seem plainly trivial, nonetheless they are assumptions): – it is impossible to imagine any knowledge about a physical object, gained in other than experimental way (i.e. beyond any measurement); – it is impossible to ﬁnd an “empirical mediator”, which would enable the observation of an object without disrupting its state signiﬁcantly and hence without causing the uncertainty. It is noteworthy that the fact of disruption of an object state in the process of measuring is not necessarily connected with microphysics and remains true in the macroscopic cases. This problem did not surface in the classical mechanics, because the inﬂuence of the interference between an object and a measuring device is “negligibly small” there. (3) Uncertainty as an effect of the properties of micro-objects. According to this interpretation, the uncertainty principle would express a certain objective feature of nature, namely the fact that such characteristics like position and momentum are not applicable to the objects of the micro-world, considered within quantum mechanics [Wichmann 1971, 34]. Thus, there is no point in talking about position 7

This is an imaginary (and actually impossible) example, but what is meant here is to illustrate problems connected with the act of measurement.

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and momentum of a quantum particle, because such particle simply doesn’t have these properties. The uncertainty principle would therefore express a fundamental restriction, immanently rooted in the very nature of the objects under examination [cf. Romanow-Broniarek 1978, 229], and it would indicate the boundary, beyond which classical ideas and notions of classical physics cannot be extrapolated. Among various approaches to the uncertainty principle, we can ﬁnd opinions, which signiﬁcantly limit too far-reaching conclusions drawn from it. Heisenberg’s uncertainty principle follows from quantum mechanics, and hence it is valid only on the ground of this theory. It is enclosed “within the description of nature provided by quantum mechanics” [van Name 1962]. Hence, if we accept this theory, we, indeed, will arrive at the conclusion that the position and momentum of a particle cannot be known, at the same time, with unlimited accuracy. The reverse implication doesn’t hold, though: the conclusions concerning the correctness of this or that theory of the quantum world do not follow from Heisenberg’s uncertainty principle. Thus, it is illogical to maintain that this principle forces us to accept a given form of the theory of quantum mechanics as absolutely valid. If the uncertainty principle seems to impose no restrictions on the possible theories of micro-world, it cannot impose such restrictions on the way of the existence of things, either8. It concerns something more than just our knowledge but still nothing more than real physical processes [Feyerabend 1960, 27]. The strong expression that the uncertainty “is rooted in the things themselves” may, if at all, be used in the sense physicists attribute to it, namely: “Physical reality is all that may be captured with the use of means available in physics” [Blanché 1969, 56-57].

8

The question whether uncertainty is epistemological or ontological is the matter of discussion [e.g. Tanona 2004]. It seems that any particular ontological engagement of the uncertainty principle may be rightly called to doubt [see for example: Fraley 1994; Morikawa 2007].

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3.2. Interpretations of quantum mechanics Quantum mechanics is, in its fundamental form, like any other theory in physics, a set of mathematical formulas. This mathematical formalism becomes physics through some interpretation of mathematical formulas it contains [cf. Weizsäcker 1980]. Hence, the discussion of the deterministic or indeterministic character of quantum mechanics arises only in connection with an interpretation of this theory [cf. Hajduk 1965, 57; Mazierski 1972, 314]. Before such an interpretation is chosen, such general judgments as: “Wave mechanics is indeterministic in nature” cannot be justiﬁed [Mazierski 1979, 76]. Interpretations of quantum mechanics can roughly be divided into two groups. The ﬁrst group includes those which claim that quantum mechanics is a theory of individual processes [Aleksandrow 1953, 135-136; Głódź 1979, 40], while the second one includes those regarding quantum mechanics as a theory of large sets of micro-objects. In the second case, the term “quantum statistics” used to be suggested. An interpretation of quantum mechanics involves attributing some physical meaning to the mathematical formulas of this theory. The most often considered problems are: the question what the so-called wave function (the solution of the Schrödinger’s equation, a fundamental one in quantum mechanics) represents, and the sense of Heisenberg’s uncertainty principle9. 3.2.1. Schrödinger’s interpretation This approach, coming from the author of the wave mechanics10, takes into account the squared amplitude of a wave function (|Ψ|2), 9

The list of interpretations of quantum mechanics provided below is not complete. We do not take into account the non-standard (although often discussed) interpretations, e.g. the ones by David Bohm and Hugh Everett [see for example Birman 2009, 209-211]. New interpretations still appear too [e.g. Ghose 2009; Lombardi, Castiliano 2008]. 10 Historically, the ﬁrst approach to the quantum world was the so-called “matrix mechanics”, yet it is much more mathematically complicated than the wave scheme; and as these descriptions are equivalent, the one by Schrödinger soon became the standard approach.

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interpreting this quantity as the density of electron’s charge11. Thus, this conception goes towards a kind of a “substantialist” direction. For what it suggests is that an electron exists in a form of “blur”, the so-called “electron cloud”. This interpretation was supported by the famous wave-particle dualism, according to which an electron, exhibiting both corpuscular and wave properties, is actually neither a particle nor a wave; rather, it is something completely different, something which appears as a wave in one type of experiments and as a particle in another. Then, if an electron doesn’t have to be a particle, we can describe it as the “electron cloud”, and we can interpret |Ψ|2 as the density of the electric charge within this cloud. Although this interpretation had to be rejected as inconsistent with some experimental ﬁndings [Feynman et al. 1963, 21-26], it is worth to note that such an interpretation would make quantum mechanics a deterministic theory. If we know the wave function of a given electron at the moment t0, we can also calculate it for any other moment t. And since this function determines the space where an electron is (in the blur form of the cloud of charge), then the theory itself fulﬁls the requirements of a deterministic theory [cf. Sławianowski 1969, 142-143]. 3.2.2. Probabilistic interpretation In our present discussion we need to introduce the distinction between the probabilistic and the statistical interpretation. The probabilistic one belongs to the ﬁrst group of interpretations, i.e. to those, which regard quantum mechanics as a theory of individual phenomena or single objects, while the statistical interpretation belongs to the second group, regarding quantum mechanics as a theory of large sets of objects. This distinction allows to avoid numerous misunderstandings connected with common intuitions about the term “statistical”. However, there are authors who call the interpretation discussed here a “statistical interpretation” [e.g. Szczęsny, Urbaniec 1988, 231]. According to the probabilistic interpretation, the wave function represents a real quantum state of micro-object and the square of the 11

Here and in further analyses, we refer only to the most straightforward example, i.e. to the description of a free electron.

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wave function modulus determines certain probability concerning a particle, e.g. the probability of ﬁnding it within a given space. This very interpretation made many accept indeterminism in quantum physics. The wave function expresses the state of a single microobject, on the one hand, but on the other, it only allows for calculating the probabilities of given states in the future. 3.2.3. The interpretation of quantum ensembles According to this conception, the wave function is also a characteristics of an individual particle, but not “in itself”, but in the sense of its belonging to the so-called statistical ensemble [Błochincew 1953, 62; Błochincew 1954, 66]. Yet, the vicious circle error seems unavoidable here, as the statistical ensemble, in turn, is understood as a set of particles being in the same state described by a given wave function. 3.2.4. Statistical interpretation Unlike the previous interpretations, this one treats quantum mechanics as a theory describing not single micro-particles but rather the behaviour of large amounts of them. “Quantum mechanics is not the theory of a real process, which a particular micro-object is subject to; rather, it illustrates adequately only the behaviour of a set of microobjects” [Terlecki 1953, 21; cf. Pechenkin 2002]. We should note that, within this interpretation, Heisenberg’s uncertainty principle determines only the relation between the dispersion of some quantities within large sets of particles. Thus, one cannot deduce from it any restrictions concerning single events, because nothing prevents single values of the pairs of quantities, the uncertainty principle connects, from being strictly determined [Fayerabend 1960, 30-31]. Within such framework, quantum mechanics would be nothing more than a statistical method of calculating some values. Statistical character of such theory may be underlain by the individually determined phenomena. Such a statistical theory provides then a kind of an average of individual effects [Sławianowski 1965, 40]. And the other way round: there is no contradiction between applying a deterministic theory and using statistical

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methods, which the “proper” statistical mechanics is an example of: the behaviour of some system is basically possible to describe within the theory of the deterministic type, yet, for practical reasons, using the statistical description is sufﬁcient and more convenient. The properties of the system, found for the purposes of such conception, can be insufﬁcient to apply a deterministic prediction; yet, this doesn’t exclude the possibility of describing this system within a deterministic theory. 3.2.5. Copenhagen interpretation This, probably the most popular interpretation, opposes the views that quantum mechanics is a theory of objective phenomena. Within this interpretation, the state of a system is not an objective property, but only a relation to the measuring devices [Feyerabend 1960, 45]. Here, the wave function has a kind of a double meaning: it describes a certain fact and expresses our knowledge about this fact. The probabilities, which the theory uses, do not result from the properties of the electron itself but from our imprecise knowledge about it [Heisenberg 1999]. This probability turns into certainty as a result of our observation when our knowledge of the system changes suddenly. The act of observation “chooses” a concrete case out of numerous ones, which have been only probable so far. A special consequence of such approach is the claim that we can talk only about what happens in the act of measurement. What happens between measurements is unknown. For example, it is impossible even to think of a position that an electron has in between measurements. As a comment to this approach, de Broglie wrote that quantum mechanics theory describes adequately only stationary states but it fails to describe the transitions between them. By declaring that these transitions surpass the space-time frame, quantum mechanics just hides its inadequacy [Blanché 1969, 50]. Heisenberg’s uncertainty principle is interpreted in a special way, too. Referring to the relationship between this principle and measurement disruptions, these disruptions are given a kind of ultimate character. The uncertainty of position and momentum is supposed to be the objective characteristics of nature. What matters here is not the fact that, because of some more or less objective reasons, we are unable to determine

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position and momentum, but the fact that these quantities do not exist, in the case of electron, or rather they do not exist simultaneously [Wichmann 1971]. Thus, the uncertainty principle is formulated as an objective law of nature; and it is often understood that way, by both supporters and opponents of the Copenhagen interpretation. Yet, we should strongly emphasize that no claim within the subjectivist Copenhagen interpretation, can be attributed the characteristics of objectivity, as the whole interpretation goes in the anti-realistic direction. It seems implausible to maintain that there is an objective regularity connecting some properties of an object, if these properties, being the relation to the measuring devices, are not objective in themselves12.

4. Conclusion It is a widespread view that while the classical mechanics is the ﬂagship of deterministic theories, the quantum mechanics is an icon of indeterministic ones. However, it appears that indeterminism of quantum mechanics is limited, at least in the sense that it depends on the interpretation of this theory (with its crucial elements like the wave function and Heisenberg’s uncertainty principle) one accepts. The developments in the research of the micro-world made some interpretations more credible than others, while some of them were totally rejected. Nonetheless, even the claim that indeterminism is irremovable from the description of the micro-world doesn’t imply the negation of the most general formula of the philosophical causality principle, namely, that each event has its cause. For judging the presence or lack of causes is raising an ontological thesis concerning real world. And theses of this kind do not directly follow from the characteristics of the scientiﬁc description of this world, regardless of how accurately they are captured. In other words, there is no direct implication between theses of the epistemology of scientiﬁc knowledge and those of the ontology of the real world. 12

It is worth noting that the authors of the Copenhagen interpretation didn’t agree with one another as far as its proper meaning is concerned [Camilleri 2006; 2007]. According to some authors, there are good reasons for rejecting this interpretation in general [Norris 2001; Putnam 2005].

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