Undergrad Quantum Ball and Cup - Thought Experiment

[Morbert]

These are not strictly interpretational questions, but more a prelude to such.

In the ball and cup analogy, there is a probability associated with each cup and the cups move towards the "measurement device"" (bar). Is that aspect representative of the predictions of QM? My understanding is that, for any given position in the experimental set-up, there is an associated probability of measuring the system at that position, at a given time. Is this the case? Do the probabilities for the cups change [within individual runs of the experiment] as the cup advances, or do they remain the same?

Also, let's say for the first run of the experiment, are the associated probabilities the same for each position or is it more likely to be measured in some positions than others? E.g. say, is it more likely to be measured at cup A than cup E?

After the first measurement, do the probabilities for each cup change?

There isn't any particular distinction between classical and quantum physics in this scenario. The probabilities will change as the cups are turned over, in the sense that each time a cup is turned over, new information is made available to the observer which can be used to update probabilities. E.g. The probability that the ball will be found under cup 3 is $\mathbf{Tr}\left[\rho\Pi_3\right]$ at the start of the experiment. If cup one is overturned and turns up empty, the probability changes to $\mathbf{Tr}\left[\not\Pi_1\rho\not\Pi_1\Pi_3\right]$

 

[Lynch101]

Not very much.
It’s seldom effective to use macroscopic objects in forming a mental model of a quantum system. One difficulty is that the ball is not a simple point particle that we can drop into Schrodinger’s equation and solve for $\psi(x,t)$, the way we would if this were a five-well problem with Hamiltonian $p^2/2m+V(x)$ and initial state being a superposition of equal amplitude in each well. Instead, the ball is something like $10^{23}$ individual particles interacting with one another as well as the potential walls formed by the cups.

Even if we could prepare the system in a pure state superposition with equal probability of the multi-particle ball being in each cup, the forward evolution of that system won’t be anything like the idealized point particle solution. It will very quickly decohere into a classical ball in one cup and we just don’t know which; this state provides no insight into the predictions of QM.

Thanks for that clarification Nugatory. I should probably have specified that the thought experiment wasn't meant to be used to infer anything at the macroscopic level. The ball in this case is meant to represent the idealised point particle upon measurement, not to be treated as a multi-particle system. The cups are just meant to represent the fact that there is a probability associated with each position and that we don't know the position of the particle until it is measured.

The question I'm asking re: QM predictions, might be thought of in terms of a "map of predictions". I'm wondering if QM makes probabilistic predictions only for where the particle will be measured on the screen or if it makes predictions for the space between the preparation device and the screen.

My understanding is that it does give us this "map of predictions" and not just predictions at the screen. It would also make sense because we can just imagine moving the screen forward, towards the preparation device. I just wanted to check that my understanding of this is correct or if there is some nuance that I'm not picking up on.

 

[Lynch101]

There isn't any particular distinction between classical and quantum physics in this scenario. The probabilities will change as the cups are turned over, in the sense that each time a cup is turned over, new information is made available to the observer which can be used to update probabilities. E.g. The probability that the ball will be found under cup 3 is $\mathbf{Tr}\left[\rho\Pi_3\right]$ at the start of the experiment. If cup one is overturned and turns up empty, the probability changes to $\mathbf{Tr}\left[\not\Pi_1\rho\not\Pi_1\Pi_3\right]$

Thanks Morbert. I'm not trying to get at the idea that individual cups are overturned during individual runs of the experiment, rather whether the probability is the same for each cup, for each individual run of the experiment.

For example, let's say it's the first run of the experiment and there are 5* cups. Is the probability for the position of the particle the same for each cup (20%), or in that individual run of the experiment (with no cups overturned) does QM predict different probabilities for different cups? E.g.
Cup 1 = 20%
Cup 2= 30%
Cup 3 = 10%
Cup 4 = 15%
Cup 5 = 25%

*The cups represent the possible positions the particle could be measured in and the number can be scaled to represent the number of possible positions predicted by QM.

 

[Morbert]

For example, let's say it's the first run of the experiment and there are 5* cups. Is the probability for the position of the particle the same for each cup (20%), or in that individual run of the experiment (with no cups overturned) does QM predict different probabilities for different cups? E.g.
Cup 1 = 20%
Cup 2= 30%
Cup 3 = 10%
Cup 4 = 15%
Cup 5 = 25%

That depends on the preparation. An experimenter could prepare the experiment such that the probability for each cup is 20% or they could prepare the experiment such that the probability is different for each cup.

 

[Lynch101]

That depends on the preparation. An experimenter could prepare the experiment such that the probability for each cup is 20% or they could prepare the experiment such that the probability is different for each cup.

Ah right. Thank you for the clarification.

Do the different interpretations propose different reasons for the differences in probability, for each position? I would be inclined to presume yes, but presumptuousness is probably ill advised, particularly with regard to QM

In relation to the idea of a "map of probabilities", I would distinguish this from say a "wall of probabilities", where a "wall of probabilities" would represent the predictions on the measurement device/screen only. A "map of probabilities" would include the space between the preparation device and the screen which register the particles. Am I right in thinking that QM predicts such a "map of probabilities"?

 

[Morbert]

Ah right. Thank you for the clarification.

Do the different interpretations propose different reasons for the differences in probability, for each position? I would be inclined to presume yes, but presumptuousness is probably ill advised, particularly with regard to QM

In relation to the idea of a "map of probabilities", I would distinguish this from say a "wall of probabilities", where a "wall of probabilities" would represent the predictions on the measurement device/screen only. A "map of probabilities" would include the space between the preparation device and the screen which register the particles. Am I right in thinking that QM predicts such a "map of probabilities"?

QM can be used to compute probabilities for the single-time measurement event at the end of the experiment. QM can also be used to compute probabilities for possible histories of the system between preparation and measurement. Different interpretations might attribute different significance to histories, detections etc

 

[Lynch101]

QM can be used to compute probabilities for the single-time measurement event at the end of the experiment. QM can also be used to compute probabilities for possible histories of the system between preparation and measurement. Different interpretations might attribute different significance to histories, detections etc

Thanks for that clarification. Does some of this pertain to the consistent histories approach?

Are there cases where, for non-FTL interpretations, the past lightcone of the single-time measurement event (STME), could be used to [retrospectively] determine that some of the predictions that had been made, were not actually possible; because they lay outside the past lightcone of the event?

I'm thinking where the the STME occurs at the extreme left of the screen, would there be positions [to the extreme right*] that had a non-zero probability which lie outside the past lightcone of the STME?

*extreme right of the experimental set-up, not the screen.

 

[PeterDonis]

for non-FTL interpretations

What do you mean by "non-FTL interpretations"? If we are talking about relativistic QM, i.e., QFT, no FTL signaling is a prediction of the basic math of QM, independent of any interpretation; so all interpretations of QM must be consistent with that.

 

[Lynch101]

What do you mean by "non-FTL interpretations"? If we are talking about relativistic QM, i.e., QFT, no FTL signaling is a prediction of the basic math of QM, independent of any interpretation; so all interpretations of QM must be consistent with that.

Apologies, it was just a very shorthand ways of trying to capture any interpretations that might have features such as that of Bohmian Mechanics, as you mentioned previously.

In the pilot wave, which can cause the ball to swerve due to information propagated at speeds faster than light from events far away.

Am I right in thinking that in some specific cases, some of the predicted positions would lie outside the past light cone of the measurement event?

 

[PeterDonis]

Am I right in thinking that in some specific cases, some of the predicted positions would lie outside the past light cone of the measurement event?

In non-relativistic QM (which is the framework in which Bohmian mechanics was developed), there is not a no FTL signaling theorem; non-relativistic QM is perfectly happy to predict FTL changes in observables.

In relativistic QM, which is the only context in which a no FTL signaling theorem for QM exists, there is not even an accepted formulation of the Bohmian interpretation. But as long as it's an interpretation of QM, it will make the same experimental predictions, which means it will obey the no FTL signaling theorem.

 

[Lynch101]

In non-relativistic QM (which is the framework in which Bohmian mechanics was developed), there is not a no FTL signaling theorem; non-relativistic QM is perfectly happy to predict FTL changes in observables.

In relativistic QM, which is the only context in which a no FTL signaling theorem for QM exists, there is not even an accepted formulation of the Bohmian interpretation. But as long as it's an interpretation of QM, it will make the same experimental predictions, which means it will obey the no FTL signaling theorem.

Thanks for that clarification. I've encountered the no FTL signaling before alright and have read some of the debates concerning the FTL influences of Bohmian Mechanics. I think mine is a more basic question, however.

If I'm understanding this aspect of the predications of QM correctly, I'm thinking that, in certain specific cases, some of the predictions for the position of a quantum system would lie outside the past light cone of the actual measurement. Would that be correct?

Without presuming anything related to signaling.

 

[PeterDonis]

I'm thinking that, in certain specific cases, some of the predictions for the position of a quantum system would lie outside the past light cone of the actual measurement.

Don't you mean future light cone?

 

[Lynch101]

Don't you mean future light cone?

No, the past lightcone.

Let's say before the first run of the experiment, QM makes probabilistic predictions about the position of the system.

After the actual measurement is made we can then map the past lightcone of the measurement event and compare what the QM predictions were. I'm thinking that some of the predictions will lie outside the past lightcone of the measurement event.

 

[PeterDonis]

After the actual measurement is made we can then map the past lightcone of the measurement event and compare what the QM predictions were. I'm thinking that some of the predictions will lie outside the past lightcone of the measurement event.

This could be the case (for example, if the experiment involved a beam splitter that could direct a photon to one of two detectors at opposite ends of the lab, so either of the two possible detection events, whose probabilities would each be 1/2 in the simplest case, would be outside the past light cone of the other). So what?

 

[Lynch101]

This could be the case (for example, if the experiment involved a beam splitter that could direct a photon to one of two detectors at opposite ends of the lab, so either of the two possible detection events, whose probabilities would each be 1/2 in the simplest case, would be outside the past light cone of the other). So what?

Is it the case for specific measurements of the double-slit experiment?

My interpretation is that, at least for certain individual measurement events, QM predicts a non-zero probability of measuring the system/particle in a position which lies outside the past lightcone of the measurement event.

I might be interpreting that aspect incorrectly, which is why I was seeking clarification.

I think I understand how this would be interpreted under Bohmian Mechanics and certain collapse theories. Am I right in saying that BM ascribes the non-zero probability to a lack of information, while certain collapse theories say the system was spread out in space and collapsed FTL to a single position, upon measurement.

I'm not sure how it would be interpreted in QFT or MWI, say, that there was a non-zero probability of measuring the particle in a position outside the past lightcone of the measurement event.

If I'm interpreting that aspect of the predictions correctly.

 

[PeterDonis]

Is it the case for specific measurements of the double-slit experiment?

Meaning, individual impacts of particles on the detector screen? Yes, it could be.

My interpretation is that, at least for certain individual measurement events, QM predicts a non-zero probability of measuring the system/particle in a position which lies outside the past lightcone of the measurement event.

No. Go and read what you quoted from me again, carefully. Note that it does not talk about just one measurement event. It talks about two measurement events, which are spacelike separated. Before the experiment is run, QM will predict a nonzero probability of detection at both events. But that does not mean QM predicts that a particle will travel FTL from one event to the other. It just means there are two possible detections that could be made, only one of which will actually happen.

 

[Lynch101]

No.. Go and read what you quoted from me again, carefully. Note that it does not talk about just one measurement event. It talks about two measurement events, which are spacelike separated. Before the experiment is run, QM will predict a nonzero probability of detection at both events. But that does not mean QM predicts that a particle will travel FTL from one event to the other. It just means there are two possible detections that could be made, only one of which will actually happen.

Apologies, I was trying to focus on a single run of the double-slit experiment where electrons are sent [in one direction] towards a single screen, via two slits in an intervening screen. The one which results in an interference pattern building up on the detection screen after many runs of the experiment.

I think this is the one being referred to here, is that correct?

Meaning, individual impacts of particles on the detector screen? Yes, it could be.

My understanding is, in that particular experimental set-up, QM would predict that there was a non-zero probability of measuring the system/particle in a position which lies outside the past lightcone of the measurement event.

Is that understanding correct? If so, I think I understand how it is interpreted under BM and certain collapse interpretations but I'm not sure how that would be interpreted under interpretations such as QFT and MWI.

It might just be that I'm interpreting that aspect of the predictions incorrectly and that all positions with a non-zero probability are within the past lightcone of the measurement event.

 

[PeterDonis]

I think this is the one being referred to here, is that correct?

Yes. Each individual electron is observed to hit the screen at one particular place.

My understanding is, in that particular experimental set-up, QM would predict that there was a non-zero probability of measuring the system/particle in a position which lies outside the past lightcone of the measurement event.

Go read my post #46 again, carefully. You keep asking the same question even though I have already responded to it.

Part of the problem here is the way you are phrasing your question. Once you have an actual measurement event, i.e,. an event in spacetime where an actual measurement took place and an actual result was observed, the fact that, before that measurement took place, QM predicted a nonzero probability for a result to be observed at some other event that is outside the past light cone of the event where an actual measurement result was observed, is irrelevant. So talking about the past light cone of the actual measurement event as though it meant something with regard to predictions that QM made before the measurement was made, is pointless.

I strongly suggest that you take a step back and think about the actual question you want an answer to, and ask that question directly instead.

 

[Lynch101]

Go read my post #46 again, carefully. You keep asking the same question even though I have already responded to it.

OK, I'll to formulate it in terms of your example.

the fact that, before that measurement took place, QM predicted a nonzero probability for a result to be observed at some other event that is outside the past light cone of the event where an actual measurement result was observed, is irrelevant. So talking about the past light cone of the actual measurement event as though it meant something with regard to predictions that QM made before the measurement was made, is pointless.

I strongly suggest that you take a step back and think about the actual question you want an answer to, and ask that question directly instead.

The question I'm asking is just how to interpret the given facts. Ultimately it's a question of meaning. In that context, I don't think the given facts are irrelevant, since they are what are being interpreted in the first place. The past light cone is not pointless in the context of relativity, so I presume it wouldn't be pointless in the context of relativistic quantum mechanics.If we take your example above, of the beam splitter, with the 50% probability of ending up at either detector, the different interpretations ascribe different meanings to those probabilities. Bohmian Mechanics, for example, says the probabilistic predictions represent a lack of information. In truth, the photon really went towards one detector. So, in truth, there wasn't really a genuine possibility of measuring it at the other detector, that just represents our lack of information about the system.

Certain collapse interpretations appear to say that, in truth, the system went in both directions but spontaneously collapsed to a single position. This spontaneous collapse involved some sort of FTL propagation.

For relativistic interpretations* - and this could be where my misinterpretation lies - I would have expected that the system could only ever have been measured somewhere within its past light cone. My understanding was that, the measurement event could only have been caused by "something" within the past light cone.

This is what leads me to an interpretational question. Does the non-zero probability mean there was a genuine possibility the system could have been measured outside the past light cone of the measurement event, or does it simply represent a lack of information on our part?

 

[PeterDonis]

The question I'm asking is just how to interpret the given facts.

Ok, but QM predictions of probabilities are not facts. So if you want to focus on facts, you shouldn't even be talking about predictions of probabilities.

The past light cone is not pointless in the context of relativity, so I presume it wouldn't be pointless in the context of relativistic quantum mechanics.

I didn't say it was pointless. I said it was irrelevant to the particular thing you appeared to be focusing on. Which, as noted above, is a prediction of probabilities, not a fact.

If we take your example above, of the beam splitter, with the 50% probability of ending up at either detector, the different interpretations ascribe different meanings to those probabilities.

Ok, fine, if that's what you want to ask about, you should just ask about it. There's no need to go wandering off into irrelevancies about past light cones.

Bohmian Mechanics, for example, says the probabilistic predictions represent a lack of information.

Yes. The particle always has one, deterministic trajectory. However, as I have already noted, there is no accepted relativistic version of Bohmian mechanics. So if you're asking about relativistic QM, there is not an accepted Bohmian interpretation of that.

Certain collapse interpretations appear to say that, in truth, the system went in both directions but spontaneously collapsed to a single position.

No. Collapse interpretations, meaning interpretations that say collapse is a real physical process, say that about collapse of the wave function. There are no "positions" independent of the wave function. There are no hidden particles as there are in Bohmian mechanics.

This spontaneous collapse involved some sort of FTL propagation.

Not in any meaningful sense, since collapse intepretations still have to satisfy the no signaling theorem in QM. However, it is true that, just as with Bohmian mechanics. no collapse interpretation of this type that I'm aware of has an accepted relativistic version. So there is an open issue with such interpretations regarding how they work with relativistic QM.

For relativistic interpretations* - and this could be where my misinterpretation lies - I would have expected that the system could only ever have been measured somewhere within its past light cone.

First, once again, this is irrelevant to the scenario you keep talking about, which is, for example, a photon passing through a beam splitter and having 50% probability of being detected by each of two detectors, one in each output arm of the beam splitter. In such an experiment, we already know that only one of the two detectors will register a photon on each run, so there is literally no possibility at all of a photon being detected at two spacelike separated events. You don't even need relativity or any rule about "no FTL travel" for this; it's literally required just by the experimental setup itself. And it therefore tells you nothing at all about whether "the system could only ever have been measured somewhere within its past light cone". You really need to take a step back and think more clearly about this.

Second, the supposed rule you give here for relativistic interpretations isn't a matter of interpretation at all. It's a matter of the basic math of relativistic QM, i.e., QFT. And what the basic math of QFT tells you is: there is no way to even formulate this question because there is no way of identifying "the same particle" at different events in QFT. QFT is a theory of fields, not particles. "Particles" are just particular field states with particular observable manifestations. If you have two measurement events, event A measuring "one electron here" and event B measuring "one electron here", there is no way to tell that those two electrons are "the same" electron. Particles don't have little identifiers on them that keep track of them. All you can say is that there was an electron present at event A and an electron present at event B. You cannot say they were "the same" electron. (And you cannot say they were not the same electron either.)

My understanding was that, the measurement event could only have been caused by "something" within the past light cone.

Causality in QFT is more subtle than that. QFT actually does not have a rule that anything that happens at a given event can only be caused by something in the past light cone of that event. All QFT says is that measurements at spacelike separated events must commute, i.e., their results must not depend on the order in which they are made. (This rule makes obvious sense since the time ordering of spacelike separated events is frame dependent, so there is no invariant fact of the matter about which one occurs first.) QFT does not forbid causal connections between spacelike separated events, as long as what happens at those events does not depend on their ordering.

Does the non-zero probability mean there was a genuine possibility the system could have been measured outside the past light cone of the measurement event, or does it simply represent a lack of information on our part?

Your photon/beam splitter experiment, and the 50% chance of a photon being detected at either of two spacelike separated events, is irrelevant to this whole question. See above.

 

[gentzen]

Certain collapse interpretations appear to say that, in truth, the system went in both directions but spontaneously collapsed to a single position.

Can you be more specific, which concrete collapse interpretation you actually have in mind here?

But maybe that is the wrong question. Why do you want to understand QM in terms of some experiment with "nearly" no inherently quantum features? My impression is that you will only ever get interpretations of classical probability from such an experiment. So is your "real" question what the different interpretations would say, if you apply them in a context where classical probabilities would be sufficient?

 

[Lynch101]

Ok, but QM predictions of probabilities are not facts. So if you want to focus on facts, you shouldn't even be talking about predictions of probabilities.

I didn't say it was pointless. I said it was irrelevant to the particular thing you appeared to be focusing on. Which, as noted above, is a prediction of probabilities, not a fact.

Ok, fine, if that's what you want to ask about, you should just ask about it. There's no need to go wandering off into irrelevancies about past light cones.

"Fact" might not have been the clearest term to use, apologies. Would mathematical facts (as opposed to observational facts) be a better choice of words perhaps, or theoretical information? In interpretations of QM discussion is often on the interpretation of the statistical predictions. It's in that context I am trying to interpret what the probabilistic interpretations tell us, in conjunction with what an aspect of relativity tells us.

In that sense, I don't think the past light cone is irrelevant since it is that information which forms the basis of the question being asked. It's a question of how to interpret that information.

Yes. The particle always has one, deterministic trajectory. However, as I have already noted, there is no accepted relativistic version of Bohmian mechanics. So if you're asking about relativistic QM, there is not an accepted Bohmian interpretation of that.

Just to focus in on how we can interpret the probabilistic interpretations here, because it provides some context for the question re: QFT. In this case, the probabilistic predictions tell us that, in truth, there isn't really a genuine possibility of measuring the particle in either position. It is our information about the system which is incomplete.

No. Collapse interpretations, meaning interpretations that say collapse is a real physical process, say that about collapse of the wave function. There are no "positions" independent of the wave function. There are no hidden particles as there are in Bohmian mechanics.

This is obviously a bit less intuitive but I wouldn't necessarily envisage hidden particles. Am I right in saying, in these collapse theories the wave function is a representation of the physical system delocalised in space; that, in some sense, the system is not localised to a single position but is physically spread out covering multiple positions?

My understanding is that, in this case, there is no missing information and the probabilistic predictions are a function of the genuine possibility of measuring the system in any of the positions (with non-zero probability). To account for why we only ever measure the position of the system in a single position (as opposed to all the non-zero positions) these interpretations say the system, randomly and physically, "collapses" to a single position. This entails some form of physical FTL causation which cannot be used for signalling.

Not in any meaningful sense, since collapse intepretations still have to satisfy the no signaling theorem in QM.

It would be meaningful in the sense that it is the reason [according to those collapse theories] we measure the system in a single position as opposed to all the non-zero predicted positions. It would be meaningful in the sense that it is a physical process which plays a causal role in the Universe. It wouldn't be exploitable, but it does have more than just a superficial meaning, I would say.

a photon passing through a beam splitter and having 50% probability of being detected by each of two detectors, one in each output arm of the beam splitter. In such an experiment, we already know that only one of the two detectors will register a photon on each run, so there is literally no possibility at all of a photon being detected at two spacelike separated events.

You don't even need relativity or any rule about "no FTL travel" for this; it's literally required just by the experimental setup itself.

At least this much I do get None of them say that both detectors will register a measurement event.

Looking at this in terms of the different interpretations [excluding the past light cone], while I wouldn't call them intuitive, I can make some sense of what Bohmian Mechanics and certain collapse theories say. I'm just less clear on what QFT says.

BM appears to say that both detectors don't truly have a genuine possibility of registering the measurement event. It's our incomplete information which makes it appear that way. This explains why we only end up with a single measurement outcome.

Certain collapse theories appear to say there is a genuine possibility of measuring at A or B but random, physical, FTL collapse of the wave function explains why we only get a single measurement event.

I'm not entirely clear how QFT explains the single measurement outcome. Unlike BM, it doesn't appear to imply that the probabilistic predictions are the result of incomplete information. FWICG, it says there is a genuine possibility of measuring the system at either location. This sounds similar to certain collapse theories, but the collapse theories explain this through FTL collapse of the physically delocalised system (represented by the wave function). Is there a similar explanation associated with QFT?

The subsequent question, with regard to the past light cone is just an extension of the question of whether there was a genuine possibility of measuring the system at all non-zero positions. Given that some of them lie outside the past light cone, how can we interpret that information?

Second, the supposed rule you give here for relativistic interpretations isn't a matter of interpretation at all. It's a matter of the basic math of relativistic QM, i.e., QFT. And what the basic math of QFT tells you is: there is no way to even formulate this question because there is no way of identifying "the same particle" at different events in QFT. QFT is a theory of fields, not particles. "Particles" are just particular field states with particular observable manifestations. If you have two measurement events, event A measuring "one electron here" and event B measuring "one electron here", there is no way to tell that those two electrons are "the same" electron. Particles don't have little identifiers on them that keep track of them. All you can say is that there was an electron present at event A and an electron present at event B. You cannot say they were "the same" electron. (And you cannot say they were not the same electron either.)

I'm not necessarily talking about separate events, as opposed to the probability of a measurement event. It's more a question of whether there was a genuine possibility of measuring the field state at all of the non-zero locations (similar to what collapse interpretations might say); or no genuine possibility (similar to BM).

My understanding is that QFT says there was a genuine possibility, but it's different from collapse interpretations. Collapse interpretations put forward a relatively clear (if unintuitive) explanation as to the origin of the probabilities and the single measurement outcome. I'm not clear on what the alternative explanation is according to QFT.

Causality in QFT is more subtle than that. QFT actually does not have a rule that anything that happens at a given event can only be caused by something in the past light cone of that event. All QFT says is that measurements at spacelike separated events must commute, i.e., their results must not depend on the order in which they are made. (This rule makes obvious sense since the time ordering of spacelike separated events is frame dependent, so there is no invariant fact of the matter about which one occurs first.) QFT does not forbid causal connections between spacelike separated events, as long as what happens at those events does not depend on their ordering.

It's probably my misinterpretation, but does this not allow for FTL causation, if the causal influence can come from outside the past light cone?

 

[Lynch101]

Can you be more specific, which concrete collapse interpretation you actually have in mind here?

I don't recall the particular names of the collapse theories. It's mostly been from discussions on here. PD has clarified a general idea with regard to certain collapse interpretations, so I would take it as a more general case of "any collapse interpretation to which the above applies".

But maybe that is the wrong question. Why do you want to understand QM in terms of some experiment with "nearly" no inherently quantum features? My impression is that you will only ever get interpretations of classical probability from such an experiment. So is your "real" question what the different interpretations would say, if you apply them in a context where classical probabilities would be sufficient?

I'm not sure I understand. The double-slit experiment does have quantum features. I'm trying to get an understanding of how to interpret the information that some of the positions predicted for the system lie outside the past light cone of the final measured position.

 

[DrChinese]

1. Certain collapse interpretations appear to say that, in truth, the system went in both directions but spontaneously collapsed to a single position. This spontaneous collapse involved some sort of FTL propagation.

2, Does the non-zero probability mean there was a genuine possibility the system could have been measured outside the past light cone of the measurement event, or does it simply represent a lack of information on our part?

1. What is propagating FTL? In your examples with the beam splitter, I don't see anything that qualifies. The "nonlocal" effect is the absence of a detection "there" when there is a detection "here", if you want to call that nonlocal. But nothing propagates.

2. Again, I don't see what is outside of any past light cone in your example.

On the other hand, there is no requirement that quantum effects are constrained to a past light cone. You can have entangled photon pairs in which the individually detected photons have never appeared in the other's past light cone.

 

[Lynch101]

1. What is propagating FTL? In your examples with the beam splitter, I don't see anything that qualifies. The "nonlocal" effect is the absence of a detection "there" when there is a detection "here", if you want to call that nonlocal. But nothing propagates.

You're right apologies. Collapse interpretations say that the causal influence is instantaneous (FTL), don't they? As opposed to "propagating" at some finite FTL speed.

2. Again, I don't see what is outside of any past light cone in your example.

There is a position that had a non-zero probability assigned to it, which lies outside the past light cone. This is what I'm looking to interpret.

A BM-like explanation might say there wasn't really a genuine possibility of measuring it in that position. The probability represents incomplete information on our part. A collapse-like explanation might say there was a genuine possibility of measurement but instantaneous-action-at-a-distance explains why there was a genuine possibility it could have been measured outside the past light cone.

Is there a BM- or collapse-like explanation for QFT? One which says how it was a genuine possibility to make a measurement at all of the non-zero positions or how it was not genuinely possible?

On the other hand, there is no requirement that quantum effects are constrained to a past light cone. You can have entangled photon pairs in which the individually detected photons have never appeared in the other's past light cone.

I think this is slightly different. In Peter's example there is only a single photon.

 

[PeterDonis]

It's in that context I am trying to interpret what the probabilistic interpretations tell us, in conjunction with what an aspect of relativity tells us.

I've already answered that. Go back and read what I said about causality and spacelike separated measurements commuting in QFT. Again, that is all independent of any interpretation.

Most of the literature on QM interpretations, unfortunately, uses non-relativistic QM as a framework, so it doesn't discuss the issue you are raising with how QM interpretations interact with relativity. So all we really have is the interpretation-independent rules I've already described.

 

[PeterDonis]

I don't think the past light cone is irrelevant

It's irrelevant in the particular scenario you have chosen. So if you want to make it relevant, you'll need to find another scenario that illustrates why.

 

[PeterDonis]

the probabilistic interpretations here,

in these collapse theories

Certain collapse theories

Please give specific references for which interpretations/theories you are talking about. (And note that some "theories", like the GRW stochastic collapse model, are not interpretations of QM, they are different theories that make different predictions about some experimental results from those of standard QM.) In order to say anything about what particular interpretations do or do not say, we need to have some kind of valid reference as a basis for discussion. That is part of the rules of this subforum.

 

[PeterDonis]

I'm not entirely clear how QFT explains the single measurement outcome.

QFT is not an interpretation of QM. It's relativistic QM. It doesn't "explain" single measurement outcomes at all, any more than basic non-relativistic QM, independent of any interpretation, does. QFT just makes predictions.

Please read my previous post about the lack of QM interpretation literature that uses QFT, instead of non-relativistic QM, as a framework.

 

[PeterDonis]

does this not allow for FTL causation, if the causal influence can come from outside the past light cone?

What it allows is not well described by the term "FTL causation", since it cannot be used to send any signals or otherwise influence any outcomes. The no signaling theorem is still true in QFT. QFT basically just says that, since the actual rule is that spacelike separated measurements commute, it is impossible to say that spacelike separated measurements cannot cause each other. But it is also impossible to say that they can cause each other. QFT simply makes no claim either way. As I noted in my previous post, QFT is not an interpretation of QM. It's just relativistic QM. It doesn't make claims about metaphysical concepts like "cause": it just makes predictions. The "spacelike separated measurements commute" rule (and its converse, that timelike or null separated measurements do not have to commute) is the closest thing QFT has to "causality".