Bell's theorem, QFT, and the Relativity of Simultaneity

[Lynch101]

TL;DR Summary

Help understanding how the relativity of simultaneity differs from classic relativity to QFT, with reference to the outcomes of a Bell test.

I've been slowly grinding away with what I can about quantum mechanics and QFT. I'm not sure how far I've gotten but I've come up against a bit of a roadblock concerning how the relativity of simultaneity applies in QFT with specific reference to the outcome of Bell tests.

My misunderstanding is best outlined by way of the familiar thought experiment.

Thought Experiment
The classic thought experiment is of the relatively moving observers, Alice on a train and Bob on the platform They pass each other at some point O, where O is equidistant between two light sources. Two flashes of light are emitted simultaneously in Bob's frame. In Alice's frame, the two flashes are not simultaneous. Instead, the flash to the front of the train (A) happens first and the flash to the rear happens second (B).

As they pass each other at point O, in Alice's frame of reference, flash A will already have happened while, for Bob, it will not yet have happened i.e. it will be in his future. Similarly, as the train moves past and the flashes happen simultaneously in Bob's frame, flash B will still be in Alice's future.

I had been looking at stuff about Bell's theorem and I was wondering why this reasoning doesn't apply to a Stern Gerlach run, where the exposure of the Stern Gerlach plate? My thought process has the exposure event being simultaneous with the flashes of light in Bob's frame, and located together with the light source A. My understanding was that, when Alice passes point O, flash A and the exposure of the Stern Gerlach plate will already have happened in her reference frame but will not yet have happened in Bob's. This would seem to imply that that the outcome of the Bell test is set before the experiment is completed.

Unfortunately, I'm not familiar enough with QFT to know why the above reasoning doesn't apply.

Another barrier is my lack of mathematics, so I try to work with [hypothetical] real world scenarios to understand what observers will observe, or what is "true about the world" based on these real world examples.

Questions:

• - Are events which are simultaneous in one frame, still non-simultaneous in a relatively moving frame? (I'm fairly certain the answer is yes, but just
• in case there are any clarifications on this point)
• 
  
• - In the first thought experiment with Alice and Bob, when they pass each other at point O will flash A [still] already have happened for Alice, but
• not yet for Bob (under QFT)
• 
  
• - With the exposure of the Stern Gerlach plate simultaneous with the flashes, when Alice and Bob pass each other at point O, will the exposure
• event already have happened in her reference frame, but not yet in Bob's?

 

[PeroK]

Summary:: Help understanding how the relativity of simultaneity differs from classic relativity to QFT, with reference to the outcomes of a Bell test.

I've been slowly grinding away with what I can about quantum mechanics and QFT. I'm not sure how far I've gotten but I've come up against a bit of a roadblock concerning how the relativity of simultaneity applies in QFT with specific reference to the outcome of Bell tests.

My misunderstanding is best outlined by way of the familiar thought experiment.

Thought Experiment
The classic thought experiment is of the relatively moving observers, Alice on a train and Bob on the platform They pass each other at some point O, where O is equidistant between two light sources. Two flashes of light are emitted simultaneously in Bob's frame. In Alice's frame, the two flashes are not simultaneous. Instead, the flash to the front of the train (A) happens first and the flash to the rear happens second (B).

As they pass each other at point O, in Alice's frame of reference, flash A will already have happened while, for Bob, it will not yet have happened i.e. it will be in his future. Similarly, as the train moves past and the flashes happen simultaneously in Bob's frame, flash B will still be in Alice's future.

I had been looking at stuff about Bell's theorem and I was wondering why this reasoning doesn't apply to a Stern Gerlach run, where the exposure of the Stern Gerlach plate? My thought process has the exposure event being simultaneous with the flashes of light in Bob's frame, and located together with the light source A. My understanding was that, when Alice passes point O, flash A and the exposure of the Stern Gerlach plate will already have happened in her reference frame but will not yet have happened in Bob's. This would seem to imply that that the outcome of the Bell test is set before the experiment is completed.

Unfortunately, I'm not familiar enough with QFT to know why the above reasoning doesn't apply.

Another barrier is my lack of mathematics, so I try to work with [hypothetical] real world scenarios to understand what observers will observe, or what is "true about the world" based on these real world examples.

Questions:

• - Are events which are simultaneous in one frame, still non-simultaneous in a relatively moving frame? (I'm fairly certain the answer is yes, but just
• in case there are any clarifications on this point)
• 
  
• - In the first thought experiment with Alice and Bob, when they pass each other at point O will flash A [still] already have happened for Alice, but
• not yet for Bob (under QFT)
• 
  
• - With the exposure of the Stern Gerlach plate simultaneous with the flashes, when Alice and Bob pass each other at point O, will the exposure
• event already have happened in her reference frame, but not yet in Bob's?

I think you have probably understood the relativity of simultaneity. Note, however, that the cause and effect in something like the SG experiment are not affected by this. In fact the statement "has already happened in Alice's frame at some distant point" has no physical significance. It may sound like "has already happened" has some physical significance but it doesn't. It's what's called a coordinate dependent statement.

This has some bearing on Bell's theorem, since any attempt to attribute a causal link between two spacelike separated events runs into the relativity of simultaneity.

You don't need QFT (thankfully) to understand any of this.

 

[Lynch101]

I think you have probably understood the relativity of simultaneity. Note, however, that the cause and effect in something like the SG experiment are not affected by this. In fact the statement "has already happened in Alice's frame at some distant point" has no physical significance. It may sound like "has already happened" has some physical significance but it doesn't. It's what's called a coordinate dependent statement.

This has some bearing on Bell's theorem, since any attempt to attribute a causal link between two spacelike separated events runs in
You don't need QFT (thankfully) to understand any of this.

Ah, OK. I'm familiar with reference frame dependent statements, but I had been led to believe something somewhat different about the physicality of events. That might have been down to the philosophical prejudice of the source though. If you don't mind, can I outline the understanding I have, based on what I've been told. You might be able to point out where my understanding is falling down.

In the thought experiment above, at some point prior to Alice and Bob passing each other at point O - let's call it point M - the outcome of the Stern Gerlach run is actualised/crystalised/set in stone - this is where the terminology fails me - it is an observable phenomenon, in Alice's reference frame (on the train). I'm probably going to butcher the terminology here, but I find that by using it and having it corrected I learn to use it more precisely - could we say that the outcome of the SG run is an event on the hyperplane of events comprising Alice's frame, simultaneous with the event of Alice at point M? This would have physical significance, wouldn't it?

According to Bob's frame of reference, when Alice is at point M, the outcome of the SG run would not be actualised (in his frame). As above, can we say it is not on the hyperplane of event simultaneous with Alice at point M? If Bob were a student of relativity however, he would know (or later calculate) that prior to the outcome of the SG run in his frame, and prior to Alice and he crossing paths at point O, the outcome of the SG run is known in Alice's frame, or at least is knowable. Would he attribute physical significance to it in this way?

 

[PeterDonis]

In the thought experiment above, at some point prior to Alice and Bob passing each other at point O - let's call it point M - the outcome of the Stern Gerlach run is actualised/crystalised/set in stone

No. There is no single "point" involved. The two measurements take place at two different points in spacetime, and those two different points in spacetime are spacelike separated, so there is no invariant fact of the matter about the order in which they take place. This also means the results of the experiments cannot depend on the order in which they take place (since there is no such invariant order), and they don't.

See further comments below.

could we say that the outcome of the SG run is an event on the hyperplane of events comprising Alice's frame, simultaneous with the event of Alice at point M? This would have physical significance, wouldn't it?

No. "Simultaneous" has no physical significance; it is frame-dependent.

This also means there is no global concept of "now" in relativity. There is no global concept of "when events get actualized" (or whatever term you want to use). The only physically meaningful connections between events are causal connections--which events are in the past or future light cones of which other events.

If Bob were a student of relativity however, he would know (or later calculate) that prior to the outcome of the SG run in his frame, and prior to Alice and he crossing paths at point O, the outcome of the SG run is known in Alice's frame, or at least is knowable. Would he attribute physical significance to it in this way?

He can attribute physical significance to the fact that, when Alice makes her measurement, she knows its result. But he doesn't need relativity to tell him that.

He cannot attribute physical significance to the "time", in his frame, that Alice's measurement takes place, relative to readings on his clock, because that has nothing to do with any causal connection between him and Alice. The only causal connection would be that if Alice sends him a message telling him of the result of her measurement, he will receive it when it has traveled to him no faster than light--in other words, when the event of Alice making the measurement enters his past light cone.

 

[PeroK]

could we say that the outcome of the SG run is an event on the hyperplane of events comprising Alice's frame, simultaneous with the event of Alice at point M? This would have physical significance, wouldn't it?

The point is that "now" at some other location has no physical significance. To take my favourite example (you may have heard it before!).

You have Alice and Bob, say, considering a distant planet a long way away. Alice has some some of high-speed vehicle that she can scoot backwards and forwards in. When they consider "now" on that distant planet, it's so far away that Alice's "now" at that distant planet changes by $\pm 100$ years every time she changes direction(!)

As far as Bob's concerned it's 2020 on that distant planet. As far as Alice is concerned, as she passes Bob traveling one way it's 1920 on that distant planet and when she passes him the other way it's 2120 on that distant planet. We can assume that Bob and the distant planet are effectively at rest (and we are assuming flat spacetime for the sake of this argument).

Now, you could argue that there is some physical significance to the history of that distant planet every time Alice changes direction. You could argue that 200 years of history are alternately wiped out and then recur. And, when she gets tired of scooting around and joins Bob, it's back to 2020 on that distant planet.

Or, you can come to the conclusion that I come to that "now" on that distant planet has no physical significance in these cases. History is not being wiped out and replayed at Alice's whim. And although it's tempting to see "now" on that distant planet as something physically meaningful, it isn't.

 

[Lynch101]

Thank you for the reply Peter.

No. There is no single "point" involved. The two measurements take place at two different points in spacetime, and those two different points in spacetime are spacelike separated, so there is no invariant fact of the matter about the order in which they take place. This also means the results of the experiments cannot depend on the order in which they take place (since there is no such invariant order), and they don't.

Sorry, I'm not sure I'm interpreting this correctly. I might be confusing the situation by talking about points. For the sake of helping me to understand this clearer, I'm thinking of markers laid out along the train tracks, where Bob is standing at the marker with the letter 'O' painted on it. The SG plate is located to the right and is painted with, let's say 'S'.

I try to introduce the invariance by way of two flashes of light which are simultaneous in Bob's frame. One light source is located along the tracks and is painted with, say 'K' - such that the two light sources are equidistant from Bob. The flashes of light occur simultaneously in Bob's frame and both are simultaneous with the exposure event of the SG plate. So that, when the flash of light event at S occurs, the exposure event on the SG plate also occurs.

No. "Simultaneous" has no physical significance; it is frame-dependent.

This also means there is no global concept of "now" in relativity. There is no global concept of "when events get actualized" (or whatever term you want to use). The only physically meaningful connections between events are causal connections--which events are in the past or future light cones of which other events.

It was partially in this context of the absence of a global "now" that I have learned about the features of relativity. Someone was explaining the consequences of the absence of a global "now" and it is partly this which had led me to the understanding I am trying to articulate. This might be part of my issue. But it is the consequence of this absence of a global "now" that I am trying to get at and what it means for the possible outcomes of an SG run.

Also, my improper use of terminology here might mean that I'm not explaining it properly here, or it could be the source of my misunderstanding.

I'm thinking in terms of the physical significance of events. Let's say, Alice's stubs her toe when she passes the marker with K painted on it. To Alice, this is a physically significant event. At the moment she stubs her toe, the exposure event happens simultaneously, in her reference frame. This exposure event would be as physically significant as her stubbing her toe or colloquially, equally real.

In more philosophical terms, and in the context of there being no universal "now", at the moment Alice stubs her toe, as she passes the K marker, the SG exposure is a real and physically significant event in the Universe

He can attribute physical significance to the fact that, when Alice makes her measurement, she knows its result. But he doesn't need relativity to tell him that.

He cannot attribute physical significance to the "time", in his frame, that Alice's measurement takes place, relative to readings on his clock, because that has nothing to do with any causal connection between him and Alice. The only causal connection would be that if Alice sends him a message telling him of the result of her measurement, he will receive it when it has traveled to him no faster than light--in other words, when the event of Alice making the measurement enters his past light cone.

Maybe I'm incorrectly interpreting this but I think I may have inadvertently confused the issue by using Alice and Bob somewhat out of their natural habitat. In this example, Alice is not doing her own SG run, she is observing Bob do his. Gina is back in the lab while Alice is on sabbatical and traveling the cosmos on relativity railways

It's meant as a bit of a hybrid of the classic relativity thought experiment of the relatively moving observers, but one of the observers is doing an SG run. The flashes of light which are simultaneous in Bob's frame are also simultaneous with the SG exposure event - the flashes of light are more to help me visualise and explain the idea.

In the context of the absence of a global "now", at the moment she passes the marker K there is a simultaneous event which is in Alice's "now". That is the exposure event or the outcome of Bob's SG run.

At the moment that Alice passes the maker K, according to Bob's reference frame, the exposure is not in Bob's "now" it is in Bob's future.

If both "nows" are equally real, or the events in each "now" are equally, physically significant, it would mean that the outcome of Bob's SG run is fixed prior to it occurring in his frame of reference.That is based on the understanding of the relativity of simultaneity I have developed up until now, so there must be some issue with it. I just can't identify why myself.

 

[Lynch101]

Thank you for the responses PeroK.

The point is that "now" at some other location has no physical significance. To take my favourite example (you may have heard it before!).

You have Alice and Bob, say, considering a distant planet a long way away. Alice has some some of high-speed vehicle that she can scoot backwards and forwards in. When they consider "now" on that distant planet, it's so far away that Alice's "now" at that distant planet changes by $\pm 100$ years every time she changes direction(!)

As far as Bob's concerned it's 2020 on that distant planet. As far as Alice is concerned, as she passes Bob traveling one way it's 1920 on that distant planet and when she passes him the other way it's 2120 on that distant planet. We can assume that Bob and the distant planet are effectively at rest (and we are assuming flat spacetime for the sake of this argument).

Now, you could argue that there is some physical significance to the history of that distant planet every time Alice changes direction. You could argue that 200 years of history are alternately wiped out and then recur. And, when she gets tired of scooting around and joins Bob, it's back to 2020 on that distant planet.

Or, you can come to the conclusion that I come to that "now" on that distant planet has no physical significance in these cases. History is not being wiped out and replayed at Alice's whim. And although it's tempting to see "now" on that distant planet as something physically meaningful, it isn't.

I have learned about the consequences of relativity mainly through examples like this, and other thought experiments and I am familiar with the basic mathematics behind it.

As Alice is zooming around on her vehicle and she passes Bob the first time, would it also be 1920 for Bob? If he is at rest relative to the distant planet, would Alice's zooming around not mean that, when she passes Bob the second time 100 years has passed for him?

This sounds like a variation on the twin paradox.

 

[PeterDonis]

Let's say, Alice's stubs her toe when she passes the marker with K painted on it. To Alice, this is a physically significant event.

Yes.

At the moment she stubs her toe, the exposure event happens simultaneously, in her reference frame.

The "simultaneously" part is not physically significant. It's just an artifact of her choice of coordinates. No physical observable, no result of any measurement, no physically significant event depends on it.

This exposure event would be as physically significant as her stubbing her toe or colloquially, equally real.

The exposure event itself is a physically significant event, yes. But the exposure event being simultaneous in Alice's frame with Alice stubbing her toe is not physically significant, as above. The only physically significant relationship between those two events (Alice stubbing her toe and the exposure event) is that they are spacelike separated, hence neither one can causally affect the other. That is true independent of any choice of coordinates. But the events being "simultaneous" is not.

In this example, Alice is not doing her own SG run, she is observing Bob do his.

Then she will observe Bob doing his run when the light signals emitted from that event reach her. Until that happens, the only physically significant thing she can say about Bob doing his run is that no causal effect from that event (Bob doing his run) has reached her yet. She can choose coordinates and say, based on those coordinates, that Bob is doing his run "now" at a particular time by her clock, but there is no physical significance to that statement; it's just an artifact of her choice of coordinates.

If both "nows" are equally real, or the events in each "now" are equally, physically significant

Neither "now" is physically significant. Individual events are, but "now" is not. See above.

That is based on the understanding of the relativity of simultaneity I have developed up until now, so there must be some issue with it. I just can't identify why myself.

The issue is that you are attributing physical significance to "now". There isn't any.

 

[DrChinese]

...could we say that the outcome of the SG run is an event on the hyperplane of events comprising Alice's frame, simultaneous with the event of Alice at point M? This would have physical significance, wouldn't it?

(My comments only relate in the sense that we are talking about a Bell test of some type involving Alice and Bob, and various relativistic considerations.)

When you say "has physical significance" the problem is defining that statement within a Bell test. Consider that we explicitly construct the following scenarios:

a. Alice measures first, in all reference frames.
b. Bob measures first, in all reference frames.
c. Alice and Bob measure at the same time, in all reference frames.

Since QM makes the same statistical predictions in these 3 cases, how would you determine that there is any different "physical significance" to them? You can't, and that is why it is meaningless to attempt to model what happens in those terms.

Also: You commented previously that the outcomes must be predetermined (or some variation of that). That was the EPR conclusion too, but Bell showed that could not be the case either (ignoring interpretations that explicitly restore predetermination).

 

[PeroK]

As Alice is zooming around on her vehicle and she passes Bob the first time, would it also be 1920 for Bob? If he is at rest relative to the distant planet, would Alice's zooming around not mean that, when she passes Bob the second time 100 years has passed for him?

No, that's not the idea. You probably do need to learn what the relativity of simultaneity means.

Alice is effectively colocated with Bob. If you imagine Bob's reference frame as a set of clocks lined up in both directions, all synchronised in Bob's frame, then Bob's clocks are not synchronised in Alice's frame. They are progressively more out of sync the further away they are. Depending on Alice's direction of motion the clocks on one side will be advanced and on the other side lagging.

You may need to go back to square one and try to understand the basic principles of SR.

 

[PeterDonis]

When you say "has physical significance" the problem is defining that statement within a Bell test. Consider that we explicitly construct the following scenarios:

a. Alice measures first, in all reference frames.
b. Bob measures first, in all reference frames.
c. Alice and Bob measure at the same time, in all reference frames.

Scenario c. is impossible as you state it ("at the same time, in all reference frames"). I would assume that what you actually meant was something like: "c. Alice's and Bob's measurements are spacelike separated, so their time ordering is different in different frames". I'll assume that rewording in what follows.

Since QM makes the same statistical predictions in these 3 cases, how would you determine that there is any different "physical significance" to them?

In the particular case of SG measurements on two particles in the singlet state, you can't, yes.

However, there are plenty of cases, in general, that can be constructed in which there will be a difference between scenarios a. and b., i.e., a difference depending on the ordering of Alice's and Bob's measurements. But there are no cases in which results in scenario c. will depend on the ordering of Alice's and Bob's measurements (since that ordering is not frame invariant in scenario c.). So in general, it can make a difference whether Alice's and Bob's measurements are spacelike separated or not.

 

[Lynch101]

The "simultaneously" part is not physically significant. It's just an artifact of her choice of coordinates. No physical observable, no result of any measurement, no physically significant event depends on it.The exposure event itself is a physically significant event, yes. But the exposure event being simultaneous in Alice's frame with Alice stubbing her toe is not physically significant, as above. The only physically significant relationship between those two events (Alice stubbing her toe and the exposure event) is that they are spacelike separated, hence neither one can causally affect the other. That is true independent of any choice of coordinates. But the events being "simultaneous" is not.

Then she will observe Bob doing his run when the light signals emitted from that event reach her. Until that happens, the only physically significant thing she can say about Bob doing his run is that no causal effect from that event (Bob doing his run) has reached her yet. She can choose coordinates and say, based on those coordinates, that Bob is doing his run "now" at a particular time by her clock, but there is no physical significance to that statement; it's just an artifact of her choice of coordinates.Neither "now" is physically significant. Individual events are, but "now" is not. See above.
The issue is that you are attributing physical significance to "now". There isn't any.

OK. I take that, although I'm not sure I can fully reconcile it yet with what I have previously learned about relativity.

When I came to relativity first it was from a more Newtonian position, in the sense that I would have viewed the world as having operating within a global now. I learned about relative time and how relativity of simultaneity showed that this view was incorrect, that there was no Universal time and therefore, no universal "now". This was explained to me in a variety of ways including thought experiments such as the above and worldlines in 4D spacetime.

One of the ways in which it was clarified was by personalising it, which did help to clarify it for me. It was said that if we consider our own personal now, let's say on our 30th birthday, just looking around, feeling, and experiencing the present moment, this is what we would consider our "now". If it was a global "now", the whole universe would exist on our 30th birhtday. Our past, would no longer exist and our future would not yet exist. The Universe would be constantly evolving just as we continually age.

However, if there is no global "now" that coincides with our 30th birthday, as relativity and the relativity of simultaneity necessitate, it would mean that either our past or our future would have to exist, along with our present. If only our present existed, then it would be a global now.

It was explained to me that relativity meant that such a perspective with a "now" could not be true, hence our past and/or future must exist, just as our present exists - whatever form that may be. It was explained that this was true for all objects in the universe i.e. that past, present, and future states all co-exist in 4D Minkowski spacetime and that the the locus of all events that make up our history (and that of every object) extend through spacetime as world lines.I was then applying this thinking to the Stern Gerlach plate and its world line.

 

[Lynch101]

(My comments only relate in the sense that we are talking about a Bell test of some type involving Alice and Bob, and various relativistic considerations.)

When you say "has physical significance" the problem is defining that statement within a Bell test. Consider that we explicitly construct the following scenarios:

a. Alice measures first, in all reference frames.
b. Bob measures first, in all reference frames.
c. Alice and Bob measure at the same time, in all reference frames.

Since QM makes the same statistical predictions in these 3 cases, how would you determine that there is any different "physical significance" to them? You can't, and that is why it is meaningless to attempt to model what happens in those terms.

Also: You commented previously that the outcomes must be predetermined (or some variation of that). That was the EPR conclusion too, but Bell showed that could not be the case either (ignoring interpretations that explicitly restore predetermination).

Thank you for the reply Dr.

My reasoning that they must be predetermined is based on my (probably errneous) application of what I have learned about the relativity of simultaneity and the world lines of objects in spacetime.

One of the contexts in which I learned about the relativity of simultaneity was in juxtaposition to the Newtonian idea of the global "now" or universal present moment. A personalised example was given where I was told to consider my present moment, right now. It helped at the time to anchor it to an event such as my 30th birthday.

It was explained that if there was a global "now" on my 30th birthday, then the whole universe existed in that global now - more so that the configuration of the universe at that moment, including my 30th birhtday was what constituted the global "now". It meant that the Universe continually evolved comprising only a single moment, just as we tend to experience.

It was explained to me that relativity overturned this view and there was no global present moment, or "now". This, therefore, necessitated that what I consider to be my past - or the past configuration of the Universe - and what I consider to be my future (future universal state) must be as equally real - what ever that term ends up meaning - as my present.

I was told that this is true for all objects in the universe and that the locus of all events that make up our history extend through 4D Minkiwski spacetime as a world line, with each event along the world line being equally real.

It is this reasoning that I am applying to the Stern Gerlach plate in a Bell test. If all events on the world line of the SG plate extend through spacetime and are equally real, then the outcome event would be set prior to the experiment.I am having trouble reconciling the two.

 

[PeterDonis]

I was told that this is true for all objects in the universe and that the locus of all events that make up our history extend through 4D Minkiwski spacetime as a world line, with each event along the world line being equally real.

@Lynch101 you might want to read this Insights article:

https://www.physicsforums.com/insights/block-universe-refuting-common-argument/

The view you are describing corresponds to the "block universe" view, and, as I show in the article, that view is not required by relativity. There are other possibilities.

As a model, yes, special relativity uses 4-d Minkowski spacetime, in which objects and observers follow particular worldlines. But the model makes no claims about which events are "real" to which observers at which points on their worldlines.

If all events on the world line of the SG plate extend through spacetime and are equally real, then the outcome event would be set prior to the experiment.

This is conflating the "block universe" view with determinism. The two are not the same.

Also, the "block universe" view comes from relativity, i.e., from a non-quantum theory which is deterministic; whether you consider the future to be as "real" as the past or not, in relativity the future is determined by the past. But that is not necessarily true in quantum mechanics, and you cannot just apply concepts from non-quantum physics to quantum mechanics and expect them to work. In fact, nobody has a way of completely reconciling what we know of quantum mechanics with a simple "spacetime" viewpoint; quantum phenomena like the violation of the Bell inequalities in experiments do not admit of any such simple interpretation.

 

[DrChinese]

... the outcome event would be set prior to the experiment.

As strange as it sounds, Bell tests can be run in which Alice and Bob run their tests BEFORE entanglement is generated. (The experimental demonstration of this would be better discussed in a separate thread.) So clearly, the order of events has nothing to do with the QM predictions.

On the other hand, it does seem to violate our world view of causality. Which in turns connects to our view of Special Relativity. The problem here is that time is not a factor, and ordering is not a factor. Also, quantum outcomes are random and statistical. So there is no sense that anything occurs in which relativity is a factor at all. It might, but there is absolutely no evidence to support that assertion. The only relevant variable in a Bell test is the relationship between what Alice chooses to measure, and what Bob chooses to measure.

 

[Lynch101]

No, that's not the idea. You probably do need to learn what the relativity of simultaneity means.

Alice is effectively colocated with Bob. If you imagine Bob's reference frame as a set of clocks lined up in both directions, all synchronised in Bob's frame, then Bob's clocks are not synchronised in Alice's frame. They are progressively more out of sync the further away they are. Depending on Alice's direction of motion the clocks on one side will be advanced and on the other side lagging.

You may need to go back to square one and try to understand the basic principles of SR.

Thanks PeroK, I have a decent understanding of that aspect of relativity of simultaneity. If Alice tries to synchronise her clocks, for example, two spatially separated clocks at either end of the train. She sends a light pulse from the mid-point, where she is located to each clock, simultaneously. Both light pulses return to the mid-point and Alice's clock are synchronised in her frame.

However, in Bob's reference frame the light pulse takes a longer time to reach the mirror at the front of the train because that mirror is moving away from the light pulse. The clock at the rear of the train is set running first, because the rear of the train is advancing towards the light pulse. This means that the clocks are out of sync because the clock at the rear of the train is set ticking before the clock at the front of the train.

This is due to the different distances that each light pulse has to travel to the respective clocks (shorter to the back, longer to the front). This issue is canceled out on the return trip (longer from the back, shorter from the front) meaning both signals return to Alice simultaneosuly - just as they do in her frame. Hence why they are synced in Alice's frame but not in Bob's.

I must be interpreting the thought experiment incorrectly. It sounded to me like a variation on the twin "paradox", where one twin speeds away from the Earth and then returns to an older twin.

 

[PeroK]

Thanks PeroK, I have a decent understanding of that aspect of relativity of simultaneity. If Alice tries to synchronise her clocks, for example, two spatially separated clocks at either end of the train. She sends a light pulse from the mid-point, where she is located to each clock, simultaneously. Both light pulses return to the mid-point and Alice's clock are synchronised in her frame.

However, in Bob's reference frame the light pulse takes a longer time to reach the mirror at the front of the train because that mirror is moving away from the light pulse. The clock at the rear of the train is set running first, because the rear of the train is advancing towards the light pulse. This means that the clocks are out of sync because the clock at the rear of the train is set ticking before the clock at the front of the train.

This is due to the different distances that each light pulse has to travel to the respective clocks (shorter to the back, longer to the front). This issue is canceled out on the return trip (longer from the back, shorter from the front) meaning both signals return to Alice simultaneosuly - just as they do in her frame. Hence why they are synced in Alice's frame but not in Bob's.

I must be interpreting the thought experiment incorrectly. It sounded to me like a variation on the twin "paradox", where one twin speeds away from the Earth and then returns to an older twin.

Yes. This is now a statement about time and simultaneity between the two reference frames. It's not just a quirk of one particular experiment.

Likewise from the train frame (Alice) the clocks in Bob's frame are out of sync. Imagine clocks extending out in both directions. If Alice keeps going at constant speed, Bob's clocks in front of her are ahead of Bob's clocks behind her.

But, if Alice gets her train to change direction rapidly and move in the opposite, then the lack of synchronicity of Bob's clock is reversed in Alice's new frame. But, as far as Bob is concerned nothing has happened to his clocks: they are physically untouched. So, Alice's change of perspective on what Bob's clocks read can be seen asa purely coordinate (non-physical) effect. As can the lack of synchonicity in the first place.

 

[PeterDonis]

I must be interpreting the thought experiment incorrectly.

It depends on which thought experiment; you have mentioned more than one.

In the thought experiment where Alice and Bob are each at rest in an inertial frame for all time (but at rest in different frames, since they are in relative motion), and Bob sees Alice's clocks as not synchronized (which you are analyzing correctly, as far as I can see), Alice and Bob can only ever meet once. For them to meet more than once, one of them would have to stop moving inertially (fire rockets or something like that), meaning they would no longer be at rest in an inertial frame for all time.

In the twin paradox, the two twins are not both at rest in an inertial frame for all time. At least one of them (the "traveling twin" in the standard twin paradox) has to turn around, meaning he has to stop moving inertially for at least some portion of his trip. That is what allows him to meet up again with the stay-at-home twin after they have already met once (at the start of the trip).

In the scenario where Alice and Bob each run a SG experiment on one of two particles that are in an entangled state, Alice and Bob are both at rest in the same inertial frame, so there is no issue of relative motion at all. Relativity is not even involved in the usual analysis of that scenario; the issues it raises are all to do with quantum mechanics, not relativity. But, as has already been noted, you can't apply concepts like determinism, which makes sense in the context of non-quantum relativity, to a quantum mechanical experiment.

 

[DrChinese]

Scenario c. is impossible as you state it ("at the same time, in all reference frames")...

When both measurements are taken in the same place, one before/after/simultaneously etc., I would say that there would be no ambiguity.

The point is that regardless of how you construct Alice and Bob's reference frames, there are no discernible differences to what is reported for the Bell test results. There is no evidence of any element of causality whatsoever in such an experiment. Does Alice's measurement influence Bob's outcome? Or vice versa? There is no way to tell, no causality evident. Further, the outcomes are random (as far as we know) so no causality there either.

 

[PeterDonis]

When both measurements are taken in the same place, one before/after/simultaneously etc., I would say that there would be no ambiguity.

Since in the usual treatment each measurement is a separate event (distinct point in spacetime), it is impossible for them both to be at exactly the same place and at exactly the same time, in any frame. And there will be only one frame in which they happen either at the same place (if they are timelike separated) or at the same time (if they are spacelike separated); in all other frames, they will happen at neither the same place nor at the same time.

If you consider both measurements as happening at exactly the same point in spacetime, then I suppose there is no ambiguity, but only because you have, so to speak, blurred your vision so as to avoid seeing any.

The point is that regardless of how you construct Alice and Bob's reference frames, there are no discernible differences to what is reported for the Bell test results.

Yes, for that particular scenario. But one can easily construct scenarios in which the order of making the measurements does make a difference in the results. The only restriction imposed by relativity is that the order cannot make a difference in the results for measurements that are spacelike separated. The Bell test happens to satisfy the much more general property, not required by relativity, that the order of making the measurements does not affect the results at all, regardless of how the measurement events are related in spacetime.

 

[DrChinese]

1. If you consider both measurements as happening at exactly the same point in spacetime, then I suppose there is no ambiguity...

2. Yes, for that particular scenario. But one can easily construct scenarios in which the order of making the measurements does make a difference in the results.

1. The point is that when there is no ambiguity in the ordering, there is no difference anyway in the statistical results.

2. No Bell experimental results are affected by the ordering of Alice's measurement, Bob's measurement, or even when the entanglement occurs. If you know of any such experiment that concludes differently, I'd be mighty interested to read about it.

What I am saying is simple: there is no aspect of special relativity that figures into the results of a Bell test. So you can do anything you want to the reference frames, and nothing changes in the way of apparent causality. Because there isn't any.

 

[Lynch101]

@Lynch101 you might want to read this Insights article:

https://www.physicsforums.com/insights/block-universe-refuting-common-argument/

The view you are describing corresponds to the "block universe" view, and, as I show in the article, that view is not required by relativity. There are other possibilities.

As a model, yes, special relativity uses 4-d Minkowski spacetime, in which objects and observers follow particular worldlines. But the model makes no claims about which events are "real" to which observers at which points on their worldlines.

Thank you Peter, that article is great. I wish I had discovered that when I first came to relativity it would probably save me a lot of unlearning now .

I had a read through the thread as well but I still have a few questions, if you wouldn't mind if I put them to you? I find that when I discuss a topic, presenting my understanding of it and having my errors pointed out helps me to develop a better understanding of it.

I was thinking, if you had the requisite privileges to re-open the thread, that would save having another thread on the Block Universe here. It might also add to what is already there.

I understand the point about the additional assumption which leads the block universe and I have a bit of a handle on the past light cone stuff, but I still have a few questions that would be great to tease out. It would certainly help with the unlearning progress.

Also, the "block universe" view comes from relativity, i.e., from a non-quantum theory which is deterministic; whether you consider the future to be as "real" as the past or not, in relativity the future is determined by the past. But that is not necessarily true in quantum mechanics, and you cannot just apply concepts from non-quantum physics to quantum mechanics and expect them to work. In fact, nobody has a way of completely reconciling what we know of quantum mechanics with a simple "spacetime" viewpoint; quantum phenomena like the violation of the Bell inequalities in experiments do not admit of any such simple interpretation.

Ah, I see. Thank you. I was under the impression that QFT had fully incorporated Minkoswki spacetime.

 

[PeterDonis]

If you know of any such experiment that concludes differently

Of course I don't know of any Bell test experiment that concludes differently, because, as I've already agreed, there isn't one.

I'm just pointing out that, for the case in which the measurement events are not spacelike separated, the property that the order of the measurements does not affect the results is not a general property of any QM experiment whatever; it is only a property of the particular class of experiments that we are calling "Bell tests".

 

[PeterDonis]

if you had the requisite privileges to re-open the thread

If you mean the discussion thread on the block universe Insights article, no, that thread is way too old to be reopened. If you have questions about the article, you can start a new thread in the relativity forum, and reference either the article itself, or any particular posts in the closed discussion thread, that you want to ask about.

I was under the impression that QFT had fully incorporated Minkoswki spacetime.

It has, in the sense that Minkowski spacetime defines the 4-d geometry in which events have to fit. (Actually, you can also do QFT on other background spacetimes, not just Minkowski spacetime.) But it does not share the determinism of non-quantum relativity theory.

 

[Lynch101]

As strange as it sounds, Bell tests can be run in which Alice and Bob run their tests BEFORE entanglement is generated. (The experimental demonstration of this would be better discussed in a separate thread.) So clearly, the order of events has nothing to do with the QM predictions.

On the other hand, it does seem to violate our world view of causality. Which in turns connects to our view of Special Relativity. The problem here is that time is not a factor, and ordering is not a factor. Also, quantum outcomes are random and statistical. So there is no sense that anything occurs in which relativity is a factor at all. It might, but there is absolutely no evidence to support that assertion. The only relevant variable in a Bell test is the relationship between what Alice chooses to measure, and what Bob chooses to measure.

Thank you Dr.

I was under the impression that QFT fully incorporated Special Relativity, no?

 

[Lynch101]

If you mean the discussion thread on the block universe Insights article, no, that thread is way too old to be reopened. If you have questions about the article, you can start a new thread in the relativity forum, and reference either the article itself, or any particular posts in the closed discussion thread, that you want to ask about.

Oh, perfect. I'll do that. Thank you!

It has, in the sense that Minkowski spacetime defines the 4-d geometry in which events have to fit. (Actually, you can also do QFT on other background spacetimes, not just Minkowski spacetime.) But it does not share the determinism of non-quantum relativity theory.

As in, QFT doesn't share the determinism of classic relativity?

Relativity of simultaneity still plays a role though, right? Presumably that is a characteristic feature of Minkowski spacetime?

 

[DrChinese]

I was under the impression that QFT fully incorporated Special Relativity, no?

Correct, it does. But it has no application to Bell tests (as compared to the non-relativistic version). Bell tests are sort of the poster child for some of the biggest mysteries of the quantum world. Such as how (and if) causality applies in physics.

 

[Lynch101]

Correct, it does. But it has no application to Bell tests (as compared to the non-relativistic version). Bell tests are sort of the poster child for some of the biggest mysteries of the quantum world. Such as how (and if) causality applies in physics.

I have been going through some literature on Bell tests but I haven't heard that question before, about whether or not causality applies in physics.

 

[PeterDonis]

QFT doesn't share the determinism of classic relativity?

That's correct, since QFT is a quantum theory and quantum mechanics in general does not share the determinism of classical relativity.

 

[PeroK]

As in, QFT doesn't share the determinism of classic relativity?

Relativity of simultaneity still plays a role though, right? Presumably that is a characteristic feature of Minkowski spacetime?

SR is a theory of space and time. There is noting inherently deterministic about the phenomena playing out on that background. Particle decay, for example, is inherently non-deterministic. It may take quantum theory to explain it fully, but you can study particle collisions and decay with simply SR and non-deterministic rules. Like the random energies in the beta decay that led to the discovery of the neutrino.

As far as SR is concerned, time dilation, length contraction and relativity of simultaneity are key elements that are all subsumed into the Lorentz transformation. QFT deals with Lorentz invariant quantities. All the basics of SR are therefore inherent in the theory through Lorentz invariance.

 

[PeterDonis]

Relativity of simultaneity still plays a role though, right?

QFT generally does not even use inertial frames and the accompanying concepts like relativity of simultaneity. It tends to use a formalism in which everything is written in invariant form, i.e., without requiring any choice of frame at all. It uses invariant concepts like spacelike separation of events, but not frame-dependent ones like simultaneity.

 

[DrChinese]

Of course I don't know of any Bell test experiment that concludes differently, because, as I've already agreed, there isn't one.

I'm just pointing out that, for the case in which the measurement events are not spacelike separated, the property that the order of the measurements does not affect the results is not a general property of any QM experiment whatever; it is only a property of the particular class of experiments that we are calling "Bell tests".

I'm with you on this all the way.

I sort of thought from the title of the thread that we were speaking of Bell as the background. It is something of a special case where time ordering of events is not a factor to the statistical predictions, and neither is reference frame (at least in traditional spin versions).

 

[DrChinese]

I have been going through some literature on Bell tests but I haven't heard that question before, about whether or not causality applies in physics.

A subject better discussed in the Quantum Interpretations subforum. You will find that this subject stirs up some very strong opinions. After all, QM only makes statistical predictions. And there is no currently known theoretical angle to making a specific prediction in a single instance. (Ignoring interpretations...)

 

[Lynch101]

A subject better discussed in the Quantum Interpretations subforum. You will find that this subject stirs up some very strong opinions. After all, QM only makes statistical predictions. And there is no currently known theoretical angle to making a specific prediction in a single instance. (Ignoring interpretations...)

hahaha thanks Dr. I'll check that out for sure!

 

[vanhees71]

Oh, perfect. I'll do that. Thank you!
As in, QFT doesn't share the determinism of classic relativity?

Relativity of simultaneity still plays a role though, right? Presumably that is a characteristic feature of Minkowski spacetime?

QFT as any quantum theory is not deterministic but probabilistic. It's still causal though by construction.

The difference between classical and quantum descriptions of reality are all in the notion of what's called a "state". In classical physics you have determinism, and the exact knowledge about the state of the system at one time implies the knowledge about the values of all possible observables you can measure on this system at this time and, due to the equations of motion, also for all later times. On the fundamental level you have a very strong version of determinism and causality, i.e., it's sufficient to now the state exactly at one time, and then you know, through solving the equations of motion, the state exactly at any later time (causality), and to know the exact state of the system implies that all possible observable quantities have well-defined values (determinism).

In QT the notion of "state" is different. You still have causality (even in the strong form of locality in time), i.e., knowing the exact state of a system at one time through the equations of motion implies to know the exact state of the system at any later time too.

Knowing the exact state, however, does not imply that all observables take determined values. The only thing you know when knowing the exact quantum state are probabilities for the outcome of measurements of any observable of the system.

In relativistic physics causality means that an event can only be causally connected to another event if they are time-like (or light-like) separated. This is incorporated in all realistic QFTs in terms of the microcausality condition, which means that the Hamilton-density operator has to commute with all local observables at space-like distances of their mutual arguments. This ensures Poincare invariance, causality, and unitarity of the S-matrix as well as the linked-cluster principle. In this sense this type of local relativistic QFTs incorporates the causality structure of (special-)relativistic spacetime, and that's why there is no discrepancy between inseparability (described by entanglement of far-distant parts of quantum systems in Bell experiments) and relativistic causality, and that's also verified in a whole plethora of very accurate and fascinating Bell-test experiments.