The thermal interpretation of quantum physics

[Greg Bernhardt]

This happens whenever you quote or reply to part of an answer, and this part contains formulas; these then appear as a mess, as in post #308 by @vanhees71. It is a bug since long... (@Greg Bernhardt - can something be done about it?)

It's not a bug but a limitation. Equations are not simple text, but equation code that is formatted by CSS. When you highlight to quote or reply it's a simple javascript browser function that just copies the highlight text. If there is an equation there is no function for the browser to also copy the underlying equation code. When these is an equation, always use the regular reply link.

 

[stevendaryl]

But it should be stressed that the plate just fixes the observable "position" of the measured electron. If you consider the SGE, as usual, as a measurement of the corresponding spin component, the point is the (nearly) 100% entanglement between position (pointer variable) and spin component (measured observable). There's nothing mysterious in this, but it can be predicted by using quantum dynamics only. There's no mystery about the SG experiment and the involved measurement devices (a magnet with the appropriately tuned magnetic fields and a screen to collect the particles).

The mystery, as I have said, is that quantum mechanics predicts that if the device interacting with a spin-up electron leads to a state in which there is a black spot on the left photographic plate, and if the device interacting with a spin-down electron leads to a state in which there is a spot on the right plate, then the device interacting with an electron that is in a superposition of spin-up and spin-down would lead to a superposition of the two macroscopic states. The additional claim that only one of the two outcomes attains means that your "minimal interpretation" is either inconsistent (which I think it actually is) or that there is a mysterious macro/micro distinction such that macroscopic variables are treated differently than microscopic variables.

 

[vanhees71]

There is no mystery. It's all completely explained with quantum dynamics. After the particle has run through the magnet providing an appropriate magnetic field the position of the particle and the measured spin component are (nearly, i.e., with high precision but never really exactly) 100% entangled. There is no mystery to have two partial beams after the magnet nor that each partial beam has (almost) determined values of the spin component in the expected direction. It's one of the very few examples which can be exactly calculated even analytically.

 

[DarMM]

There is no mystery. It's all completely explained with quantum dynamics. After the particle has run through the magnet providing an appropriate magnetic field the position of the particle and the measured spin component are (nearly, i.e., with high precision but never really exactly) 100% entangled. There is no mystery to have two partial beams after the magnet nor that each partial beam has (almost) determined values of the spin component in the expected direction. It's one of the very few examples which can be exactly calculated even analytically.

By what mechanism do the spins directions agree no matter direction is choosen? How do two randomly generated spacelike separated outcomes always agree?

 

[vanhees71]

Yes; see post #135 for how this is viewed by the thermal interpretation.

But there is some mystery about how Nature manages to get the right correlations in experimental tests of long distance entanglement (the case under discussion here). Quantum mechanics predicts the right correlations, but does not explain so far how it is possible that these are actually obtained!

What is the mystery? There is none. QT predicts these calculations and they are verified at an astonishing level of significance. I do not understand, where the mystery should be. It's just the prepatation of entangled states which leads to these correlations.

This is also a very nice example for what I'm still missing in your interpretation. For the statistical interpretation it's easy to understand, how entangled states can be prepared. Let's take the most simple example. Just produce a neutral pion and wait until it decays. It's most easily described in its rest frame, i.e., you have a state of zero momentum (with some small uncertainty of course, because momentum eigenstates, i.e., plane waves are no proper but generalized states only) and 0 angular momentum. It decays with almost 100% probability to two photons, obeying the conservation laws, i.e., the photons have (within the uncertainty of momentum) back-to back momenta and total angular momentum 0. The latter property makes the polarizations in any direction 100% correlated but also maximally uncertain, i.e., the single-photon polarization state is that of completely unpolarized photons, but still there are the 100% correlations, i.e., measuring the polarization of each of the photon in the same direction you always get opposite results, i.e., if the one photon is horizontally polarized the other one is necessarily vertically polarized and vice versa. It's completely undetermined which measurement outcome you'll have, before having done the measurement, and you can do the measurement at as far distant places you want (provided there's nothing charged around with which the photons may interact and changing the state before being measured) but the 100% correlation is imprinted due to the preparation of these photons.

As I said, there's no mystery within the statistical minimal interpretation. Now two questions:

(a) how do you interpret this situation, i.e., the preparation of the biphoton state and subsequent measurement of the single-photon polarizations within your statistical interpretation, if it's not allowed to interpret the formal mathematical manipulations statistically?

(b) What's the mystery due to the thermal interpretation, which is obviously absent in the minimal statistical interpretation?

 

[DarMM]

What is the mystery? There is none. QT predicts these calculations and they are verified at an astonishing level of significance. I do not understand, where the mystery should be. It's just the prepatation of entangled states which leads to these correlations.

Yes, but it doesn't explain the mechanism by which these correlations are satisfied. What you're saying is akin to saying that situation A:
"Stick of dynamite, a lit match, a wall"
is correlated with the following situation B at later times:
"Collapsed wall"
And that there is no mystery here, simply the correlation.

People want the mechanism, i.e. "heated nitroglycerine explodes and the explosion collapses the wall".

 

[A. Neumaier]

What is the mystery? There is none. QT predicts these calculations and they are verified at an astonishing level of significance. I do not understand, where the mystery should be. [...] the 100% correlation is imprinted due to the preparation of these photons.

As I said, there's no mystery within the statistical minimal interpretation.

This has nothing at all to do with the statistical interpretation. Blind trust in the formalism of quantum mechanics removes the mystery no matter which interpretation.

You simply lost the sense of mystery because you trust the quantum mechanical calculations as confirmed by experiments and do not look for any understanding beyond that. Very well; then there is nothing more to discuss.

 

[A. Neumaier]

how do you interpret this situation, i.e., the preparation of the biphoton state and subsequent measurement of the single-photon polarizations

Since you never replied to my interpretation of the simpler Stern-Gerlach experiment in post #135 (given upon your request) I don't see any point in interpreting for you this more complex situation. You just ignore my interpretations and only rant against my dismissal of unobserved statistics.

 

[vanhees71]

Yes, but it doesn't explain the mechanism by which these correlations are satisfied. What you're saying is akin to saying that situation A:
"Stick of dynamite, a lit match, a wall"
is correlated with the following situation B at later times:
"Collapsed wall"
And that there is no mystery here, simply the correlation.

People want the mechanism, i.e. "heated nitroglycerine explodes and the explosion collapses the wall".

What's "the mechanism"? It's just a reproducible experience that "heated nitroglycerine explodes and the explosion collapses the wall". You can of course dig for "deeper explanations", i.e., try to derive this observation from more fundamental knowledge about the molecules making up nitroglycerine, but you'll always end at one point of the most fundamental knowledge, where there is no more deeper explanation of "a mechanism" simply because it's the most fundamental knowledge we currently have, and that's always based on the reproducibility of some observations. The natural sciences are all empirical sciences. That there are amazingly simple mathematically describable "fundamental laws" is one of these empirical findings. As Einstein famously said, the most incomprehensible fact about nature is that it is comprehensible in the sense that there are these amazingly simple laws which can be precisely formulated mathematically.

 

[DarMM]

What's "the mechanism"? It's just a reproducible experience that "heated nitroglycerine explodes and the explosion collapses the wall".

Yes, but the point is that for many people the current account in QM is missing the "heated nitroglycerine explodes and the explosion collapses the wall " part.

This is even formally the case, where the QM correlations violate the Reichenbach principle of a common cause. There's no event you can condition on that removes the correlations, which is taken as typical of an "explanation" in statistics.

 

[DarMM]

As Einstein famously said, the most incomprehensible fact about nature is that it is comprehensible in the sense that there are these amazingly simple laws which can be precisely formulated mathematically.

I have to say I definitely don't belong to whatever elite club considers Quantum Yang-Mills theories "simple"!

 

[vanhees71]

I would introduce quantum mechanics with the qubit, which is just 19th century optics. This produces the density operator, the Hilbert space, the special case of pure states, Born's rule (aka Malus' law), the Schrödinger equation, and the thermal interpretation - all in a very natural way.

That's precisely how I started my QM lecture for teacher students last semester. Of course, I used the statistical minimal interpretation as soon as it came to the case of very much dimmed light, when single photon events start to be visible (of course with the caveat that there are not single photons prepared but low-intensity coherent states, of course without being able at this very introductory stage to give a precise definition of coherent states).

To deepen the understanding, one can discuss classical mechanics in terms of the Lie algebra of phase space function given by the negative Poisson bracket, and then restrict to a rigid rotor, described by an so(3) given by the generators of angular momentum. This example is the one given in the last two paragraphs of post #63, and also provides the Lie algebra for the qubit.

Next one shows that this Lie algebra is given by a scaled commutator. This generalizes and defines the Lie algebras that describe quantum mechanics. Working out the dynamics in terms of the q-expectations leads to the Ehrenfest equations. Then one can introduce the Heisenberg, Schrödinger, and interaction picture and their dynamics.

That's one way to look at the formalism. I've no problems with that, but it does not provide an interpretation, as you promise by calling the whole endeaver "thermal interpretation".

Then one has everything, without any difficult concepts beyond the Hilbert space and the trace, which appeared naturally. There is no need yet to mention eigenvalues and eigenvectors (these come when discussing stationary states), the subtle problems with self-adjointness (needed when discussing boundary conditions), and the spectral theorem (needed when defining the exponentials $U(t)=e^{\pm itH}$). The latter two issues are completely absent as long as one works within finite-dimensional Hilbert spaces; so perhaps doing initially some quantum information theory makes sense.

Well, here I'm lost already. The very purpose of the above given starting point with polarization measurements was to get to the eigenvectors and eigenvalues and Born's rule. I don't see, how you can avoid eigenvectors and eigenvalues in the foundations. That's how everything, including expectation values and the quantum dynamics, is defined, providing the necessary minimal interpretation, giving the connection between what's observed in nature and the formalism.

The very fact that you can formulate the mathematical description of time evolution in different pictures shows that you need both the states and also the eigenvectors to finally derive what's observable (in the standard interpretation the probabilities for the outcome of measurements given a state in terms of a preparation). Neither the state (statistical operator) alone nor the eigenvectors (of operators representing observables) alone refer to any observable quantity within the standard statistical interpretation.

The calculations are of course identical, since calculations are not part of the interpretation.

But the interpretation of the calculation is different: In the thermal interpretation, the Ag field is concentrated along the beam emanating from the source, with a directional mass current. The beam is split by the magnetic field into two beams, and the amount of silver on the screen at the end measures the integrated beam intensity, the total transported mass. This is in complete analogy to the qubit treated in the above link. Particles need not be invoked.

You just use other words to describe what also the minimal statistical interpretation describes. The state describes a beam of Ag atoms. I don't know as what it's interpreted in your thermal interpretation precisely, but in the minimal statistical interpretation it's clear: There is a cylinder like region in space, where you have a high probability to find a silver atom with some momentum distributed around the cylinder axis, and these distributions are probability distributions within the statistical interpretation. What else are they in your thermal interpretation? Do you just ignore the atomistic nature of the Ag atoms and just interpret it as a classical density and velocity distribution? Wouldn't this be like the early interpretation by Schrödinger, which however is not consistent with the observation that single Ag atoms just make a single spot on a screen (as in Stern's and Gerlach's experiment) but do not give a smeared distribution, which only occurs after you accumulate very many Ag atoms? As I already stated before, to interpret the expectation values (also those of local quantities like charge, current, or energy densities within QFT) as the observables is contradicting in that very cases, where QT really becomes important, namely whenever the atomistic nature of matter (as well as radiation!) becomes resolved. I think the title + subtitle of Schwinger's QM book brings it to the point: "Quantum Mechanics - Symbolism for atomistic measurements"!

Sorry, for having overseen this nice posting for so long.

 

[stevendaryl]

There is no mystery. It's all completely explained with quantum dynamics. After the particle has run through the magnet providing an appropriate magnetic field the position of the particle and the measured spin component are (nearly, i.e., with high precision but never really exactly) 100% entangled. There is no mystery to have two partial beams after the magnet nor that each partial beam has (almost) determined values of the spin component in the expected direction. It's one of the very few examples which can be exactly calculated even analytically.

I don't think you're addressing what I said. Quantum mechanics predicts that if you treat a measuring device as a quantum system (which you should) then it will not make a nondeterministic transition into one or the other pointer states. The nondeterminism implied by Born's rule only applies when you treat the measuring device as a classical system that can only be in one macroscopically distinguishable state.

 

[A. Neumaier]

The very purpose of the above given starting point with polarization measurements was to get to the eigenvectors and eigenvalues and Born's rule. I don't see, how you can avoid eigenvectors and eigenvalues in the foundations.

Stokes didn't need them, neither did I in my account of the work of Malus and Stokes. Nevertheless, the whole phenomenology of a qubit was there.

Neither the state (statistical operator) alone nor the eigenvectors (of operators representing observables) alone refer to any observable quantity within the standard statistical interpretation.

Only because you think again in terms of the statistical interpretation, which you want to teach your students. In contrast, I want to introduce the students to the thermal interpretation, where the true, approximately observable values are the Stokes parameters (and not any eigenvalues!), of which the erratic events on the screen give very poor but slightly significant approximations only, which become reproducible (and hence deserve to be called measurements) only after averaging over many events. In this case, one indeed gets a good approximation of some component of the Stokes vector, proving that the Stokes vector can be observed.

I don't see, how you can avoid eigenvectors and eigenvalues in the foundations.

But I did avoid them! Nowhere any eigenvalue or eigenvector appeared!

The state describes a beam of Ag atoms. I don't know as what it's interpreted in your thermal interpretation precisely, but in the minimal statistical interpretation it's clear: There is a cylinder like region in space, where you have a high probability to find a silver atom with some momentum distributed around the cylinder axis, and these distributions are probability distributions within the statistical interpretation. What else are they in your thermal interpretation?

Something completely different, based on quantum fields rather than a particle picture; this makes the probabilistic interpretation irrelevant. The thermal interpretation dismisses the view that single events imply single particles. That's the whole purpose of the discussion in Section 3.4 of Part III, which shows that there are no convincing grounds (only historical ones) to do so. The thermal interpretation replaces this view by the intuition of fields probed by quantum buckets - see Post #272. The quantum buckets (aka bistable systems leading to single detection events) measure the rate of flow of the silver field, but at low rates only very coarsely.

Do you just ignore the atomistic nature of the Ag atoms and just interpret it as a classical density and velocity distribution? Wouldn't this be like the early interpretation by Schrödinger, which however is not consistent with the observation that single Ag atoms just make a single spot on a screen

The resulting interpretation indeed resembles that of Schrödinger; see post #273, except that it takes a quantum field point of view and hence has access to beables describing correlations, which Schrödinger didn't consider - he wanted a description in fully classical terms.

to interpret the expectation values (also those of local quantities like charge, current, or energy densities within QFT) as the observables is contradicting in that very cases, where QT really becomes important, namely whenever the atomistic nature of matter (as well as radiation!) becomes resolved.

With the thermal interpretation in place of the statistical interpretation, there is no longer a contradiction. The experiments that need statistics can all be explained in terms of the quantum bucket intuition, as in this example.

 

[vanhees71]

I don't think you're addressing what I said. Quantum mechanics predicts that if you treat a measuring device as a quantum system (which you should) then it will not make a nondeterministic transition into one or the other pointer states. The nondeterminism implied by Born's rule only applies when you treat the measuring device as a classical system that can only be in one macroscopically distinguishable state.

There is no indeterministic transition in what I said. To the contrary all is determined by unitary time evolution. The preparation of the spin component with an (almost accurately) determined value ($1/2$ or $-1/2$ nothing in between) by splitting of the beam leading to (almost) 100% position-spin-component entanglement works through the unitary time evolution. Nowhere does one make any approximate classical description of the motion of the atom (which however is a pretty good description in this case by the way, but that's not the point here).

 

[A. Neumaier]

Nowhere does one make any approximate classical description of the motion of the atom

But you make one of the detector, which is formally entangled but you treat it as being in one of two definite states, which are not continuously connected.

 

[vanhees71]

Well, the detector is simply some plate, where you catch the Ag atoms to measure there position using a microscope. Of course, one can make a problem out of this simple procedure too, but for which purpose?

 

[A. Neumaier]

Well, the detector is simply some plate, where you catch the Ag atoms to measure there position using a microscope. Of course, one can make a problem out of this simple procedure too, but for which purpose?

For the purpose of checking whether the formal Rules of Quantum Mechanics together with the formal postulates of an interpretation justify this simple heuristic (of treating the plate classically). This is the measurement problem - on a heuristic level there is none.

The devil is always in the details!

 

[stevendaryl]

There is no indeterministic transition in what I said.

Well, the minimal interpretation claims that a measurement always produces an eigenvalue of the corresponding operator, with a probability given by the Born rule. But when you analyze the measurement process quantum mechanically, that's not true.

That's why I say that the minimal interpretation is inconsistent.

 

[ftr]

But when you analyze the measurement process quantum mechanically, that's not true.

So what is true?do you mean something like what Arnold is saying.

 

[vanhees71]

Well, the minimal interpretation claims that a measurement always produces an eigenvalue of the corresponding operator, with a probability given by the Born rule. But when you analyze the measurement process quantum mechanically, that's not true.

That's why I say that the minimal interpretation is inconsistent.

Can you specify an experiment where this contradiction occurs? If this were true, I'm sure it would make a big sensation since it would prove QT wrong, making a "revolutionary" new theory necessary. So far, there seems not to be any such sensation.

 

[stevendaryl]

Can you specify an experiment where this contradiction occurs? If this were true, I'm sure it would make a big sensation since it would prove QT wrong, making a "revolutionary" new theory necessary. So far, there seems not to be any such sensation.

No, people have been living with this contradiction for nearly 100 years. It doesn't bother them any more.

Asking for an experiment in which a contradiction shows up doesn't make any sense. A contradiction is a property of a theory. The real world can't have any contradictions.

 

[stevendaryl]

So what is true?do you mean something like what Arnold is saying.

I don't. Quantum mechanics in its standard formulation is just inconsistent. As I have said before, it's a "soft" inconsistency.

 

[*now*]

These papers are about the notion of temperature in classical general relativity. What should this have to do with my papers?

I think the question was more curiosity on my part given how the effect has been considered in literature concerning the thermal time hypothesis than commentary on the TI papers, so could be removed along with follow ups like this reply. The 2nd paper (4.3) of TI mentions that gravity should be discussed in a more detailed account of the universe and so touch on the open question of quantum gravity, but that the papers offer a consistent framework for such discussions. Some thermal time hypothesis papers consider that temporal aspect thermodynamically and in non-general-relativistic physics, and the effect is compared in terms of Boltzmann Gibbs equilibrium state and general relativistic statistics, generalising to stationary spacetime. There may be some parallels with perspectival accounts, like allowing for different pictures and views like the statistical minimal one, or in comparisons of the effect with the TI. It might be relevant or useful, or not.

Quantum mechanics predicts the right correlations, but does not explain so far how it is possible that these are actually obtained!

What of attempts so far?

 

[lukesfn]

Sorry late reply...

In relativistic quantum field theory, q-expectations of fields refer to single measurements, all fields are local and objective, and single measurements are fully explained through the effects of coarse-graining and the resulting dissipation.

That was non sequitur. I prefer to think of expectations values applying to individual measurements myself.

However, maybe I was looking at TI too much through the lenses of the Ensemble interpretation. I can see how TI could apply to single measurement results, where on my terms it would be compatible with unique objective measurement results, but non-local. (I’d have to call extended objects explicitly non local)

Trying to understand TI is an interesting thought exercise, however I can’t help but feel it has a lot of unnecessary baggage, obfuscation, and new definitions, where it could have been more simple and more general, although I suppose some people will find it all well motivated, after all, it could be argued that all interpretations introduce unnecessary baggage.

It all feels a bit backwards from how I like to think about things, even as I try to understand it, I end up changing it to fit better with my thinking, so it probably isn't the most helpful way of looking at things for me. Anyway, I doubt my contributions are particularly helpful here.

 

[ftr]

Can you specify an experiment where this contradiction occurs? If this were true, I'm sure it would make a big sensation since it would prove QT wrong, making a "revolutionary" new theory necessary. So far, there seems not to be any such sensation.

I think it all boils down to what experiment proves that the position of a particle is an eigenvalue of the corresponding operator. can you name one?

 

[A. Neumaier]

the position of a particle is an eigenvalue of the corresponding operator.

The position operator has a purely continuous spectrum, hence no eigenvalues.

 

[ftr]

So what experiment determines this specrum?

 

[A. Neumaier]

So what experiment determines this spectrum?

Every real number is in the spectrum of the position operator, so the part of Born's rule you refer to is here trivially valid.

 

[ftr]

Do you mean no experiment is needed to validate?

 

[ftr]

Also do you agree that say if we do measurement for a particle in a box we can confirm the density function?

 

[A. Neumaier]

I think it all boils down to what experiment proves that the position of a particle is an eigenvalue of the corresponding operator. can you name one?

Do you mean no experiment is needed to validate?

Also do you agree that say if we do measurement for a particle in a box we can confirm the density function?

Please ask about such elementary things in a different thread. They have nothing to do with the thermal interpretation.

 

[ftr]

Ok, I will.

 

[DrDu]

The official description of the thermal interpretation of quantum physics can be found in my just finished papers

Foundations of quantum physics I. A critique of the tradition,
Foundations of quantum physics II. The thermal interpretation,
Foundations of quantum physics III. Measurement.

They are also accessible through the arXiv at
arXiv:1902.10778 (Part I), arXiv:1902.10779 (Part II), arXiv:1902.10782 (Part III).

If you are short of time, start reading at post #260. DarMM gave in post #268 a nice summary of the thermal interpretation. The simplest quantum system, a qubit, was already described by Stokes 1852, in terms essentially equivalent to the thermal interpretation.

Three reviews (Part I, Part II, Part III) are on PhysicsOverflow, together with some comments by me.

The articles are very interesting. Nevertheless I do not like the style, especially of paper I.
It insinuates that there is only one universal "traditional" way of learning QM which follows the steps listed in 5.2.
Although it is more than 30 years now that I learned QM, this was certainly not the way I learned it.

 

[stevendaryl]

I think it all boils down to what experiment proves that the position of a particle is an eigenvalue of the corresponding operator. can you name one?

It's more interesting with an operator that has discrete eigenvalues, such as angular momentum. Experiments can confirm that a measurement of any component of angular momentum always yields an integer or half-integer multiple of $\hbar$.

The point I have made is that this prediction of quantum mechanics mixes up some things that are true by definition and some things that are empirically verified.

By definition, a device can only be said to measure an observable $A$ if distinct values of $A$ lead to macroscopically distinguishable states of the measuring device. If $A$ has eigenvalues $a_1, a_2, ...$, then that means that for each $j$, there is a corresponding distinct macroscopic state of the device $S_j$ such that if the system being measured is initial in an eigenstate of $A$ with value $a_j$, then the device will make a transition into macroscopic state $S_j$. That's the definition of what it means to measure $A$.

So the rule saying that measurements always produce eigenvalues of the observable being measured follows from the definition of "measure", plus the linearity of the evolution of quantum states, plus the macroscopic rule: If a macroscopic system would, by Schrodinger's equation be in a superposition of macroscopically distinguishable states, then it will be found to be in one or the other of those states, with probabilities given by the square of the corresponding amplitude of the wave function of the macroscopic system.

In other words, the empirical content of the Born rule is implied by the claim that every system evolves unitarily according to Schrodinger's equation, except that macroscopic systems are always observed to be in states with definite values for all macroscopic quantities (with probabilities given by the square of the amplitude corresponding to each value). There is no need for the Born rule to apply to all observables; it is enough to apply it to macroscopic observables.