Entanglement & Wave Function Collapse

[Lynch101]

TL;DR Summary

Wave function collapse and the relativity of simultaneity

This thread is to look at the notion of wave function collapse and relativity of simultaneity. The other thread I started on QFT has helped to clarify a lot, so hopefully this one can do the same.

I may have this all wrong, but I will outline my question and hopefully someone can point out where I've gone astray.

Thought Experiment

The standard thought experiment with Alice and Bob each being sent one of a pair of entangled particles. I think I've seen it formulated before whereby [in a given referecence frame], Alice and Bob measure the particles simultaneously. Then, in relatively moving reference frames the order of them measuring the particles changes depending on the motion of the frame (as a result of relativity of simultaneity).

From my understanding, the wave function for each of them collapses the instant it is measured by one of them, but because they cannot communicate/signal each other faster than the speed of light, there is no violation of causality. Am I even in the right ball park with this?Questions

• What about in the case where only one of them makes a measurement: let's say Bob just doesn't bother to measure his particle. Does the wave function for his particle still collapse?
• If so, and in accordance with the relativity of simultaneity, will there be a reference frame in which the wave function of Bob's particle spontaneously collapses and causes the collapse of Alice's particle?
• Is the wave function in QM completely non-physical?

Again, am I even in the right city with this one (not to mention the right ball park)?

 

[DrChinese]

No one is actually sure if there is a physical thing called "wave function collapse". To a certain extent, it is interpretation dependent - hopefully you are familiar with some of these already (Copenhagen, MWI, Bohmian, etc).

Whatever collapse is, there is no current method to expose exactly when it occurs - or when it becomes irreversible.

Lastly: there is no apparent difference in saying Alice causes collapse versus Bob causes collapse regardless of the order of measurement, and regardless of reference frame. I would say that strict causality is not present, but most of those here do not agree with that assessment. Again, it is interpretation dependent.

 

[DarMM]

Summary: Wave function collapse and the relativity of simultaneity

• What about in the case where only one of them makes a measurement: let's say Bob just doesn't bother to measure his particle. Does the wave function for his particle still collapse?
• If so, and in accordance with the relativity of simultaneity, will there be a reference frame in which the wave function of Bob's particle spontaneously collapses and causes the collapse of Alice's particle?
• Is the wave function in QM completely non-physical?

Whether the wavefunction is physical depends on the interpretation. In the standard Copenhagen view it is not. As such in those views collapse is not a physical process.

Other views have the wavefunction as real, but no collapse fundamentally like Many Worlds or Bohmian Mechanics.

 

[DarMM]

I would say that strict causality is not present

What exactly do you mean here?

 

[Nugatory]

From my understanding, the wave function for each of them collapses the instant it is measured by one of them, but because they cannot communicate/signal each other faster than the speed of light, there is no violation of causality.

Collapse is not part of the mathematical formalism of quantum mechanism. It's one way of interpreting what might or might not be going on behind the scenes, and like all interpretations we only introduce it because it makes it easier (or just more comfortable for our classically-trained brains) to think about the problem at hand. So if it's not helping you understand a particular problem, you can reasonably just decide not to use it on that problem - and as you're finding out, instantaneous collapse is a remarkably unhelpful way of thinking about entanglement problems (and generally any situation in which we make spacelike-separated measurements).

All that quantum mechanics actually says is that after we've measured one member of the pair, we know what the result of the corresponding measurement on the other would be, if it that measurement is actually made. It is explicitly silent on what mechanism could produce those correlations (although Bell's theorem precludes just about anything that is consistent with both relativity and our classical intuition).

 

[DrChinese]

What exactly do you mean here?

There is no experimental manner to distinguish between [A causes B] or [B causes A] in any scenario that can be constructed. For example: A & B are in the same reference frame, and A occurs first. You cannot conclude A causes B by any experimental means. It is equally accurate to say B causes A (since neither case can be distinguished). That would defy strict causality. Again, this is not an opinion shared by most here (I prefer to label such differences in opinion, while many do not).

 

[DarMM]

Collapse is not part of the mathematical formalism of quantum mechanism

I was always taught collapse was just another name for state reduction and thus is a part of the formalism. The interpretation of it as a physical process is what is not.

Do you use "state reduction" or something similar for the part of the formalism where the state is updated upon measurements and "collapse" only for viewing that as a physical process?

 

[DarMM]

There is no experimental manner to distinguish between [A causes B] or [B causes A] in any scenario that can be constructed. For example: A & B are in the same reference frame, and A occurs first. You cannot conclude A causes B by any experimental means. It is equally accurate to say B causes A (since neither case can be distinguished). That would defy strict causality. Again, this is not an opinion shared by most here (I prefer to label such differences in opinion, while many do not).

In a spacelike separated case yes you can't argue for causality in either case. And then I assume you are bringing this over to even timelike separations.

I would have thought that neither A or B cause each other's results was a fairly standard view. That's what it is in Copenhagen for example.

 

[Lynch101]

No one is actually sure if there is a physical thing called "wave function collapse". To a certain extent, it is interpretation dependent - hopefully you are familiar with some of these already (Copenhagen, MWI, Bohmian, etc).

I am familiar with them, thank you. I think I have a decent grasp of them (for a beginner that is).

Whatever collapse is, there is no current method to expose exactly when it occurs - or when it becomes irreversible.

Lastly: there is no apparent difference in saying Alice causes collapse versus Bob causes collapse regardless of the order of measurement, and regardless of reference frame. I would say that strict causality is not present, but most of those here do not agree with that assessment. Again, it is interpretation dependent.

But what if either Bob or Alice simply don't make a measurement? Let's say Bob just doesn't bother going to the lad that day, or whenever. Does the wave function of his particle still collapse?

I'm just realising as I write this, that Bob probably isn't necessary to the procedure, but if he doesn't set up the detection equipment, does Alice measuring her particle have any [for want of a better word] effect on Bob's particle?

 

[Nugatory]

Yes, I do try to be careful to use the term "state reduction" as you suggest. Anecdotal evidence (but hanging out on PF for a few years means a lot of anecdotes in that evidence) suggests that most people asking this question are assuming that "collapse" is a real physical process that can have real physical "effects" on the other particle, and trying to use the word to mean anything else leads ot confusion.

 

[Lynch101]

Collapse is not part of the mathematical formalism of quantum mechanism. It's one way of interpreting what might or might not be going on behind the scenes, and like all interpretations we only introduce it because it makes it easier (or just more comfortable for our classically-trained brains) to think about the problem at hand. So if it's not helping you understand a particular problem, you can reasonably just decide not to use it on that problem - and as you're finding out, instantaneous collapse is a remarkably unhelpful way of thinking about entanglement problems (and generally any situation in which we make spacelike-separated measurements).

All that quantum mechanics actually says is that after we've measured one member of the pair, we know what the result of the corresponding measurement on the other would be, if it that measurement is actually made. It is explicitly silent on what mechanism could produce those correlations (although Bell's theorem precludes just about anything that is consistent with both relativity and our classical intuition).

Thank you. I think this helps to clarify a lot of the issues I was having, with this question and questions pertaining to QFT.

Does the emboldened part imply that any mechanism that could produce those correlations will likely contradict relativity? This sounds like what is stated in other quotes [I referenced in another thread], but I didn't quite know how to parse them.

 

[DarMM]

Yes, I do try to be careful to use the term "state reduction" as you suggest. Anecdotal evidence (but hanging out on PF for a few years means a lot of anecdotes in that evidence) suggests that most people asking this question are assuming that "collapse" is a real physical process that can have real physical "effects" on the other particle, and trying to use the word to mean anything else leads ot confusion.

@vanhees71 and myself had a similar discussion recently. I genuinely just had collapse as a synonym for state reduction. I see from reading previous threads that some other users have "collapse" in the same meaning as me, i.e. just state updating.

I'll separate them in future.

 

[DarMM]

Does the emboldened part imply that any mechanism that could produce those correlations will likely contradict relativity? This sounds like what is stated in other quotes, but I didn't quite know how to parse them.

One type of mechanism will contradict Relativity. There are others that do not.

The Copenhagen view is that there is no mechanism, in the sense that whatever is occurring is not a mathematically describable causal process.

 

[Nugatory]

Does the emboldened part imply that any mechanism that could produce those correlations will likely contradict relativity?

Much much much more likely that the problem is with our classical intuition.

 

[Lynch101]

One type of mechanism will contradict Relativity. There are others that do not.

The Copenhagen view is that there is no mechanism, in the sense that whatever is occurring is not a mathematically describable causal process.

Ah, I see. Thank you. A lot of it is so much clearer now.

Am i right in thinking that it boils down to a question of realism vs anti-realism?

 

[Lynch101]

Much much much more likely that the problem is with our classical intuition.

Ah, my apologies. I read that wrong.

Am I right in thinking the question boils down to realism vs anti-realism?

In what way might our classical intuition be wrong?

EDIT: is it that our classical intuition might be wrong in thinking that there must be a mechanism i.e. hidden variables theory?

 

[DarMM]

Ah, my apologies. I read that wrong.

Am I right in thinking the question boils down to realism vs anti-realism?

One aspect of this does involve whether QM is Representational or Non-Representational. I use "Representational" as Realism makes it sound like one is arguing about whether things exist.

 

[atyy]

@vanhees71 and myself had a similar discussion recently. I genuinely just had collapse as a synonym for state reduction. I see from reading previous threads that some other users have "collapse" in the same meaning as me, i.e. just state updating.

I consider it standard to use collapse for state reduction. I would say that collapse is part of the mathematical formalism of quantum mechanics.

 

[Lynch101]

One aspect of this does involve whether QM is Representational or Non-Representational. I use "Representational" as Realism makes it sound like one is arguing about whether things exist.

Ah yes. I've encountered that terminology recently.

You mentione collapse mechanisms that don't contradict relativity, which ones are those?

 

[DarMM]

I consider it standard to use collapse for state reduction. I would say that collapse is part of the mathematical formalism of quantum mechanics.

That's actually what I would have said as well and what I was taught. But others take collapse to mean "viewing state reduction as a physical process". It was actually yourself I was referring to when I said:

other users have "collapse" in the same meaning as me, i.e. just state updating

 

[DarMM]

Ah yes. I've encountered that terminology recently.

You mentione collapse mechanisms that don't contradict relativity, which ones are those?

Superdeterministic, Retrocausal and Acausal ones.

 

[Lynch101]

Superdeterministic, Retrocausal and Acausal ones.

cheers, more stuff for me to try and get my head around before running back here with ELI5 questions

 

[Nugatory]

Am I right in thinking the question boils down to realism vs anti-realism?

Depends on what you mean by "realism"... Bell shows that any theory that meets certain criteria cannot match the results of quantum mechanics. You may decide that these criteria correspond to what you mean by "realism", but if you find yourself in an argument about this, you're arguing about categorization not physics.

In what way might our classical intuition be wrong?

@darmm gave one example above:

The Copenhagen view is that there is no mechanism

. Another is that most laypersons' first intutive reaction to entanglement is to imagine something similar to Bertelmann's socks, and that doesn't work. More generally, the entire notion that unmeasured quantities don't exist is distinctly at odds with classical intuition.

 

[Lynch101]

Depends on what you mean by "realism"... Bell shows that any theory that meets certain criteria cannot match the results of quantum mechanics. You may decide that these criteria correspond to what you mean by "realism", but if you find yourself in an argument about this, you're arguing about categorization not physics.

I would take realism to mean something along the lines of the idea espoused by Lee Smolin that there is something going on in the individual experiments of QM which the statistical model doesn't capture.

@darmm gave one example above:. Another is that most laypersons' first intutive reaction to entanglement is to imagine something similar to Bertelmann's socks, and that doesn't work. More generally, the entire notion that unmeasured quantities don't exist is distinctly at odds with classical intuition.

OK, so it would appear to be a matter of some mechanism which contradicts relativity or no mechanism at all. Am I reading that right?

I would be inclined to say that the emboldened part is somewhat tautological insofar as a quantity is necessarily a measurement. Would this mean that the representationalist/realist approach vs the anti-poisition, would be that something exists there but we can't measure it vs nothing exists there because we cannot measure it?

 

[DarMM]

OK, so it would appear to be a matter of some mechanism which contradicts relativity or no mechanism at all. Am I reading that right?

No. It's one of:

1. No Mechanism
2. A Mechanism that is nonlocal and will violate relativity in general
3. Retrocausal Mechanism
4. Superdeterministic Mechanism
5. Acausal Mechanism
6. Multiple Worlds

 

[Lynch101]

No. It's one of:

1. No Mechanism
2. A Mechanism that is nonlocal and will violate relativity in general
3. Retrocausal Mechanism
4. Superdeterministic Mechanism
5. Acausal Mechanism
6. Multiple Worlds

That is excellent! thank you!

 

[DarMM]

I would take realism to mean something along the lines of the idea espoused by Lee Smolin that there is something going on in the individual experiments of QM which the statistical model doesn't capture

Everybody thinks there is something going on. "Realism" is a technical term in the philosophy of physics referring to whether you can capture that "something" in mathematical terms that describe what it is actually like.

As I said though I prefer the term "Representational" as opposed to "Realist" because Realist causes the exact confusion you are having here.

 

[Lynch101]

Everybody thinks there is something going on. "Realism" is a technical term in the philosophy of physics referring to whether you can capture that "something" in mathematical terms that describe what it is actually like.

As I said though I prefer the term "Representational" as opposed to "Realist" because Realist causes the exact confusion you are having here.

The idea that there is no mechanism of wave function colllapse or the notion that unmeasured quantities don't exist somewhat implies that there is "nothing to see" i.e. noting going on.

 

[Lynch101]

With regard to the question from the OP, where only one of the entangled particles is measured, does this measurement produce correlations in the other particle which suggest that the wave function has collapsed?

 

[DarMM]

The idea that there is no mechanism of wave function colllapse or the notion that unmeasured quantities don't exist somewhat implies that there is "nothing to see" i.e. noting going on.

No it doesn't. Wave function collapse can be viewed epistemically and measurement quantities can "not exist" prior to measurement because they are created by the experimental context. None of these imply nothing is going on.

 

[Lynch101]

No it doesn't. Wave function collapse can be viewed epistemically and measurement quantities can "not exist" prior to measurement because they are created by the experimental context. None of these imply nothing is going on.

I would agree with that, but it appears to be tautological that measurement quantities don't exist until they are measured. I think we can reasonably ask the question though, what is the state of the system prior to being measured?

 

[DarMM]

I would agree with that, but it appears to be tautological that measurement quantities don't exist until they are measured.

It's not tautological because in classical theories the values of measured quantities exist prior to their measurement.

 

[PGaccount]

I would agree with that, but it appears to be tautological that measurement quantities don't exist until they are measured. I think we can reasonably ask the question though, what is the state of the system prior to being measured?

In quantum theory, the measurements (interactions with the apparatus) are what define the behavior of the system. There is no sharp separation between these interactions and an "independent behavior" of the system. So there is no question of the measured values existing or not existing before these interactionscht.

 

[Lynch101]

It's not tautological because in classical theories the values of measured quantities exist prior to their measurement.

Apologies, could you ELI5? It's not an issue I have given any consideration to before, so I'm clear on how that is i.e. I would not be able to explain why that is the case. In what sense do they have values before being measured? Is it that we can predict their values?

I'm probably misinterpreting what is being said, but the system must be in some state prior to being measured. The idea that measured quantities do not exist prior to their measurement seems tautological in this sense, or at least doesn't address the question of the state of the system prior to measurement.

 

[DarMM]

could you ELI5?
In what sense do they have values before being measured?

In classical mechanics a particle might have some momentum $p$ as it moves along. When you measure it you get a value $p^{'}$ close to the actual momentum of the particle. So the measured result is a recording, up to experimental noise, of the momentum value the particle had before it was measured. Thus there was a value for momentum before you measured it.

This is not the case in Quantum Theory.