The thermal interpretation of quantum physics

[A. Neumaier]

Thanks for posting a link to that essay. I think Bell summarizes pretty well what I find unsatisfactory about most textbook descriptions of quantum mechanics.

My summary of what I find unsatisfactory in most textbook descriptions is given in Section 5.2 of Part I. It intersects Bell's in some respects but not in others.

 

[A. Neumaier]

How does the Ehrenfest-Tolman effect affect this?

https://journals.aps.org/pr/abstract/10.1103/PhysRev.35.904
https://journals.aps.org/pr/abstract/10.1103/PhysRev.36.1791

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

 

[julcab12]

"The thermal interpretation gives a natural, realistic meaning to the standard formalism of quantum mechanics and quantum field theory in a single world, without introducing additional hidden variables"

This is a satisfying take on whole ensemble of QM. I'm satisfied with fields and statistical side of the story. I hope a get the picture right. Approximate position, eigenstate doesn't exist? Everything is an approximation no need for collapse or silent on it. It is still considered on the genre of statistical intepretation of QM. Does it relate to equipartition theorem (all modes of excitation carry heat).

 

[DarMM]

Just to understand. Take a particle reaction like $\pi^{+} \rightarrow \mu^{+} + \nu_{\mu}$. In the thermal interpretation I assume what is happening here is that locally devices probe $\pi^{+}, \mu^{+}, \nu_{\mu}$ fields (of course these are not fundamental fields, but let's ignore that for now). Via interaction with the fields each of the devices' slow modes are placed into a bistable state and environmental noise triggers these to decay into the detection/non-detection states?

 

[A. Neumaier]

I'm satisfied with fields and statistical side of the story. I hope a get the picture right. Approximate position, eigenstate doesn't exist? Everything is an approximation no need for collapse or silent on it. It is still considered on the genre of statistical intepretation of QM. Does it relate to equipartition theorem (all modes of excitation carry heat).

Eigenstates do not matter, except for computational purposes. Every observable quantity has an associated intrinsic state-dependent uncertainty within which it can be (in principle) determined. It is meaningless to ask for more accuracy, just as it is ridiculous to ask for the position of an apple to mm accuracy. Statistics enters whenever a single value has too much uncertainty, and only then. In this case, the uncertainty can be reduced by calculating means, as within classical physics. Collapse is the continuous but very fast change of the coarse-grained state in a dissipative environment. There is no relation to the equipartition theorem.

 

[A. Neumaier]

Just to understand. Take a particle reaction like $\pi^{+} \rightarrow \mu^{+} + \nu_{\mu}$. In the thermal interpretation I assume what is happening here is that locally devices probe $\pi^{+}, \mu^{+}, \nu_{\mu}$ fields (of course these are not fundamental fields, but let's ignore that for now). Via interaction with the fields each of the devices' slow modes are placed into a bistable state and environmental noise triggers these to decay into the detection/non-detection states?

At each time $t$ you have three operator-valued effective 4-currents A,B,C (for simplicity, to avoid having to write Greek letters and/or indices). When the reaction center is at the origin, the reaction A$\to$B+C proceeds as follows: At large negative times the A-density (q-expectation of the time component of the 4-current) is concentrated along the negative z-axis, and the A-current (q-expectation of the 3-vector of space components of the 4-current) is concentrated along the positive z-axis; the 4-currents B and C essentially vanish.

If the reaction happened (which depends on the details of the environment) then, at large positive times, the 4-current A is negligible, the B-density and C-density are concentrated along two (slightly diverging) rays emanating from the origin in such a way that momentum conservation holds, and the B-current and C-current are concentrated along these rays, too. Otherwise, at large positive times, the A-density is concentrated along the positive z-axis, and the A-current is concentrated along the positive z-axis, too, and the 4-currents B, C remain negligible. During the reaction time when the fields are concentrated near the origin, one can interpolate the asymptotic happening in an appropriate way; no problems there. The details are defined by the interaction.

The manifold of slow modes splits into a basin corresponding to the decayed state (with two continuous angle parameters labeling the possible modes) one basin corresponding to the undecayed state. The metastable transition state at time zero determines together with the environmental fluctuations which basin is chosen and which direction is taken. This is comparable to what happens to bending a classical thin iron bar through longitudinal pressure in a random direction, though in that case the bar must bend, so that there is only one basin, with modes labelled by a single angle. In both cases, one of the continuous labels appears due to the rotational symmetry of the setting around the z-axis. In the case of the decay reaction, the second continuous label arises through another, infinitesimal symmetry at the saddle point at the origin.

 

[A. Neumaier]

Via interaction with the fields each of the devices' slow modes are placed into a bistable state and environmental noise triggers these to decay into the detection/non-detection states?

If the reaction happened (which depends on the details of the environment) then, at large positive times, the 4-current A is negligible, the B-density and C-density are concentrated along two (slightly diverging) rays emanating from the origin in such a way that momentum conservation holds, and the B-current and C-current are concentrated along these rays, too.

Actually, this is only one of the possible scenarios, probably what happens if the decay happens inside a dense medium (a secondary decay in a bubble chamber, say).

For a collision experiment in vacuum, there is probably not enough environmental interaction near zero, and after reaching the collision region, the B,C fields rather should take (in case of a reaction happening) a rotational symmetric shape. In this case, the path like particle nature appears only later when the spherical fields reach a detector. The metastability of the detector forces the two spherical fields to concentrate along two paths, and momentum conservation makes these paths lie weighted-symmetric to the z-axis (would be geometrically symmetric when the decay products have equal mass). The details are those reported in Mott's 1929 paper (ref. [35] of Part I).

In both cases, the detection process creates the seeming particle nature of the observation record.

 

[ftr]

spherical fields reach a detector

Are these physical fields, what is this field composed of.

 

[A. Neumaier]

Are these physical fields, what is this field composed of.

Fields are not really composed of anything (except perhaps in some formal sense of other fields). They tell about properties of Nature at arbitrary spacetime points.

In the present case, the fields of interest are the effective fields given by the currents of the particles involved in the reaction.

 

[ftr]

So in essence particles are fields of nothing but numbers sometimes localised and others extended greatly, correct.

 

[A. Neumaier]

So in essence particles are fields of nothing but numbers sometimes localised and others extended greatly, correct.

No.

In general, fields are just themselves, not composed of other stuff. The temperature field in a room is not composed of anything but describes how warm it is in different places. Similar for other fields, e.g. the water level of the moving surface of a lake, or the salt concentration in the lake. They are not composed of water but describe properties of the lake.

Electron fields and other fundamental stuff are not much different in principle, only in their quantum properties.

Partcles are moving localized aspects of fields, described by bloblike or beamlike currents. The paths they travel are often more real than the particles themselves. Think of rain pouring down or of moving water wavelets, but don't take the imagery too seriously!

 

[ftr]

Particles are moving localized aspects of fields

And Fields are aspects of what?

 

[DarMM]

And Fields are aspects of what?

They're just fields as such, same as they are in classical field theory, just the structure of their properties is different.

 

[ftr]

They're just fields as such, same as they are in classical field theory, just the structure of their properties is different.

In classical field theory temperature field is an aspect of energy of the particles. The post said that particles are aspect of fields while everybody knows that fields must be aspect of particles.

 

[DarMM]

In classical field theory temperature field is an aspect of vibration energy of the particles. The post said that particles are aspect of fields while everybody knows that fields must be aspect of particles.

In QFT in general, not specifically the Thermal Interpretation, the fields aren't generally "aspects of particles". There are several states that don't really admit a particle interpretation, particles only emerge at asymptotic times, the particle content is observer dependent (i.e. Unruh effect). I don't see how the fields are aspects of particles.

 

[A. Neumaier]

And Fields are aspects of what?

They are aspects of what we can observe.

 

[A. Neumaier]

In classical field theory temperature field is an aspect of energy of the particles.

No. This holds only for ideal gases, but not for the temperature of liquid water, say, as it figures in the Navier-Stokes equations.

everybody knows that fields must be aspect of particles.

Everybody who looks deeper knows that the fundamental theory of Nature is quantum field theory, and not quantum particle theory. Particles are described in terms of fields.

 

[ftr]

I don't see how the fields are aspects of particles.

Ever since I was born in QM theory world I was taught that particles and fields are dual description, and since we say here is a particle and not here is a field I presume that fields are aspects of particles.

 

[DarMM]

Ever since I was born in QM theory world I was taught that particles and fields are dual description

I don't see how that could be possible in general interacting field theories which have states without a particle decomposition.

 

[A. Neumaier]

we say here is a particle and not here is a field I presume that fields are aspects of particles.

Informally, we say here is a particle (mainly because of tradition), but looking at the math involved in their relativistic description one finds that the particle picture is purely figurative, while everything is expressed in terms of fields.

 

[ftr]

I don't see how that could be possible in general interacting field theories which have states without a particle decomposition.

Informally, we say here is a particle (mainly because of tradition), but looking at the math involved in their relativistic description one finds that the particle picture is purely figurative, while everything is expressed in terms of fields.

First I hear that fields are fiction(i.e. mathematical), now I hear that particles are fiction.
then this post

They are aspects of what we can observe

The interpretation was suppose to make things clear, was it?
edit: ok I admit this has made me to think a lot harder.

 

[A. Neumaier]

First I hear that fields are fiction(i.e. mathematical), now I hear that particles are fiction.

In some sense, only Nature is real, and all talk about it is already fiction. In any case, particles are more superficial fiction than quantum fields. Nobody ever has seen a particle. We just imagine it as a tiny cannon ball or a tiny wavelet, or whatever...

The interpretation was suppose to make things clear, was it?

The thermal interpretation is supposed to resolve the issues with the traditional interpretations, primarily the measurement problem.

Clarity will rule only 5-10 years after a single interpretation is accepted by the majority, and textbooks are rewritten accordingly. Thus you need to be patient.

The only shortcut is to learn to understand things from the ground, starting with the math, rather than from what you hear people say.

 

[julcab12]

First I hear that fields are fiction(i.e. mathematical), now I hear that particles are fiction.
then this postThe interpretation was suppose to make things clear, was it?

Fields are real and particles blurry bundles of real in approximation. The usual convention is coined behavior, depending on how you view it. For loopy guys- are interactive, transformative via timelike slices-- Thermal Time (Still Blurry Though). In terms of field--mathematical abstraction are often so closely related to "real" stuff that they're confused with each other. A vector is not real, a force is. But we're so used to vector forces, we swap them carelessly. We can do so only because we know forces behave (with an extremely fine approximation) as vectors, but vectors are not real. Vector fields are not real, for the same reasons vectors are not real; the electrical field is real and you could feel it if you had the right organs. Hilbert spaces are not real, superposition is.

 

[ftr]

Fields are real

Although "real" is hard to define, but typically in physics we mean that something that has certain property that can be measured directly or indirectly. I don't know of any experiment that has measured electron field and typically the fields are expressed using imaginary numbers.

 

[A. Neumaier]

I don't know of any experiment that has measured electron field

Then you can learn something new!

Atomic force microscopy displays the surface of the electron cloud around a nucleus, not a number of tiny electron particles surrounding the nucleus. See ''Does an atom mostly consist of empty space?'' from my theoretical physics FAQ.

 

[ftr]

Then you can learn something new!

That is what attracts me to science, I get very bored when I sail an open sea. What is the unit of measurement.

P.S. I don't see a single sentence that says "electron field" in your first reference.

 

[DarMM]

I forgot to ask this. Is the Thermal Interpretation contextual?

If I have a set of nine devices for a four level system that represent one of the nine orthogonal bases in Cabello's proof of Kochen-Specker. And "let us say" that to keep determinism we end up with a contextual assignment whereby projector $P_5$ is assigned a value of $1$ (i.e. is the result that will occur) when measured as part of operator $A$, but assigned a value of $0$ when measured as part of operator $B$. This determination $\nu(P_5,A) = 1$ implicitly includes the full dynamics of the environment, since it is just a statement of the value that will obtain.

How does this contextuality arise in the thermal interpretation? I assume it is that given a fixed environmental state $\rho_E$ the metastable states on devices implementing $A$ and $B$ are different enough that under influence from the environment one will decay onto the $P_5$ component of the slow manifold and the other will not.

 

[A. Neumaier]

That is what attracts me to science, I get very bored when I sail an open sea. What is the unit of measurement.

P.S. I don't see a single sentence that says "electron field" in your first reference.

It talks about forces. Forces are vector fields (generalizing the gravitational forces familiar to anyone). The detailed force measured depends on the instrument, but they are all calculated from the interaction with the electron field (plus the Coulomb fields of the nuclei).

 

[A. Neumaier]

I forgot to ask this. Is the Thermal Interpretation contextual?

Of course, since quantum mechanics is. The stochastic influences depend on the environment, which is the context. No two environments are identical. (But conventional contextuality discussions are not applicable since they assume sharp outcomes, while the thermal interpretation is about explaining when sharp outcomes should be expected.)

Note that the thermal interpretation gives no details, only the conceptual intuition needed to turn each specific problem into a precise problem of statistical mechanics. To find out how the slow manifold looks like is for each case a separate statistical mechanics problem.

In Part III, I discussed two particular measurement situations treated by AB&N and B&P, respectively. The techniques generalize, but have not yet been applied to generic measurement situations which would allow to treat not only particular cases but fairly general settings.

Thus there is still a lot of research potential in the application of the thermal interpretation.

 

[DarMM]

Of course, since quantum mechanics is.

I think this is a difference of phrasing. Quantum Mechanics (in the typical view) retains nonconextuality by sacrificing determinism, i.e. there are sets of projectors to which one cannot assign elements of ${0,1}$ noncontextually. Either you give up determinism, i.e. assign real values elements of $[0,1]$, or you accept the contextuality.
Although some call any violation of either contextuality.

Regardless the explanation is as I expected. Have you read:
Heywood, P., & Redhead, M. L. G. (1983). Nonlocality and the Kochen-Specker paradox. Foundations of Physics, 13(5), 481–499

It contrasts the different forms of locality implied by different methods of having contextuality, i.e. ontological vs environmental contextuality.

 

[A. Neumaier]

Have you read:
Heywood, P., & Redhead, M. L. G. (1983). Nonlocality and the Kochen-Specker paradox. Foundations of Physics, 13(5), 481–499

I had studied the Kochen-Specker theorem in detail, but didn't read all of the surrounding literature.

I lost interest in quantum-logic related results (though I read the book Quantum logic by Karl Svozil and more) long ago, when I realized that quantum logic is a very poor logic in which not even implication is sensibly defined. Thus one can make only the most primitive logical arguments. The fact is that all predictive power in quantum physics comes from applying classical logic to get results about q-expectations, and nothing but confusion comes from considering quantum logic.

 

[A. Neumaier]

Three reviews (Part I, Part II, Part III) of my three papers are now on PhysicsOverflow, together with some comments by me.

 

[Mentz114]

[..]

I discussed two particular measurement situations treated by AB&N and B&P, respectively. The techniques generalize, but have not yet been applied to generic measurement situations which would allow to treat not only particular cases but fairly general settings.

Thus there is still a lot of research potential in the application of the thermal interpretation.

I have to say it looks incredibly hard. I doubt if a general theory is possible.
I looked at buying a copy of the B&P book but the earliest delivery date for a new one is June !
I'm not sure if Breuer et al (2015) is cited in the Thermal papers but it gives a foretaste and is available on arXiv.

Non-Markovian dynamics in open quantum systems
Heinz-Peter Breuer, Elsi-Mari Laine, Jyrki Piilo, Bassano Vacchini

arXiv:1505.01385v1 [quant-ph] 6 May 2015

I like very much the re-synthesis of QT in the Thermal interpretation. Dropping particles gets rid of a lot of Platonic nonsense. Nice move.

 

[A. Neumaier]

I looked at buying a copy of the B&P book but the earliest delivery date for a new one is June !
I'm not sure if Breuer et al (2015) is cited in the Thermal papers but it gives a foretaste and is available on arXiv.

H. P. Breuer & F. Petruccione,
Stochastic dynamics of open quantum systems: Derivation of the
differential Chapman-Kolmogorov equation,
Physical Review E51, 4041-4054 (1995).

is freely online and related to what I discuss. But it works with pure states rather than with the mixed states required for the thermal interpretation.

 

[A. Neumaier]

I looked at buying a copy of the B&P book

You may wish to look at bookfinder! (But your shipping country and hence the prices may be different.)
I wonder why used copies may be more expensive than new ones by a large factor...