A question regarding the Copenhagen interpretation.

[atyy]

Why shouldn't this be possible? Of course the time evolution of any free two-photon system is unitary and can be done analytically, or do I misunderstand your question?

Let's say, from your example, the state is $|\Psi \rangle =\frac{1}{\sqrt{2}} (|HV \rangle-|V H \rangle)$.

Let's say Alice measures her photon to be H, the state collapses to $|\Psi \rangle = |HV \rangle$.

The collapse is non-unitary, and affects Bob's density matrix. Can we describe this situation without collapse? I have seen examples for teleportation, which was initially worked out with collapse, and unitary descriptions were later found. Is there a unitary description here?

 

[vanhees71]

Can you prove somehown that the state collapses? I cannot, and I don't see why it should. When Alice's photon is measured, it's usually absorbed in the photo multiplier used to register it. So why should there be a two-photon state after her measurement at all?

The only thing you can say is that when Alice measures a horizontally polarized photon (condition), Bob must necessarily find a vertically polarized photon.

In other words: The conditional probability for Bob to find hi photon to be vertically provided Alice's photon is measured to be horizontally polarized is 1 (and that it's horizontally polarized is necessarily 0) of course.

If you want to know, from quantum theory, what's going on at the measurement, you have to solve the very complicated interaction of the photons with Alice's and/or Bob's measurement apparati. This is, however not necessary to understand the conditional probabilities described above. They follow simply from Born's rule and elementary probability theory.

 

[atyy]

Can you prove somehown that the state collapses? I cannot, and I don't see why it should. When Alice's photon is measured, it's usually absorbed in the photo multiplier used to register it. So why should there be a two-photon state after her measurement at all?

The only thing you can say is that when Alice measures a horizontally polarized photon (condition), Bob must necessarily find a vertically polarized photon.

In other words: The conditional probability for Bob to find hi photon to be vertically provided Alice's photon is measured to be horizontally polarized is 1 (and that it's horizontally polarized is necessarily 0) of course.

If you want to know, from quantum theory, what's going on at the measurement, you have to solve the very complicated interaction of the photons with Alice's and/or Bob's measurement apparati. This is, however not necessary to understand the conditional probabilities described above. They follow simply from Born's rule and elementary probability theory.

Let's say Alice does a non-demolition measurement.

 

[bohm2]

Let's say Alice does a non-demolition measurement.

If I'm understanding you, I've read (e.g. Vaidman) that this can't be done because such a non-demolition measurement would violate Einstein causality.

 

[atyy]

If I'm understanding you, I've read (e.g. Vaidman) that this can't be done because such a non-demolition measurement would violate Einstein causality.

There are some non-demolition measurements that are impossible, and I'm not sure the exact one I wrote is possible. For example, the non-demolition measurement of a non-Abelian Wilson loop is not possible, as shown in http://arxiv.org/abs/hep-th/0110205 following Vaidman, Aharonov and Albert.

However, there should be systems for which it is possible to do a non-demolition measurement on one particle in an EPR experiment. For example, http://arxiv.org/abs/0706.1232 (p3) give the example where the state is $|\Psi \rangle =\frac{1}{\sqrt{2}} (|10\rangle-|01\rangle)$. After Alice measures her particle to be 1, the state collapses to $|\Psi \rangle = |10\rangle$

Also http://arxiv.org/abs/quant-ph/9502005 and http://arxiv.org/abs/1308.0477 consider versions of Bell tests with sequential measurements on pairs of particles, so I think a non-demolition measurement should be possible for some systems.

 

[StevieTNZ]

Technically the state would be (if we only measure one particle) |state> = |H>|apparatus shows V> - |V>|apparatus shows H>

 

[vanhees71]

Well, but this state collapse then is just the adaption of Alice's knowledge from her non-demolition measurement. Nothing has instantaneously happen with Bob's photon, at least as long standard QED is right, according to which the interaction of Alice's photon with her measurement apparatus is local. To let Bob know her measurement Alice needs to send the information to him, which signal takes at least the time L/c, when Bob is at a distance L from Alice. So there is no FTL communication possible by just doing the local measurement at Alice's photon, and no violation of the causality structure of SRT is implied.

 

[atyy]

Well, but this state collapse then is just the adaption of Alice's knowledge from her non-demolition measurement. Nothing has instantaneously happen with Bob's photon, at least as long standard QED is right, according to which the interaction of Alice's photon with her measurement apparatus is local. To let Bob know her measurement Alice needs to send the information to him, which signal takes at least the time L/c, when Bob is at a distance L from Alice. So there is no FTL communication possible by just doing the local measurement at Alice's photon, and no violation of the causality structure of SRT is implied.

I agree that wave function collapse does not lead to any FTL communication of classical information, and there is no violation of special relativity.

At any rate, I take back my claim in post #16 that in interpretations with a classical/quantum cut, EPR can be described without collapse or non-unitary time evolution of the wave function.

 

[stevendaryl]

What I find unsatisfactory about the interpretation of quantum mechanics as a probabilistic theory is that probabilities are probabilities of events. Either it's a probability of something being true, or its a probability of something happening. In the case of quantum mechanics, it's not clear what the probabilities are probabilities for. Associated with a wave function \Psi, an observable \hat{O}, and an eigenvalue o_i of \hat{O}, there is a corresponding probability p_i. But is this a probability that something is true? Is there a probability of p_i that the observable has value o_i? I would say no, that is not a correct interpretation. Observables don't have definite values in quantum mechanics until they are measured (or prepared to have those values). If you prepare a spin-1/2 particle so that it is spin-up in the z-direction, it has a 50% probability associated with having spin-up in the x-direction. But it doesn't actually have a spin in the x-direction prior to measuring it. (If it did, that would be a hidden variable, which is ruled out by Bell-type inequalities.)

So the probabilities for quantum mechanics are not associated with a probability of something being true. Then what are they probabilities for? They are probabilities of measuring something. The probability p_i is the conditional probability that you will measure \hat{O} to have value o_i, given that you choose to measure that observable. That's fine as a heuristic, but what does it really mean? The difficulty for me is that measurements themselves are physical interactions, presumably described by quantum mechanics. There is no more reason for the statement "The measurement of \hat{O} produced value o_i" to have a definite truth value than "\hat{O} has value o_i". I feel that a theory is still at the ad hoc stage if it must rely on the distinction between measurements and other interactions.

The closest thing to a objective interpretation of quantum mechanics that does not rely on ad hoc nonlocal interactions of ad hoc distinctions between measurements and other interactions is the "consistent histories" interpretation (which I think of as a variant of the Many-Worlds Interpretation). The wave function of the universe evolves continuously according to Schrödinger's equation (or the quantum-field theoretic generalization) until decoherence splits it into effectively disjoint parts. At that point, we can choose to interpret the wave function probabilistically, as an ordinary probability distribution on alternative histories.

But I find that not completely satisfying either. For one thing, the notion of "effectively disjoint alternative histories" is fuzzy. It depends on the likelihood of being able to observe interference effects between alternatives. For another thing, it seems weird that we have to wait for decoherence to do its thing before we can interpret what is going on.

 

[atyy]

I feel that a theory is still at the ad hoc stage if it must rely on the distinction between measurements and other interactions.

Yes, it is widely agreed that quantum mechanics has a measurement problem, which within Copenhagen is rooted in the need to make a classical/quantum cut, with the measuring apparatus on the classical side.

Also I agree that attempts to say that in interpretations with a classical/quantum cut, that wave function collapse is exclusively updating of knowledge, and that the physical system is not evolving, are so far not convincing. If it were, then quantum theory in such interpretations would be standard probability theory, and it isn't.

 

[Jilang]

Why do we refer to a quantum/classical cut rather than a boundary condition? Is that what measurement effectively is?

 

[atyy]

Why do we refer to a quantum/classical cut rather than a boundary condition? Is that what measurement effectively is?

We do have boundary conditions on the wave function, but quantum mechanics is not a theory like classical field theory, which also has boundary conditions. In classical field theory, the field potentially includes everything in the universe, including the measuring apparatus. The field is a model in which there is a single reality that changes with time. In classical field theory, we don't think there is any fundamental problem with including the measuring apparatus or the whole universe in the field, although it may be inconvenient. However, in quantum mechanics, if we try to put the measuring apparatus or the whole universe into the wave function, we get time evolution into superpositions which are not observed. To make the match to observation, we have to introduce the notion of measurement as a distinct postulate, as something that produces definite outcomes.

It may be possible to avoid the classical/quantum cut by using an interpretation such as many-worlds. However, at least for non-relativistic quantum mechanics, one can also avoid the classical/quantum cut by de Broglie-Bohm theory and its variants. Since there is not one unique way of avoiding the classical/quantum cut, and since quantum mechanics with the cut is working just fine for the moment, we can use it and are agnostic about the underlying interpretation.

 

[Jilang]

Thanks atyy, my question is more along the lines of why we regard the preparation of the state as an initial boundary condition for the wavefunction, but why we don't talk of the measurement as being a final boundary condition.

 

[atyy]

Thanks atyy, my question is more along the lines of why we regard the preparation of the state as an initial boundary condition for the wavefunction, but why we don't talk of the measurement as being a final boundary condition.

There is one formulation of quantum mechanics in which something like this is the case, if I understand it correctly: http://arxiv.org/abs/0706.1232. I believe it is more a calculational method, like the path integral, than it is an interpretation. I think Dr Chinese has read this article quite carefully, so he could answer questions on it. But if you would like to disucss this, perhaps it'd be better to start a new thread.

In the more textbookish way of thinking, a measurement causes the wave function to collapse, and collapse is not governed by the Schroedinger equation, so if the particle still exists after the measurement, it isn't enough to set the measurement as a boundary condition, since unitary evolution is violated.

 

[Jilang]

Thanks atyy. I will read the article and I might start a new post.

 

[DevilsAvocado]

[my bolding]

In this minimal interpretation there is thus no "spooky action at distance" or a "collapse of the state" necessary to explain the 100% correlation of the photons' polarization since this 100% was already prepared when the photons were created by parametric down conversion and not by Alice's and/or Bob's measurement of the polarization state of their single photons.

In the whole description of this EPR experiment nowhere a collapse assumption or action at a distance is necessary and thus there's no EPR paradox.

Further, nobody denies the "nonlocal correlations" known as entanglement. The point is that these are correlations but not nonlocal interactions. To the contrary, the most successful theories, like the Standard Model of elementary particles, are local relativistic quantum field theories. This precisely resolves the EPR paradox as explained in my previous posting. The correlations are already there from the very beginning of the experiment, i.e., due to the preparation of the two photons in the entangled polarization state and it's not caused by the measurement of one of the photon's polarization. So there is no need for an action at a distance of the far-distant photon with the apparatus located where the other photon is registered.

Before Bob measures the polarisation of his photon, he doesn't know it, and the polarizaton is not determined at all. He also doesn't know anything about Alice's photon, and it's indetermined as well. Now at the moment when Bob measures his photon's polarization, he also knows Alice's photon's polarization. The reason for this correlation between Alice's and Bob's photon polarization is, however not Bob's measurement but the preparation in the entangled state by the parametric down conversion in the very beginning.

This is confusing...? Are you talking about the 1935 EPR picture??

What you are saying is obviously not true after 1964, and Bell's groundbreaking paper "On the Einstein Podolsky Rosen paradox". The 1935 picture is only valid for prefect alignments/perfect correlations; i.e. it does not work for any other settings...

 

[bohm2]

The interesting question is what is responsible for the EPR correlations. I mean how does nature do that 'trick'?

 

[stevendaryl]

[my bolding]
This is confusing...? Are you talking about the 1935 EPR picture??

What you are saying is obviously not true after 1964, and Bell's groundbreaking paper "On the Einstein Podolsky Rosen paradox". The 1935 picture is only valid for prefect alignments/perfect correlations; i.e. it does not work for any other settings...

There's a confusion about the meaning of "indeterminate". If you say that before Bob detects the photon, its polarization is indeterminate, you could be making an epistemological statement, that Bob doesn't know the polarization. Or you could be making a statement about the photon---that it doesn't have a polarization. After Bob does detect a horizontally-polarized photon, the state of Alice's photon + filter + detector becomes determined: She will definitely not measure a vertically-polarized photon. There are similarly two interpretations to this "becomes determined": (1) Bob learns about Alice's situation, or (2) Alice's situation changes to a situation in which the polarization is definite.

The two interpretations of the words "indeterminate" and "determined" are both unsatisfactory, in my opinion. If you view them as purely epistemological, so it's just a matter of Bob learning facts that are already true, then that would seem to imply a "hidden variables" model, which is ruled out by Bell's inequality. If you view them as not purely epistemological, but as actually about the state of the photons, then it would seem that Bob's measurement has an effect on the distant photon. Which is the "spooky action at a distance". Neither alternative is very attractive.

 

[DevilsAvocado]

The interesting question is what is responsible for the EPR correlations. I mean how does nature do that 'trick'?

I have absolutely no idea, and as a petite 'remedy' – we are in good company of über-smart people like Anton Zeilinger...

I think that Bohmian mechanics has some sort of "real explanation" (do you know?), but not in detail how the non-locality is 'implemented', and anyhow, there are serious trouble with RoS as soon as you make "real stuff" being there and influencing other distant "real stuff".

As Lee Smolin writes in his latest book:

To describe how the correlations are established, a hidden-variables theory must embrace one observer’s definition of simultaneity. This means, in turn, that there is a preferred notion of rest. And that, in turn, implies that motion is absolute. Motion is absolutely meaningful, because you can talk absolutely about who is moving with respect to that one observer—call him Aristotle. Aristotle is at rest. Anything he sees as moving is really moving.
End of story.
In other words, Einstein was wrong. Newton was wrong. Galileo was wrong. There is no relativity of motion.
This is our choice. Either quantum mechanics is the final theory and there is no penetrating its statistical veil to reach a deeper level of description, or Aristotle was right and there is a preferred version of motion and rest.

It's hard and very interesting – I'm glad to live in these interesting times! ;)

 

[DevilsAvocado]

There are similarly two interpretations to this "becomes determined": (1) Bob learns about Alice's situation, or (2) Alice's situation changes to a situation in which the polarization is definite.

The two interpretations of the words "indeterminate" and "determined" are both unsatisfactory, in my opinion.

I agree, there is no satisfactory explanation for EPR-Bell. You could refer to MWI to get rid of the whole problem, but to me this is at the same level as superdeterminism or the anthropic principle.

Basically, you could introduce even more weirdness to get rid of the EPR-Bell weirdness, or you could just "give up" and say - Shut up and calculate! ;)


P.S: My 'objection' to vanhees's posts was that it looks like he's talking about the 1935 picture of "gloves in a box", and of course this picture make it possible to refer to a common source as an explanation of the correlations, whereas this breaks down as soon as you go one step further to the Bell picture.

 

[vanhees71]

Just a comment to "indeterminism". Quantum theory clearly tells you, which observables have a definite value (i.e., are determined) and which not, given the state of the system, because you can calculate the probability of finding a definite value. If there is one value, for which you get the probability 1, this is the determined value of that variable otherwise not, and the observable is indetermined. The determination or nondetermination of a certain observable is thus due to the preparation of the system in the (pure or mixed) state.

Further, I never have discussed something contradicting Bell's achievements. Of course, the correlations according to entanglement are in perfect agreement with Bell, and these correlations are naturally described by the quantum-theoretical formalism and are well-established empirically (including the violation of Bell's inequality, excluding local deterministic hidden-variable models with very high significance).

With the Aspect-Zeilinger setup of polarization-entangled photons, detected by far distant observers "Alice and Bob", I've described previously, you can also perform high-precision Bell-experiments. You only have to rotate one of the polarization foils against the other. At certain relative angles you get maximal violations of Bell's inequality for the photon polarization. This is all encoded in the quantum-theoretical state and thus, according to the minimal statistical interpretation, inherent in the preparation procedure, leading to the preparation of the photon pair in the entangled state and not due to any kind of collapse of the state due to one observer's measurement of the polarization of his photon.

 

[DevilsAvocado]

Further, I never have discussed something contradicting Bell's achievements.

Good, then we are on the same page, since one of Bell's achievements was to rule out the "common source explanation" in EPR, which was the main fuel of the 20 year long Bohr–Einstein debates.

 

[EskWIRED]

The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.'

Where can I learn more about this difficulty in QM?

 

[atyy]

Where can I learn more about this difficulty in QM?

The measurement problem - the need for a classical/quantum cut within the Copenhagen interpretation, and the use of two different postulates for dynamics given by the Schroedinger equation and wave function collapse are described in:

Bell, Against 'measurement'
http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf

Laloe, Do we really understand quantum mechanics?
http://arxiv.org/abs/quant-ph/0209123 (see the section "Difficulties, paradoxes", on p13)

 

[vanhees71]

Good, then we are on the same page, since one of Bell's achievements was to rule out the "common source explanation" in EPR, which was the main fuel of the 20 year long Bohr–Einstein debates.

What do you mean by "common source explanation"? In some sense the entangelment in the two-photon example we discuss here is due to a common source of the two photons by parametric downconversion.

 

[atyy]

What do you mean by "common source explanation"? In some sense the entangelment in the two-photon example we discuss here is due to a common source of the two photons by parametric downconversion.

The entangled state is not a local common source in the sense of Bell.

http://arxiv.org/abs/0901.4255 (Eq 2)
Gisin, Foundations of Physics, 42, 80-85, 2012

Special relativity does forbid "nonlocality", but it does not forbid quantum nonlocality. Thus quantum mechanics is nonlocal in the sense of Bell. However, it is not nonlocal in the sense of violating special relativity. Rohrlich and Popescu discuss these different definitions of locality/nonlocality http://arxiv.org/abs/quant-ph/9508009 (Foundations of Physics, 24, 379-385, 1995).

 

[DevilsAvocado]

What do you mean by "common source explanation"? In some sense the entangelment in the two-photon example we discuss here is due to a common source of the two photons by parametric downconversion.

Yes absolutely, the two photons are entangled due to a "common source" (even if it nowadays is possible to entangle photons that have never met, i.e. entanglement swapping), but this common source can never be used as an explanation of the correlations, because the correlations are ruled by the relative angle between the two space-like separated polarizers (outside each other's light cone), in the form of Malus' law: cos²(a-b)

I.e. there is no ("normal") way to know the measurement settings for Alice & Bob in advance; hence the "common source explanation" will get you nowhere.

It "worked" for 1935 EPR, because they only considered perfect correlations, it doesn't work today.

 

[bhobba]

but it does not forbid quantum nonlocality.

If QM is non local is very interpretation dependent - that's the import of Bells Theorem and Einsteins error. QM rules out naive-reality ie local realism. If you reject realism (ie properties do not exist independent of observation) then locality is saved. If you keep it then locality is gone. But SR is still saved since it can't be used to send information which is what's required to sync clocks.

Basically all Bell type 'experiments' are doing is observing systems with spatial extent, and because of how its arranged if one thing in the system has a property on observation, so does the other thing - but they are spatially separated.

I have two pieces of paper, one black, and one white and put them in envelopes. I randomly send one to one person, and another to a different person. If any of those people open their envelope they immediately know what the other person will get when they open their envelope. Their is nothing Earth shattering going on. Same with Bell type experiments, with the twist we can't say it has the property of blackness or whiteness until observation.

Griffiths book - Consistent Quantum Theory discusses it from this interesting perspective:
https://www.amazon.com/dp/0521539293/?tag=pfamazon01-20

Thanks
Bill

 

[atyy]

If QM is non local is very interpretation dependent - that's the import of Bells Theorem and Einsteins error. QM rules out naive-reality ie local realism. If you reject realism (ie properties do not exist independent of observation) then locality is saved. If you keep it then locality is gone. But SR is still saved since it can't be used to send information which is what's required to sync clocks.

Basically all Bell type 'experiments' are doing is observing systems with spatial extent, and because of how its arranged if one thing in the system has a property on observation, so does the other thing - but they are spatially separated.

I have two pieces of paper, one black, and one white and put them in envelopes. I randomly send one to one person, and another to a different person. If any of those people open their envelope they immediately know what the other person will get when they open their envelope. Their is nothing Earth shattering going on. Same with Bell type experiments, with the twist we can't say it has the property of blackness or whiteness until observation.

Griffiths book - Consistent Quantum Theory discusses it from this interesting perspective:
https://www.amazon.com/dp/0521539293/?tag=pfamazon01-20

Thanks
Bill

Bell nonlocality is simply the violation of the Bell inequalities, and the existence of the measurement result, the measurement choice, the independence of the measurement choice, and the existence of a variable used to predict the probabilities. Certainly the inequality cannot be violated if any of these quantities don't exist, or a probability distribution cannot be defined over them. However, it does not require that black or white exist before the measurement, only that black or white exist after the measurement. The hidden variable can be the wave function itself. If one by fiat excludes the wave function from entering the inequality (and defines that as the wave function being not real) then perhaps one can escape the conclusion that quantum mechanics violates the inequality. Take a look at Eq 2 in http://arxiv.org/abs/0901.4255 (Foundations of Physics, 42, 80-85, 2012). I agree that one can use nonreality of the measurement results to avoid Bell nonlocality, but I don't think vanhees71 was challenging the violation of the Bell inequalities.

 

[DevilsAvocado]

If QM is non local is very interpretation dependent - that's the import of Bells Theorem and Einsteins error.

For once, there are thousands of thoroughly and professional experiments, settling the options left for us to consider, i.e. the experimental results has nothing to do with interpretations as such, and the fact is – Bell's theorem is a mathematical proof – not specifically 'tied' to QM, or any interpretation. There is one task left – to close loopholes simultaneously – but no one could seriously expect any different outcome (as this would be a bigger surprise than anything else).

(At least) one of these three options has to be abandoned:

• Locality
• Realism
• Free will*

*I.e. give up our freedom to choose (random) settings, which would conduce to Superdeterminism.

If you reject realism (ie properties do not exist independent of observation) then locality is saved.

True, but there is one "little" problem left – unless one pursues the "Shut up and calculate!" methodology – one ought to explain how this works, and this (for sure) is not an easy task, not even for fairly 'vague' interpretations. Some attempts are Holism & Nonseparability, Two-state vector formalism, Relational Blockworld, etc. These are all very interesting but quite "nasty creatures", that has very little or nothing to do with standard QM...

If you keep it then locality is gone. But SR is still saved since it can't be used to send information which is what's required to sync clocks.

True, but if you keep realism in favor of locality, you have "real stuff" out there, that must act according to Relativity of Simultaneity, and then you will surely run into trouble with SR, trying to define a preferred version of motion and rest. Catch-22.

I have two pieces of paper, one black, and one white and put them in envelopes. I randomly send one to one person, and another to a different person. If any of those people open their envelope they immediately know what the other person will get when they open their envelope. Their is nothing Earth shattering going on. Same with Bell type experiments, with the twist we can't say it has the property of blackness or whiteness until observation.

I'm quite baffled by this... you surely know things that I have absolutely no clue on... but this is wrong, entirely wrong... and this is the same "trap" that vanhees seems to have fallen into... weird...

This picture of envelopes or boxes with only two possible values (i.e. black/white [cards] or left/right [gloves]), is the old 1935 EPR picture. It is proven wrong beyond any discussion.

The new Bell picture is more like the complete spectrum of the rainbow, and the final definite colors are correlated *only* by the *relative* angle *between* the settings of the two space-like separated polarizers of Alice & Bob.

... ...