I The thermal interpretation of quantum physics

[A. Neumaier]

They deserve the name of beables, but not beables in the Bell sense. For instance, as you quoted, Bell required that "beables need not of course resemble those of, say, classical electron theory; but at least they should, on the macroscopic level, yield an image of the everyday classical world". I don't see how your bilocal beables, on the macroscopic level, yield an image of the everyday classical world.

I don't see either how a Bohmian particle position yields on the macroscopic level an image of the everyday classical world. Only certain things computable from beables (in Bell's sense) are required to yield on the macroscopic level an image of the everyday classical world.

Note also that ''classical'' does not exclude ''nonlocal''. The mass of the Earth is a very nonlocal classical beable, and Bell mentioned explicitly the total energy of a bounded system as a nonlocal beable.

Thus the thermal bilocal beables are as much beables in Bell's sense as Bohmian particles. But unlike the latter, they are not local.

 

[ftr]

I don't understand your question.

There is just one way in which something is real - it exists and has properties independent of what we think about it. Our subjective views are approximations to the real.

Ok. I will be bold, what is the ontology of field, just numbers. I think this has a bearing on what is meant by beable.

 

[julcab12]

I think we must ignore some bounds of what it means local or nonlocal. Everything is approximation. Much like in open sets; continuous infinitely small patches, but with blurred contours. Forget any classical picture of a particle like a ball or point, it is very rough approximation, forget wavefunction, it is less rough approximation, currently, we understand all particles as excitation of some field, imagine it as a wave of a sea, there is no sense of sailing in which point it is, or how wide it is. TI offers some 'temporary' relief to some weirdness of QM.

 

[A. Neumaier]

Ok. I will be bold, what is the ontology of field, just numbers. I think this has a bearing on what is meant by beable.

In the thermal interpretation, one says (by definition) that the q-expectations of operators acting on the state space of a quantum system (in particular of fields) exist objectively, define real (actual) properties (beables) of the system, thus defining an ontology. Having the ontology, one can draw conclusions, for example about what can be known (observed) about a quantum system, and how accurately.

In my view, there is nothing more to ontology than this.

 

[Demystifier]

I don't see either how a Bohmian particle position yields on the macroscopic level an image of the everyday classical world.

This may help: https://en.wikipedia.org/wiki/Pointillism

 

[A. Neumaier]

This may help: https://en.wikipedia.org/wiki/Pointillism

It just illustrates what I said before, that macroscopic beables with a classical meaning are composed of certain nonclassical beables. But the single Bohmian beable has no classical macroscopic meaning. Thus Bell cannot have meant that every beable must have a classical macroscopic meaning.

 

[Demystifier]

It just illustrates what I said before, that macroscopic beables with a classical meaning are composed of certain nonclassical beables. But the single Bohmian beable has no classical macroscopic meaning. Thus Bell cannot have meant that every beable must have a classical macroscopic meaning.

Of course not. He meant that collection of many microscopic beables must have a classical macroscopic meaning.

But the thermal interpretation, or any interpretation with bilocal beables, is different. A bilocal beable means that "having a dot here" and "having a dot there" is not the same as "having dots here and there". Maybe it's my lack of imagination, but I cannot imagine pointilism painting with such a property.

Anyway, pointilism painting is a great metaphor for Bohmian beables, I think we can agree on that.

 

[A. Neumaier]

pointilism painting is a great metaphor for Bohmian beables

Yes, but not for the beables in the thermal interpretatiton.

A bilocal beable means that "having a dot here" and "having a dot there" is not the same as "having dots here and there".

The thermal interpretation embodies the classical truth ''There is more to the whole than to the parts'', which is also observed in nonlocal entanglement experiments.

 

[Demystifier]

Yes, but not for the beables in the thermal interpretatiton.

The thermal interpretation embodies the classical truth ''There is more to the whole than to the parts'', which is also observed in nonlocal entanglement experiments.

Thanks for the discussion, now I think I understand what the thermal interpretation is.

 

[N88]

The thermal interpretation embodies the classical truth ''There is more to the whole than to the parts'', which is also observed in nonlocal entanglement experiments.

How is the word "nonlocal' defined in the TI? Is it required [or redundant and can be dropped] in the above phrase "nonlocal entanglement experiments"?

 

[A. Neumaier]

How is the word "nonlocal' defined in the TI? Is it required [or redundant and can be dropped] in the above phrase "nonlocal entanglement experiments"?

I used the word informally.
You may replace "nonlocal" by "long distance" in the above phrase, to get a more precise rendering of the intended meaning.

 

[N88]

I used the word informally.
You may replace "nonlocal" by "long distance" in the above phrase, to get a more precise rendering of the intended meaning.

Thank you. Is it too much to hope that TI can be formulated and discussed without reference to that (in my experience) "many-times confusing" word?

 

[A. Neumaier]

Thank you. Is it too much to hope that TI can be formulated and discussed without reference to that (in my experience) "many-times confusing" word?

In the three papers I am fairly careful with my words. Read Section 4 of Part II. But it doesn't make sense to avoid the word.

Nonlocal simply means referring to multiple, not infinitely close locations.

 

[Demystifier]

Noise from the environment causes it to quickly decay into one of the slow mode manifolds giving a discrete outcome not fully reflective of $\langle A\rangle$.

Where can I see a simple general quantitative explanation of why exactly that happens?
By simple I mean not longer than a couple of pages, by general I mean referring to a wide class of cases, by quantitative I mean containing equations (not merely verbal hand waving). Mathematical rigor is not required.

 

[cube137]

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. Post #484 is my very short summary and post #479 contains links to my explanations of the connections between theory and experiments. Open problems related to the thermal interpretation are discussed in post #293.

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

In Februray 20, 2016. I started the thread "Neumaier quantum 101" to get a handle of the thermal interpretation. It's nice to know Neumaier has even developed it further. I wrote this then:

https://www.physicsforums.com/threads/neumaier-quantum-101.858289/
"For example you have detectors in a circle and a photon was emitted from the center. Does the photon travel with a trajectory to a particular detector or does it travel as wave.. if wave.. what is the meaning it travels as wave function.. upon detection.. it only appears at one detector (the wave function collapses). In your view.. what really happened?"

Neumaier described it" It travels as a wave, as one knows since Huygens 1690. It doesn't appear on the detector; it disappears there, and the transmission of energy leaves random spots at a rate determined by the impinging energy density.".

But why only one spot appear and not two simultaneously? Won't it be possible to put the above under experimental test or scrutiny as it is the most graphic ramifications yet of the thermal interpretation? Before delving even to greater and densest depth. We must deal with the above first.

 

[Demystifier]

But why only one spot appear and not two simultaneously?

My post above is asking the same question in a different form.

 

[stevendaryl]

Where can I see a simple general quantitative explanation of why exactly that happens?
By simple I mean not longer than a couple of pages, by general I mean referring to a wide class of cases, by quantitative I mean containing equations (not merely verbal hand waving). Mathematical rigor is not required.

My feeling is that it doesn't happen. The wave function by linearity cannot evolve from a superposition of two possibilities to a choice of one possibility or the other.

There is a trick that can be performed that makes it almost seem as if this happens. If a microscopic superposition interacts with a macroscopic system (such as a measurement device), you can no longer describe the situation as a pure state of the microscopic system. So you form the density matrix and trace out the environmental degrees of freedom. The resulting reduced density matrix looks as if the system is in a mixed state, which can be interpreted as the system being in one or other possibilities with a particular probability for each. But that does not actually mean that the environment has selected one of the possibilities; if you enlarge the "system" to include the environment, you will see that it is still a pure state.

At least, that's the way things work in nonrelativistic quantum mechanics. @DarMM tells me that in QFT you can have the situation where you have essentially mixed-state density matrices that cannot be interpreted as arising from any pure state.

 

[Demystifier]

The wave function by linearity cannot evolve from a superposition of two possibilities to a choice of one possibility or the other.

I think here one has a different idea in mind. Suppose that initially a subsystem is in a superposition of the ground state and an excited state. When you couple it to the environment, the subsystem decays continually into the ground state only. This explains why do we finally find the subsystem in a definite state of energy, and not in a superposition or mixture of different energies. The problem with that, as I see it, is that in 50% cases of energy measurements we should finally find the subsystem in the excited state, which the decay above cannot explain.

 

[DarMM]

At least, that's the way things work in nonrelativistic quantum mechanics. @DarMM tells me that in QFT you can have the situation where you have essentially mixed-state density matrices that cannot be interpreted as arising from any pure state.

Yes, for the local algebras in QFT all states are mixed states, no pure states exist. In the sense that for all states $\omega$ and observables $A$, there always exists another pair of states $\omega_1$ and $\omega_2$ such that:
$$\omega\left(A\right) = \frac{1}{2}\omega_{1}\left(A\right) + \frac{1}{2}\omega_{2}\left(A\right)$$
So every state can always be thought of as "Classical Ingorance" of two others if one wishes.

However my view is that thinking of density matrices as ignorance of the "true" pure state is wrong even in non-relativistic QM as if they were you would expect the space of density matrices to be (isomoprhic to) $\mathcal{L}^{1}\left(\mathcal{H}\right)$ with $\mathcal{H}$ the quantum Hilbert space.

 

[Demystifier]

I guess the answer to my question above is the following. The dynamics of the open subsystem is described not only by a single Hamiltonian, but also by a series of Lindblad operators. The consequence, I guess, is that there are many (rather than one) stable states to which the system can finally decay. To which one it will decay depends on fine details of the initial state that in practice cannot be known exactly, so they play a role of "hidden variables".

 

[A. Neumaier]

Where can I see a simple general quantitative explanation of why exactly that happens?
By simple I mean not longer than a couple of pages, by general I mean referring to a wide class of cases, by quantitative I mean containing equations (not merely verbal hand waving). Mathematical rigor is not required.

I guess the answer to my question above is the following. The dynamics of the open subsystem is described not only by a single Hamiltonian, but also by a series of Lindblad operators. The consequence, I guess, is that there are many (rather than one) stable states to which the system can finally decay. To which one it will decay depends on fine details of the initial state that in practice cannot be known exactly, so they play a role of "hidden variables".

The detailed dynamics of an open system is governed by a (piecewise deterministic or quantum diffusion) stochastic process of which a Lindblad equation is only a summary form. See, e.g., the book by B&P cited in Part III, which has lots of (not fully rigorous) formulas and lots of examples.

For measurement settings, if one assumes the noise to be small (weak coupling to the environment), there is a deterministic dissipative part which makes the system generically move into a fixed point; each fixed point corresponding to a measurement outcome. If the detector (e.g., a bubble chamber) is initially in a metastable state, there is an ambiguity into which fixed point it is mapped, and this ambiguity is resolved randomly by the noise in the stochastic process. This is analogous to a ball balanced on the top of a hill, which moves under noise into a random direction, eventually ending up at the bottom of one of the valleys.

 

[A. Neumaier]

But why only one spot appear and not two simultaneously?

Conservation of energy, together with the instability of macroscopic superpositions and randomly broken symmetry forces this, just as a classical bar under vertical pressure will bend into only one direction. See Subsection 5.1 of Part III and the similar discussion around this post.

Won't it be possible to put the above under experimental test or scrutiny as it is the most graphic ramifications yet of the thermal interpretation?

This is just a more complicated form of the usual test at two locations, and only complicates the setting without adding substance. Every particle collider makes similar experiments, not with photons but with massive particles, and one always observes that symmetry is broken. Whether this symmetry is discrete or continuous is in the present context of secondary importance.

 

[A. Neumaier]

The wave function by linearity cannot evolve from a superposition of two possibilities to a choice of one possibility or the other.

In the thermal interpretation, beables (q-expectations) are quadratic in the wave function, hence cannot be superimposed. They are always definite numbers that are approximately measureable.

The two possiblities come from the fact that the reduced dynamics of system plus detector has two fixed points, and one of them is reached as explained in the previous few posts.

 

[Demystifier]

The detailed dynamics of an open system is governed by a (piecewise deterministic or quantum diffusion) stochastic process of which a Lindblad equation is only a summary form. See, e.g., the book by B&P cited in Part III, which has lots of (not fully rigorous) formulas and lots of examples.

For measurement settings, if one assumes the noise to be small (weak coupling to the environment), there is a deterministic dissipative part which makes the system generically move into a fixed point; each fixed point corresponding to a measurement outcome. If the detector (e.g., a bubble chamber) is initially in a metastable state, there is an ambiguity into which fixed point it is mapped, and this ambiguity is resolved randomly by the noise in the stochastic process. This is analogous to a ball balanced on the top of a hill, which moves under noise into a random direction, eventually ending up at the bottom of one of the valleys.

My problem is that I don't see how to reconcile it with the non-stochastic description of decoherence which, in a measurement setting, typically predicts evolution not to a single fixed point (one measurement outcome) but to an incoherent superposition of all fixed points (all possible measurement outcomes, as in the many-world interpretation).

I agree that influence of unknown degrees of freedom can effectively be described by an appropriate stochastic model, but it doesn't mean that any stochastic model is appropriate. In particular, a stochastic model that predicts evolution to a single fixed point is probably not appropriate for the purpose of solving the measurement problem. Perhaps it can be appropriate as a description of the phenomenological fact that we do observe single measurement outcomes, but such a model doesn't really solve the measurement problem. Instead, it merely assumes that somehow it is already solved by more fundamental non-stochastic means, so that one is allowed to use stochastic models for practical purposes.

Related to this, at page 25 of part III of your paper you say:
"The thermal interpretation claims that this influences the results enough to cause all randomness in quantum physics, so that there is no need for intrinsic probability as in traditional interpretations of quantum mechanics."
This might be the central claim of thermal interpretation, but I am not at all convinced that this claim is true.

 

[A. Neumaier]

My problem is that I don't see how to reconcile it with the non-stochastic description of decoherence which, in a measurement setting, typically predicts evolution not to a single fixed point (one measurement outcome) but to an incoherent superposition of all fixed points (all possible measurement outcomes, as in the many-world interpretation).

This is because the analysis of decoherence works on the coarser level of Lindblad equations rather than on the finer level of the underlying stochastic piecewise deterministic process (PDP) of B&P.

I agree that influence of unknown degrees of freedom can effectively be described by an appropriate stochastic model, but it doesn't mean that any stochastic model is appropriate. In particular, a stochastic model that predicts evolution to a single fixed point is probably not appropriate for the purpose of solving the measurement problem.

There is no choice. The deterministic dynamics of the universe and the properties of system and detecor force everything, including the form of the reduced stochastic process. If a quantity with discrete spectrum is measured one ends up with a PDP, if it is continuous, wih a quantum diffusion process.

such a model doesn't really solve the measurement problem. Instead, it merely assumes that somehow it is already solved.

Only if you create the model by guessing. If you create it by coarse-graining the true dynamics, one gets a solution to the measurement problem.

Related to this, at page 25 of part III of your paper you say:
"The thermal interpretation claims that this influences the results enough to cause all randomness in quantum physics, so that there is no need for intrinsic probability as in traditional interpretations of quantum mechanics."
This might be the central claim of thermal interpretation, but I am not at all convinced that this claim is true.

Read B&P to get the necessary mathematical background!

 

[Demystifier]

This is because the analysis of decoherence works on the coarser level of Lindblad equations rather than on the finer level of the underlying stochastic piecewise deterministic process (PDP) of B&P.

But decoherence can be described at an even more fundamental level, without the Lindblad equation and withoud stochastic processes. See e.g. Schlosshauer's book, Chapters 2 and 3. This more fundamental level typically predicts incoherent superposition of all possible measurement outcomes.

 

[ftr]

Arnold, I just saw this, does it have any relation to your interpretation since it also talks about thermal interpretation.

 

[atyy]

If I am right, then this stochastic approach doesn't really solve the measurement problem but rather assumes that somehow it is already solved.

I haven't studied the thermal interpretation, so am not commenting on it directly. However, it is reasonable to conceive solving the measurement problem by postulating the stochastic equation directly, eg. under some circumstances CSL (non-Copenhagen) and the continuous measurement formalism (Copenhagen) produce the same equation.
https://en.wikipedia.org/wiki/Belavkin_equation

 

[Demystifier]

However, it is reasonable to conceive solving the measurement problem by postulating the stochastic equation directly

I agree with that, for instance the GRW theory is of that kind. But the thermal interpretation is not of that kind.

 

[A. Neumaier]

But decoherence can be described at an even more fundamental level, without the Lindblad equation and withoud stochastic processes. See e.g. Schlosshauer's book, Chapters 2 and 3. This more fundamental level typically predicts incoherent superposition of all possible measurement outcomes.

I meant with ''on the coarser level of Lindblad equations'' anything based on a deterministic approximate dynamics for the reduced density matrix. I don't have Schlosshauers book at hand but believe he only works on this level. On the other hand, B&P produce a stochastic dynamics for the reduced density matrix, which has a greater resolution power.

I haven't studied the thermal interpretation, so am not commenting on it directly. However, it is reasonable to conceive solving the measurement problem by postulating the stochastic equation directly, eg. under some circumstances CSL (non-Copenhagen) and the continuous measurement formalism (Copenhagen) produce the same equation.

I agree with that, for instance the GRW theory is of that kind. But the thermal interpretation is not of that kind.

B&P produce such an equation by coarse-graining from a unitary dynamics rather than postulating it directly. Some of my claims about the thermal interpretation rely on this.