I Spooky action at a distance and various interpretations of QT

[J O Linton]

TL;DR Summary

By analysing a simple experiment involving entangled photons I wish to explore which, if any, of the various interpretations of QT violate locality (i.e. involve spooky action at a distance)

By analysing a simple experiment involving entangled photons I wish to explore which, if any, of the various interpretations of QT violate locality (i.e. involve spooky action at a distance)
Consider the following idealised scenario: A source S produces entangled pairs of photons A and B such that the plane of polarisation is random but the two photons are at right angles. Photon A impinges on a vertical polaoid P1 placed 1m from the source, a short distance behind which is a detector D1. Photon B impinges on a similar vertical polaroid P2 placed 2 m from the source behind which is a second detector D2. We are interested in the times and circumstances under which both detectors respond together.
I believe that I am right in saying that if the photons were purely classical (i.e. not entangled) both detectors would fire 12½% of the time but since the two photons are entangled and their planes of polarisation are at right angles, QT predicts that the two detectors will never fire together.
On a very simplistic interpretation of QT this effect may be explained as follows: When the two photons leave the source they are in a superposition of an infinite number of states with their polarisation planes in all possible directions (but always at right angles to each other); when photon A reaches P1 a 'measurement' of its plane of polarisation is made and the wavefunction partially collapses into just two possible states with equal propbability: in one, photon A passes through P1 with it plane of polarisation vertical while photon B is absorbed because its plane of polarisation is horizontal; in the other, photon A is absorbed and photon B passes through P2. Later when the detectors are examined, the wavefunction collapses still further into one or other of these possibilities.
To my mind, this interpretation does not violate locality because all that happens when photon A passes through or is absorbed by P1 is that a large number of alternative possibilities are simply ruled out. No information is passed from A to B.
First, is my analysis of the situation correct and second, how would the experiment be explained by an adherent of the Many Worlds interpretation or indeed any other popular interpretation of QT?

 

[PeterDonis]

By analysing a simple experiment involving entangled photons I wish to explore which, if any, of the various interpretations of QT violate locality (i.e. involve spooky action at a distance)

First you need to define what you mean by "violate locality". If you mean "violate the Bell inequalities" then all interpretations of QM violate locality because QM itself does.

 

[Christian Thom]

I agree with you, but with the mechanism you propose, the measurement you make changes the reality. In fact, reality is determined by the measurement you make and that is the reason Bell's theorem doesn't apply.

 

[J O Linton]

I had hoped to avoid all mention of Bell's inequality despite the apparent similarity in the experimental setup. I am not trying to assert or deny the existence of 'hidden variables'. I am trying to focus on locality - a property which depends on your metaphysical interpretation of QT and is quite independent of whether or not QT violates Bells inequality.

 

[PeterDonis]

I am trying to focus on locality

And in order to do that, you have to tell us what you mean by that term. Anyone with even a passing familiarity with the literature in this area should know that the term "locality" has at least as many different definitions as there are quantum physicists. Given the many different definitions of this term, you cannot use it as though it had a single accepted meaning. You have to tell us what you mean by it.

 

[PeterDonis]

reality is determined by the measurement you make

This statement, to the extent that it is meaningful at all, is only true for certain QM interpretations.

 

[Christian Thom]

I had hoped to avoid all mention of Bell's inequality despite the apparent similarity in the experimental setup. I am not trying to assert or deny the existence of 'hidden variables'. I am trying to focus on locality - a property which depends on your metaphysical interpretation of QT and is quite independent of whether or not QT violates Bells inequality.

Precisely, I just wanted to emphasize that it is a way to reconcile locality and the fact that Bell's inequalities are violated, but at the cost of admitting that reality is determined by measurements.

 

[PeterDonis]

I just wanted to emphasize that it is a way to reconcile locality and the fact that Bell's inequalities are violated

For one definition of "locality", yes. But not for others. As I have already pointed out, one definition of "locality" is simply "the Bell inequalities are not violated", so on this definition any violation of the Bell inequalities is a violation of locality.

 

[Christian Thom]

For one definition of "locality", yes. But not for others. As I have already pointed out, one definition of "locality" is simply "the Bell inequalities are not violated", so on this definition any violation of the Bell inequalities is a violation of locality.

I would say that for me locality is that there is a place and a time where the state of the system is determined.

 

[PeterDonis]

I would say that for me locality is that there is a place and a time where the state of the system is determined.

It seems impossible for any spatially extended entangled quantum system (of which the system described in the OP is an example) to satisfy this definition, since in an entangled system, the individual subsystems have no definite state by themselves, only the full system does, and the full system does not have a single location.

 

[J O Linton]

I agree with you both that 'locality' is not well defined - but then it is a metaphysical concept, not a physical one. What I have in mind when I speak of a violation of locality is what Einstein would have objected to - namely the transfer of information instantaneously (or at superluminal speed) from one place to another. I have also tried to suggest that the 'simplistic' interpretation of QT does not violate this concept of 'locality' because it involves the removal of possible states/outcomes/worlds etc rather than the transfer of information.

What I would like to know is how adherents of other interpretations of QT would explain the results of the experiment I have described and whether their explanations would or would not require some form of superluminal communication between the two photons.

 

[Christian Thom]

It seems impossible for any spatially extended entangled quantum system (of which the system described in the OP is an example) to satisfy this definition, since in an entangled system, the individual subsystems have no definite state by themselves, only the full system does, and the full system does not have a single location.

Locality means precisely (for me) that there is a time where it has. For example the interaction having produced the particles. After that, the state(s) evolve deterministically following the Schrödinger equation and may spread out largely, but is determined.

 

[PeterDonis]

I agree with you both that 'locality' is not well defined

That's not what I said. I said there are different possible definitions, so you need to tell us which one you are using. "Not well defined" implies that there is no possible definition, which is not the case.

then it is a metaphysical concept, not a physical one

The different "locality" definitions in the literature are all physical concepts; they're just different physical concepts.

What I have in mind when I speak of a violation of locality is what Einstein would have objected to - namely the transfer of information instantaneously (or at superluminal speed) from one place to another.

That just shifts the problem to what your definition of "information" is; there are different definitions in the literature, so you need to tell us which one you are using. (And no, that does not mean "information" is not well defined, any more than "locality".)

 

[Christian Thom]

I agree with you both that 'locality' is not well defined - but then it is a metaphysical concept, not a physical one. What I have in mind when I speak of a violation of locality is what Einstein would have objected to - namely the transfer of information instantaneously (or at superluminal speed) from one place to another. I have also tried to suggest that the 'simplistic' interpretation of QT does not violate this concept of 'locality' because it involves the removal of possible states/outcomes/worlds etc rather than the transfer of information.

What I would like to know is how adherents of other interpretations of QT would explain the results of the experiment I have described and whether their explanations would or would not require some form of superluminal communication between the two photons.

If I may answer in their place, I think they would evoke the collapse of the common wave-function of the two photons; it seems to me that is the standard answer to this situation.

 

[PeterDonis]

What I would like to know is how adherents of other interpretations of QT would explain the results of the experiment I have described

If this is the question you want answered, you can just ask it, without any of the other baggage about ambiguous terms like "locality" and "information". (Some QM interpretations do not even use those terms at all.)

and whether their explanations would or would not require some form of superluminal communication between the two photons.

"Superluminal communication" as a term has the same issue as "information", since it means communicating information faster than light.

 

[PeterDonis]

Locality means precisely (for me) that there is a time where it has.

So as long as the photons originally came from a common source at a single location, they satisfy "locality"? This is a clear definition, but it's also useless, since it says nothing whatever about what happens to the photons after they separate spatially, and that's where the issue is.

 

[Christian Thom]

So as long as the photons originally came from a common source at a single location, they satisfy "locality"? This is a clear definition, but it's also useless, since it says nothing whatever about what happens to the photons after they separate spatially, and that's where the issue is.

As I said : "After that, the state(s) evolve deterministically following the Schrödinger equation and may spread out largely, but is determined."

 

[PeterDonis]

all that happens when photon A passes through or is absorbed by P1 is that a large number of alternative possibilities are simply ruled out.

This looks like an intepretation in which the quantum state (or wave function) represents our knowledge about the system, rather than the system itself; ruling out possibilities is something that happens in our mental model.

how would the experiment be explained by an adherent of the Many Worlds interpretation

In the MWI, all possible results happen for both measurements; the entanglement between the photons just determines which results coexist in each world. So there would be a world in which photon A passes through P1 and is detected at D1, and photon 2 is absorbed at P2; and there would be a world in which photon A is absorbed at P1, and photon 2 passes through P2 and is detected at D2.

 

[PeterDonis]

As I said : "After that, the state(s) evolve deterministically following the Schrödinger equation and may spread out largely, but is determined."

If you adhere to this strictly, you end up with the many worlds interpretation, in which there is never any wave function collapse at all, it's just unitary evolution (which is indeed deterministic) all the time. Is that the position you are taking? That only the MWI is consistent with your definition of "locality"?

 

[PeterDonis]

I think they would evoke the collapse of the common wave-function of the two photons

Not in the many worlds interpretation, since there is no collapse in that interpretation.

 

[Christian Thom]

If you adhere to this strictly, you end up with the many worlds interpretation, in which there is never any wave function collapse at all, it's just unitary evolution (which is indeed deterministic) all the time. Is that the position you are taking? That only the MWI is consistent with your definition of "locality"?

Not at all. I should have added "until another interaction happens" interaction (or measurement) which in fact determines the reality as proposed in this thread.

 

[J O Linton]

I accept that it is important to define what we are talking about and that terms like 'locality' and 'information' can be defined in different ways so let us talk about SAAAD (Spooky action at a distance) which is quite deliberately left a bit vague. From what you have both said I am inclined to believe that both my 'simplistic' interpretation of QT and the MWI avoid having to postulate anything like SAAAD because each state of the system (or 'world') already contains all the information needed to determine its subsequent evolution.
On the other hand an interpretation such as the Pilot Wave interpretation quite explicitly uses what I have called SAAAD. What language would an adherent of the Pilot Wave Interpretation use to explain my experiment?

 

[PeterDonis]

I should have added "until another interaction happens"

At which point the system is spatially extended so your definition of "locality" doesn't apply to the system as a whole any more; it only applies to individual subsystems.

 

[martinbn]

I agree with you both that 'locality' is not well defined - but then it is a metaphysical concept, not a physical one. What I have in mind when I speak of a violation of locality is what Einstein would have objected to - namely the transfer of information instantaneously (or at superluminal speed) from one place to another. I have also tried to suggest that the 'simplistic' interpretation of QT does not violate this concept of 'locality' because it involves the removal of possible states/outcomes/worlds etc rather than the transfer of information.

What I would like to know is how adherents of other interpretations of QT would explain the results of the experiment I have described and whether their explanations would or would not require some form of superluminal communication between the two photons.

This might be of interest to you.
https://en.wikipedia.org/wiki/No-communication_theorem

 

[PeterDonis]

let us talk about SAAAD (Spooky action at a distance) which is quite deliberately left a bit vague

If it's vague I don't see the point of talking about it.

From what you have both said I am inclined to believe that both my 'simplistic' interpretation of QT and the MWI avoid having to postulate anything like SAAAD because each state of the system (or 'world') already contains all the information needed to determine its subsequent evolution.

In the MWI this is true. However, I don't see how it's true in your "simplistic" interpretation because in that interpretation the "state" does not determine anything; it's just our knowledge about the system. The state changes when a measurement is made because our knowledge about the system changes, not because the state has determined any evolution of anything.

 

[PeterDonis]

On the other hand an interpretation such as the Pilot Wave interpretation quite explicitly uses what I have called SAAAD.

If you can say which interpretations use SAAAD and which don't, it isn't vague.

What language would an adherent of the Pilot Wave Interpretation use to explain my experiment?

They would say that the pilot wave enforces the perfect anti-correlation between the measurements on the two photons by connecting the two measurements.

 

[Christian Thom]

At which point the system is spatially extended so your definition of "locality" doesn't apply to the system as a whole any more; it only applies to individual subsystems.

That's true, because at that point the entanglement is broken.

 

[PeterDonis]

at that point the entanglement is broken.

On certain interpretations, yes. But not, for example, in the MWI.

 

[Christian Thom]

On certain interpretations, yes. But not, for example, in the MWI.

I place myself in the interpretation of this thread, not MWI.

 

[PeterDonis]

I place myself in the interpretation of this thread, not MWI.

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

 

[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.