Undergrad Is the Following How Most Students Think of Einstein's View Of QM

[vanhees71]

I first became interested in QM just after finishing my degree and reading In Search of Schrodinger's Cat by John Gribbon. He suggested if you want the detail studying Dirac's Principles of QM and Von-Neumann's Mathematical Foundations. Bad move. Von-Neumann was a breeze - it simply was an extension of Hilbert's spaces I had done as one of my subjects - but Dirac was another matter - especially after Von-Neumann's scathing attack on his math. I originally sided with Von-Neumann and thought Dirac mathematically dubious - how wrong I was - but that took a few years to dawn on me. BTW to newbies do not learn QM from either of those books - get them later for your reference library - Gribben was wrong - other books are MUCH better to start with. Anyway Gribben discussed Bell at length but no detail in Von-Neumann or Dirac.

Thanks
Bill

It's a bit ironic. Of course von Neumann gave the first mathematical strict formulation of QT within then standard Hilbert-space theory. Dirac's physicist's approach to what is today called distributions of course was irresistable for mathematicians to make rigorous, because it worked so well. The $\delta$ distribution was, however, not first invented by Dirac but already earlier by Sommerfeld in some paper about electrodynamics. I don't go into the physical part of von Neumann's book, which I'd not recommend to study at all ;-).

 

[vanhees71]

There is a conjecture (asymptotic safety http://www.percacci.it/roberto/physics/as/faq.html) that quantized Einstein-Hilbert action is renormalizable in a non-perturbative sense. If someone proved that conjecture, would you then say that QT is complete?

Yes, when there is a working quantum theory of gravitation in accordance with all observables, I'd say there's no incompleteness left.

 

[Demystifier]

Yes, when there is a working quantum theory of gravitation in accordance with all observables, I'd say there's no incompleteness left.

But what if there are two different renormalizable theories of quantum gravity, both of which are consistent with currently existing experimental data? The two theories may have different predictions at very high energies, but with current technologies such high energies cannot be achieved in the laboratories. It that was the case, would you say that QT is complete today?

 

[vanhees71]

Then it's of coarse a question, which of the two theories is correct (or maybe whether neither of them is correct), which has to be decided somehow by experiment (maybe astronomical observations). I think one of the reasons, why there's no satisfactory quantum theory of gravitation, is that there are no observations of "quantum-gravity effects". All observed about gravity is well-described with classical GR, because gravitational interactions play only a major role for macroscopic objects, and so far classical GR (usually tested in the PPN formalism as far as binary systems are concerned, which provide the most accurate tests of GR, including pulsar timing as well as the LIGO/VIRGO measurements of gravitational waves from BH-BH, BH-NS, and (maybe) BH-NS mergers).

 

[Elias1960]

I'm confused. What do you think the EPR paper proved?

I'm confused for decades concerning what the EPR paper might have proven. I can't tell!

That from realism (in the quite weak but well-defined variant of the EPR criterion) and Einstein causality it follows that QT is incomplete.

 

[vanhees71]

For me the EPR criterion is far from eing well-defined and clear in its meaning. It starts with the assumption that we can measure something without disturbing the object, which is impossible even in the classical realm. So the criterion about "reality" is just an empty phrase at best.

In the quantum realm it's obvious that we cannot measure anything without disturbing it such that the disturbance can be neglected. If we deal with, e.g., an elementary charge (e.g., a proton) and want to measure properties of the proton, e.g., its position we need either another charged particle we can scatter at the proton, and we cannot make the electric charge of this particle smaller than that of the proton, i.e., using the em. force between charges to measure the position, we cannot do that without disturbing the proton considerably, or we use an uncharged particle, like a photon with the well-known consequences discussed by Heisenberg (and in more detail by von Weizsäcker) in the famous "Heisenberg-microscope gedankenexperiment".

The same holds the more for "preparation procedures" defining states of an elementary particle, preparing the particle in a state with a rather well defined position the standard Heisenberg uncertainty principle tells us that its momentum must be rather indetermined and vice versa. So you cannot prepare a particle in a pretty well defined position without disturbing it in such a way that it's momentum stays pretty well defined too.

That's not only a prediction of QT but an experimental fact which is not in accordance with the very assumption in what EPR consider "realistic". So their notion of realism implies that if there's something real, it's not in accordance with our experience, which is however not in accordance with the very fact that we can describe all this experience in very accurate agreement with this very experience by QT. We can even use these quantum-theoretical predictions to manufacture fancy equipment like lasers, semi-conductor based electronics, etc. I'd say the "realism" of QT (i.e., inherent randomness of the outcome of measurements on undetermined observables) is much more in accordance with "reality" than EPR's idea of realism as far as it is well-defined at all.

 

[RUTA]

For me the EPR criterion is far from eing well-defined and clear in its meaning. It starts with the assumption that we can measure something without disturbing the object, which is impossible even in the classical realm. So the criterion about "reality" is just an empty phrase at best.

From this I infer that you would likewise claim classical physics is not well-defined? We talk about the properties of classical objects in the absence of measurement as well.

 

[PeterDonis]

from realism (in the quite weak but well-defined variant of the EPR criterion) and Einstein causality

What are the definitions of "realism" and "Einstein causality"?

 

[EPR]

The EPR argument aimed to prove that particles have well defined values before measurement and thus QT was incomplete. But their thought experiment only confirmed that they don't have, giving further credence to QM. This is a very major stumbling block towards building an ontology from the bottom up.

 

[Elias1960]

What are the definitions of "realism" and "Einstein causality"?

The definition of realism is what made the EPR paper famous:

We shall be satisfied with the following criterion, which we regard as reasonable: If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quality, then there exists an element of physical reality corresponding to this physical quantity.

Another important definition given in that paper is that of completeness:

Every element of the physical reality must have a counterpart in the physical theory.

For Einstein causality, as far as it is relevant for the EPR argument, Bell has found the following quote:

"But on one supposition we should, in my opinion, absolutely hold fast: the real factual situation of
the system $S_2$ is independent of what is done with the system $S_1$, which is spatially separated from the former." A. EINSTEIN in Albert Einstein, Philosopher Scientist, (Edited by P. A. SCHILP) p. 85,
Library of Living Philosophers, Evanston, Illinois (1949).

The EPR paper itself simply presumes that one can arrange the two systems in a way that one can be sure that they no longer interact.

For this purpose let us suppose that we have two systems, I and II, which we permit to interact from the time t=0 to t=T, after which time we suppose that there is no longer any interaction between the two parts.
...
On the other hand, since at the time of the measurement the two systems no longer interact, no real change can take place in the second system in consequence of anything which may be done to the first system.

This is, in fact, a side effect of the non-optimal choice of what is measured (P and Q). Before measuring some Q, we are not in a position to say that they both have space-time positions A and B which exclude any interactions by Einstein causality. This part of the argument can be made only in the much better later arrangement where spin is measured and both A and B have well-defined locations in spacetime.

 

[PeterDonis]

The definition of realism is what made the EPR paper famous

For Einstein causality, as far as it is relevant for the EPR argument, Bell has found the following quote

Ok, so by these definitions, the fact that violations of the Bell inequalities have been observed experimentally shows that it is impossible for both realism and Einstein causality to be true, yes?

 

[Elias1960]

Ok, so by these definitions, the fact that violations of the Bell inequalities have been observed experimentally shows that it is impossible for both realism and Einstein causality to be true, yes?

Yes.

It starts with the assumption that we can measure something without disturbing the object, which is impossible even in the classical realm. So the criterion about "reality" is just an empty phrase at best.

That means we cannot assume that the measurement made by Alice does not disturb the particle at B, even if A and B are spacelike separated? Something completely anti-relativistic which I did not expect to hear from you.

That's not only a prediction of QT but an experimental fact which is not in accordance with the very assumption in what EPR consider "realistic". So their notion of realism implies that if there's something real, it's not in accordance with our experience, which is however not in accordance with the very fact that we can describe all this experience in very accurate agreement with this very experience by QT.

I'd say the "realism" of QT (i.e., inherent randomness of the outcome of measurements on undetermined observables) is much more in accordance with "reality" than EPR's idea of realism as far as it is well-defined at all.

Both claims are in conflict with the elementary point that there exist realistic interpretations, and with dBB even a deterministic one. The realistic interpretations are in agreement with the EPR criterion, it simply does not give much once there is no strong enough notion Einstein causality to exclude that Bob's measurement distorts the particle of Alice.

 

[bhobba]

II don't go into the physical part of von Neumann's book, which I'd not recommend to study at all ;-).

Neither would I - just because of it's fame and infamous mistake about no go theorems as a reference in your library. If you have a good background in math (and I do mean good - it's just on the verge of my ability) I would consider Quantum Mechanics for Mathematicians by Leon Takhtajan. It is meant for second-year
graduate students in math - and that is its level - believe me. It adopts the approach, which goes back to Dirac, and to which I subscribe, that classical mechanics and quantum mechanics are just two realizations of what a physical theory that uses the notions of observables, states, measurement, and the time evolution dynamics would look like. Of the founders of QM it's one reason I think Dirac stands up best to modern views on QM - just a personal take. He concentrated on the math, not trying to understand it in terms of the classical world of our experience, which how to put it nicely, may not be fruitful.

The author has some parts of the book on the course he gives on it - Lectures on Quantum Mechanics - that can easily be found by an internet search. Have a look and you will appreciate what some wit said - when mathematicians get a hold of a physical theory it becomes unrecognizable to physicists. Having read a few such tome's it unfortuneately has more than a grain of truth.

I don't know why, but this jogged my memory, I have been meaning for a while now to get Weinberg's book on QM and ordered it. Despite my background in math it is likely more to my taste.

Thanks
Bill

 

[vanhees71]

From this I infer that you would likewise claim classical physics is not well-defined? We talk about the properties of classical objects in the absence of measurement as well.

Classical physics is well-defined, but an approximation. It is understandable by coarse-graining of quantum theory. The classical behavior of macroscopic observables is an emergent phenomenon and understandable in terms of statistical averaging over many microscopic degrees of freedom.

 

[vanhees71]

Yes.

That means we cannot assume that the measurement made by Alice does not disturb the particle at B, even if A and B are spacelike separated? Something completely anti-relativistic which I did not expect to hear from you.

No, that's another wrong conclusion in the EPR paper. The problem is not action at a distance but inseparability, as Einstein correctly said in his paper where he is criticizing his own EPR paper. There is no action at a distance in local relativistic QFT by construction. The observed strong correlations in Bell experiments is due to the preparation procedure of the particles in an entangled state. In the original EPR paper it's the entanglement due to momentum conservation and thus the entanglement of the particles momenta (total momentum 0 in the CM frame) and relative position. Note that these are compatible observables on the complete (!) quantum system consisting of the two particles, which in this way are indeed "inseparable" according to QT, and this made the trouble for Einstein not some spooky action at a distance.

Both claims are in conflict with the elementary point that there exist realistic interpretations, and with dBB even a deterministic one. The realistic interpretations are in agreement with the EPR criterion, it simply does not give much once there is no strong enough notion Einstein causality to exclude that Bob's measurement distorts the particle of Alice.

Despite some claims in the literature, I've not seen a convincing dBB interpretation of relativistic QFT, and for non-relativistic physics actions at a distance are no problem to begin with but the standard case.

 

[vanhees71]

Neither would I - just because of it's fame and infamous mistake about no go theorems as a reference in your library. If you have a good background in math (and I do mean good - it's just on the verge of my ability) I would consider Quantum Mechanics for Mathematicians by Leon Takhtajan. It is meant for second-year
graduate students in math - and that is its level - believe me. It adopts the approach, which goes back to Dirac, and to which I subscribe, that classical mechanics and quantum mechanics are just two realizations of what a physical theory that uses the notions of observables, states, measurement, and the time evolution dynamics would look like. Of the founders of QM it's one reason I think Dirac stands up best to modern views on QM - just a personal take. He concentrated on the math, not trying to understand it in terms of the classical world of our experience, which how to put it nicely, may not be fruitful.

The author has some parts of the book on the course he gives on it - Lectures on Quantum Mechanics - that can easily be found by an internet search. Have a look and you will appreciate what some wit said - when mathematicians get a hold of a physical theory it becomes unrecognizable to physicists. Having read a few such tome's it unfortuneately has more than a grain of truth.

I don't know why, but this jogged my memory, I have been meaning for a while now to get Weinberg's book on QM and ordered it. Despite my background in math it is likely more to my taste.

Thanks
Bill

Weinberg's QM book is a gem, as any of his textbooks. I'm only a bit puzzled, why he thinks the quantum foundations and the socalled measurement problem are still not understood. That's his conclusion of his very lucid chapter on foundational questions.

Of all the founding fathers of course Dirac is the most profound, concerning interpretational issues. It's close to my preferred shutup-and-calculate interpretation (though in his book he subscribe to collapse, but that seems to be part of the of the Copenhagen hype of the early days of QT, which I don't understand either, because it's usually very unsharp philosophical suggestion rather than objective mathematical and physical analysis).

 

[Elias1960]

No, that's another wrong conclusion in the EPR paper. The problem is not action at a distance but inseparability, as Einstein correctly said in his paper where he is criticizing his own EPR paper.

If you and Einstein think that inseparability is another problem, fine. The problem for Einstein causality does not go away if some other problem appears, they can live together nicely.

There is no action at a distance in local relativistic QFT by construction.

No, the construction is the same standard QM. So the Bell inequalities are violated too. All you have is a no signalling theorem.

Note that these are compatible observables on the complete (!) quantum system consisting of the two particles, which in this way are indeed "inseparable" according to QT, and this made the trouble for Einstein not some spooky action at a distance.

You think I have to care what made the trouble for Einstein? Is that really important? We actually know much more trouble for quantum foundations after Bell and the experiments supporting the violation of the BI. This trouble has a simple and straightforward solution, namely accepting a preferred frame, but this solution is somehow evil, anathema. Its so horrible that many people even reject realism and causality (inclusive Einstein causality, given that to name signal "causality" a causality is an exaggeration).

Despite some claims in the literature, I've not seen a convincing dBB interpretation of relativistic QFT, and for non-relativistic physics actions at a distance are no problem to begin with but the standard case.

I have given you the reference to the paper many times, if you ignore it, your choice. The point is simply that it exists without problems at least for bosons, and nobody has argued with good arguments that it doesn't. If it convinces you or not is not an issue at all.

 

[RUTA]

Classical physics is well-defined, but an approximation. It is understandable by coarse-graining of quantum theory. The classical behavior of macroscopic observables is an emergent phenomenon and understandable in terms of statistical averaging over many microscopic degrees of freedom.

My point is that classical physics makes exact predictions and uncertainty is introduced by the measurement process of those exact predictions. Likewise, QM makes exact predictions and uncertainty is introduced by the measurement of those exact predictions. That doesn’t make either theory ill-defined.

 

[.Scott]

I would not be surprised if additional constraints were discovered on how basic Physics works - beyond those described by current QM. I view the apparent "random" result from QM experiments as uncovering information - rather than manufacturing it from nothing.

Although my initial reaction to Bell's Inequality (I was around when it was published) was critical (no experiment at the time could capture a sufficient portion of the particles to exclude local explanations), I never doubted that there had to be non-local features in Physics. If information about a particle was never distributed beyond a single point at a time, how could particles ever interact?

In that sense, my tendency is to view QM as "incomplete".

 

[.Scott]

My point is that classical physics makes exact predictions and uncertainty is introduced by the measurement process of those exact predictions. Likewise, QM makes exact predictions and uncertainty is introduced by the measurement of those exact predictions. That doesn’t make either theory ill-defined.

The uncertainty is not introduced by the measurement process. It is inherent in what is being measured. The predictions that QM makes are most commonly probability distributions - not a specific result but a distribution of possible results. So when the experiment is repeated hundreds of time, QM is verified when the distribution of results matches the QM prediction.

 

[RUTA]

The uncertainty is not introduced by the measurement process. It is inherent in what is being measured. The predictions that QM makes are most commonly probability distributions - not a specific result but a distribution of possible results. So when the experiment is repeated hundreds of time, QM is verified when the distribution of results matches the QM prediction.

QM makes exact predictions of probabilities and those probabilities are then measured to within experimental uncertainty. In that sense it is as well-defined as any other theory of physics.

 

[A. Neumaier]

Classical physics is well-defined, but an approximation.

Classical mechanics is fully well-defined, but classical electromagnetism not quite.

What is not well-defined on the formal, conceptual level is the notion of measurement - neither in the classical nor in the quantum case.

This is the true incompleteness of contemporary physics. I side with Einstein.

 

[Elias1960]

What is not well-defined on the formal, conceptual level is the notion of measurement - neither in the classical nor in the quantum case.

This is the true incompleteness of contemporary physics. I side with Einstein.

No. Such complex things like measurements don't need something on the formal, conceptual level. It is the theory which decides what is observable. What counts as measurement can be left open, it has no fundamental importance.

The problem appears once one tries to use such a complex thing like measurement as a fundamental entity. It has no place on the fundamental level.

Let's note that there is also no problem with statistical theories which use measurements as a basic, fundamental notion, as long as one does not try to sell it as a fundamental, complete theory. As long as it remains clear that the measurement is something quite complex, and this complexity is simply not considered by the statistical theory (so that it is, from the start, incomplete) there is nothing to object against them.

 

[vanhees71]

If you and Einstein think that inseparability is another problem, fine. The problem for Einstein causality does not go away if some other problem appears, they can live together nicely.

In local relativistic QFTs by construction there is no problem with Einstein causality. The microcausality condition ensures that no action whatsoever can cause effects at spacelike separated events. So this problem is already solved by construction.

The inseparability is an established fact of science. With high accuracy all Bell tests ever done are in agreement with the predictions of Q(F)T: Thus we have a theory obeying Einstein locality and at the same time are in agreement with the violation of the Bell inequatlity. Everything lies indeed together nicely, but not by violating fundamental principles but providing a consistent description in terms of relativistic local QFT.

 

[vanhees71]

Classical mechanics is fully well-defined, but classical electromagnetism not quite.

What is not well-defined on the formal, conceptual level is the notion of measurement - neither in the classical nor in the quantum case.

This is the true incompleteness of contemporary physics. I side with Einstein.

What is not well-defined with classical electromagnetism? Of course the radiation reaction problem assuming point particles is something that immediately comes into mind, but this tells me only that there are no classical point particles, which is not a very surprising conclusion.

What's not understood concerning measurements? We meausure with great success things all the time. What should be a conceptual problem?

 

[A. Neumaier]

Classical physics is well-defined, but an approximation.

Classical mechanics is fully well-defined, but classical electromagnetism not quite.

No. Such complex things like measurements don't need something on the formal, conceptual level. It is the theory which decides what is observable. What counts as measurement can be left open, it has no fundamental importance.

Since the primiive notion of measurement is already built into Born's rule, the latter is conceptually vacuous without a specification on the formal, conceptual level. The latter is needed in order to give more than heuristic meaning to Born's rule.

Thus the common foundations of quantum mechanics are incomplete unless theory defines what a measurement is, and hence gives an unambigous meaning to Born's rule.

Let's note that there is also no problem with statistical theories which use measurements as a basic, fundamental notion, as long as one does not try to sell it as a fundamental, complete theory. As long as it remains clear that the measurement is something quite complex, and this complexity is simply not considered by the statistical theory (so that it is, from the start, incomplete) there is nothing to object against them.

This confirms my argument.

That's the whole point of Einstein's critique: A statistical theory is necessarily incomplete.

This includes Bohmian mechanics, which, though deterministic, is intrinsically statistical since its derivation of quantum mechanics is based on the unverifiable quantum equilibrium hypothesis.

 

[A. Neumaier]

What is not well-defined with classical electromagnetism? Of course the radiation reaction problem assuming point particles is something that immediately comes into mind

Yes, that's enough.

What's not understood concerning measurements? We measure with great success things all the time. What should be a conceptual problem?

Being successful is different from being complete. We measured things long before there was any conceptual theory at all.

 

[vanhees71]

Exactly. I don't understand what's needed conceptually to define a measurement other than what's given by the very construction of the meausurement devices in the lab. Most conceptual papers on the measurement problem lack in not giving a clear description of a real-world measurement device, such that a physicist cannot even understand where the apparent problem is.

 

[A. Neumaier]

Exactly. I don't understand what's needed conceptually to define a measurement other than what's given by the very construction of the meausurement devices in the lab.

Yes, that's evident. You are too little interested in the conceptual side of measurement to care about such an understanding.

A conceptual definition is needed to be sure of the meaning of Born's rule.

How can Born's rule state to infinite precision (since otherwise one cannot deduce from it the exact rule for expectation values) a universal fact about arbitrary measurement results - of only informally defined measurement devices that

• have a finite resolution only, a resolution that depends on the measurement device and not only on the quantity measured?
• may need days of calibration to be tuned to maximal accuracy?
• may need many pages for the justification of why they measure to the claimed high precision?
• weren't conceived of at the time the rule was formulated?

 

[vanhees71]

Again, since QT, including Born's rule, leads to a very good agreement between theory and experiment, from a physical point of view that's what justifies the rule (together with the rest of the formalism). Of course, a real-world experiment always needs the detailed study of the imperfections of the used measurement devices, but that's part of experimental physics not of concepts of the theory.