Posts Tagged ‘Entropy’

QUANTUM FLUCTUATIONS & ARROW OF TIME

January 18, 2016

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).

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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.

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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!)

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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:

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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’

Entropy & Quantum: The Relativity of States

May 17, 2015

Entropy (usual symbol S) measures the number of specific ways in which a thermodynamic system may be arranged. It measures the number of states. It is understood as a measure of disorder.

Another part of physics which worries about states is Quantum Physics. A Quantum Process is associated to a Quantum Space which turns out to be a Hilbert Space (a complete complex vector space with a metric; basically the nices, simplest high dimensional complex vector space one can conceive of). The measurement is identified with an operator (say A) in said space, which has eigenspaces and eigenvalues (Av = av; where v is a vector called an eigenvector, and a, a complex number, the eigenvalue).

Forget Cats. In Which States Is The World Really In?

Forget Cats. In Which States Is The World Really In?

[Haroche, from the ENS lab in Paris which invented optical pumping, thus the laser, 62 years ago, and Wineland, from Boulder, got the Nobel in 2012.]

Both Entropy and the Quantum suffer of the same problem, namely: what is a state? Can state be absolutely defined?

As it is, things have been all too relative.

This is exemplified in Quantum Physics with the Schrodinger Cat Paradox. A cat is put in a box, with an infernal Quantum mechanism that is supposed to gas it (shortly after, the Nazis did for real… Interesting Freudian slip that German and Austrian physicists were involved with the idea of mixtures of dead and live cats).

The question is whether mixing live and dead cat waves is a full description of the system. It obviously stretches credulity. This was the argument of Schrodinger (initiated in exchanges with Einstein).

From the point of view of the cat, inside the box, the waves, states, and chosen Quantum spaces would be quite different

My wished-for-solution?

Apply an order on Hilbert spaces, according to fullness of description, and consider only ultrafilters (in the topological sense) as genuinely representative of the best approximation of reality. Hey, nobody said we should not think big… Anyway, that’s my answer to the Multiverse and its multiversists.

Now back to entropy.

As it exists, thermodynamics is about particles. Thus, it infeodated to the problem of states in Quantum Physics. Hence solving the Quantum Cat problem solves the problem of Entropy.

Or does it?

The deepest problem subjacent to Quantum Physics is whether some sort of thermodynamics could be, and thus should be, applied to the isolated particle (I believe it could, and should).

The Haroche and Wineland methods, above, are a step in the right direction, namely measuring what the real states, the ultimate element of reality of the world, are.

So is Entropy useless? Is it physics? Yes, it is physics, just like computer science is science. Both are emergent aspects of the world. Not as fundamental as a future sub-Quantum Physics, but all the fundamentalism, and no more, that we need, much of the time.

Patrice Ayme’

Time for Cause & Effect?

December 31, 2014

Cause, effect, and time are all mysteries at this point. As far as Physics is concerned.

When I was a young chicken, learning physics, pecking around the way chicken do, I came upon “the Arrow of Time”. At the time, the question about the nature of time was all about “Entropy” and the “Second Law of Thermodynamics”. How quaint it seems now that I got much wiser!

Entropy is about “states”. The “Second Law” says that processes augment the number of states, as time goes by.

The most basic question is then: ”What is a state?”

People in thermodynamics thought they had an answer. And, in a way, they do, like a car mechanics is full of answers about the state of your car.

Mechanics Getting Weirder: Are There Wormholes?

Mechanics Getting Weirder: Are There Wormholes?

[Yes, these distorted things are distant galaxies, viewed through the wormhole. The picture, from the excellent movie “Interstellar” depicts how a wormhole in spacetime would appear at close range; the little flower is the rotating spaceship. Interstellar represents an Earth where society has pursued its way down the abyss, thanks to the anti-science, anti-rationality movement in evidence nowadays. NASA went underground… Something not far removed from its present state, where tantalizing clues for life on Mars are left unexamined, because of the anti-nuclear movement… Long story, another time.]

However, nature is a Quantum car. And mechanics have nothing to say about it. Quantum Physics has its own notion of state. Moreover, in the meantime, the very notion of time and causality came under attack. From an unexpected corner.

It was simple enough when Lorentz and Poincaré introduced the notion of “local time”. Time was relative (Poincaré Relativity Principle, 1904): it depended upon one’s state of motion. In a local frame moving fast, time slows down (relative to the friend who did not get on that speedy rocket).

Einstein then observed that if a local time was accelerated, it would also slow down. Einstein somehow hoped to extract from this “General Theory of Relativity” a cause for inertia, but he failed (and could only fail, as GTR is local, not global). He ended up with just a Theory of Gravitation (Fock), a better and much improved version of the one of 1700, true… But still GTR is articulated basically the same equation arising from Ismael Bullialdus considerations in 1645 (and then Huygens, Borelli, Hooke, etc.)

Enter Quantum Physics. There time is absolute (oops). Locally absolute over an extent. Why? Because each Quantum processes are logically and mathematically analyzed in a particular space, relative to said process, and GLOBALLY therein (here is that global concept Einstein was desperately searching for, as he craved for inertia as a global phenomenon, following Newton and Mach).

That particular space relative to that particular process is not just two dimensional (as in the famed double slit experiment), it can be pretty much anything that can be depicted as a Hilbert space (consider Dirac Spinor space).

In the past, before 1904, one could consider that if something A preceded something else B, in time, A could have “caused” B. However local time already messes up with that situation (consider closed time loops in GTR; reference: just released movie Interstellar, a respected relativist, Thorne, made discoveries while consulting for the movie).

Quantum Physics makes causation a worse consideration than ever. As it stands, the Quantum is Non-Local. No need to get into Spin and Bell, to figure that one out: the analysis in Quantum Hilbert space uses time only as a one parameter transformation group, it’s intrinsically Non-Local (hence the famed “Collapse of the Wave Packet).

If a physicist changes a spin axis on Earth, does it do something to the second member of the entangled photon pair he sent to Beta Centauri? Instantaneously? Really? No one knows for sure (and I don’t believe the “instantaneous” part), but the present Quantum formalism (sort of) says it does.

Paradoxically, all of this debate about cause and effect has become very practical, in the most fundamental domain possible, Quantum Physics. As real physics moves away from the multiverse derangement syndrome, it ponders using, as nature and biology, and even evolution do, the Quantum.

Indeed, even biology uses the Quantum to compute, and find best solutions (as was demonstrated in the case of the chlorophyll molecule; much more examples are on the way, including that will demonstrate how a type of Lamarckian evolution works).

However “what causes what” has stood in the way of making Quantum Computers. Real physicists and engineers have been trying to get a handle on causation. One wants to isolate the process of computation, yet get it impacted by complicated inputs, and only these.

Time to spend some money on all this (that means re-direct the economy that way).

Patrice Ayme’