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On the thermal interpretation of quantum mechanics

+ 4 like - 1 dislike
2467 views

I got an email by Gerard t'Hooft concerning my thermal interpretation of quantum mechanics (see my Thermal Interpretation FAQ, Chapter 10 of my quantum mechanics book  or  the section Foundations independent of measurements from my theoretical physics FAQ). He asked me the following questions:

[Concerning the "thermodynamic interpretation,] all I could find about that is that it  neatly follows Copenhagen in "dodging the question" about what is really going on. All you have to do is work with density matrices if you don't like wave functions.
Fine, but how then do space and time develop curvature? Do we have to dodge the question what that curvature really is?

I want to make models of Planckian scale physics. For that, I need to know what space and time are like. Writing curvature in terms of non-commuting operators produces problems for me that I want cleared out of the way.

Could you explain in concise terms what your thermodynamic interpretation is, and  why you prefer that? Don't you also need an infinite universe of universes? What  happens when a measurement is done?

asked Oct 27, 2014 in Theoretical Physics by Arnold Neumaier (12,355 points) [ revision history ]
edited Dec 19, 2014 by dimension10

3 Answers

+ 5 like - 0 dislike

was recently introduced to Neumaiers interesting/ deep new interpretations of QM by Thomas Klimpel / (se). it appears to me they are quite well developed and on the surface similar to/ meshing with soliton theory which goes back decades but a definitive history seems to remain to be written.

Neumaier refers to a "hydrodynamical" interpretation, but at heart its a fluid dynamical system. there are recent very major advances in this theory by Anderson/ Brady. am surprised nobody has cited them yet wrt the Neumaier interpretation. highly recommend reading them in depth.

the near-obvious interpretation which no one has pointed out much it seems is that space itself is the fluid! this seems to be an interpretation also dating to Majorana

it is worth listing many famous/ influential quantum scientists who regarded or intuited QM theory as likely, or possibly/ conceivably having some kind of realistic "interpretation" other than the Copenhagen interpretation, and further even pointing to some "deeper theory". many of these views are generally downplayed/ deemphasized/ narrowly cited in typical historical accounts if even referred to at all.

  • Einstein
  • De Broglie
  • Schroedinger
  • Bohm
  • Bell
  • T'Hooft

T'Hooft asks specifically what happens during a measurement? the zen question of the 20th century continuing into the 21st. an analogy could be made to something like a sound microphone hooked up to a digitizer. this is a purely classical system but exhibits a wave/ particle duality. the least significant bit of binary samples of sounds by the microphone follows a photon-like law of converting analog, wave-based sound energy into digital counting. this analogy likely can be pushed much further with real mathematical/ experimental analysis (but of course can anticipate much skepticism in this regard, however invite further dialog/ investigation on this also).

following are some references that support the soliton theory of reality and mesh broadly/ compatibly with the Neumaier fluid dynamical ideas/ interpretation. my personal conjecture is that (along the following lines) classical experiments/ analogies/ correspondences further than those cited below can continue to be devised/ explored (along with leveraging the full power all other classic attack techniques/ directions such as mathematics, philosophy etc) that help reveal an ulterior quantum mechanical reality, & encourage/ urge others with similar aims to join in this pioneering research project/ program.

answered Dec 19, 2014 by vzn (80 points) [ revision history ]

@Vzn,

Thank you for the useful and provocative material, which indeed gives excellent food for thought. After reading it I did some further searching and came across this page: http://iopscience.iop.org/1742-6596/504/1

It includes the proceedings of the EmQM13 conference (Emergent Quantum Mechanics 2013, 3–6 October 2013, Vienna), which include interesting material about QM foundations research that might complement the papers you recommended above nicely.

[EDIT: I updated the link to point to the main page with the actual proceedings].

Ciao,
Paolo

thx! fyi some further elaboration/ discussion with TK on the microphone/ sound digitizer & new QM pov/ interpretations contd in se physics chat room: toy models of QM

update, had a long discussion with TK et all in the chat room, have turned up many other relevant, even striking refs meantime, recently wrote up all this/ summarized in a large new synthesis. superclassical/ emergent QM, recent developments, rough outline/ overview/ leads

new highlights: Borns rule/ nonlocality measurements in classical statistical systems, experiments proposed to measure the reality of the quantum wavefunction (Cavalcanti et al), liquid helium anomalies experimentally measured maybe related to soliton theory, related physics.se questions survey, etc

+ 3 like - 0 dislike

The main novelty in the thermodynamic interpretation is to regard that what is usually called an ensemble mean as in fact being an observable value. Thus quantum mechanics is at the same time a classical and a quantum theory; the natural hidden variables are Wigner-type multi-correlation functions.

For example, the classical hydrodynamic equations are obtained by looking only at field values (and projects the remainder away), and the Boltzmann equation is obtained by looking only at local 2-point correlators (and projects the remainder away). Adding local multi-momentum fields accounting for multparticle collisions adds observables that are more and more difficult to observe, and if all multimomentum fields are present, we have the full gamut of hidden (but in fact not so hidden) variables. Their dynamics is described by quantum field theory; in fact by generalized Wigner transforms of the Wightman n-point functions. 

Clearly the field values in hydrodynamics are observable in a classical sense, though not very accurately. On the other hand, in a quantum field theory, where operators are space-time dependent, it is impossible to obtain a true ensemble, as we cannot repeat experiments at the same space-time position. Thus in quantum field theory, ensembles are purely fictitious.

A quantum theory of gravity must account for quantum mechanics of large bodies, such as a star. But the interpretation problems are already apparent for much smaller bodies, such as a glass of water. Each particular glass of water in equilibrium is a single quantum system, but all the observables we customarily ascribe to it according to classical mechanics are true observables of the system, observable in the single instance, without having to postulate ensembles in the statistical sense. 

The thermal interpretation extends this to all quantum phenomena. A measurement is simply the recording of field values of some classical apparatus, described as part of the dissipative quantum system consisting of the apparatus and the system of interest, with the environment already projected out. This ensures that measurement values are definite and  irreversible. Moreover, traditional analyses of observed quantum measurement processes imply that this interpretation of measurements gives a correct account of the observation of microscopic systems (though the traditional measurement terminology there is very different). 

Regarding physics at the Planck scale, I think that spacetime is most likely a classical 4-dimensional manifold. There is a single universe whose states are given by a density matrix, a semidefinite trace class operator on some (most likely nonseparable) Hilbert space. Whatever we observe are classical values of fields (though usually called expectation values or correlation functions) depending on a space-time point and zero or more momenta. In particular, gravity (and hence curvature) is just another field, as this is the way it appears on the observable level. This is both fully local and fully compatible with the thermal interpretation.

Why I prefer this interpretation? Once one has gotten rid of the traditional brain-wash about quantum observables and quantum measurements, one can see that everything corresponds to how we actually observe things - by looking at extended objects and their (in essence hydrodynamic) variables.

How these extended objects respond to the microscopic systems under study cannot be part of the foundations but must be seen as the result of an analysis in terms of quantum statistical mechanics. Thus claiming that we observed a discrete particle with spin when we in fact observed a blob on a screen is something that needs to be explained rather than postulated. (In the thermal interpretation, this is interpreted instead as the observation of a continuous field by means of an apparatus that only allows discrete responses with an intensity-depending rate.) It turns out that the connection becomes stochastic due to the nature of the quantum dynamics rather than due to an intrinsic randomness in quantum mechanics.

answered Oct 27, 2014 by Arnold Neumaier (12,355 points) [ revision history ]
edited Oct 27, 2014 by Arnold Neumaier
Most voted comments show all comments

Do you see this approach to measurement in other interpretations of QM? I've often thought that we construct QM from measurements, not that we construct measurements from QM (which is a significant part of what I take from your account here). An aspect that you don't address here is that we typically engineer material objects and their electronic environment so that they undergo thermodynamic transitions under more delicate changes of their environment than would likely occur without human intervention.

I presume you saw Padmanabhan's arXiv:1410.6285v1 [gr-qc] 23 Oct 2014, "Emergent Gravity Paradigm: Recent Progress", which I take to be enough similar in approach to be of interest. There are numerous others pursuing this kind of approach, of course.

I think one might pay some attention to the different symmetry groups of quantum fluctuations and of thermal fluctuations, respectively 3+1-dimensional Poincaré and 3-dimensional spatial Euclidean+1-dimensional temporal translations, when talking about thermodynamics.

I can’t help but noting that the “Thermodynamic Interpretation” is not an interpretation at all, but a prescription. Yes, I know how to calculate the most likely results of any experiment if someone gives me the Hamiltonian. But what is it that actually happened? That’s the dodged question. In most quantum theories, the “quantum state of the universe (note added)” is a wave function defined in the universe of all universes. That’s too large for me, particularly now that I know that, with some more effort, one can construct models that live in a single universe roughly resembling ours.

@Peter Morgan, I'm afraid I do not agree with you. As for numbers, black hole holography strongly suggests that the square of 10-35 meters is the smallest space for a single bit of info, and the good old speed of light (3.108 m/s) is the speed limit. Also, if you take all known symmetry principles into account (GR, local Lorentz and what have you), our Planck length models seem to be overdetermined rather than underdetermined - I frankly don't regard string theories as rigorous enough to serve as useful models. This is why I think we don't have to wait for experiments to tell us what it might be that's happening at Planck scales.

To measure an ensemble expectation $\langle \Phi(t,x)\rangle$ one has to measure $\Phi(t,x)$ multiple times and taking averages. But this is impossible since each repetition happens either at a different time or at a different location.

You'll find certainty nowhere except in mathematics, and even there only if you accept the assumptions.

There is no error in what you quote from ''How do atoms and molecules look like?''. Indeed, I gave a number of references that highly respected experimentalists interpret the electron density of a molecule as a charge density. This is consistent with my thermal interpretation.

And there is no question that the density of an electron in the ground state is spherical.

This has nothing to do with shooting projectiles on the atom. This has been done by Rutherford, who concluded that atoms are nearly empty. But it only means that electrons don't scatter much.

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Arnold, I got confused with your FAQ because I did not find a certainty there. Besides, there is an erroneous passage:

''quantum mechanics specifies the probability of finding an electron at position x relative to the nucleus. This probability is determined by $|\psi(x)|^2$, where $\psi(x)$ is the wave function of the electron given by Schroedinger's equation. The product of $-e$ and $|\psi(x)|^2$ is usually interpreted as charge density, because the electrons in an atom move so fast that the forces they exert on other charges are essentially equal to the forces caused by a static charge distribution $-e|\psi(x)|^2$.''

It is on the contrary - to "see" such a static picture, the projectile velocity should be much higher than $v_0$. Then the first Born approximation deals with unperturbed $\psi$ squared solely.

If the projectile is slow, it inevitably polarizes the atom and at each distance $R$  to the atom the atomic wave function will be $R$-and $Z_{proj.}$-dependent.

I think you are joking about "spherical charge cloud" around the nucleus.

Those experimentalists who deal with X-rays extrapolate too much!

I do not say the "negative charge cloud" in the ground state is not spherical. I meant the presence of a "positive charge cloud" too, which is determined with the same wave function.

It was funny - when I was reporting this "positive charge cloud" picture at a seminar in 1985, people could not understand why the nucleus should rotate around the atomic center of mass if the electron cloud (configuration) is absolutely spherically symmetric.

And, of course, those "clouds" are only meaningful when they are such in calculations. In particular, in the first Born approximation for scattering problems.

+ 0 like - 0 dislike

I found a very simple way to present the basics: Instead of interpreting expectations as a concept meaningful only for frequent repetition under similar conditions, I interpret it for a single system in the following way, consistent with the practice of thermal statistical mechanics, with the Ehrenfest theorem in quantum mechanics, and with the obvious need to ascribe to particles created in the lab an approximate position even though it is not in a position eigenstate (which doesn't exist).

The basic thermal interpretation rule says:

Upon measuring a Hermitian operator $A$, the measured result will be approximately $\bar A=\langle A\rangle$ with an uncertainty at least of the order of $\sigma_A=\sqrt{\langle(A−\bar A)^2\rangle}$. If the measurement can be sufficiently often repeated (on an object with the same or sufficiently similar state) then $\sigma_A$ will be a lower bound on the standard deviation of the measurement results.

Compared to the Born rule (which follows in special cases), this completely changes the ontology: The interpretation applies now to a single system, has a good classical limit for macroscopic observables, and obviates the quantum-classical Heisenberg cut. Thus the main problems in the interpretation of quantum mechanics are neatly resolved without the need to introduce a more fundamental classical description.

Recent additional material on the thermal interpretation of quantum mechanics is referenced in my Thermal interpretation FAQ

answered May 26, 2016 by Arnold Neumaier (12,355 points) [ revision history ]

Yes, you did it!

Concerning 't Hooft's question: "I know how to calculate the most likely results of any experiment if someone gives me the Hamiltonian. But what is it that actually happened?", I can safely say that nobody understands even Classical Mechanics. (I mean, the measurement process and its description with some equations.) As soon as we understand Classical Mechanics, we will be better prepared to understanding QM, in my opinion.

Thanks @ArnoldNeumaier for recommending (in the Thermal Interpretation FAQ) L. Sklar's book "Physics and Chance" book, which seems excellent at a first glance. Sklar's most recent book also seems good. I am trying to understand the thermal interpretation, questions forthcoming.

Note - once again I posted this comment as an answer. Yes, one should be more careful, we are all attention-challenged these days and but I guess the user interface could be improved to make it clear when one is posting an answer and when a comment. How about asking the user to confirm? "Please confirm that you want to post this as an answer/comment. If you wanted to post a comment/answer instead, please follow this link."

@GiulioPrisco: You may post your (useful) suggestion about the answer box on meta, and it will be considered by our system developer @polarkernel.

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