Undergrad Quantum physics vs Probability theory

[vanhees71]

What else do you need? I also don't need a collapse to understand the fascinating Bell measurements with entangled (multi-)photon states either. The correlation is simply not caused by local interactions of the photons with the measurement devices but is already there due to the preparation in the initial entangled state (though the single-photon properties like polarization states are maximally uncertain, i.e., maximum-entropy mixed states).

 

[QLogic]

What else do you need?

Beyond the S-matrix? This is basically equivalent to saying why would you need to be able to handle finite time processes in QFT. I think our fundamental theory should be able to handle finite-time processes, otherwise how could finite time events dealt with non-rel QM be considered limiting cases of QFT.

I also don't need a collapse to understand the fascinating Bell measurements with entangled (multi-)photon states either.

Of course you don't need collapse to understand Bell correlations and of course the correlations are not caused by local interactions. The point is that you claimed state-reduction has problems with relativistic QFT. I'm saying that it has been mathematically proven that it does not.

However take a complicated multiparticle entangled state, not just the pairs in a simple Bell experiment. Something like the more general correlations considered by Gisin with $L$ particles, $M$ observables and $N$ outcomes also known as $(L,M,N)$ Bell secnarios in the literature.

You have an initial entangled state, then measurements are performed on $R$ of the particles. How do you model the correlations conditioned on these observations for the remaining $L - R$ particles without the state update rule?

 

[vanhees71]

How can it not have problems with relativistic causality, if you claim that instantaneously by measuring a photon's polarization at point A, another photon which is most likely to be registered at a far distant place B, the state collapses from the entangled state before the measurement which is something like
$$[\hat{a}^{\dagger}(\vec{p},H) \hat{a}^{\dagger}(\vec{p}',V)-\hat{a}^{\dagger}(\vec{p}',H) \hat{a}^{\dagger}(\vec{p} V)]|\Omega \rangle$$
to a "product state", which is something like
$$\hat{a}^{\dagger}(\vec{p},H) \hat{a}^{\dagger}(\vec{p}',V) |\Omega \rangle$$
(modulo normlization factors and integration over the momenta such as to have proper wave packets rather than generalized momentum eigenstates of course)?

 

[QLogic]

How can it not have problems with relativistic causality...rest of post

It's just the standard no-signalling results extended to QFT where it's a bit harder to prove. $B$ is not able to infer $A$'s choice of observable from the statistics of observables local to $B$. Thus there is no violation of causality.

That updating of the state is just standard QM where conditioned on one of $A$'s results the global state is a product state. It doesn't mean that $B$ over multiple runs of the experiment can ever learn anything about $A$'s results.

Of course in QFT we never have product states locally anyway, but that's a separate point.

Also how do you model the statistics of the $L - R$ particles conditioned on results on $R$ of them that I mentioned above?

 

[QLogic]

Or are such failures the failure of the assumptions made in modeling phenomena with classical probability theory - for example, assuming events are independent when they (empirically) are not.

But the success of pre-probabilities does not imply that classical probability theory won't work. It does imply that modeling certain physical phenomena is best done by thinking in terms of pre-probabilities instead of making simplifying assumptions of independence and applying classical probability theory directly.

What kind of dependence did you have in mind, the ignoring of which leads to errors?

 

[vanhees71]

It's just the standard no-signalling results extended to QFT where it's a bit harder to prove. $B$ is not able to infer $A$'s choice of observable from the statistics of observables local to $B$. Thus there is no violation of causality.

That updating of the state is just standard QM where conditioned on one of $A$'s results the global state is a product state. It doesn't mean that $B$ over multiple runs of the experiment can ever learn anything about $A$'s results.

Of course in QFT we never have product states locally anyway, but that's a separate point.

Also how do you model the statistics of the $L - R$ particles conditioned on results on $R$ of them that I mentioned above?

Yes sure, from the very foundations of local (microcausal) QFT it's clear that no problems can occur, but just putting the assumption of "state collapse" on top (and it's completely unnecessary too!) destroys this consistency of the formalism.

Look at the concrete experiments: You make a measurement protocol at each of the places and then evaluate them afterwards and postselect the different events. There's no collapse necessary to explain these outcomes but just Born's rule to calculate the probabilities for the outcomes of measurements and compare it with the result of the experiment.

 

[QLogic]

Yes sure, from the very foundations of local (microcausal) QFT it's clear that no problems can occur, but just putting the assumption of "state collapse" on top (and it's completely unnecessary too!) destroys this consistency of the formalism.

It's a theorem found in Hamhalter's book that it doesn't.

Look at the concrete experiments: You make a measurement protocol at each of the places and then evaluate them afterwards and postselect the different events. There's no collapse necessary to explain these outcomes but just Born's rule to calculate the probabilities for the outcomes of measurements and compare it with the result of the experiment.

Of course. However what if one has observed only a subset of the particles and you wish to model the statistics of future experiments. Again as I said if only $R$ have been measured and you wish to model the statistics of the remaining $L - R$, how is this done without conditioning/state reduction?

The classical analogue of what you're arguing is that in probability theory one doesn't need conditioning. I can't see how that is valid.

 

[vanhees71]

Obviously again I don't understand what you are asking. Of course one needs conditioning in both classical and quantum statistics. Is this about philosophical quibbles about the meaning of probabilities in general? If so, it doesn't belong into the quantum physics forum at all (not even into the interpretation subforum).

 

[atyy]

Yes sure, from the very foundations of local (microcausal) QFT it's clear that no problems can occur, but just putting the assumption of "state collapse" on top (and it's completely unnecessary too!) destroys this consistency of the formalism.

Wrong.

Look at the concrete experiments: You make a measurement protocol at each of the places and then evaluate them afterwards and postselect the different events. There's no collapse necessary to explain these outcomes but just Born's rule to calculate the probabilities for the outcomes of measurements and compare it with the result of the experiment.

Whatever you call it, there is no unitary time evolution of the quantum state.

 

[atyy]

Obviously again I don't understand what you are asking. Of course one needs conditioning in both classical and quantum statistics. Is this about philosophical quibbles about the meaning of probabilities in general? If so, it doesn't belong into the quantum physics forum at all (not even into the interpretation subforum).

Rubbish. It is you that rejects standard QM.

 

[QLogic]

Is this about philosophical quibbles about the meaning of probabilities in general?

No. Not remotely.

In every textbook of either quantum mechanics or quantum information that I have read one has state updating as either an axiom or for some quantum information books a very early theorem (books can use different basic axioms). In quantum information state updating is used all the time to condition on measurements.

There are also solid mathematical proofs that state updating is compatible with relativity.

Thus I cannot make sense of the statement that one doesn't need state updating since every textbook has it or the statement that it is incompatible with special relativity since it provably is not.

Of course one needs conditioning in both classical and quantum statistics

Now I am extra confused. State updating is how you condition in quantum probability. They're synonyms. How can you accept conditioning and reject state updating.

What does conditioning without the usual state updating/projection postulate look like since you are advocating this?

Rubbish. It is you that rejects standard QM.

That's what it looks like to me. Perhaps I am mistaken though.

 

[QLogic]

What do you think about Streater's Classical and Quantum Probability?

The famous paper by Redei and Summers is the most cited introduction:
https://arxiv.org/abs/quant-ph/0601158

Here you can see several differences between classical and quantum probability, such as the much stricter conditions under which conditional expectations exist as well as more well known features like entanglement.

 

[vanhees71]

Wrong.
Whatever you call it, there is no unitary time evolution of the quantum state.

Then you change QT to a new theory!

 

[vanhees71]

No. Not remotely.

In every textbook of either quantum mechanics or quantum information that I have read one has state updating as either an axiom or for some quantum information books a very early theorem (books can use different basic axioms). In quantum information state updating is used all the time to condition on measurements.

There are also solid mathematical proofs that state updating is compatible with relativity.

Thus I cannot make sense of the statement that one doesn't need state updating since every textbook has it or the statement that it is incompatible with special relativity since it provably is not.Now I am extra confused. State updating is how you condition in quantum probability. They're synonyms. How can you accept conditioning and reject state updating.

What does conditioning without the usual state updating/projection postulate look like since you are advocating this?That's what it looks like to me. Perhaps I am mistaken though.

I guess it's again some misunderstanding. For me "collapse" is the assumption that by a measurement the state instantaneously changes as a physical process affecting properties of far remote parts of the system instantaneously and this clearly violates causality in relativistic physics. No such thing is needed to calculate conditional probabilities, and the Bell experiments done with entangled photon states are well described within usual local QED without the assumption of such instaneous actions at a distance at all. Also in the evaluation of the real-world experiments you use measurement protocols taken locally and compare them afterwards to choose the wanted subensembles of measured photons. That's the famous "postselection" or "delayed-choice properties" being discussed all the time in Bell experimental setups, all confirming the predictions of QT. We had a long debate about this a while ago discussing several real-world experiments (quantum eraser, entanglement swapping etc.), all of which can be described without invoking a collapse and in accordance with local relativistic QFT.

So, if you say the collapse is compatbible with local relativistic QFT you must mean something different than I assumed above.

 

[QLogic]

For me "collapse" is the assumption that by a measurement the state instantaneously changes as a physical process affecting properties of far remote parts of the system instantaneously and this clearly violates causality in relativistic physics

This explains it then. For you the word "collapse" is interpretation loaded and you are rejecting that interpretation. That's fine I won't go into that.

I just meant the usual state reduction axiom is compatible with relativity where I am taking it in its purely "everyday use" sense of what conditioning looks like in Quantum Theory. Thus I thought you were rejecting conditioning which I couldn't make sense of. Where as you are saying it shouldn't be viewed as process but simply as conditioning.

I think there's no actual disagreement here then.

 

[QLogic]

All would be well, in fact, if some bright mathematician in the 19th century had invented complex probability spaces before QM forced it out. Then, QM would rely on classical PT. It's just that classical PT would have been already enriched by complex probability amplitudes!

You might find it interesting that Bruno De Finetti in his paper:

De Finetti, B. (1937). A proposito di “correlazione.” Supplemento Statistico ai Nuovi problemi
di Politica, Storia ed Economia, 3: 41–57.

recast probability theory in terms of Hilbert spaces and actually found the Tsirelson bound about 40 years before Tsirelson. He even gave these probabilities a non-classical reading. Just a nice note of history.

 

[Stephen Tashi]

For me "collapse" is the assumption that by a measurement the state instantaneously changes as a physical process affecting properties of far remote parts of the system instantaneously and this clearly violates causality in relativistic physics. No such thing is needed to calculate conditional probabilities, and the Bell experiments done with entangled photon states are well described within usual local QED without the assumption of such instaneous actions at a distance at all.

If we say that the calculation of a conditional probability is valid, do we accept that there is some physical process that causes the condition to affect the calculation? - perhaps not a process that is modeled by instantaeous action-at-a-distance. Or does the calculation merely imply a mental process on the part of the person calculating that is physical only in the sense the person calculating is implemented by a physical process? (As Thomas Aquinas wrote: "... for I can think of France and afterwards of Syria, without ever thinking of Italy, which stands between them. Therefore much more can an angel pass from one extreme to another without going through the middle.")For example, suppose I have a value for the probability that it rains on a randomly selected day in February. If I select a day at random and notice it is a cloudy morning, I can revise the probability to be the probability that it rains on a randomly selected day in February that has a cloudy morning. ( I see nothing subjective about such a revision. A scientific theory predicts certain results based on certain "givens". Getting a different answer when different information is given is no more subjective that getting different answers for problem 1 and problem 25 in a textbook.) My own mental agility is the only limitation on how quickly I revise the probability. However, thinking classically, I also imagine that there is some physical process that takes place which makes days with cloudy mornings statistically different that the general population of days. In thinking this way, must I be implicitly thinking of hidden variables?

For example, the paper by Ohanian https://arxiv.org/pdf/1703.00309.pdf deals with the collapse of probability distributions in spacetime, but he uses an example of a card game which seems (to me) to employ "hidden variables" in the form of the cards: "the pre-collapse merely affects what we know when and where, but it does not affect the ultimate outcome of the game—who wins and who loses—which is predetermined by the initial conditions imposed by the initial mailing of the playing cards.".

 

[vanhees71]

It's hard to discuss in such generality. It's better you pick some example of a real-lab experiment. Then it's clear how it works. In the usual Bell measurements like the delayed-choice quantum eraser experiment all you do is to choose subensembles based on the local measurements by Alice and Bob on each of "their" photons (which are simply defined as those photon of the pair measured at the detector placed at A's and B's position in space).

Your weather example makes it very clear that there's nothing mysterious in changing the probabilities given new information. If I have probability for rain on an arbitrary day in February (given by weather data through statistical evaluation just looking at all days of many Februaries in the past), it's of course different from the probability for rain on a day in February which starts cloudy in the morning (again given by whether data through statistical analysis taking into account only all cloudy-in-the-morning days of many Februaries in the past, which is a choosen subensemble of the former). There's nothing collapsing here nor is there anything mysterious that the two probabilities are different.

For me there's also no mystery in the probabilities provided by quantum-theoretical calculations: Of course the probabilities for the outcome of a measurement depend on the selection of the ensembles with different chosen conditions.

 

[atyy]

It's hard to discuss in such generality. It's better you pick some example of a real-lab experiment. Then it's clear how it works. In the usual Bell measurements like the delayed-choice quantum eraser experiment all you do is to choose subensembles based on the local measurements by Alice and Bob on each of "their" photons (which are simply defined as those photon of the pair measured at the detector placed at A's and B's position in space).

Your weather example makes it very clear that there's nothing mysterious in changing the probabilities given new information. If I have probability for rain on an arbitrary day in February (given by weather data through statistical evaluation just looking at all days of many Februaries in the past), it's of course different from the probability for rain on a day in February which starts cloudy in the morning (again given by whether data through statistical analysis taking into account only all cloudy-in-the-morning days of many Februaries in the past, which is a choosen subensemble of the former). There's nothing collapsing here nor is there anything mysterious that the two probabilities are different.

For me there's also no mystery in the probabilities provided by quantum-theoretical calculations: Of course the probabilities for the outcome of a measurement depend on the selection of the ensembles with different chosen conditions.

@vanhees71's statements on this are generally misleading. He rejects collapse to save locality, but locality cannot be saved unless one rejects "reality". However, there is no clear rejection of "reality" in his statements. In fact, he generally conveys the impression that interactions are all local, which cannot be the case (unless one tries something else like many-worlds, or something else),

 

[PeterDonis]

Moderator's note: Thread moved to the quantum foundations and interpretations forum.

 

[Stephen Tashi]

For me there's also no mystery in the probabilities provided by quantum-theoretical calculations: Of course the probabilities for the outcome of a measurement depend on the selection of the ensembles with different chosen conditions.

It's difficult (for me) to express any distinction between QM calculations and the viewpoint you describe, but there are papers that assert that the Schrödinger Eq. is not equivalent to a stochastic process. (e.g. http://www.physik.uni-augsburg.de/theo1/Talkner/Papers/Grabert_PRA_1979.pdf ).

By a "classical" stochastic process, I shall mean this: I imagine a collection of deterministic processes and classify them to be examples of "the same" process $S$. The processes each evolve deterministically in time. To this concept, I add the concept of genuine probability by saying that when I do an experiment on such a process, I pick one of the examples $S$ at random, giving each example an equal probability of being chosen.

From this point of view, if I measure some variable $x$ involved in $S$ at time $t$ then the probability that $x = 5$ at time $t= 2$ may differ from the probability that $x = 5$ at time $t$ given that I also measured $x = 4$ at time $t=1$. The distinction between those probabilities doesn't require any notion that my measurement at time $t=1$ changed the physical state of the process. The distinction between the probabilities is explained by the fact that knowing $x=4$ at $t=1$ reveals that the example we are observing is a member of a proper subset of the examples initially available for selection.

It's hard to discuss in such generality. It's better you pick some example of a real-lab experiment. Then it's clear how it works. In the usual Bell measurements like the delayed-choice quantum eraser experiment all you do is to choose subensembles based on the local measurements by Alice and Bob on each of "their" photons (which are simply defined as those photon of the pair measured at the detector placed at A's and B's position in space).

I don't understand which experiments make a distinction between the above description of a classsical stochastic process and a theory that involves hidden variables. Each example of a classical stochastic process can be thought of as sequence of measurements (e.g. (t=0,x=6), (t=1,x=4),...). There is no explicit hidden variable whose value at t = 0 determines the values of the example at later times. Perhaps there is a clever and abstract way to define such a variable. For example, if I imagine a way to map each example to a distinct real number, then the value of that real number trivially determines all values in the sequence for that example.

 

[vanhees71]

Of course, QT-time evolution is not equivalent to a stochastic Markov process. Why should it be? I don't see any convincing interpretation of the QT probabilities in terms of classical statistical processes, at least not within a local and/or Markovian framework. There was this idea of a stochastic interpretation by Nelson, but I've never found this very convincing.

It's the other way around: The QT description of many-body systems is the so far most fundamental, and the classical statistics can be derived via various levels from QT rather than the other way around.

 

[EPR]

How can this proposal explain something as basic as quantum tunneling as a purely stochastic/deterministic process?

 

[vanhees71]

Which proposal? QM describes quantum tunneling (of course not as stochastic-determinic process).

 

[EPR]

The proposal that classsical stochastic processes can explain quantum tunning.

 

[vanhees71]

They can't!

 

[OCR]

QM describes quantum tunneling (of course not as. . . process)

They can't!

Perhaps you should engage your spellchecker, so we know without ambiguity. . . they can't ?Thank you, and,

Carry on .

.

 

[vanhees71]

I don't know, what you want. I clearly stated that quantum tunneling cannot be described by a stochastic-deterministic process but only with QT.

 

[OCR]

I clearly stated that quantum tunneling cannot be described by a stochastic-deterministic process but only with QT.

Works for me. . . . Carry on. . . . ✔

.

 

[vanhees71]

In which sense does it work for you?

One should remember what "tunnelling" in the strict sense means: It means that a particle prepared in an energy eigenstate can, with some non-zero probability, be registered in regions that are classically forbidden for a particle of this specific energy. There's no way to describe this classically, because it violates classical physics (the energy-conservation law).

It's also not the same as, e.g., overcoming a potential barrier of a particle (as in the famous Kramers's problem) due to thermal fluctuations, which is completely in accordance with classical mechanics and energy conservation because the particle gains some energy from the heat bath to overcome the potential barrier. It's an open system, and thus energy conservation doesn't hold for the particle alone, i.e., it can exchange energy with the heat bath and thus with some probability overcome the barrier. That's a stochastic process, which can be described as a usual Markovian Langevin process (but also as one with colored noise and some memory effect [1]).

[1]
B. Schüller, A. Meistrenko, H. van Hees, Z. Xu, C. Greiner, Kramers's escape rate within a non-Markovian description
Ann. Phys. (NY) 412, 168045 (2019)
arXiv: 1905.09652 [hep-ph]