I The thermal interpretation of quantum physics

[A. Neumaier]

Paradoxically, although claiming to provide a new interpretation, you never tell us its content. It's not enough to write down the formalism and forbid to use the 93 years old accepted probabilistic interpretation without providing a new one. If @DarMM 's posting #268 provides the correct interpretation of your interpretation, it's the more confirmed that it is still the usual probabilistic one too.

You never listened to the content descriptions I gave (last in #263 and #266).

Of course I don't forbid anything; so you can always add probabilistic interpretations. DarMM's summary is essentially correct; I'll point to small corrections later. It never assumes anything probabilistic; thus one doesn't need it.

Unlike you, I allow people to dismiss statistical connotations in all situations where no actual measurement results are averaged over - without loss of physics but with a resulting improvement of the foundations. No irreducible probability, no dependence of the foundations on measurement, the same clarity in the association of predictions and experimental results. But the traditional foundational problems are gone!

You, of course, never saw any foundational problems in the statistical interpretation. This is because you are far more liberal in the use of intuition than strict adherence to the axioms in any statistical foundations would allow. At this level of liberality in the discussion we agree. But many others (e.g., @Stevendaryl, or Steven Weinberg) were never satisfied with such liberal (and hence poorly defined) foundations. The thermal interpretation is for those.

Our whole discussion shows that I didn't miss anything in the thermal interpretation, and really covered the actual physical usage of the quantum formalism.

 

[A. Neumaier]

Thermal Interpretation Summary Redux

Excellent summary, thanks!

7. In measurements our devices (for reasons given in the next point) unfortunately only become correlated with a single point within the world tube or blurred range of a property. This gives measurements on quantum systems discrete results that don't faithfully represent the "tubes". Thus we must reconstruct them from multiple observations.

The ''single point'' here is of course also a blurred point only, as a detector always responds to a small space-time region and not to a point only. The measurement result will often be discrete, however, due to the reasons given in point 8.

It is like measuring the rate of water flow into a basin by the number of buckets per unit time needed to keep the water at a roughly fixed level of height. As long as there is enough flow the bucket is very busy and the flow is measured fairly accurately. But at very low rates it is enough to occasionally take out one bucket full of water and the bucket number is a poor approximation of the flow rate unless one takes very long times.

Photocells and Geiger counters act as quantum buckets, by the same principles.

 

[A. Neumaier]

Question for @A. Neumaier , do higher statistics like skew and kurtosis give one further structure of the world tube?

The world tube is just a visualization, even a fuzzy one since it cannot be said how many sigmas the world tube is wide. I don't think skewness and kurtosis are valuable on this fuzzy visualization level.

Rather, the next level of naturally visualizable detail would be to think of the particle's world tube as being actually a moving cloud of mass (or energy, or charge, etc.), with mass density $\rho(z)=\langle m\delta(x_k-z)\rangle$ for a distinguishable particle $k$ inside a multiparticle system. For a single particle state, this would be $\rho(z)=m|\psi(z)|^2$, recovering Schrödinger's intuition about the meaning of the wave function. Of course, this is already the field picture, just in first quantized form.

Mathematically, of course, there is no world tube at all but just a host of loosely related beables. One family of them is the reference path $\langle x(t)\rangle$. It has a clear intuitive meaning (as the path one sees at low resolution), just as the reference path of a classical donut traced out by the center of mass, though in both cases nothing is precisely at the reference path.

 

[ftr]

For a single particle state, this would be ρ(z)=m|ψ(z)|2ρ(z)=m|ψ(z)|2\rho(z)=m|\psi(z)|^2, recovering Schrödinger's intuition about the meaning of the wave function. Of course, this is already the field picture, just in first quantized form

I most definitely agree with this picture based on the example I gave in post #255. The only thing is that your system does not tell exactly what is going on in detail in that small region, my idea supplements and give the interpretation of the "line" picking distances as energy which upon calculation adds to mass according to good old Einstein's formula.

P.S. I think you were right Arnold. The wavefunction is nothing, only density has a physical reality.

 

[A. Neumaier]

does not tell exactly what is going on in detail in that small region

Nothing exact can be said. Differences of the order of the uncertainty are physically meaningless.

 

[ftr]

Nothing exact can be said. Differences of the order of the uncertainty are physically meaningless.

So what do you think of this
https://www.newscientist.com/articl...en-atom-youre-on-quantum-camera/#.UeSbfW2i18E

 

[A. Neumaier]

So what do you think of this
https://www.newscientist.com/articl...en-atom-youre-on-quantum-camera/#.UeSbfW2i18E

They say, ''Rather than taking an image of a single atom, they sampled a bunch of atoms. '' Thus they are explicitly averaging over many atoms. It is like creating an average picture of a human face...

 

[vanhees71]

Unlike you, I allow people to dismiss statistical connotations in all situations where no actual measurement results are averaged over - without loss of physics but with a resulting improvement of the foundations. No irreducible probability, no dependence of the foundations on measurement, the same clarity in the association of predictions and experimental results. But the traditional foundational problems are gone!

Again, just to understand, because I think this is the main source of our mutual misunderstanding:

Let's take my example for the measurement of a current with a galvanometer. From a quantum-theoretical point of view electric current consists of the motion of many conduction electrons in a wire at room temperature.

My point of view is that at a microscopic level you have a many-electron system, and the current density is described by the operator
$$\hat{j}^{\mu}(x)=-e \bar{\psi}(x) \gamma^{\mu} \psi(x).$$
What's measured by the galvanometer is the expectation value
$$J^{\mu}(x) = \mathrm{Tr} (\hat{\rho} \hat{j}(x)),$$
where $\hat{\rho}$ is a statistical operator at (or close) to thermal equilibrium, i.e., something like $\propto \exp[-(\hat{H}-\mu \hat{Q})/T]$.
Now the galvanometer provides the current,
$$I=\int \mathrm{d} \vec{f} \cdot \vec{J}$$
right away as a pointer reading, because it is providing the above formally noted expectation value due to precisely resolving the measured quantity at this level of resolution.

This is within the standard statistical interpretation of the formalism. Now, how does your thermal interpretation explain this situation, if it denies the validity of the statistical arguments.

 

[DarMM]

Again, just to understand, because I think this is the main source of our mutual misunderstanding:

Let's take my example for the measurement of a current with a galvanometer. From a quantum-theoretical point of view electric current consists of the motion of many conduction electrons in a wire at room temperature.

My point of view is that at a microscopic level you have a many-electron system, and the current density is described by the operator
$$\hat{j}^{\mu}(x)=-e \bar{\psi}(x) \gamma^{\mu} \psi(x).$$
What's measured by the galvanometer is the expectation value
$$J^{\mu}(x) = \mathrm{Tr} (\hat{\rho} \hat{j}(x)),$$
where $\hat{\rho}$ is a statistical operator at (or close) to thermal equilibrium, i.e., something like $\propto \exp[-(\hat{H}-\mu \hat{Q})/T]$.
Now the galvanometer provides the current,
$$I=\int \mathrm{d} \vec{f} \cdot \vec{J}$$
right away as a pointer reading, because it is providing the above formally noted expectation value due to precisely resolving the measured quantity at this level of resolution.

This is within the standard statistical interpretation of the formalism. Now, how does your thermal interpretation explain this situation, if it denies the validity of the statistical arguments.

In the thermal interpretation $J^{\mu}(x)$ (or a smeared version thereof) is a quantity itself not the average outcome for an indeterminate quantity.

 

[vanhees71]

Hm, well, that's just the usual sloppy language of some textbooks on QM to identify the expectation values with the actually observed quantities. I think there's much more behind Arnold's interpretation, which however I still miss to understand :-(.

 

[DarMM]

The Thermal Interpretation isn't identifying $J^{\mu}(x)$ with the observed quantity, it's saying that it is an actual property of the system.

The whole notion of statistics in the TI arises because, as mentioned in my summary, the observed quantities don't accurately reflect this underlying ontic quantity.

 

[A. Neumaier]

how does your thermal interpretation explain this situation

OK. Let us reconsider your example for the measurement of a current with a galvanometer. From a quantum field theoretical point of view, the electric current consists of the motion of the electron field in a wire at room temperature. The thermal interpretation says that at any description level you have an electron field, and the theoretically exact current density is described by the distribution-valued beable (q-expectation)
$$J^{\mu}(x) = \mathrm{Tr} (\hat{\rho} \hat{j}(x))$$
determined by the current operator
$$\hat{j}^{\mu}(x)=-e :\bar{\psi}(x) \gamma^{\mu} \psi(x):,$$
where the colons denote normal ordering and $\hat{\rho}=e^{-S/k_B}$ is the density operator describing the exact state of the galvanometer plus wire. (I usually don't write hats over the operators, but kept them when copying your formulas.)

At this level of description there is no approximation at all; the latter is introduced only when one replaces the exact $S$ by a numerically tractable approximation. At or close to thermal equilibrium, it is well-established empirical knowledge that we have $S \approx (H+PV-\mu N)/T$ (equality defines exact equilibrium). We can substitute this (or a more accurate nonequilibrium) approximation into the defining formula for $J(x)$ to compute a numerical approximation.

Measurable by the galvanometer is a smeared version
$$J^{\mu}_m(x) =\int dz\ h(z) J^{\mu}(x+z)$$
of the exact current density, where $h(z)$ is a function that is negligible for $z$ larger than the size of the current-sensitive part of the galvanometer. The precise $h$ can be found by calibration (as discussed earlier). You didn't explain what your $\vec f$ refers to, but taking your formula as being correct with an appropriate $\vec f$, the galvanometer provides (ignoring the reading uncertainty) the current
$$I=\int \mathrm{d} \vec{f} \cdot \vec{J_m}$$
right away as a pointer reading.

This is without the standard statistical interpretation of the formalism. I made nowhere use of any statistical argument, treating the trace simply as a calculational device - as you do it for defining field correlations.

The only averaging is the smearing needed for mathematical reasons to turn the distribution-valued current into an observable vector, and for physical reasons since the galvanometer is insensitive to very high spatial or temporal frequencies. Note that this smearing has nothing to do with coarse-graining or averaging over microscopic degrees of freedom: It is also needed in (already coarse-grained) classical field theories. For example, in hydromechanics, the Navier-Stokes equations generally have only weak (distributional) solutions that make numerical sense only after smearing. Thus the quantum situation is in the thermal interpretation no different from the classical situation (except that there are many more beables than in the classical case).

Hm, well, that's just the usual sloppy language of some textbooks on QM to identify the expectation values with the actually observed quantities. I think there's much more behind Arnold's interpretation, which however I still miss to understand :-(.

I can see nothing sloppy in my arguments.

 

[vanhees71]

My problem is that there is no physical motivation given for all the formal mathematical manipulations you do. It's of course all right formally, but to understand, why you are doing all these manipulations you need an interpretation, which you still don't provide since you simply say it's not the usual statistical interpretation behind it, but you still don't say, what instead is behind these manipulations. I don't think we come to a conclusion about these different pictures of what an interpretation in principle should provide, repeating the same arguments over and over again.

 

[A. Neumaier]

I consider orthodox quantum mechanics to be incomplete (or maybe inconsistent) [...]
Alice and Bob prepare an electron so that it is a superposition of spin-up and spin-down. Alice measures the spin. According to orthodox quantum mechanics, she either gets spin-up with such-and-such probability, or she gets spin-down with such-and-such probability.
But Bob, considering the composite system of Alice + electron

Orthodox quantum mechanics applies without problems when only a single quantum system is considered, as the Copenhagen interpretation requires.

Inconsistencies appear (only) when one considers simultaneously a quantum system and a subsystem of it (as in your example). The standard foundations (which work with pure states only and treat mixed states as states of incomplete knowledge, with classical uncertainty about the true pure state) simply do not cater appropriately for this situation. The reason is discussed in detail in Subsection 3.5 of Part I of my series of papers. In short, the standard foundations assert

(S1) The pure state of a system (at a given time) encodes everything that can be said (or ''can be known'') about the system at this time, including the possible predictions at later times, and nothing else.

On the other hand, common sense tells us

(S2) Every property of a subsystem is also a property of the whole system.

Now (S1) and (S2) imply

(S3) The pure state of a system determines the pure state of all its subsystems.

But (S3) is denied by the standard foundations, since knowing the pure state of an entangled system does not tell us anything at all about the pure state of its constituents. Nothing in the literature tells us anything about how to determine the pure state of a subsystem from the pure state of a system (except in the idealized, unentangled situation). Not even that - not a single property of a subsystem alone can be deduced from the pure state of the full system if the latter is completely entangled (which is the rule for multiparticle systems)!

The conclusion is that in the standard foundations, we have in place of (S2)

(S??) No property of a subsystem is also a property of the whole system.

This absurd conclusion causes the well-known foundational problems.

Not only that - taken at face value, (S??) would mean that the quantum state of a physics lab has nothing to do with the quantum states of the equipment in it, and of the particles probed there!

This is very strange for a science such as physics that studies large systems primarily by decomposing them into its simple constituents and infers properties of the former from collective properties of the latter.

The thermal interpretation avoids all these problems by taking the state to be an arbitrary monotone linear functional defining q-expectations (thus allowing for mixed states), and the (functions of ) q-expectations of operators as the properties of a system. The properties of a subsystem are then simply the (functions of) q-expectations of operators that act on the subsystem alone. Thus the properties (S1)-(S3) - with the word ''pure'' dropped - are trivially valid!

 

[stevendaryl]

Orthodox quantum mechanics applies without problems when only a single system is considered, as the Copenhagen interpretation requires.

I would say, on the contrary, that the Copenhagen interpretation always involves at least two systems: the system being measured and the measuring device.

The thermal interpretation avoids all these problems by taking the state to be an arbitrary monotone linear functional (allowing for mixed states), and the (functions of ) q-expectations of operators as the properties of a system. The properties of a subsystem are then simply the (functions of) q-expectations of operators that act on the subsystem alone. Thus the properties (S1)-(S3) - with the word ''pure'' dropped - are trivially valid!

Yes, I appreciate that. But I don't completely understand it. If you have, for example, an entangled pair of spin-1/2 particles, $\sqrt{\frac{1}{2}} (|ud\rangle - |du\rangle)$, and someone measures the spin of the first particle, then the result would seem to be something that is not computable from expectations and correlations.

 

[A. Neumaier]

My problem is that there is no physical motivation given for all the formal mathematical manipulations you do. It's of course all right formally, but to understand, why you are doing all these manipulations you need an interpretation, which you still don't provide since you simply say it's not the usual statistical interpretation behind it, but you still don't say, what instead is behind these manipulations.

You have the same problem when introducing in your research work Green's functions as purely calculational tools, deferring the interpretation in terms of experiments to results derived from the formal manipulations.

I don't think we come to a conclusion about these different pictures of what an interpretation in principle should provide, repeating the same arguments over and over again.

I demand from an interpretation only that it gives a clear interface between the theoretical predictions and the experimental record, and in this respect the thermal interpretations serves very well.

People were always doing those formal manipulations where history has shown that it works, while the intuition associated with the formal manipulations changed. Maxwell derived his equations from intuition about a mechanical ether; we think of this today as crutches that are no longer needed, and in fact are detrimental for a clear understanding.

Thus whether or not someone accompanies the formal manipulations with intuitive blabla - about microscopic degrees of freedom, or virtual particles popping in and out of existence, or Bohmian ghost variables, or many worlds, or whatever - is a matter of personal taste. I prefer to cut all this out using Ockham's razor, and leave it to the subjective sphere of individual physicists.

 

[vanhees71]

The orthodox quantum mechanics (which for me is the formalism + the minimal statistical interpretion, i.e., that flavors of Copenhagen that do not envoke some esoterical "quantum-classical cut" nor an even more esoterical "collapse of the state") work perfectly well, because orthodox quantum mechanics does not claim that there are only pure states.

Of course, you have maximal possible knowledge about a system only, if you have prepared it in a pure state. If you now prepare a composite system, described in a product space $\mathcal{H}_1 \otimes \mathcal{H}_2$, with the Hilbert spaces referring to the parts, in a pure state $\hat{\rho}=|\Psi \rangle \langle \Psi \rangle$ you have maximal possible knowledge about this composite systems.

If you choose to ignore one of the parts, by definition you through away information, by choosing to ignore the other part of the system. Then, in general, of course the partial system you choose to consider, is not prepared in a pure state, but in the state given by the partial trace, i.e., if you only like to take notice of part 1 of the system, you describe it, according to the basic definitions of probability theory, by the mixed state given by the partial trace,
$$\hat{\rho}_1=\mathrm{Tr}_2 \hat{\rho}.$$

 

[DarMM]

@A. Neumaier what do you consider the open problems of the Thermal Interpretation?

Establishing that devices in certain canonical scenarios have the metasability properties and slow mode disconnected manifolds required? And also that these in fact lead to discrete outcomes whose long run frequencies have an average equal to the true value $\langle A\rangle$? i.e. that in certain states the device will fall into one slow mode more frequently for example.

 

[vanhees71]

You have the same problem when introducing in your research work Green's functions as purely calculational tools, deferring the interpretation in terms of experiments to results derived from the formal manipulations.I demand from an interpretation only that it gives a clear interface between the theoretical predictions and the experimental record, and in this respect the thermal interpretations serves very well.

People were always doing those formal manipulations where history has shown that it works, while the intuition associated with the formal manipulations changed. Maxwell derived his equations from intuition about a mechanical ether; we think of this today as crutches that are no longer needed, and in fact are detrimental for a clear understanding.

Thus whether or not someone accompanies the formal manipulations with intuitive blabla - about microscopic degrees of freedom, or virtual particles popping in and out of existence, or Bohmian ghost variables, or whatever - is a matter of personal taste. I prefer to cut all this out using Ockham's razor, and leave it to the subjective sphere of individual physicists.

I don't have a problem to define Green's functions. Why should I have a problem? They are calculational tools, as are, e.g., the potentials in electromagnetism which are not observable as well. There are plenty of calculational objects in theoretical physics which do not directly refer to observables. Why should I have problems introducing them to help to calculate predictions for observables?

It's also clear that you can get correct theories from wrong heuristics, as your example of the historical derivation of Maxwell's equations from mechanistic aether models show. Of course, here we have also a perfect example, how physicists are forced to change their heuristics and the interpretation with progress in science: Maxwell himself finally abandoned his own mechanistic aether interpretation. As is well known, the aether was completely abandoned only much later after Einstein's discovery of special relativity, which also lead to a change of interpretation in terms of relativistic space-time descriptions.

The only thing, I still find lacking with your "thermal interpretation" is that it doesn't provide an interpretation at all but just tries to sell the formalism as the interpretation. It precisely does not provide what you yourself defined as the purpose of any interpretation, namely the link between the formalism and the observable facts in the lab!

 

[A. Neumaier]

the Copenhagen interpretation always involves at least two systems: the system being measured and the measuring device.

But the measurement device is treated classically, not in terms of a quantum state.

Yes, I appreciate that. But I don't completely understand it. If you have, for example, an entangled pair of spin-1/2 particles, $\sqrt{\frac{1}{2}} (|ud\rangle - |du\rangle)$, and someone measures the spin of the first particle, then the result would seem to be something that is not computable from expectations and correlations.

The measurement result is primarily a property of the detector, and is computable - up to measurement errors - from the state of the detector (e,g., from the position $\langle q\rangle$ of the center of mass $q$ of the pointer).

As an approximate measurement of the first particle, it is a poor approximation (binary, with large uncertainty) of the the z-component of the spin of the first particle, which - in the thermal interpretation - is the real number $\langle J_3\rangle=\langle i\sigma_3\rangle$.

To reduce the uncertainty one can measure the spin of a whole ensemble of $N$ particles and compute the ensemble average, thereby reducing the uncertainty by a factor of $\sqrt{N}$. For large $N$ this provides a statistical interpretation of the q-expectation.

 

[stevendaryl]

But the measurement device is treated classically, not in terms of a quantum state.

Okay. But that has to be an approximation, because the measurement device is made out of electrons and protons and photons, just like the system being measured.

The measurement result is primarily a property of the detector, and is computable - up to measurement errors - from the state of the detector (e,g., from the position $\langle q\rangle$ of the center of mass $q$ of the pointer).

I don't see how that can be true. In an EPR twin-pair experiment, if Alice measures spin-up for her particle along the z-axis, then Bob will measure spin-down along that axis. The details of Bob's measuring device seem completely irrelevant (other than the fact that it actually measures the z-component of the spin).

 

[vanhees71]

It's of course not true. A measurement device by definition and construction (that's half of the very art of experimentalists, the second being the art of evaluating the measurement results properly, including an estimate of the statistical (sic!) and systematic errors) after interacting with the system to be measured, provides some information of the measured observable of the system.

The most simple example is the Stern-Gerlach experiment. The measurement device is the magnet, leading to an (approximately!) entanglement of the position of the particle (pointer variable) and the spin component in the direction of the (homogeneous part of) the magnetic field. This means to measure that spin component you just have to collect the particles (in the original Frankfurt experiment Ag atoms) on a screen and look at the position. As you see, here the pointer variable is in the very particle itself, namely its position. There's no need for any classical approximation whatsoever (except for the final step of "collecting" the particle on the screen).

 

[A. Neumaier]

what do you consider the open problems of the Thermal Interpretation?

Establishing that devices in certain canonical scenarios have the metasability properties and slow mode disconnected manifolds required? And also that these in fact lead to discrete outcomes whose long run frequencies have an average equal to the true value $\langle A\rangle$? i.e. that in certain states the device will fall into one slow mode more frequently for example.

Yes, this kind of things, which are argued in my papers only qualitatively. I listed some open problems at the end of the Conclusions of Part III. Also, the AB&N work is too complex to be studied in depth by many, and finding simpler scenarios that can be analyzed in a few pages (so that they are suitable for courses in quantum mechanics) would be worthwhile.

 

[stevendaryl]

It's of course not true. A measurement device by definition and construction (that's half of the very art of experimentalists, the second being the art of evaluating the measurement results properly, including an estimate of the statistical (sic!) and systematic errors) after interacting with the system to be measured, provides some information of the measured observable of the system.

The most simple example is the Stern-Gerlach experiment. The measurement device is the magnet, leading to an (approximately!) entanglement of the position of the particle (pointer variable) and the spin component in the direction of the (homogeneous part of) the magnetic field. This means to measure that spin component you just have to collect the particles (in the original Frankfurt experiment Ag atoms) on a screen and look at the position. As you see, here the pointer variable is in the very particle itself, namely its position. There's no need for any classical approximation whatsoever (except for the final step of "collecting" the particle on the screen).

I would say that there SHOULD be no need for any classical approximation, if quantum mechanics were consistent and complete.

 

[vanhees71]

It's of course a challenge, but I don't think that there are any principle problems in understanding macroscopic measurement devices (as in this example the screen used to collect the Ag atoms) quantum theoretical since measurement devices are just macroscopic physical systems as anything around us, and these are quite well understood in terms of quantum many-body theory. I'd say condensed-matter physics is one of the most successful branches of physics, and its very successful research is precisely dealing with the quantum theoretical understanding of the classical properties of macroscopic systems, and measurement devices are just such macroscopic systems manipulated by experimentalists and engineers to enable their use as measurement devices.

That's why I was so inclined to the "thermal interpretation" at first, because I thought it just takes this usual point of view of the macroscopic behavior being described by quantum-many body theory in terms of appropriate coarse-graining procedures, which is a generically statistical-physics argument. Then I learned in this discussion, that I completely misunderstood the three papers, because it's precisely how I should NOT understand the interprtation, but now I'm lost since I've no clue what the interpretation now is meant to be.

 

[A. Neumaier]

Okay. But that has to be an approximation, because the measurement device is made out of electrons and protons and photons, just like the system being measured.

Yes, but Copenhagen says nothing about the nature of this approximation. It takes definite classical measurement values as an irreducible fact. The measurement problem begins precisely when one wants to derive this fact rather than postulate it.

I don't see how that can be true. In an EPR twin-pair experiment, if Alice measures spin-up for her particle along the z-axis, then Bob will measure spin-down along that axis. The details of Bob's measuring device seem completely irrelevant (other than the fact that it actually measures the z-component of the spin).

Well, you surely agree that the pointer position can be calculated (in principle) from the state of the measurement device at the time the reading is done. This has nothing at all to do with what is measured, it is only the fact that the pointer is somewhere where it can be read.

What you and I don't see is how precisely Bob's detector knows which pointer reading to display to conform to the correlated quantum statistics. Somehow, Nature does it, and since we haven't found any deviation from quantum physics, it is presumably a consequence of the Schrödinger dynamics of the state of the universe. In Subsections 4.4 and 4.5 of Part II, I discussed the sense in which this can be partially understood: the extendedness of quantum systems (entangled long-distance states are very fragile extended systems) together with conditional knowledge make things reasonably intelligible to me. In any case, it is in full agreement with the requirements of relativity theory.

 

[stevendaryl]

I would say that there SHOULD be no need for any classical approximation, if quantum mechanics were consistent and complete.

The basic postulate of the minimal interpretation of quantum mechanics is: If you measure an observable, then you will get an eigenvalue of the corresponding operator. But if measurement is definable in terms of more basic concepts, then that rule should be expressible in terms of those more basic concepts.

So for example, an observable is measured when it interacts with a macroscopic system (the measuring device) so that the value of that observable can be "read off" from the state of the macroscopic system. In other words, the microscopic variable is "amplified" to make it have a macroscopic effect.

So the rule about measurement producing an eigenvalue boils down to a claim that a macroscopic measurement device is always in one of a number of macroscopically distinguishable states.

So the minimal interpretation of QM, it seems to me, is equivalent to the following:

Any system, no matter how complex, evolves according to unitary evolution with the exception that a macroscopic system is always in one of a number of macroscopically distinguishable states. If unitary evolution would put the system into a superposition of macroscopically distinguishable states, then the system will pick one, with probability given by the square of the amplitude corresponding to that possibility.

This way of stating the Born rule is, as far as I know, exactly equivalent in its empirical content to the minimal interpretation. But it differs in that it does not claim that measurements produce eigenvalues. That is a derivable consequence (from the definition of "measurement" plus the rules for unitary evolution). So I actually think that this formulation is better. But it explicitly makes a distinction between macroscopic and microscopic observables. This distinction is already implicit in the minimal interpretation, but is hidden by the lack of a clear definition of "measurement".

 

[A. Neumaier]

I don't have a problem to define Green's functions. Why should I have a problem? They are calculational tools, as are, e.g., the potentials in electromagnetism which are not observable as well. There are plenty of calculational objects in theoretical physics which do not directly refer to observables. Why should I have problems introducing them to help to calculate predictions for observables?

But why do you demand more for my calculational tools, the q-expectations? Justify them exactly in the same way as you justify your definition of Green's function, and you'll understand me.

The only thing, I still find lacking with your "thermal interpretation" is that it doesn't provide an interpretation at all but just tries to sell the formalism as the interpretation. It precisely does not provide what you yourself defined as the purpose of any interpretation, namely the link between the formalism and the observable facts in the lab!

I only claim that some of the q-expectations give predictions for actual observations, and how these are to be interpreted is fully specified in my posts #263, #266, and #278 (and elsewhere).

 

[stevendaryl]

Well, you surely agree that the pointer position can be calculated (in principle) from the state of the measurement device at the time the reading is done. This has nothing at all to do with what is measured, it is only the fact that the pointer is somewhere where it can be read.

Let's look at the specific case: You have an electron sent through a Stern-Gerlach device. Depending on the electron's spin, it either is deflected left, and makes a black dot on a photographic plate on the left, or is deflected right, and makes a black dot on a photographic plate on the right.

If the electron is deflected left, then it WILL make a dot on the left plate. So the details of the photographic plate just don't seem relevant, other than the fact that its atoms are in an unstable equilibrium so that a tiny electron can trigger a macroscopic state change.

 

[A. Neumaier]

Let's look at the specific case: You have an electron sent through a Stern-Gerlach device. Depending on the electron's spin, it either is deflected left, and makes a black dot on a photographic plate on the left, or is deflected right, and makes a black dot on a photographic plate on the right.

If the electron is deflected left, then it WILL make a dot on the left plate. So the details of the photographic plate just don't seem relevant, other than the fact that its atoms are in an unstable equilibrium so that a tiny electron can trigger a macroscopic state change.

I completely agree. But this doesn't invalidate what I said:

That there is a dot on the left, say, is a property of the plate that is computable from the state of the plate at the time of looking at it to record the event. For the state of the plate with a dot on the right is quite different from the state of the plate with a dot on the left or that without a dot. Hence the state differentiates between these possibilities, and hence allows one to determine which possibility happened.

The only slighly mysterious thing is why Alice can predict Bob's measurement. Here I don't have a full explanation, but only arguments that show that nothing goes wrong with relativistic causality.

Note also that the prediction comes out correct only when the entangled state is undisturbed and the detector is not switched off at the time the photon hits - things that Alice cannot check until having compared notes with Bob. Thus her prediction is not a certainty but a conditional prediction only.