Where does a quantum experiment *begin*?

[ShayanJ]

Also note that there's no collapse of the state as a whole via the measurement of either A or B. It's only such that if A finds H, she knows that B's photon will be found to have polarization B, but for Bob that doesn't change anything, i.e., the only thing he knows is that he will find with probability 50% either H or V. Also A finds with 50% probability H. So everything is consistent, and there is no spooky action at a distance, which is implied by the assumption of a collapse, but as you see, we don't need the collapse to understand the correlations. Further according to QT you cannot say more about the outcome of these measurements than the said probabilities, and the understanding is that the polarization of the single photons is really maximally indetermined.

What you describe doesn't need collapse only if we make the assumption that the quantum state is subjective, so after A measures her photon, she assigns a pure state to the B's photon but B himself assigns a mixed state to his photon. Otherwise if you want to assume that the quantum state is objective, your own description leads to collapse.

 

[Demystifier]

If the collapse is not caused by the interaction between the measured system and the measurement device, by what is it caused then?

I think that, by "collapse", @atyy means what I call the "update". The update is nothing but a thinking tool. The update is a process in the mind of a person who thinks about results of measurement and their interpretation in terms of quantum theory. There is no update without a person who understands some quantum physics. At the neurological level, the relevant processes in the brain can very well be described by local classical physics. In this sense, the update is caused by local interactions between different parts of the brain. For the update, one does not even need a real measurement in the laboratory. It is sufficient to think about thought experiments. As a theoretical physicist, I make quantum updates very often.

 

[vanhees71]

What you describe doesn't need collapse only if we make the assumption that the quantum state is subjective, so after A measures her photon, she assigns a pure state to the B's photon but B himself assigns a mixed state to his photon. Otherwise if you want to assume that the quantum state is objective, your own description leads to collapse.

Sure. That's the same with "classical probabilities". If I through a dice the probaility to get "6" is 1/6 and I may look at it and find it shows "6". Then the probability is 1 for showing 6, but if I don't let you see the result, all you can do is still to assign the probability 1/6 to get "6". That's nothing specific to QT probabilities.

 

[ShayanJ]

I think that, by "collapse", @atyy means what I call the "update". The update is nothing but a thinking tool. The update is a process in the mind of a person who thinks about results of measurement and their interpretation in terms of quantum theory. There is no update without a person who understands some quantum physics. The relevant processes in the brain can very well be described by local classical physics. In this sense, the update is caused by local interactions between different parts of the brain. For the update, one does not even need a real measurement in the laboratory. It is sufficient to think about thought experiments. As a theoretical physicist, I make quantum updates very often.

The problem with these discussions between you,atyy and vanhees71 (with helpful comments from stevendaryl of course!) that come up from time to time, continues exactly the same and never comes to a conclusion, is collapse is never exactly defined by you and atyy. In this thread I can see at least three different meanings to the concept of collapse and I'm never sure which one you two are talking about. So I think its better that you two come to a consensus about this before another discussion with vanhees71!

 

[Demystifier]

The problem with these discussions between you,atyy and vanhees71 (with helpful comments from stevendaryl of course!) that come up from time to time, continues exactly the same and never comes to a conclusio, is collapse is never exactly defined by you and atyy. In this thread I can see at least three different meanings to the concept of collapse and I'm never sure which one you two are talking about. So I think its better that you two come to a consensus about this before another discussion with vanhees71!

You are absolutely right!
But I think I explained pretty well that by "collapse" I really mean the mental process which would better be called the update. And I think @atyy has the same meaning in mind. If we could all agree to call it update, and not to use the dirty c-word, I think the problems would disappear.

 

[ShayanJ]

But I think I defined pretty well that by "collapse" I really mean the mental process which would better be called the update.

Do you agree that in the description given in the post #210, only A has to update the state she assigns to B's photon and B doesn't update the state he assigns to his photon?

I think @atyy has the same meaning in mind.

I doubt it!

I don't discuss this because if all you have is unitary evolution, you will end up with unitary evolution of the universe with all the problems of interpretation including MWI etc.

 

[Demystifier]

My aim in this thread is to defend the minimal interpretation or shut up and calculate because it works.

The only honest way to defend the shut-up-and-calculate doctrine is to shut up and calculate. Obviously, this is not what you are doing.

 

[vanhees71]

You are absolutely right!
But I think I explained pretty well that by "collapse" I really mean the mental process which would better be called the update. And I think @atyy has the same meaning in mind. If we could all agree to call it update, and not to use the dirty c-word, I think the problems would disappear.

Well, then we agree, and can stop the discussion. I'm pretty sure, however, that atyy has another meaning of collapse in mind, because he always denies the fundamental concept of locality of interactions in relativistic local QFT (at least I understand his arguments in that way).

 

[Demystifier]

An experiment happens in the lab and not in Hilbert space.

I agree. But I think it is still not clear where do quantum interactions happen? In the lab? In the Hilbert space? Somewhere else?

 

[vanhees71]

Well interactions happen in the lab too. You can have an entire universe consisting of particles not interacting with any of our detectors at all. It's completely irrelevant to us then, because it has no effect whatsoever to detectors in the lab!

 

[Demystifier]

Well, then we agree, and can stop the discussion. I'm pretty sure, however, that atyy has another meaning of collapse in mind, because he always denies the fundamental concept of locality of interactions in relativistic local QFT (at least I understand his arguments in that way).

Then let us wait for him to clarify his position.

 

[ddd123]

Come on, if you say there is a collapse, it can only be caused by the interaction of the particle with the measurement apparatus. If you say there is no interaction, you cannot measure anything.

How about the Elitzur-Vaidman bomb tester? 1/4 of the time a measurement without interaction occurs. If there were interaction, the bomb would explode. If there weren't measurement, you wouldn't know that the bomb works.

Thanks for the long reply above but what I meant involved compound measurements. In your modelling, with two successive measurements you have to change your psi in between non-unitarily to get to a prediction consistent with the experimental result. What I think atyy is saying is this: for the time being minimal has to include collapse as a postulate, otherwise you're simply hoping that it would not be necessary if you modeled the measurement device quantum mechanically. You haven't proven that state vector reduction is not necessary, you hope it isn't.

 

[Demystifier]

Well interactions happen in the lab too.

Well, I find it confusing. You have defined interactions very precisely in a mathematical language, in terms of local Lagrangians (e.g. QED). But I don't see Lagrangians in the lab. So if you claim that interactions happen in the lab, and not in the Hilbert space, then it looks as if you need a new definition of interaction.

 

[Demystifier]

How about the Elitzur-Vaidman bomb tester? 1/4 of the time a measurement without interaction occurs. If there were interaction, the bomb would explode. If there weren't measurement, you wouldn't know that the bomb works.

Perhaps the Elitzur-Vaidman bomb does not involve an interaction in the lab. But it definitely involves an interaction that happens in the Hilbert space.

 

[vanhees71]

Sure, you have a theory with all its math. The theory predicts the outcome of measurements (in the case of QT probabilities for finding certain values of observables), which you can compare with observations. If the predictions are correct (within the uncertainties of measurements and statistics) you call it a successful theory and use it to design further experiments etc.

An interaction happens, e.g., at the LHC every time two protons out of the two beams collide and also the produced particles are registered by the detectors through interactions of them with the detector. Of course, there's nowhere a Fock space, action functionals and the like mathematical abstracta involved.

As already in Newtonian mechanics, you call "interactions" (or "forces") what causes changes of states, and that's well observable in the lab! If I kick a ball, it will move with a different momentum than before, which is a well observable fact about the ball and the (in this case electromagnetic) interaction of my foot with the ball.

 

[Demystifier]

you call "interactions" (or "forces") what causes changes of states, and that's well observable in the lab!

What do you mean "states"?
States in the lab, such as actual position of a macroscopic pointer?
Or states in the Hilbert space, such as |pointer up> + |pointer down>?

A related question: Are quantum forces deterministic or random?

 

[vanhees71]

Sure, states in the lab. Physics is about states in the lab. That's why I always write a state is represented by a statistical operator or an observable is represented by a self-adjoint operator in a Hilbert space etc. Of course this refers to the mathematical formalism. An observable itself is defined operationally by a measurement procedure (or an equivalence class of measurement procedures). Analogously states are defined as equivalence classes of preparation procedures.

 

[Demystifier]

Sure, states in the lab.

Fine, so states in the lab can change. These changes are caused by local forces. The local forces may act in a non-deterministic way. Am I right so far?

But changes are not the only thing observed in the lab. Another observed thing are correlations between the changes. So what causes the correlations? Are correlations also caused by those local forces?

 

[atyy]

Come on, if you say there is a collapse, it can only be caused by the interaction of the particle with the measurement apparatus. If you say there is no interaction, you cannot measure anything.

But that interaction is not in the Hamiltonian. So if you say the "local interaction" of QFT is well-specified by the mathematical formalism, I will say that the Hamiltonian does not specify any interaction between the measurement apparatus and the quantum system at all. Since collapse does not affect the Hamiltonian, it does not cause any nonlocal interaction at all.

 

[vanhees71]

Fine, so states in the lab can change. These changes are caused by local forces. The local forces may act in a non-deterministic way. Am I right so far?

But changes are not the only thing observed in the lab. Another observed thing are correlations between the changes. So what causes the correlations? Are correlations also caused by those local forces?

Sure, the correlations are also caused by some interactions (see my description of the preparation procedure for polarization-entangled two-photon states).

 

[vanhees71]

But that interaction is not in the Hamiltonian. So if you say the "local interaction" of QFT is well-specified by the mathematical formalism, I will say that the Hamiltonian does not specify any interaction between the measurement apparatus and the quantum system at all. Since collapse does not affect the Hamiltonian, it does not cause any nonlocal interaction at all.

It's not in the Hamiltonian, because you choose not to describe it, but take the functioning of the measurement device for granted. Of course, as long as a theory (here relativstic local QFT) is not known to have limits of applicability (which for sure it has, but it's not known yet), I've all reason to believe that also the interaction between the measured object and the measurement device is ruled by the laws described by the theory. Hence, this interactions are the very same local interactions used in the Hamiltonian.

E.g., to describe the creation of a polarization-entangled photon pair with (in-medium) QED, you have to make a model Hamiltonian (as done by Hong and Mandel in the mid 1980ies) and see whether it correctly describes satisfactorily the observed (statistical!) facts about these pairs (which to my knowledge it does). As long as there is not an experiment showing that the creation of entangled photon pairs cannot be described by these standard QED local interactions, I keep it as the valid description. The same holds true for the theory of photon detection, which are also very well described using the standard local QED interactions.

 

[Demystifier]

That's why I always write a state is represented by a statistical operator or an observable is represented by a self-adjoint operator in a Hilbert space etc.

So interaction is represented by Lagrangian. (And Lagrangian can be represented as an operator in the Hilbert space.) Is that correct?

But is that representation faithful? Is there a 1-1 correspondence between
i) observed change in the lab (cat dies), and
ii) change represented by local interaction in the Hilbert space (|cat alive>+|cat dead>)?

 

[zonde]

Moreover, the model uses a different method to embedd the probabilities into a Kolmogorov space. It doesn't use marginals, but rather conditionals.

I would like to check if I understand correctly what you mean with conditionals (as opposed to marginals). With conditionals you mean that only measurement results are embedded in probability space (and there is no reference to $\lambda$ that Bell used)?

As I said, the use of subsequences in frequency versions of the inequality amounts exactly to the use conditionals in the probability setting. You can't just select a subsequence and expect it to be distributed in the same way as the original sequence. This assumption must be made in all proofs of the inequality. The inequality can't be proved without this assumption.

I'm not sure about what assumption you are talking. Can you try to reword it? Alice's subsequences under identical measurement settings at Alice's side but for different measurement settings at Bob's side can be identical. This is required by locality condition.

 

[ddd123]

Perhaps the Elitzur-Vaidman bomb does not involve an interaction in the lab. But it definitely involves an interaction that happens in the Hilbert space.

But then it is a non local one.

 

[vanhees71]

So interaction is represented by Lagrangian. (And Lagrangian can be represented as an operator in the Hilbert space.) Is that correct?

But is that representation faithful? Is there a 1-1 correspondence between
i) observed change in the lab (cat dies), and
ii) change represented by local interaction in the Hilbert space (|cat alive>+|cat dead>)?

The only thing QT tells you, given the state described by the ket you wrote down, is the probability for the cat being dead or alive after a certain time putting the poor animal into the box. It's not clear in which sense there is a "1-1 correspondence". I'd say, since I can check the prediction of the probabilities only on a sufficiently large ensemble with a given statistical significance there is a 1-1 correspondence at best with such ensembles.

 

[Demystifier]

But then it is a non local one.

It depends on what do you mean by "non-local". There is no entanglement, so it is local in the Bell sense.

 

[Demystifier]

The only thing QT tells you, given the state described by the ket you wrote down, is the probability for the cat being dead or alive after a certain time putting the poor animal into the box. It's not clear in which sense there is a "1-1 correspondence". I'd say, since I can check the prediction of the probabilities only on a sufficiently large ensemble with a given statistical significance there is a 1-1 correspondence at best with such ensembles.

So there is a 1-1 correspondence at the level of large ensembles, but not at the level of single measurements. Even a single change in the lab is supposed to be caused by a force, but that single-change lab-force is not always faithfully represented by local QFT in the Hilbert space. Would you agree?

 

[vanhees71]

This is an empty question since QT doesn't tell you anything about a single event except probabilities. The interaction itself is described in the formalism by the Hamiltonian and as such is 1-1 (up to equivalence like gauge invariance or similar equivalences).

 

[Demystifier]

This is an empty question since QT doesn't tell you anything about a single event except probabilities.

But I don't ask a question about quantum theory. Quantum theory works in the Hilbert space, and I don't ask a question about Hilbert space. I ask a question about forces in the lab. And lab, as you said, does not live in the Hilbert space. So why would my question about lab be an empty question? Fine, the question cannot be answered by quantum theory. But this is a defect of the theory, not a defect of the question. If some question cannot be answered by quantum theory, it doesn't mean that the question is empty. It means that we need a different theory.

Or perhaps you take for granted that there is no and there will never be a theory behind quantum theory? (I hope you don't.)

Or if anything is empty at all, it is the intersection between my question and the quantum theory. But the question as such is not empty.

 

[Demystifier]

The interaction itself is described in the formalism by the Hamiltonian and as such is 1-1

You are contradicting yourself. You said that all changes in the lab are caused by interactions. If so, then even single measurement changes are described by interactions. Yet, you said that single measurement changes are not represented by quantum interactions. Therefore, some interactions in the lab are not represented by quantum interactions. In other words, the representation is not 1-1. Q.E.D.