QFT made Bohmian mechanics a non-starter: missed opportunities?

[martinbn]

Of course, you must be able to say (to some accuracy at least) that each single realization of the system is prepared in this state.

May be as a sloppy way of phrasing it. But strictly you cannot. That is the point of being an ensemble interpretation.

 

[Morbert]

Of course, you must be able to say (to some accuracy at least) that each single realization of the system is prepared in this state.

This is fine to say loosely since everyone will know what you mean. But strictly, according to a minimalist ensemble interpretation, we don't assign any significance to a single system. $|\psi\rangle$ only refers to an ensemble of identically prepared systems, not the state of each member of the ensemble, though the distinction is not always important.

This is also why collapse is not real under this interpretation. Arguably, even time-evolution is not real. All that is physical is the preparation and the dataset once the measurements or sequences of measurements are concluded.

 

[Demystifier]

If you dont know what an ensemble interpretation is, then you shouldnt make statments about it.

I think I know what it is (I think @vanhees71 agrees with me on that), I just don't know what you mean by it. Perhaps you would like to explain it to us?

 

[vanhees71]

Obviously it's not clear what "the ensemble interpretation" is since you also deny that it is possible to prepare single representants of an ensemble in a given state. If this were true, you couldn't use QT at all to describe real-world experiments. That's obviously wrong.

For me the ensemble interpretation means that the only meaning of the quantum state are to provide probabilities for the outcome of measurements on equally prepared systems. The preparation procedure refers to single instances that constitute the ensemble.

 

[vanhees71]

This is fine to say loosely since everyone will know what you mean. But strictly, according to a minimalist ensemble interpretation, we don't assign any significance to a single system. $|\psi\rangle$ only refers to an ensemble of identically prepared systems, not the state of each member of the ensemble, though the distinction is not always important.

This is self-contradictory. How can you prepare each single system "identically" such that it is described by some state $\hat{\rho}$? To build an ensemble you must be able to prepare each single system in such a way to build this ensemble, right?

This is also why collapse is not real under this interpretation. Arguably, even time-evolution is not real. All that is physical is the preparation and the dataset once the measurements or sequences of measurements are concluded.

Of course time-evolution is real. How else do you explain that standard S-matrix theory works in HEP?

 

[martinbn]

I think I know what it is (I think @vanhees71 agrees with me on that), I just don't know what you mean by it. Perhaps you would like to explain it to us?

You say that a single particle has the givne state. That contradicts the main idea of the ensemble interpretation.

 

[vanhees71]

No, it doesn't. How do you come to this idea?

 

[martinbn]

Obviously it's not clear what "the ensemble interpretation" is since you also deny that it is possible to prepare single representants of an ensemble in a given state. If this were true, you couldn't use QT at all to describe real-world experiments. That's obviously wrong.

You can prepare representatives, but they are not in the state. Only ensembles can have states.

For me the ensemble interpretation means that the only meaning of the quantum state are to provide probabilities for the outcome of measurements on equally prepared systems. The preparation procedure refers to single instances that constitute the ensemble.

This sounds more like Copenhagen.

 

[Demystifier]

This is one of the happiest moments in my life, @vanhees71 and me agree against @martinbn .

 

[vanhees71]

You can prepare representatives, but they are not in the state. Only ensembles can have states.

They are representatives of the state you use to describe the ensemble, or how else do you explain the tremendous success of QT in application to real-world observations of Nature?

This sounds more like Copenhagen.

That may well be. The Copenhagen interpretation cover such a wide range of unsharp defined interpretations that nearly all interpretation fall into that category. For me even the ensemble interpretation is quite in the Copenhagen spirit.

 

[Morbert]

This is self-contradictory. How can you prepare each single system "identically" such that it is described by some state $\hat{\rho}$? To build an ensemble you must be able to prepare each single system in such a way to build this ensemble, right?

Given some equivalence class of preparations, you can of course prepare an individual system, but it has no significance. All that is significant is an ensemble of such systems.

Of course time-evolution is real. How else do you explain that standard S-matrix theory works in HEP?

My wording here was probably too strong. What I mean is the significance of time-evolution is the establishment of the frequencies and correlations we expect to see in an experimental dataset, based on the preparation, as opposed to a fine-grained account of the history of a system.

 

[martinbn]

They are representatives of the state you use to describe the ensemble, or how else do you explain the tremendous success of QT in application to real-world observations of Nature?

Yes, this is true. But the individual particles are not in the state. The state does not describe induviduals, just ensembles.

That may well be. The Copenhagen interpretation cover such a wide range of unsharp defined interpretations that nearly all interpretation fall into that category. For me even the ensemble interpretation is quite in the Copenhagen spirit.

 

[martinbn]

This is one of the happiest moments in my life, @vanhees71 and me agree against @martinbn .

If being wrong makes you happy, congrats.

 

[Demystifier]

Yes, this is true. But the individual particles are not in the state. The state does not describe induviduals, just ensembles.

The state describes what we know about the individuals, this is common to Copenhagen, ensemble and Bohmian interpretation. The three interpretations only differ on whether this knowledge is complete or not.

 

[vanhees71]

Yes, this is true. But the individual particles are not in the state. The state does not describe induviduals, just ensembles.

That doesn't make sense. Just take the definition by Ballentine in his textbook:

Postulate 2. To each state there corresponds a unique state operator. The
average value of a dynamical variable $\hat{R}, represented by the operator$\hat{R}, in
the virtual ensemble of events that may result from a preparation procedure
for the state, represented by the operator $\hat{\rho}$, is
$$\langle R \rangle = \frac{1}{\mathrm{Tr} \hat{\rho}} \mathrm{Tr} (\hat{R} \hat{\rho}).$$

Of course he goes on to make the usual definition for the state operator (or statistical operator): It must be a positive semidefinite self-adjoint operator with a finite trace, and it's customary to properly normalize it right away such that $\mathrm{Tr} \hat{\rho}=1$.

 

[vanhees71]

The state describes what we know about the individuals, this is common to Copenhagen, ensemble and Bohmian interpretation. The three interpretations only differ on whether this knowledge is complete or not.

But isn't it complete in any of these interpretations? The Bohmian trajectories are just deriable from the state, i.e., they don't provide any additional "knowledge" not already contained in the states, right?

 

[martinbn]

The state describes what we know about the individuals, this is common to Copenhagen, ensemble and Bohmian interpretation. The three interpretations only differ on whether this knowledge is complete or not.

Well, no, it is not in the ensemble interpretation.

 

[martinbn]

That doesn't make sense. Just take the definition by Ballentine in his textbook:Of course he goes on to make the usual definition for the state operator (or statistical operator): It must be a positive semidefinite self-adjoint operator with a finite trace, and it's customary to properly normalize it right away such that $\mathrm{Tr} \hat{\rho}=1$.

Where does he say that the state describes the individual?!

 

[Demystifier]

But isn't it complete in any of these interpretations? The Bohmian trajectories are just deriable from the state, i.e., they don't provide any additional "knowledge" not already contained in the states, right?

The Bohmian trajectory (singular, not plural) for a single particle is derivable from the state, given its initial position. But the initial position is not derivable, so the initial position is the additional information not present in Copenhagen and ensemble interpretations.

 

[vanhees71]

Then please give a reference, where your flavor of the ensemble representation is clearly stated. Obviously it's not the one, Ballentine defines in his book (and already in his RMP).

 

[vanhees71]

The Bohmian trajectory (singular, not plural) for a single particle is derivable from the state, given its initial position. But the initial position is not derivable, so the initial is the additional information not present in Copenhagen and ensemble interpretations.

That's of course true. In the minimal interpretation such a situation is described by a state (preparation procedure) where the particle is well localized, i.e., you have a sharply peaked "density matrix", $\rho(\vec{x},\vec{x})=\langle \vec{x}|\hat{\rho}|\vec{x} \rangle$, which of course doesn't constrain the state itself very much.

 

[martinbn]

Then please give a reference, where your flavor of the ensemble representation is clearly stated. Obviously it's not the one, Ballentine defines in his book (and already in his RMP).

Why! Your quote doesn't contradict anything i said. Please provide a reference where in an ensemble interpretation the state describes the individual!

 

[vanhees71]

I didn't say that the state describes the individual, but I said that the state is associated to each individual in the sense that it refers to preparation procedures that allow to prepare ensembles described by this state.

I can only again refer to Ballentines book and precisely the quote I've given above. Also see the text following it:

The quantum state description may be taken to refer to an ensemble
of similarly prepared systems. One of the earliest, and surely the most
prominent advocate of the ensemble interpretation, was A. Einstein. His
view is concisely expressed as follows [Einstein (1949), quoted here without
the supporting argument]:
“The attempt to conceive the quantum-theoretical description as
the complete description of the individual systems leads to unnatural
theoretical interpretations, which become immediately unnecessary
if one accepts the interpretation that the description refers to
ensembles of systems and not to individual systems.”

 

[Demystifier]

Well, no, it is not in the ensemble interpretation.

It looks as if you are saying that the ensemble interpretation says absolutely nothing about the individuals. But individuals clearly exist (at least as individual measurement outcomes), so such a version of ensemble interpretation would say nothing about the things that exist. I'm pretty much confident that this is not what Ballentine had in mind.

 

[vanhees71]

Also have a look at the RMP paper, which has it in very precise and efficiently formulated form:

https://doi.org/10.1103/RevModPhys.42.358

 

[Demystifier]

I particularly like the following quote from the Ballentine's paper above: "Thus it is most natural to assert that a quantum state represents an ensemble of similarily prepared systems, but does not provide a complete description of an individual system."

 

[vanhees71]

The question, whether the description is complete or not, is of course somewhat mute. I think, a physical theory is as long considered complete as long there are no observational contradictions to its predictions and as it describes all phenomena. In this sense QT is of course incomplete, because it doesn't provide a satisfactory description of the gravitational interaction. It's, however, not incomplete, for the single reason that it provides "only" probabilistic descriptions for the outcome of measurements on "ensembles of similarly prepared systems". Of course, any probabilistic description says only something about such ensembles, because without ensembles you cannot test the probabilistic description, i.e., "you need enough statistics", which is why, e.g., the LHC was upgraded to "higher luminosities" and the then necessary higher DAQ rates to be handled by the detectors. However, this probabilistic description doesn't need to be a priori "incomplete". It may well be that Nature is inherently probabilistic and thus in this sense "completely" described by probabilistic laws. For me the outcomes of all the Bell experiments, in accordance with Q(F)T, are a strong indication that this might in fact be true!

 

[Demystifier]

In this sense QT is of course incomplete, because it doesn't provide a satisfactory description of the gravitational interaction.

My conjecture/hypothesis is that the key to quantum gravity might be the idea that classical spacetime symmetries are not valid at the quantum level. Bohmian mechanics served as an inspiration, but I defended this conjecture/hypothesis within standard QM, in
https://arxiv.org/abs/2301.04448

 

[WernerQH]

Of course, you must be able to say (to some accuracy at least) that each single realization of the system is prepared in this state.

@martinbn has correctly noted the sloppiness of this statement, and your reference to Ballentine is definitely not the one he asked for.

The word "state" refers to an idealization, to a "typical" or "average" particle, and certainly not to individual members of the ensemble. Its purpose is to convey the correlations that we regularly observe between "preparation" and "measurement" events. Quantum theory is about the correlations between events. On "what's going on" between events the theory is remarkably silent -- we are supposed to take all possibilities occurring in the meantime into account.

 

[vanhees71]

Then, how do you explain that in fact experimentalists can prepare with high accuracy definite states of individual systems?

 

[martinbn]

Then, how do you explain that in fact experimentalists can prepare with high accuracy definite states of individual systems?

Do you actually realise how inconsistent your statements are!

 

[WernerQH]

Then, how do you explain that in fact experimentalists can prepare with high accuracy definite states of individual systems?

Of course there are correlations, and we wouldn't have evolved without a keen sense for them. (Think of Pavlov's dog!)

"Definite" states of "individual systems" are constructions of your mind that it foists on the real world.

 

[vanhees71]

That doesn't make sense. Quantum opticians can with high precision prepare entangled photon pairs or how else do you explain the precise confirmation of the quantum-theoretical predictions? I don't see, what's inconsistent with Balentine's standard interpretation of the quantum state as being descriptions of preparation procedures of individual systems.

 

[WernerQH]

That doesn't make sense.

Exactly! Perhaps you should read Ballentine more carefully.

 

[vanhees71]

I didn't mean that Ballentine makes no sense but your claim that the standard interpretation of the state within the minimal interpretation were wrong. You also didn't clearly specify, what you think the "right" interpretation is.