Compatibility of Quantum Mechanics and Special Relativity

[Mal Cevalo]

Hello,

In my free time, I've been learning about an eclectic range of topics (ie. French History, Kinetic Theory etc.). Most recently I've been focused on Quantum Mechanics, which happens to be most complex topic I've ever looked at. Typically I write up summaries after reading from various sources, however this time I'm a little worried my summary might not be accurate.

Would it be possible to run through my summary below and point out any factual errors? (not so worried about bad grammar or spelling as its only for me)

In 1905, Albert Einstein devised the Special Theory of Relativity, which postulates:

1. There is no variation in laws of physics for all inertial frames of reference.
2. The speed of light in a vacuum is the universal speed limit of all objects and information.​

By 1935, it had become evident to Einstein, along with his colleagues Podolsky and Rosen, that Quantum Mechanics appeared to conflict with Special Relativity; with the trio expressing their concerns in the paper “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?”

Their key concern was regarding a phenomenon now known as Quantum Entanglement. For entangled particles interact instantaneously with each other, when one is measured for its spin, resulting in the latter’s measurement having the opposite spin, if both are measured along the same axis.

Einstein et al referred to this as “spooky action at a distance” as Quantum Mechanics implied entangled particles could be separated by astronomical distances, without any impact on its instantaneity. This seems to breach the second postulate of Special Relativity, as it appears information is transmitted between the two particles faster than the speed of light.

To avoid what they saw as a breach of the Second Postulate. It was proposed that prior to separation, these entangled particles effectively pre-plan to have opposite spins when measured along the same axis, in what is referred to as “hidden information”.

It wasn’t until 1964, that John Bell devised a test, which could rule out “hidden information” as being the mechanism behind “spooky action at a distance”. All credible Bell test experiments that have since been undertaken have contradicted the "hidden information" explanation.

While instantaneous interaction between entangled particles seems to defy Special Relativity. Orthodox interpretations of Quantum Mechanics, do not consider this interaction to count as true information exchange, as the spin of the particle measured first is random.

All help is much appreciated : )

 

[jfizzix]

The factual errors I see (if they can be counted as such) are as follows:

The second postulate of special relativity is not that the speed of light in a vacuum is a universal speed limit, but rather, that the speed of light in a vacuum is the same in all inertial frames of reference.
The first postulate is correct.
That the speed of light is a cosmic speed limit comes from those two postulates.

If I wanted to be really nit-picky, I'd also point out that Einstein doesn't actually mention "spooky action at a distance" in the original EPR paper, though he does later.

All in all, it's a good summary, though.

 

[forcefield]

Quantum Mechanics implied entangled particles could be separated by astronomical distances

No. Measurement devices can be separated. It is the measurement results that are "entangled". I don't know Special Relativity well enough to comment on the compatibility.

 

[jfizzix]

No. Measurement devices can be separated. It is the measurement results that are "entangled". I don't know Special Relativity well enough to comment on the compatibility.

Measurement results are not entangled.
The correlations in the measurement results prove (with high probability) that there's entanglement shared between the pair of particles, assuming enough identically prepared particle pairs to get good measurement statistics.

If the particles were not entangled, there's a limit to how strong the measurement correlations can be. Finding stronger correlations than this limit rules out the possibility that the pairs are not entangled, or at least, makes the probability of such a scenario vanishingly small.

 

[forcefield]

Measurement results are not entangled.
The correlations in the measurement results prove (with high probability) that there's entanglement shared between the pair of particles, assuming enough identically prepared particle pairs to get good measurement statistics.

If the particles were not entangled, there's a limit to how strong the measurement correlations can be. Finding stronger correlations than this limit rules out the possibility that the pairs are not entangled, or at least, makes the probability of such a scenario vanishingly small.

You are assuming an entangled pair of particles. Can you prove that they have separated before entanglement ends ? Like Bohr has been claimed to have said, "there is no quantum world", implying that there are no entangled particles.

 

[jfizzix]

You are assuming an entangled pair of particles. Can you prove that they have separated before entanglement ends ? Like Bohr has been claimed to have said, "there is no quantum world", implying that there are no entangled particles.

Violating a Bell inequality does not require assuming entangled pair of particles.
The violation shows that the correlations between measurement outcomes of separated detectors cannot be explained by a Local Hidden Variable (LHV) model.
If the joint quantum state of a pair of particles is separable (not entangled), then the measurement correlations would also have to obey an LHV model. This is why violating a Bell inequality shows that the particle pairs being measured by these detectors must be entangled.

The measurement events localize the position of each particle to its respective detector (which is also when the entanglement is destroyed). If the detectors are separated by a vast distance, then at the time of the detection, the particles must also be separated by a vast distance as well.

I can't argue for or against what Bohr may or may not have said.
In my experience, saying that two particles are entangled, and saying that the quantum state describing the two particles is entangled is saying the same thing.

 

[PeterDonis]

instantaneous interaction between entangled particles seems to defy Special Relativity

The correlations between measurements on entangled particles at spacelike separated events, which violate the Bell inequalities, do not require "instantaneous interaction". The interaction between the particles happened in the past, when they were entangled.

What the observed violations of the Bell inequalities do force us to do is to sharpen up our understanding of what consistency between quantum mechanics and special relativity actually requires. The proper framework for addressing this is quantum field theory, and in QFT, the key requirement is that measurements at spacelike separated events must commute--that is, the results cannot depend on the order in which the measurements are carried out. Measurements on entangled particles at spacelike separations satisfy this requirement, so any appearance that the correlations between them "defy" SR is only an appearance; there is no actual inconsistency.

 

[bhobba]

Measurements on entangled particles at spacelike separations satisfy this requirement, so any appearance that the correlations between them "defy" SR is only an appearance; there is no actual inconsistency.

Nice - hadn't thought of it that way before.

My view is as per this thread:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/

You should really exclude correlations from the start so no issue arises.

But having discussed that one a number of times I know opinons vary.

Thanks
Bill

 

[zonde]

The correlations between measurements on entangled particles at spacelike separated events, which violate the Bell inequalities, do not require "instantaneous interaction". The interaction between the particles happened in the past, when they were entangled.

What the observed violations of the Bell inequalities do force us to do is to sharpen up our understanding of what consistency between quantum mechanics and special relativity actually requires. The proper framework for addressing this is quantum field theory, and in QFT, the key requirement is that measurements at spacelike separated events must commute--that is, the results cannot depend on the order in which the measurements are carried out. Measurements on entangled particles at spacelike separations satisfy this requirement, so any appearance that the correlations between them "defy" SR is only an appearance; there is no actual inconsistency.

Well, I agree that there is no inconsistency between SR and entanglement phenomena. However there is inconsistency between entanglement and very popular interpretation of SR that speed of light is fundamental speed limit i.e. no physical effect can propagate faster than light.

 

[vanhees71]

There is no contradiction with this either! Only if you assume collapse as a physical ("ontic") process rather than an update of the knowledge of the local (!) observer ("epistemic"), you run into contradictions, and that's why Einstein was completely right in criticizing that branch of the Copenhagen interpretations which includes a collapse.

 

[zonde]

Bell inequalities are formulated and experimentally tested without any need for such an assumption.

 

[Boing3000]

However there is inconsistency between entanglement and very popular interpretation of SR that speed of light is fundamental speed limit i.e. no physical effect can propagate faster than light.

SR speed limit applies to things that moves. Entanglement do not propagate "effect". An entangled property seems to be non-local, meaning it have no coordinate and thus have no speed.

 

[bhobba]

SR speed limit applies to things that moves. Entanglement do not propagate "effect". An entangled property seems to be non-local, meaning it have no coordinate and thus have no speed.

SR applies to the speed information can be sent. Specifically its the ability to sync clocks.

That said that view is not what I use to explain SR - this is my preferred approach:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Thanks
Bill

 

[vanhees71]

Bell inequalities are formulated and experimentally tested without any need for such an assumption.

Of course. All you need is the minimal statistical interpretation, and there entanglement, inseparability, long-range correlations etc. etc. lead to no contradictions with the special relativistic causality structure of spacetime. Our standard relativistic QFTs are precisely constructed in such a way as to avoid such contradictions (microcausality, locality of interactions, linked-cluster principle all hold!).

 

[zonde]

SR applies to the speed information can be sent. Specifically its the ability to sync clocks.

Clock synchronization in SR is just a convention. You are free to adopt different conventions of clock synchronization for different reference frames and it will have no effect on predictions of SR. You will just have more cumbersome formulations of physical laws.

 

[zonde]

Of course. All you need is the minimal statistical interpretation, and there entanglement, inseparability, long-range correlations etc. etc. lead to no contradictions with the special relativistic causality structure of spacetime. Our standard relativistic QFTs are precisely constructed in such a way as to avoid such contradictions (microcausality, locality of interactions, linked-cluster principle all hold!).

Bell inequalities can not be constructed by only considering statistics. Contradiction with special relativistic causality structure of spacetime appears only when you consider individual events.

 

[Boing3000]

SR applies to the speed information can be sent. Specifically its the ability to sync clocks.

Tanks, I'll read that note carefully. But I find "information" way too vague a term. If it can be "sent", mustn't this "information" consist of some entity obeying the laws of conservation (meaning it cannot change locally without changing its value in the RHS of the Einstein field Equation).

Otherwise said, let's say we entangle a HUGE amount of electrons, and isolate the two group (A & B) far away. Then we measure group B (all a once because we have a HUGE number of detector). If there is a "real" change (whatever the speed of that effect) in group A, I bet some form of gravitational wave should be emitted from group A (due to the sudden change (as from group B))
If there is only some "pure information" change (like a (unmeasured yet) random distribution turned into another one), it obviously count as "pure information" if no change actually occurs at site A (or B for that matter). In short I wonder if there is information with no "weight" attached.

The extension of this thought experiment would be to wait that we measure at once group A (because only then the the correlation are "realized"). Meaning that if there is a true conservation of quantity of "up & down", the "change in correlation" is waiting in limbo to popup on measuring device.
As angle of all the detectors will actually decide the actual final information gathered, I think there is no such conservation of "information bits". That's how I understood Bell's implication about non-locality anyway, and the relation with SR/GR, (no propagating effect, because nothing move)

 

[vanhees71]

Bell inequalities can not be constructed by only considering statistics. Contradiction with special relativistic causality structure of spacetime appears only when you consider individual events.

Exactly, and QT makes only probabilistic predictions, which are testable via statistics (ensembles).

 

[atyy]

There is no contradiction with this either! Only if you assume collapse as a physical ("ontic") process rather than an update of the knowledge of the local (!) observer ("epistemic"), you run into contradictions, and that's why Einstein was completely right in criticizing that branch of the Copenhagen interpretations which includes a collapse.

Wrong. Collapse is consistent with quantum special relativity.

Quantum special relativity is consistent with "physical effects" traveling faster than the speed of light.

 

[bhobba]

If there is a "real" change (whatever the speed of that effect) in group A, I bet some form of gravitational wave should be emitted from group A (due to the sudden change (as from group B))

Well first I don't understand what you are gettting at, but as far as I can, here is what I think.

We have what's called the cluster decomposition property that lies at the foundation of QFT:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574

You can't sent information instantaneously.

As Weinberg says: the fundamental principles of physics (indeed, of all science) that experiments that are sufficiently separated in space have unrelated results…

Now this is thread about SR, but if you want to discuss Bell etc that's really outside this threads scope. It has been discussed many many times - you can look it up - but if you want to go through it again start a new thread. But basically in the cluster decomposition property as explained in the link correlations are specifically excluded and all Bell is, is a correlation.

Thanks
Bill

 

[Boing3000]

Well first I don't understand what you are gettting at

I was illustrating the difference between physical quantities that SR applies to, and those that aren't. Those quantities covered by SR are also covered by GR. The sloppy language of zonde post #9 is common place everywhere on the internet. "Action" "effect" "propagation" "distance" "speed" are not valid arguments for an incompatibility between SR and QM because entanglement as none of these properties. The correlation is (non-local). My thought experiment is just a way to test it using GR (because SR don't apply), and not QM.

I take a very small issue with "information" of your post, but using "it" to synchronize clock is a perfectly fine criteria. I suggest a simpler definition like "change".

You can't sent information instantaneously.

Indeed, because correlation don't change, they are. And thing that can be sent, move (although "instantaneous" is not really a speed either)
And also because maximally entangle multi particles state don't exist (because then you could retest the correlation for a change)

 

[zonde]

The sloppy language of zonde post #9 is common place everywhere on the internet. "Action" "effect" "propagation" "distance" "speed" are not valid arguments for an incompatibility between SR and QM because entanglement as none of these properties.

Who is arguing about incompatibility between SR and QM? It seems like you are implying that I am arguing for that. But I am not.
And I don't think it makes sense to attach "properties" to abstract term like "entanglement". But certainly we can speak about distance between two detection events (in lab restframe) and we can say that they are either spacelike or timelike separated.

 

[vanhees71]

Of course it makes perfect sense to "attach properties" to terms like "entanglement". In science only well-defined terms with clearly stated properties have a place, and entangled states have a very clear meaning, and nowadays you can't call them abstract anymore since in each quantum-optics lab they concretely prepare, e.g., polarization-engangle photon pairs via parametric downconverision en masse!

 

[Boing3000]

Who is arguing about incompatibility between SR and QM? It seems like you are implying that I am arguing for that. But I am not.

OK, my mistake then. The statement I obviously don't understood was this one:

However there is inconsistency between entanglement and very popular interpretation of SR that speed of light is fundamental speed limit i.e. no physical effect can propagate faster than light.

As indeed no physical effect can propagate faster than light, I assume you attribute speed and propagation to entanglement.

And I don't think it makes sense to attach "properties" to abstract term like "entanglement". But certainly we can speak about distance between two detection events (in lab restframe) and we can say that they are either spacelike or timelike separated.

As vanhees71 also remarked, I have no idea what you meant to say here. Entanglement is a well define process that occurred at one single event. The firther detection space/time separations events are irrelevant.

 

[zonde]

Of course it makes perfect sense to "attach properties" to terms like "entanglement". In science only well-defined terms with clearly stated properties have a place, and entangled states have a very clear meaning, and nowadays you can't call them abstract anymore since in each quantum-optics lab they concretely prepare, e.g., polarization-engangle photon pairs via parametric downconverision en masse!

Sorry, sloppy statement. I meant physical properties like "distance" or "speed".

 

[zonde]

As indeed no physical effect can propagate faster than light,

As I see experiments have demonstrated results that falsify this statement.

I assume you attribute speed and propagation to entanglement.

No. Your statement is sloppy. Entanglement is joined statistical property of two particle state. To speak about speed or propagation we have to speak about individual particles in entangled pairs. It does not make sense to say that two particle property propagates from one particle to the other one.

Entanglement is a well define process that occurred at one single event. The firther detection space/time separations events are irrelevant.

The whole point of Bell inequality violation is to demonstrate that this can not be the case.

 

[martinbn]

As I see experiments have demonstrated results that falsify this statement.

Like what?

 

[zonde]

Like what?

Loophole free violations of Bell inequalities.

 

[martinbn]

Loophole free violations of Bell inequalities.

What propagates there?

 

[zonde]

What propagates there?

Whatever it is that can affect measurement result of individual photon (or electron).

 

[martinbn]

Whatever it is that can affect measurement result of individual photon (or electron).

That is very vague. Your claim was that there is something that propagates. I asked what it was. Your answer is whatever it is. Very unsatisfying. Let me ask the question this way. How do we know that there is something at all that propagates faster than light?

 

[Boing3000]

As I see experiments have demonstrated results that falsify this statement.

Your respond to martinbn is more than vague, it is incorrect. What affect measurement of individual photon is a polarization filter. Have we observed such a filter goes faster than light ? As far as effect is concerned what is that effect exactly and what speed does it have ? A number will do (**).

No. Your statement is sloppy. Entanglement is joined statistical property of two particle state. To speak about speed or propagation we have to speak about individual particles in entangled pairs. It does not make sense to say that two particle property propagates from one particle to the other one.

My statement was clear, but apparently incorrect. But then you've just make a new statement totally contradictory to what you stated previously. Now we agree completely. Although I would state "one property shared by (non-local to any of) two particles"

The whole point of Bell inequality violation is to demonstrate that this can not be the case.

Unless I am mistaken, Bell's inequality violation are tested on particle created at one single event. The demonstration tells which side off two possibilities must be true when tested elsewhere (detection space/time separations events are irrelevant whatever the effort of experimenters (delay choice etc etc))
Thus experiments show that the correlation appears to be instantaneous. (**) The number you may have mistaken for a speed is this bound.
As far as I know "instantaneous" would be synonymous to infinite speed. But infinite is not a number. By logic alone, if something (like a polarization property value) is at two places at the "same instant" it is the same thing, and don't move.

 

[zonde]

That is very vague. Your claim was that there is something that propagates. I asked what it was. Your answer is whatever it is. Very unsatisfying.

As I understand that you need a name for it. Unfortunately I can't help with that. Pick one yourself.

Let me ask the question this way. How do we know that there is something at all that propagates faster than light?

Well, we can not know that in some absolute sense. In science what we know is that certain approaches don't work. And we know approaches that work for now or work FAPP in their domains of applicability.
So from Bell inequality tests we know what approaches are not going to work. So we can look what is left when we exclude these that won't work. And then we can look which ones of these remaining approaches are consistent with scientific approach. And there are two: unbelievable coincidence and physical effect that propagates FTL.

 

[PeterDonis]

from Bell inequality tests we know what approaches are not going to work

No, from Bell inequality tests we know what kinds of theoretical models are not going to work. Theoretical models are not reality.

Even if we talk about theoretical models, however, your apparent belief that the only viable ones given the Bell inequality tests are ones with FTL propagation is incorrect. Quantum field theory predicts violations of the Bell inequalities, and it is perfectly consistent with SR and has no FTL propagation.

 

[zonde]

Your respond to martinbn is more than vague, it is incorrect. What affect measurement of individual photon is a polarization filter. Have we observed such a filter goes faster than light ? As far as effect is concerned what is that effect exactly and what speed does it have ? A number will do (**).

So you are saying I can't claim that certain theoretical models won't work without providing detailed alternative model, right?

But then you've just make a new statement totally contradictory to what you stated previously.

I am fairly sure I didn't.

By logic alone, if something (like a polarization property value) is at two places at the "same instant" it is the same thing, and don't move.

That logic would require totally novel structure of spacetime. And this would go outside philosophical basis of scientific approach.