Status of Time in Physics - MIT Mathematics

Time in Science and the Arrow of Time Einstein’s Relativity and Consequences Quantum Theory of Fields and the Fabric of Space and Time

Status of Time in Physics Ramis Movassagh Department of Mathematics, MIT/Northeastern

September 17, 2012

Ramis Movassagh

Status of Time in Physics


Outline

Time in the scientific methods Conception of time throughout history Space-time in physics Origin of space-time Measuring time Information and time Modern views of fabric of space-time

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Out - of - line

Time in psyche (perception/intensity) Time in religion Existence (now-ness, illusion of time) Reality Philosophy of time Management of time and its use Determinism with relation to free will Mythology

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What is time?

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What is time?

[mass noun] the indefinite continued progress of existence and events in the past, present, and future regarded as a whole - Oxford Dictionaries

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What is time? [mass noun] the indefinite continued progress of existence and events in the past, present, and future regarded as a whole - Oxford Dictionaries

Time is the continuing sequence of events occurring in apparently irreversible succession from the past through the present to the future and a measure of the durations and frequencies of events and the intervals between them. -Wikipedia

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What is time? [mass noun] the indefinite continued progress of existence and events in the past, present, and future regarded as a whole - Oxford Dictionaries

Time is the continuing sequence of events occurring in apparently irreversible succession from the past through the present to the future and a measure of the durations and frequencies of events and the intervals between them. -Wikipedia

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Less controversial Wiki hits

"time is what clocks measure" "time is what keeps everything from happening at once" Comment: Whoever wrote this didn’t believe in causality.

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The Scientific Method

Key element in science is experiment Confidence in experiment requires reproducibility There is a tacit assumption of homogeneity in time when performing experiments.

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The Scientific Arrogance

Zealous belief in comprehensibility of nature The Eventual Goal of Science is to provide a single theory that describes the whole universe - S. Hawking, Briefer History of Time Demanding a unified view especially developed in countries that were monotheistic (e.g. unifying forces, string theory etc.)

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Physics Physics is mainly concerned with the state and evolution in time of material particles and fields given the couplings among them.

Newton's 2nd “law of motion”

F=ma=mx

Physics (empirical)

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Math (differential equation)



Physics

Physics Physics is mainly concerned with the state and evolution in time of material particles and fields given the couplings among them. t>0

t=0

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(non) determinism

(non) determinism

Omar Khayyam (1048–1131)

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(non) determinism

And the first Morning of Creation wrote What the Last Dawn of Reckoning shall read.

Omar Khayyam (1048–1131)

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Existence Static Existence: “Block Universe” t

Person B's Life events

y

Person A's Life events

x

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Determinism Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration...

Sir Isaac Newton (1649 -1736) Principia

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Arrow of Time

Good References: ● ● ●

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S. Carroll's talks and book Schrödinger, 'what is life?' H Price, Time Arrow (Phil.)



Arrow of time

t0 Ramis Movassagh



Arrow of time

t0

Many ways of having such evolution

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t>t0



Arrow of time

?

t0

t>t0 Ramis Movassagh



Arrow of time

YES! “...You would have to wait a long time” - L. Boltzmann

t>t0

NOT Many ways of having such evolution

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t0



Micro vs. Macro States

Microstates: any particular configuration in the phase space Macrostate: sets of macroscopically indistiguishable microstates S = kB ln D Entropy is lack of information, lack of structure

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Phase Space Probabilities Second law of thermodynamics: time evolution of the state

S≥0 t > t0

t = t0

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The second law of thermodynamics

Equilibrium is death for living matter

So why is the universe so complex (life, structure, etc.) ? ?

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What is Life?

S

= kB ln D

D: amount of disorder

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What is Life?

S

= kB ln D 1 Sdrawn = kB ln = −kB ln D D D: amount of disorder

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Drawing order and pushing equilibrium away

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Drawing order and pushing equilibrium away

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Ludwig Boltzmann (1844 - 1906) ...That in Nature the transition from a probable to an improbable state does not happen equally often as the opposite transition, should be sufficiently explained by the assumption of a very improbably state of the whole universe surrounding us ...

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Universe: S(t0 )

Around big bang

Simple

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Universe S(t1 > t0 ) Around now: 1010 yrs

Around big bang

Simple

Complex

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Universe S(t2 > t1 ) 10 15 yrs

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Universe S(t3 > t2 ) > 10 100 yrs an eternal vast emptiness

Simple Ramis Movassagh



Suggesting

Magnitude

Complexity

Entropy

Time Ramis Movassagh



Plan Physics

Einstein's relativity Preserves Causality, Determinism, ...

Quantum theory Inherently probabilistic, Heisenberg's uncertainty principle, ….

Partially reconciled to quantum theory of fields

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Plan Physics

Quantum theory

Einstein's relativity Preserves Causality, Determinism, ...

Inherently probabilistic, Heisenberg's uncertainty principle, ….

1

2

Partially reconciled to quantum theory of fields

3 These have profound consequences, which we will now explore Ramis Movassagh



Einstein's Relativity and Consequences

Good References: ●

● ●

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S. Hawking, Briefer History of Time W. Rindler, 'Relativity' S. Weinberg, Gravitation



Newton’s Universe

Absolute space Absolute time

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Newton’s Universe

Absolute space Absolute time Despite his equations implying relativity. Newton was severely criticized but he remained a tough cookie because he believed God is absolute =⇒ His space and time had to be!

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Albert Einstein

Time at and after Einstein

Albert Einstein (1879 - 1955) Ramis Movassagh



Absolute , equable, mathematical ...

Time

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Space-Time

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Space-Time Relative !

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Space-Time ‫ ق‬- elative !

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Birth of Special Relativity

AE was fascinate by Maxwell’s theory that unified E & M (constancy of speed of light) It took young and hungry Einstein’s imagination and confidence to hold on to this original line of thought despite various seeming paradoxes.

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Consequences of SR

Make mechanics consistent with Maxwell’s theory =⇒ Special Theory of Relativity ! Relativity of space and time. Nothing absolute about space or time No faster than light signal (causality). Equivalence of mass and energy: E = mc 2

Unified mechanics with Electromagnetism

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Consequences of SR

Make mechanics consistent with Maxwell’s theory =⇒ Special Theory of Relativity ! Relativity of space and time Nothing absolute about space or time No faster than light signal (causality). Equivalence of mass and energy: E = mc 2

⇔

m=

E c2

Unified mechanics with Electromagnetism

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Einstein’s Universe

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A. Friedman Took Einstein’s equations at face value

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Friedman’s solution(s) of the Universe

I. Expands, slows down, contracts into a crunch II. Expands so rapidly that the gravitational attraction can never stop it (escape velocity) III. Expands rapid enough that it stops at infinite time, i.e., barely escapes the crunch doomsday None have a boundary.

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So which is it?

Recent, we see that the expansion is accelerating =⇒ NONE OF THE FRIEDMAN solutions !

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The “Big Bang”

A common feature of all solutions to Einstein’s equations is that, regardless of the future:

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The “Big Bang”

A common feature of all solutions to Einstein’s equations is that, regardless of the future: At 13.7 Billion years ago the distance between neighboring galaxies must have been zero.

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The “Big Bang”

A common feature of all solutions to Einstein’s equations is that, regardless of the future: At 13.7 Billion years ago the distance between neighboring galaxies must have been zero. All the universe must have been at a single point: the origin of space and time!

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Time Travel

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Traveling into the future

This is easy. Just wait

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Traveling into the future

This is easy. Just wait You can even fast forward into the future (so called twin paradox)

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But can we travel into the past ?!

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Closed Time-like Curves


Kurt Gödel: 1906 – 1978

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Closed Time-like Curves ●

Arguably the greatest logician of all times.

●

Very difficult patient

●

Incompleteness Theorem

●

●

Finding an inconsistency in American constitution

Kurt Gödel: 1906 – 1978

Closed time like curves (CTC)

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One way: Closed Time Like Curves

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CTC: Features of Gödel’s solution

Solution implies that the whole universe is rotating Mathematical side effect: travel a great distance and come back to a different space-time point. e.g. come back to earth and a time in the past !

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Good news is that : recent data suggests that there are no Gödel rotations, further his model doesn’t have expansion in it.

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Good news is that : recent data suggests that there are no Gödel rotations, further his model doesn’t have expansion in it. Bad news ...

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There are other ways

1

Faster than light. No go with GR.

2

Curve the space-time so much by gravitation that you create a singularity.

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Wormholes

Albert Einstein and Nathan Rosen (1935): create the bridges, In the same year: EPR predict entanglement !

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A Wormhole in a 2D universe

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Quantum Fabric of Space-Time

F. Wilczek , various books S. Carroll's book N. Arkani-Hamed , various talks IAS talk 2011 recommended

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Consequences of QFT

E ∆E

= mc 2 ∼

1 ∆t

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Consequences of QFT

E ∆E

= mc 2 ∼

⇔

m=

E c2

1 ∆t

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Vacuum: Can it get any more boring?

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Vacuum: Can it get any more boring?

e- e+

ΔE~

1 Δt

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Vacuum: It's kinda of exciting? p-

e+ p+ e-

k+ k-

μ+ μ-

~ 10

-13

– 10

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-16



This description of nature has been tremendously successful based on QFT Formulated by 1970's with fantastic set of predictions.

Now with Higgs having been verified, we have strong confidence that the standard model is an accurate description of nature to scales 10 -16

Some experiments are verified to a part in 1011

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This description of nature has been tremendously successful based on QFT Formulated by 1970's with fantastic set of predictions.

eeff

10 -11 cm Verified to an accuracy of 1/1000

I. Levine et al. , Phys. Rev. Lett. 78, 424–427 (1997)

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Vacuum: Too EXCITING

Doom of Space Time

~ 10 -33 cm ~ 10 -43 sec

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Hell breaks loose at the Planck scale Planck time Planck mass Planck length (ℓP)

5.39121 × 10−44 s 2.17645 × 10−8 kg 1.616252×10−35 m

Numbers from wikipedia

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Quantum Mechanics & Relativity

Δ E ~ 1/ Δ t

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E = m c2




Δ E ~ 1/ Δ t

E = m c2

Fluctuations become larger and larger at smaller scales.

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Δ E ~ 1/ Δ t

E = m c2


Vacuum has energy: is a hot boiling soup of particles

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Δ E ~ 1/ Δ t

E = m c2


Vacuum has energy: is a hot boiling soup of particles

Shorter distances give yet higher energies; i.e., higher energy density Λ

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Even if we don't go so small as the planck scale so we can meaningfully talk about space and time we still get a very large Λ

Predicts a Λ so large that the universe would expand a lot faster than observed

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Even if we don't go so small as the planck scale so we can meaningfully talk about space and time we still get a very large Λ

Predicts a Λ so large that the universe would expand a lot faster than observed

Λobserved ~ 10-120 Λtheory

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How is it currently explained and “understood”? ? Believe it or not we do fine tuning :

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How is it currently explained and “understood”? ? Believe it or not we do fine tuning :

Λobserved = Λtheory + Λ background Λtheory ~ - Λ background Where they agree to 120 decimal places and hence cancel !!!

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How is it currently explained and “understood”? ? Believe it or not you do fine tuning :

Ju Th st ha ere pp en ! s

Λobserved = Λtheory + Λ background Λtheory ~ - Λ background Where they agree to 120 decimal places and hence cancel !!!

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to be


Anthropic Principle (idea): Sean Carroll’s picture

But why why? Best we got is the Anthropic Principle:

The fundamental physical constants necessary to accommodate conscious life

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Anthropic Principle (idea): Sean Carroll’s picture

But why why? Best we got is the Anthropic Principle:

The fundamental physical constants necessary to accommodate conscious life

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Clocks ●

●

Oldest of man's inventions to measure time intervals smaller than ones offered by nature (e.g., a day, a lunar cycle etc.) Signature of all clocks is periodicity

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Atoms Atoms are of the same identical kind. As far as we know they don't change their properties over time. They have 'discrete' energy levels Their transitions are invariants Provide a source for high frequency 'hatching' of time.

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Atoms Atoms are of the same identical kind. As far as we know they don't change their properties over time. They have 'discrete' energy levels Their transitions are invariants Provide a source for high frequency 'hatching' of time.

Atomic Clocks: also use periodicity !

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An Atomic Transition

E±δE E

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E

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E

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E E

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Sharpen the precision Feed back To Drive the cavity

E

E ± δE E

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E

~E E

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E

~E E

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E

~E E

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State of art clocks

1

Fountain atomic clock: Microwave standars such as NIST-F1 caesium fountain loses a second in 100 million years

2

Quantum clocks: UV standard aluminum and beryllium ion clock loses a second in 3.7 billion years 1

3

1,121,015,393,207,857.4(7) Hz

In February 2010, NIST enhanced it using a single aluminum to get twice accuracy

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What is time? [mass noun] the indefinite continued progress of existence and events in the past, present, and future regarded as a whole - Oxford Dictionaries Time is the continuing sequence of events occurring in apparently irreversible succession from the past through the present to the future and a measure of the durations and frequencies of events and the intervals between them. - Wikipedia

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The World as a Fluctuation

Perhaps Boltzmann’s idea can be restored that each of these ’big bangs’ corresponds to a fluctuation in a grand-universe that is otherwise at equilibrium. Hence our world including lives, dreams and cosmology are none but an ephemeral fluctuation sparkling in a timeless existence

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Lastly... At this very moment I remain confused as to whether I should

ThankQ

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Lastly... At this very moment I remain confused as to whether I should

ThankQ or Thank you Ramis Movassagh



So let me

1 √ { ThankQi 2

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+

Thank youi }.



The Scientific Method

Key element in science is experiment Confidence in experiment requires reproducibility There is a tacit assumption of homogeneity in time when performing experiments. A good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation Karl Popper In science we are never right, we can only prove to be wrong.

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Existence “There are really four dimensions, three which we call the three planes Of Space and a fourth Time. There is however a tendency to draw an unreal distinction between the former three And the latter dimension because our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives” “That' said a very young man, making spasmodic efforts to relight his cigar over the lamp; 'that … very clear indeed.” H.G. Wells, The Time Machine (Chapter 2 SR , S. Weinberg, Gravitation)

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Cosmic Microwave Background (CMB)

We appear here 13.7 billion years later

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Cosmic Microwave Background (CMB) 379 000 years after ~ 3000 K

c c

c

c

c

c c

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c



So which is it?

Until a couple of decades ago, physicists thought it was the second type, because you expect gravity to slow it.

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So which is it?

Until a couple of decades ago, physicists thought it was the second type, because you expect gravity to slow it. Recently CMB indicates asymptotically flat universe =⇒ Third type

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So which is it?

Until a couple of decades ago, physicists thought it was the second type, because you expect gravity to slow it. Recently CMB indicates asymptotically flat universe =⇒ Third type Even more recent, we see that the expansion is accelerating =⇒ NONE OF THE FRIEDMAN solutions !

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How far can this be pushed?

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How far can this be pushed? As far as physics

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How far can this be pushed? As far as physics Planck time ∼ 10−44 sec.

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Technological limitations

Factors influencing the accuracy ●

●

●

Thermal fluctuations can pollute the photonic pure tone ● Shielding of the cavity Motion of the atoms ● Better cooling techniques: ion traps, laser cooling, etc. Impurities in the cavity

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