QUANTUM FLUCTUATIONS & ARROW OF TIME

What is time? Quantum Physics gives an answer, classical physics does not. Quantum Physics suggests that time is the set of all irreversible processes. This is a world first, so it requires some explanations. I have been thinking, hard, of these things all my life. Sean Carroll, bless his soul, called my attention to the new development that mainstream physicists are starting to pay attention to my little kingdom(so I thank him).

***

SCIENCE IS WHAT WE DO:

Sean Carroll in “Quantum Fluctuations”:

“Let’s conjure some science up in here. Science is good for the soul.”

Patrice Ayme’: Why is science good for the soul? Because the human soul is centered on finding truth. Science is truth, thus science is human. Nothing is more human than science. Science is what humans do. Another thing humans do is art, and it tries to both duplicate, distort, and invent new nature, or interpretations, interpolations, and suggestions, of and from, nature:

Claim: Quantum Interference Is An Irreversible Process, Time's Arrows All Over. Quantum Interference Goes From Several Waves, To One Geometry. Soap Bubbles Brim With Quantum Interference..

Claim: Quantum Interference Is An Irreversible Process, Time’s Arrows All Over. Quantum Interference Goes From Several Waves, To One Geometry. Soap Bubbles Brim With Quantum Interference..

SC: …what are “quantum fluctuations,” anyway? Talk about quantum fluctuations can be vague. There are really 3 different types of fluctuations: Boltzmann, Vacuum, & Measurement. Boltzmann Fluctuations are basically classical: random motions of things lead to unlikely events, even in equilibrium.

Patrice Ayme’: As we will see, or we have already seen in my own “Quantum Wave”, Quantum Fluctuations are just the Quantum Waves. Richard Feynman, at the end of his chapter on entropy in the Feynman Lectures on Physics, ponders how to get an arrow of time in a universe governed by time-symmetric underlying laws. Feynman:

“So far as we know, all the fundamental laws of physics, such as Newton’s equations, are reversible. Then where does irreversibility come from? It comes from order going to disorder, but we do not understand this until we know the origin of the order. Why is it that the situations we find ourselves in every day are always out of equilibrium?”

Patrice Ayme’: Is that really true? Are equations time-symmetric? Not really. First, equations don’t stand alone. Differential equations depend upon initial conditions. Obviously, even if the equations are time-symmetric, the initial conditions are not: the final state cannot be exchanged with the initial state.

Quantum Physics make this observation even more important. The generic Quantum set-up depends upon a geometric space S in which the equation(s) of motion will evolve. Take for example the 2-slit: the space one considers generally, S, is the space AFTER the 2-slit. The one before the 2-slit, C, (for coherence) is generally ignored. S is ordered by Quantum interference.

The full situation is made of: (C, S & Quantum interference). it’s not symmetric. The Quantum depends upon the space (it could be a so-called “phase space”) in which it deploys. That makes it time-assymmetric. An example: the Casimir Effect.

***

QUANTUM PHYSICS IS ABOUT WAVES:

Sean Carroll: “Nothing actually “fluctuates” in vacuum fluctuations! The system can be perfectly static. Just that quantum states are more spread out.”

Indeed. Quantum states are, intrinsically, more spread out. They are NON-LOCAL. Why?

One has to go back to the basics. What is Quantum Physics about? Some, mostly the “Copenhagen Interpretation” followers, claim Quantum Physics is a subset of functional analysis. (The famous mathematician Von Neumann, one of the creators of Functional Analysis, was the founder of this system of thought; this scion of plutocrats, famously, yet satanically, claimed that De Broglie and Bohmian mechanics were impossible… Von Neumann had made a logical mistake; maybe that had to do with being involved with the satanic part of the American establishment, as, by then, that Hungarian had migrated to the USA and wanted to be called “Johnny”!).

The Quantum-as-functional analysis school became dominant. It had great successes in the past. It allows to view Quantum Physics as “Non Commutative Geometry”. However, contrarily to repute, it’s not the most fundamental view. (I have my own approach, which eschews Functional Analysis.)

But let’s backtrack. Where does Quantum-as-functional-analysis come from? A Quantum system is made of a (“configuration”) space S and an equation E (which is a Partial Differential Equation). Out of S and E is created a Hilbert Space with a basis, the “eigenstates”.

In practice, the eigenstates are fundamental waves. They can be clearly seen, with the mind’s eye, in the case of the Casimir Effect with two metallic plates: there is a maximal size for the electromagnetic wavelengths between the plates (as they have to zero out where they touch the metal).

The notion of wave is more general than the notion of eigenstate (Dirac pushed, successfully, the notion of wave so far that it created space, Spinor Space, and Quantum Field Theory has done more of the same, extending the general mood of De Broglie-Dirac to ever fancier Lagrangians, energy expression guiding the waves according to De Broglie scheme).

Historically, De Broglie suggested in 1923 (several publications to the French Academy of Science) that to each particle was associated a (relativistic) wave. De Broglie’s reasons were looked at by Einstein, who was impressed (few, aside from Einstein could understand what De Broglie said; actually De Broglie French jury thesis, which had two Nobel prizes, was so baffled by De Broglie’s thesis, that they sent it to Einstein, to ask him what he thought. Einstein replied with the greatest compliment he ever made to anyone: “De Broglie has started to lift the great veil,” etc…).

The De Broglie’s wave appears on page 111 of De Broglie’s 1924 thesis, which has 118 pages (and contains, among other things, the Schrödinger wave equation, and, of course, the uncertainty principle, something obvious: De Broglie said all particles were guided by waves whose wavelengths depended upon their (relativistic) energy. An uncertainty automatically appears when one tries to localize a particle (that is, a wave) with another particle (that is, another wave!)

***

CLASSICAL PHYSICS HAS NO ARROW OF TIME:

Consider an empty space S. If the space S is made available to (classical) Boltzmann particles, S is progressively invaded by (classical) particles occupying ever more states.

Classical physicist (Boltzmann, etc.) postulated the Second Law of Thermodynamics: something called entropy augmented during any process. Problem, rather drastic: all classical laws of physics are reversible! So, how can reversible physics generate a time-irreversible law? Classical physicist have found no answer. But I did, knight in shining armor, mounted on my powerful Quantum Monster:

***

QUANTUM PROCESSES CREATE IRREVERSIBLE GEOMETRIES:

When the same space S is made available as part of a Quantum System, the situation is strikingly different. As Sean Carroll points out, the situation is immediately static, it provides an order (as Bohm insisted it did). The observation is not new: the De Broglie waves provided an immediate explanation of the stability of electronic waves around atoms (thus supporting Bohr’s “First, or Semi-Classical, Quantum Theory”.

What’s a difference of a Quantum System with a classical system? The classical system evolves, from a given order, to one, more disordered. The Quantum system does not evolve through increasing disorder. Instead, the space S, once accessed, becomes not so  much an initial condition, but a global order.

The afore-mentioned Hilbert Space with its eigenstates is that implicit, or implicate (Bohm) order. So the Quantum System is static in an important sense (from standing Quantum Waves, it sorts of vibrates through time).

Thus Quantum Systems have an intrinsic time-assymmetry (at least when dealing with cavities). When there are no cavities, entanglement causes assymmetry: once an interaction has happened, until observation, there is entanglement. Before interaction, there was no entanglement. Two classical billiards balls are not entangled either before or after they interact, so the interaction by collision is fully time reversible.

Entanglement is also something waves exhibit, once they have interacted and not before, which classical particles are deprived of.

Once more we see the power of the Quantum mindset for explaining the world in a much more correct, much simpler, and thus much more powerful way. The Quantum even decides what time is.

So far as we know, all the classical fundamental laws of physics, such as Newton’s equations, are reversible. Then were does irreversibility come from? It does NOT come, as was previously suggested, from order going to disorder.

Quite the opposite: irreversibility comes from disorder (several waves)going to order (one wave, ordered by its surrounding geometry). And we do understand the origin of the order: it’s the implicit order of Quantum Waves deployed.

You want to know the world? Let me introduce you to the Quantum, a concept of wealth, taste and intelligence.

Last and not least: if I am right, the Quantum brings the spontaneous apparition of order, the exact opposite picture which has constituted the manger in which the great cows of physics have found their sustenance. Hence the fact that life and many other complicated naturally occurring physical systems are observed to create order in the universe are not so baffling anymore. Yes, they violate the Second Law of Thermodynamics. However, fundamentally, that violated the spirit, the principle of the universe, the Quantum itself.

Patrice Ayme’

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15 Responses to “QUANTUM FLUCTUATIONS & ARROW OF TIME”

  1. 1truegarcol Says:

    conflation. confusion. conundrum.
    Why is 2nd law of thermodynamics LESS relevant than quantum theory? Tendency to increase entropy is as meaningful as the quantum vibration. And the quantum dance is as revealing as Salome’s Dance of the Seven Veils – ie, it sheds no light or understanding, but clouds the actual issue
    We live in an exciting time where the merest mathematical hypothesis can transmogrify into a full-sized description of “true reality”.
    Naturally occurring physical systems do NOT violate the second law (like evolution and crystal growth) because these systems are NOT closed.
    Non-locality MAY be irreversible; but so are dropped eggs. I’m not sure that either one is sufficient to qualify as an explanation of “time’s arrow”, though both may in fact, be the result of it.
    Sean Carroll may in fact be brilliant, but his popularizations tend to smear and misrepresent the underlying mathematics (ie, ‘truth’) – this is a real problem of translation and analogy from one language to another.
    [“Are equations time-symmetric? Not really. First, equations don’t stand alone.”] No, they are used to describe physical relationships. NONE of the classical mechanical relationships (laws of motion, gravity, electricity, magnetism, etc) have any parameter which identifies a direction of time. There is an initial condition and final condition, but the descriptive formula does not mandate a temporal direction.
    All but the 2nd law.

    • Patrice Ayme Says:

      Well look, don’t go so fast, I don’t know if you notice, but an extract of the famous Feynman lectures on physics was quoted. It’s not all Sean Carroll. I was very explicit about the problem of Second Law: the equations and Initial Conditions are all REVERSIBLE. In the end you preach that too!!!!!!!!!!!!!! Second Law does not forbid a local decrease of entropy. I point out that QUANTUM INCREASES ORDER, BECAUSE OUT OF MANY, ONE!

      My point of view explains why the egg cannot be unscrambled, classical physics does not.
      I was baffled by this problem for decades before I finally got it.

      I do not agree with Sean as far as the MWIQM. But make no mistake: you are interacting with people who have made cutting edge research on PDEs, so we know what Initial Conditions are!
      ;_)

  2. Magnema Says:

    Magnema says:
    January 16, 2016 at 11:06 pm

    @Patrice: Actually, from a differential equations standpoint, the final equation CAN be exchanged with the initial condition – there is no distinction (at least in ODEs; PDEs get a bit more technical, but in terms of fundamentally-physical PDEs, the same ideas broadly apply). The mathematical theorems are not direction-dependent. Differential equations don’t really depend on initial conditions; they depend on SOME additional constraint, but this could equally validly be ICs, FCs, or BCs (for ODEs; PDEs, again, are more complicated).

    As for the quantum, if you watch/read his time course, he talks about it; essentially, if you both “confine” the initial conditions and the final conditions (by setting up the IC and only counting certain measured FCs), then you get time-symmetric “middle conditions.” In other words: if you ask time-symmetric questions, you get time-symmetric answers – and this principle holds in all of fundamental physics (up to a few asterisks of CPT, which are of no significance to the core question).

    What you say is “ignored” about Quantum Mechanics (in the “before states” vs. “after states”) is merely ignored in most popularizations. In practice, the initial state and the final state are considered on at least near-equal ground (“near” for a few practical reasons, which are contingent on the apparent arrow of time and in no way on the fundamental physics being experimented on).

    • Patrice Ayme Says:

      Quantum Physics creates entire (Hilbert) spaces during fundamental processes, and this is what cannot be reversed. (I wrote the second part in the meantime to explain that better, hopefully answering you better.)

  3. Magnema Says:

    Magnema says:
    January 18, 2016 at 9:43 am

    @Patrice: Entanglement is (in principle) just as reversible as any other law of physics. Your assumption that things are not entangled before interaction is simply not necessarily true, generically, unless you specify that the two particles have never, through any chain of effects looking backwards in time, interacted (and even then, it is questionable). The key here is that being “entangled” is the generic case – being disentangled is actually a very special condition, which we usually specify on our problems more out of (a) a desire to simplify them or (b) simple epistemological uncertainty, in the usual statistical-mechanical sense.

    By analogy: if you have some expression awy+bwz+cxy+dxz (for a,b,c,d numbers and w,x,y,z variables), then being “disentangled” is equivalent to this expression being able to be written (ew+fx)(gy+hz) for e,f,g,h some numbers. Since the latter has nontrivial restrictions, the solution space is a lower-dimensional submanifold of the original space (in particular, “disentangled states” between two particles form a three-dimensional submanifold out of a four-dimensional state). This is why disentangled systems become entangled – because being disentangled is a highly nongeneric state which, unless explicitly preserved by the Hamiltonian, will immediately dissociate.

    In this case, generically speaking, quantum particles ARE entangled from the beginning, unless you put some additional restrictions on initial conditions, that things aren’t entangled – and even if you do so as a cosmological criterion (which I don’t think is unreasonable), for most practical experiments, everything has been interacting for long enough that it is all entangled anyway.

    As for your wave discussion: The wave equation (and the S.E., more to the point of quantum mechanics) is completely time-reversible, so you can’t get irreversibility out of that, even if you restrict to a cavity – including the Casimir effect. This is ignoring the fact that waves only get you so far in QM – in particular, waves cannot account for finite-dimensional system, and particularly not angular momentum, unlike the linear algebra approach. (I would also disagree that waves are more fundamental than eigenstates, seeing as “waves” in the sense of sine waves are simply eigenstates of a particular linear operator PDE, and even general manifold derivatives involve linear algebra… but that’s beside the point, at the end of the day, of the arguments of irreversibility.)

    • Patrice Ayme Says:

      Answer to Magnema:
      Magnema says:”Entanglement is (in principle) just as reversible as any other law of physics. ”

      Patrice Ayme: Entanglement gets un-entangled (it’s called decoherence) NON-LOCALLY. Occasionally Free Will will even be involved (say choosing the direction of polarization measurement, or a magnetic field in a Stern-Gerlach device, etc.). Without evoking Free Will, decoherence will involve a large macroscopic object, thus a large space, like a gravitational field, but with a life of its own, so to speak, thus irreversible. As Bohr would say, the Quantum System cannot be isolated when “measured” (or made to decohere).

      Non-Locality does not look reversible to me: it involves non topologically trivial “inner” geometry (see below).

      Magnema: “Your assumption that things are not entangled before interaction is simply not necessarily true, generically, unless you specify that the two particles have never, through any chain of effects looking backwards in time, interacted (and even then, it is questionable).”

      PA: The entanglement is caused by an interaction. In general. Always.

      Could the particles have been entangled before, without suspecting it? This is the last loophole in the proof of the Bell Inequality. This is the subject of present research, but many in the know do not doubt what will be found. The question has been asked in the case of Einstein-Podolski-Rosen (type) experiments (“EPR”). These involve making a measurement on an element of a pair of “particles” A and B which are entangled, yet “separated” by what I would call a “CLASSICAL DISTANCE”.

      Starting with Alain Aspect (who got the Wolf Prize in Physics for it), it has been shown that spin measurement can be made in flight, where the direction of the polarization is changed haphazardly in flight, and the measurement on A “immediately” changes B (“immediately” meaning out of the light cone of A).

      The suggestion has been made that A and B could be actually within the same much larger, much older light cone, and thus causally related in the classical relativistic sense. An esteemed team of American experimenters will thus run a version of the Aspect experiment, where the polarization direction are obtained by signals from quasars so distant from each other that they cannot plausibly be causally related.

      It seems extremely unlikely that the experiment will reveal that, after all all correlations observed and predicted (by the Quantum axiomatics) were the fruit on long set hidden causality.

      http://www.nbcnews.com/science/space/quasar-experiment-may-shed-light-quantum-physics-free-will-n45571

      As far as I know, (Quantum) entanglement arises only from interaction. Thus picking two particles haphazardly, they should NOT have, generically, a common entanglement (albeit we don’t know what they are entangled with, some could end entangled with each other).

      Because of its non-local character, Quantum entanglement is impossible to reverse. Why? It has a non-trivial geometry and topology. It’s not the (simple) one of relativistic spacetime, it is the geometry of what happened before: not the sum of all histories, just the (geometrical and topological) nature of a particular history. Once again, not the geometry of spacetime, but a subset with a non trivial topology of the geometry of much higher dimensional manifold in which spacetime is embedded (see Nash embedding theorem).

      Now for waves. I remember Dirac, initially an engineer, saying he was looking for the simplest relativistic wave (simpler that a solution of the Klein-Gordon equation, a second order PDE). it struck him that that the simplest wave had to be a first order PDE (waves on a string like sines answer to second order PDEs; other waves, such as the KdV solitons, answer to nonlinear SE PDEs: waves don’t have to be just trigonometric functions!).

      Angular momentum in its simplest form arises from spinor geometry, not linear algebra (it was discovered by Elie Cartan before World War One, in a purely geometrical setting). It’s a square root of the Riemannian metric.

      http://mathoverflow.net/questions/66681/classical-geometric-interpretation-of-spinors

      Dirac rediscovered it by postulating the simplest relativistic wave, a solution to the simplest, thus first order, Partial Differential Equation giving what can be called a wave. It’s equivalent to taking the square root of the relativistic WAVE operator (the usual Laplacian).

      https://en.wikipedia.org/wiki/Dirac_equation

      However, Michael Atiyah said:

      “No one fully understands spinors. Their algebra is formally understood but their general significance is mysterious. In some sense they describe the “square root” of geometry and, just as understanding the square root of −1 took centuries, the same might be true of spinors.”

      May I suggest the same is true of the geometry of entanglement?… With the caveat that it is irreversible?

  4. Phayes Says:

    phayes says:
    January 18, 2016 at 10:57 am

    @Patrice Ayme

    “What is Quantum Physics about? Some, mostly the “Copenhagen Interpretation” followers, claim Quantum Physics is a subset of functional analysis”

    Not so. The claim is that quantum physics is the application of (noncommutative) probability theory¹ to physics. As (Copenhagenist) Ray Streater says, “It took some time before it was understood that quantum theory is a generalisation of probability, rather than a modification of the laws of mechanics.”²

    1) Does physics need probability theory? Yes.³
    2) Does it have noncommuting observables? Yes.³
    3) P̶r̶o̶f̶i̶t̶!!! Quantum theory.

    “The notion of wave is more general than the notion of eigenstate ”

    Depending on context / definition of eigenstate it might be. It certainly isn’t more general than the notion of state and wave function states are not enough for physics (cf. Chris Isham’s Lectures on QT: “there are many examples of quantum-mechanical systems whose states cannot be represented as wave functions”).

    “The classical system evolves, from a given order, to one, more disordered. The Quantum system does not evolve through increasing disorder. ”

    Neither the quantum entropy ( https://en.wikipedia.org/wiki/Von_Neumann_entropy ) nor its classical counterpart (Gibbs entropy) increase: http://www.ucl.ac.uk/~ucesjph/reality/entropy/text.html

    ¹ https://terrytao.wordpress.com/2010/02/10/245a-notes-5-free-probability/
    ² http://arxiv.org/abs/math-ph/0002049
    ³ http://www.nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.html

    • Patrice Ayme Says:

      phayes says:
      @Patrice Ayme
      “What is Quantum Physics about? Some, mostly the “Copenhagen Interpretation” followers, claim Quantum Physics is a subset of functional analysis”

      Not so. The claim is that quantum physics is the application of (noncommutative) probability theory¹ to physics. As (Copenhagenist) Ray Streater says, “It took some time before it was understood that quantum theory is a generalisation of probability, rather than a modification of the laws of mechanics.”²

      Well, this is your opinion and that of Mr. Streater. Actually interpretations of the Copenhagen Interpretation vary considerably. You can consider:

      https://en.wikipedia.org/wiki/Copenhagen_interpretation

      As engineers are trying to make functional Quantum computers and Quantum simulators, they have to figure out exactly what causes “decoherence” or “wave function collapse”. “Interpreting” Quantum Physics has become an experimental subject.

      Quantum Physics has even been interpreted as a change of logic (with no less than Birkhoff and Von Neumann as the original authors):

      https://en.wikipedia.org/wiki/Quantum_logic

      As you can see therein, the subject is not closed. It involves now supersymmetry, supergeometry and thus non-commutative mathematics.

      Waves: first, there is no general definition of “wave”. That’s, precisely the force of the concept (whereas there is a strict definition of eigenstate, that’s a weakness). If a Quantum state has not (yet!) be demonstrated to be caused by waves, that does not mean it’s not. It just mean we don’t know. To be sure why something does not happen, one has to be sure why it does not happen. In this particular case, one would have to know more than what the Copenhagen Interpretation says. “Copenhagist” who claim to know more than Copenhagen, are not really Copenhagists. That’s rather ironical.

  5. Paul Handover Says:

    I would love to have even the vaguest understanding of any of this. Seriously! Can someone point me in the direction of anything that explains what you are discussing in layman’s terms?

    • Gmax Says:

      Those guys are far out in the philosophy of Quantum Mechanics, the Time Arrow, and all this. This is the hardest part of science where even Einstein could not break through. If Patrice is a bit right, it’s a huge paradigm change. We are watching history in the making

    • Patrice Ayme Says:

      Hi Paul! You have to understand that the problem at hand is the hardest: what are the foundations of physics? As you will see in further comments, my positions are subtle, requiring the highest level in math and physics. To boot, I claim it goes towards explaining time, no less…

  6. Gmax Says:

    So you are saying that time is irreversible, because time creates space which is irreversible? WOW! Did I get that right?

    • Paul Handover Says:

      I’m hanging on for the answer as well! Plus, and excuse the simple attempt at asking a question, if ‘classical’ physics says that processes are reversible then why cannot the omelet be returned to eggs? Or is it because an omelet, as with aging, is a simile for the passing of time? (Now I have a headache but at least that’s reversible!)

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