Undergrad Spooky action at a distance and various interpretations of QT

[Christian Thom]

The OP was not just asking about his "simplistic" interpretation. He was asking how other interpretations explain the experiment he described.

Yes, you are right, sorry.

 

[J O Linton]

In #28 Peter Donis implied that in the MWI the entanglement was not broken by the passage of photon A through P1. Can you explain what you meant by this? As I understand the MWI when the photon is emitted there are an infinite number of possible or parallel worlds in which the plane of polarisation takes all possible values. These worlds are 'coherent' and can potentially 'interfere' with each other. I am interested to know what happens to the world in which the photon is at, say, 30 degress to the vertical when A passes through P1. Does the photon in this world suddenly become vertical? Or is it that this world cesaes to exist is some sense? If the former we end up with an infinite number of identical worlds; if the latter, what is the difference between this and wavefunction collapse?

 

[Nugatory]

As I understand the MWI when the photon is emitted there are an infinite number of possible or parallel worlds in which the plane of polarisation takes all possible values.

That is not right, and may be the source of your confusion here. When the photon is emitted there is one world in which the plane of polarization has no value. When the polarization is measured this world splits into two, one in which the photon passed through the polarizer and one in which it didn’t. In the world in which the photon passed through the polarizer, the entangled partner will not pass through a polarizer at the same angle if we try.

I am interested to know what happens to the world in which the photon is at, say, 30 degress to the verticalwhen A passes through P1.

You are reasoning as if the polarization has some definite value even though it hasn’t been measured. That doesn’t work in any interpretation.

 

[J O Linton]

Thanks for this. Your answer makes a lot of sense. Clearly, however, the MWI adopts a different definition of what I consider a 'world' to be (i.e. an entity in which objects exist which have unique and measurable properties.)

You also say that there is no interpretation in which the polarisation has a definite value before it has been measured. I was under the impression that the Pilot Wave interpretation assumed that all the entities involved had definite properties at all times, but that their behaviour was in some way 'guided' by the pilot wave. More specifically, a 30 degree photon encountering a vertical polaroid would either pass or not according to the usual cos^2 rule and that the pilot wave would 'inform' photon B what had happened to A.

 

[PeterDonis]

These worlds are 'coherent' and can potentially 'interfere' with each other.

The "worlds" in the MWI cannot interfere with each other; splitting into multiple "worlds" only occurs after a measurement has been made and decoherence has occurred. The "worlds" are the different decoherent branches of the wave function and cannot interfere.

 

[Nugatory]

I was under the impression that the Pilot Wave interpretation assumed that all the entities involved had definite properties at all times

yes, I omitted a disclaimer that I usually make: “with apologies to the Bohmians” - didn’t seem necessary in this context

 

[PeterDonis]

I was under the impression that the Pilot Wave interpretation assumed that all the entities involved had definite properties at all times

The Pilot Wave does not say that all properties always have definite values, only that position always does. In fact, the Pilot Wave interpretation, strictly speaking, says that position is the only property that anything ever has; measurements that we think of as measuring something other than position are actually measuring position, we are just interpreting them as measuring something else.

For example, the result of what we think of as a polarization measurement of a photon actually depends, in this interpretation, on the position of the photon as it enters the polarizer; one set of positions results in the photon going through the polarizer, and the remaining positions result in the photon getting absorbed. We interpret this as the polarization of the photon being either parallel to or perpendicular to the orientation of the polarizer, but actually, according to the Pilot Wave interpretation, there is no such thing as "polarization" as a separate property; all we're actually measuring is the photon's position.

 

[J O Linton]

So what, exactly is the Bomian (Pilot Wave?) interpretation in this context. Does it imply some sort of SAAAD?

 

[PeterDonis]

So what, exactly is the Bomian (Pilot Wave?) interpretation in this context. Does it imply some sort of SAAAD?

The Pilot Wave interpretation is fully deterministic, so the results of all experiments that are ever done through the entire history of the universe are determined by the initial conditions. (Strictly speaking, this would be called "superdeterminism" since the initial conditions would also have to fix all of the experimental settings that will ever be made, such as the orientations of polarizers in photon polarization measurements.) A fully deterministic theory wouldn't normally be thought of as having any SAAAD.

However, the usual formulation of the Pilot Wave interpretation is non-relativistic, which means it does not limit signal speeds to the speed of light, and one of the criteria for SAAAD is usually taken to be the possibility of signals being sent faster than light. There have been some attempts to formulate a relativistic version of the Pilot Wave interpretation, but none of them have gained general acceptance.

 

[J O Linton]

I can't say that I like the sound of that!

Anyway, now that we have discussed some of the various interpretations and removed a few of the misconceptions which plague my understanding of the subject, I would beg you to consider a slight modification to my experimental setup.

A third polaroid, P3, at 45 degrees to the vertical is interposed between the source and P1.

Firstly - what is the prediction of QM as regards the possibility that the two detectors fire together? Does the passage of photon A through P3 'break the entanglement' - in which case we now have two classical photons traveling at +-45 deg towards two vertical polarizers with the possibility that both detectors fire; or is it the case that if photon A happens to pass through both P3 and P1, then photon B is still prevented from passing through P2? If so, how is this explained using the interpretations we have discussed?

 

[Nugatory]

I would beg you to consider a slight modification to my experimental setup.A third polaroid, P3, at 45 degrees to the vertical is interposed between the source and P1.

Now we're back to a question about what quantum mechanics says will happen with particular configuration of polarizers and detectors - the answer will of course be the same no matter what interpretation you choose. But before we go there, two things:
1) In your first post you said that you expected both detectors to trigger in 12.5% of your tests runs when the two photons are not entangled and 0% if they are. Where did that 12.5% come from? If I'm understanding your description properly it should be 25% in the non-entangled case: 50% probability that A passes P1, independent 50% probability that B passes P2 gives us a 25% probability that they both pass. (I do agree about the 0% for the entangled case).
2) You went out of your way to specify that P1 is closer to the source than P2. If you're doing this so that you can think in terms of the interaction with P1 happening first... Don't. The two interaction are space-like separated so there's no way of saying which one is first. If you don't get the same result no matter which photon first encounters a polarizer, you're doing something wrong.

And with that said... What do you expect to happen in your new configuration, for both the entangled and the unentangled case?

 

[Christian Thom]

That is not right, and may be the source of your confusion here. When the photon is emitted there is one world in which the plane of polarization has no value. When the polarization is measured this world splits into two, one in which the photon passed through the polarizer and one in which it didn’t. In the world in which the photon passed through the polarizer, the entangled partner will not pass through a polarizer at the same angle if we try.

You are reasoning as if the polarization has some definite value even though it hasn’t been measured. That doesn’t work in any interpretation.

I would very much like to know if there is an interpretation of QM as attributed at MWI by Linton in #32, where the world splits not on the measurements, but on the creation of particles when a symmetry would need to be broken, and where ulterior measurements only "select" one subset of this many worlds (that would be the collapse of the wave function) ? Or is it just rephrasing the standard interpretation ?

 

[J O Linton]

Now we're back to a question about what quantum mechanics says will happen with particular configuration of polarizers and detectors - the answer will of course be the same no matter what interpretation you choose. But before we go there, two things:
1) In your first post you said that you expected both detectors to trigger in 12.5% of your tests runs when the two photons are not entangled and 0% if they are. Where did that 12.5% come from? If I'm understanding your description properly it should be 25% in the non-entangled case: 50% probability that A passes P1, independent 50% probability that B passes P2 gives us a 25% probability that they both pass. (I do agree about the 0% for the entangled case).
2) You went out of your way to specify that P1 is closer to the source than P2. If you're doing this so that you can think in terms of the interaction with P1 happening first... Don't. The two interaction are space-like separated so there's no way of saying which one is first. If you don't get the same result no matter which photon first encounters a polarizer, you're doing something wrong.

And with that said... What do you expect to happen in your new configuration, for both the entangled and the unentangled case?

The 12.5% comes about because you must integrate across all possible values of the initial polarisation. This means writing down an expression for the probability of coincidence for every angle and integrating it. Of course I am assuming that the two photons are oriented at right angles, even in the 'classical' case.

I agree with you that the position of the second detector is irrelevant. I just wanted to specify the experiment in such a way as to forestall any possible discussion of this issue.

As regards the outcome of my modified experiment, I have never studied QM and am not qualified to do the necessary calculations so I genuinely don't know the answer and am very interested to be told what it is. For what it is worth I am 90% confident that the 45 degree polarizer will not break the entanglement and that the two detectors will still not fire together buit, as with so many aspects of QT, I could be wrong.

 

[Nugatory]

Of course I am assuming that the two photons are oriented at right angles, even in the 'classical' case.

Ok, I had not picked that up from the original post.

For what it is worth I am 90% confident that the 45 degree polarizer will not break the entanglement

You are mistaken. Just like the original vertically oriented one, that polarizer is measuring the polarization so ends the entanglement.

 

[J O Linton]

I am not so sure. I suspect that the action of simply passing a photon through a polarizer does not in itself constitute a measurement but that decoherence must occur as well. In other words, the measurement is only actually made when the photon is recorded by D1 or D2.

The point is absolutely crucial and it was actually to test this very point that I started this whole thread. Are you qualified in QM and have you actually calculated the result using the standard Bra-Ket rules? If not, I will, respectfully, reserve judgment until I get a reply from someone who has the appropriate skills.

 

[Nugatory]

IAre you qualified in QM and have you actually calculated the result using the standard Bra-Ket rules?

yes.

 

[J O Linton]

Excellent! Now we can really start to sort things out!

Am I right in saying that after photon A has either passed through or been absorbed by P3, there are now two equally probable possiblilities:
1. Photon A passes through through P3 and we now have two entirely classical, unentangled photons traveling towards P1 and P2, one at +45 degrees and the other at -45 degrees. The probability that both pass through P1 and P2 is therefore 25%.
2. Photon A is absorbed by P3 and there is zero probability that both detectors will fire.
The conclusion is that both detectors will fire 12.5% of the time.

Under the MWI, when A reaches P3 the original world in which the polarization of the two photons was indeterminate splits into two worlds which can no longer interfere with each other (because you say that the entanglement is broken). In one world photon A passes through P3 and in the other it is absorbed. When B reaches P2 a further split into two worlds occurs making 4 possible worlds (though not with equal probabilities). Is this correct?

 

[PeterDonis]

I would very much like to know if there is an interpretation of QM as attributed at MWI by Linton in #32, where the world splits not on the measurements

The reason the MWI has worlds splitting on measurements is that measurements are when decoherence happens.

, but on the creation of particles when a symmetry would need to be broken

QM does not say that decoherence happens on "the creation of particles when a symmetry would need to be broken", so no, there is no such interpretation.

Or is it just rephrasing the standard interpretation ?

It's not describing any intepretation that I'm aware of.

 

[PeterDonis]

that polarizer is measuring the polarization so ends the entanglement.

Note that under some interpretations, such as the MWI, measurements do not end entanglement; they only extend it to the measuring devices (and ultimately to the environment through decoherence).

 

[PeterDonis]

I suspect that the action of simply passing a photon through a polarizer does not in itself constitute a measurement but that decoherence must occur as well.

Decoherence does occur when the photon passes through the polarizer, because the polarizer might absorb the photon. Those two alternatives (passes through the polarizer vs. absorbed by the polarizer) can never interfere with each other, so they are decohered. The detector after the polarizer in this case just allows us humans to detect which alternative happened (or, in interpretations like the MWI, happened in our branch of the wave function).

If you want a device that can act on photons without decoherence, you need something like a beam splitter, where both alternatives pass through the splitter, they just come out in different directions. In that case, decoherence would not occur until a photon reached a detector, and you could make the two alternatives interfere by directing them into another beam splitter (as in, for example, a Mach-Zehnder interferometer).

The point is absolutely crucial and it was actually to test this very point that I started this whole thread.

In other words, we have spent 50 posts now going round and round about something that could have been answered in one post (I just answered it in this one), if you had just asked the question you actually wanted answered in the OP of this thread. Please bear that in mind for future discussions: if you want an answer to a particular question, just ask the question. Don't try to construct an elaborate scenario that you think will lead to an answer to the question; it might not, because you might not understand the subject well enough.

 

[Christian Thom]

The reason the MWI has worlds splitting on measurements is that measurements are when decoherence happens.QM does not say that decoherence happens on "the creation of particles when a symmetry would need to be broken", so no, there is no such interpretation.It's not describing any intepretation that I'm aware of.

Thank you for your answer.

 

[Christian Thom]

I am not so sure. I suspect that the action of simply passing a photon through a polarizer does not in itself constitute a measurement but that decoherence must occur as well. In other words, the measurement is only actually made when the photon is recorded by D1 or D2.

The point is absolutely crucial and it was actually to test this very point that I started this whole thread. Are you qualified in QM and have you actually calculated the result using the standard Bra-Ket rules? If not, I will, respectfully, reserve judgment until I get a reply from someone who has the appropriate skills.

I would think it depends on the polarizer : if the other polarization is absorbed, it might count as a measurement. If the other polarization is reflected, it could be used to reconstruct the original wave so it is not a measurement IMHO.

 

[PeterDonis]

I would think it depends on the polarizer : if the other polarization is absorbed, it might count as a measurement.

It does. See my post #50. My understanding is that this is the type of polarizer the OP was using.

If the other polarization is reflected, it could be used to reconstruct the original wave so it is not a measurement IMHO.

I think the more usual term for this type of device is "polarizing beam splitter".

 

[J O Linton]

I think, PeterDonis, you are being a little unfair on me. The 50 posts have already cleared up several misconceptions of mine which might have been missed if I had inroduced the modified experiment at the start.
But thank you all the same for confirming Nugatories statement that the polarizer does break the entanglement. And since you have not contradicted anything which I said in #47, I take it that what I said there is basically correct.

My reason for deferring the introduction of P3 was that, assuming that P3 did not break the entanglement, the case for some sort of SAAAD between the two photons would be quite strong. But since the entanglement is broken there is no need to consider this possibility any more.

 

[J O Linton]

In view of what you said in #53, if P3 was a polarizing beam splittier and the other polarization was allowed to go off into space - are you saying that the entanglement would remain and that the detectors would never fire together?

 

[PeterDonis]

The 50 posts have already cleared up several misconceptions of mine which might have been missed if I had inroduced the modified experiment at the start.

I'm not saying you should have introduced some "modified experiment" (not sure what you mean by this) at the start. I'm saying that, since the primary question you apparently wanted an answer to (going by the post of yours that I quoted) is "does decoherence occur immediately when a photon encounters a polarizer, or only when it encounters a detector after passing through a polarizer?", you could have just asked that question in your OP. You would have gotten an answer in one post, and you could have followed up with other questions with that primary point correctly understood at post #2 instead of post #50. I'm glad we have still cleared up some misconceptions of yours, but that could have been done with the thread started the way I describe too, since your follow-up questions would presumably still have included other things you asked about in this thread.

 

[PeterDonis]

thank you all the same for confirming Nugatories statement that the polarizer does break the entanglement.

I didn't say the polarizer breaks the entanglement. I said it causes decoherence. That's not the same thing. See my post #49 in response to @Nugatory.

 

[J O Linton]

So what is your response to #55?

 

[PeterDonis]

since you have not contradicted anything which I said in #47, I take it that what I said there is basically correct.

As far as the MWI part of post #47 is concerned, you need to rethink that in the light of my post #49.

The first partof post #47 looks correct to me as far as the calculation of probabilities is concerned, although some of your description in words is interpretation dependent.

 

[PeterDonis]

So what is your response to #55?

It has the same confusion between "breaking entanglement" and decoherence that I pointed out in post #57.