That’s actually not quite accurate, although that is how it is commonly interpreted. The reason it is not accurate is because Bell’s theorem simply doesn’t show there is no hidden variables and indeed even Bell himself states very clearly what the theorem proves in the conclusion of his paper.
In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.[1]
In other words, you can have hidden variables, but those hidden variables would not be Lorentz invariant. What is Lorentz invariance? Well, to be “invariant” basically means to be absolute, that is to say, unchanging based on reference frame. The term Lorentz here refers to Lorentz transformations under Minkowski space, i.e. the four-dimensional spacetime described by special relativity.
This implies you can actually have hidden variables under one of two conditions:
Those hidden variables are invariant under some other framework that is not special relativity, basically meaning the signals would have to travel faster than light and thus would contradict special relativity and you would need to replace it with some other framework.
Those hidden variables are variant. That would mean they do indeed change based on reference frame. This would allow local hidden variable theories and thus even allow for current quantum mechanics to be interpreted as a statistical theory in a more classical sense as it even evades the PBR theorem.[2]
The first view is unpopular because special relativity is the basis of quantum field theory, and thus contradicting it would contradict with one of our best theories of nature. There has been some fringe research into figuring out ways to reformulate special relativity to make it compatible with invariant hidden variables,[3] but given quantum mechanics has been around for over a century and nobody has figured this out, I wouldn’t get your hopes up.
The second view is unpopular because it can be shown to violate a more subtle intuition we all tend to have, but is taken for granted so much I’m not sure if there’s even a name for it. The intuition is that not only should there be no mathematical contradictions within a single given reference frame so that an observer will never see the laws of physics break down, but that there should additionally be no contradictions when all possible reference frames are considered simultaneously.
It is not physically possible to observe all reference frames simulatenously, and thus one can argue that such an assumption should be abandoned because it is metaphysical and not something you can ever observe in practice.[4] Note that inconsistency between all reference frames considered simulatenously does not mean observers will disagree over the facts, because if one observer asks another for information about a measurement result, they are still acquiring information about that result from their reference frame, just indirectly, and thus they would never run into a disagreement in practice.
However, people still tend to find it too intuitive to abandon this notion of simultaneous consistency, so it remains unpopular and most physicists choose to just interpret quantum mechanics as if there are no hidden variables at all. #1 you can argue is enforced by the evidence, but #2 is more of a philosophical position, so ultimately the view that there are no hidden variables is not “proven” but proven if you accept certain philosophical assumptions.
There is actually a second way to restore local hidden variables which I did not go into detail here which is superdeterminism. Superdeterminism basically argues that if you did just have a theory which describes how particles behave now but a more holistic theory that includes the entire initial state of the universe going back to the Big Bang and tracing out how all particles evolved to the state they are now, you can place restrictions on how that system would develop that would such that it would always reproduce the correlations we see even with hidden variables that is indeed Lorentz invariant.
Although, the obvious problem is that it would never actually be possible to have such a theory, we cannot know the complete initial configuration of all particles in the universe, and so it’s not obvious how you would derive the correlations between particles beforehand. You would instead have to just assume they “know” how to be correlated already, which makes them equivalent to nonlocal hidden variable theories, and thus it is not entirely clear how they could be made Lorentz invariant. Not sure if anyone’s ever put forward a complete model in this framework either, same issue with nonlocal hidden variable theories.
Indeed. I’m not completely sure what point you are trying to make, but my point is not a hidden variable point. The states can be in a perfectly correlated superposition without any hidden variables, and still not “share anything” upon collapse into an eigenstate.
I will concede that it looks a lot like one particle somehow tells the other “hey, I just collapsed into the |1> state, so now you need to as well”, but at a closer look this seems to happen on its own without any such message being shared. In particular, while the collapse of one state causes the collapse of the other, there is no physical way to distinguish between a state that was collapsed due to entanglement, and one that wasn’t. At least not until you send a sub-FTL signal to explain what happened.
So if physically, the state of particle 1 before and after particle 2 was measured is indistinguishable, how can we say that “something” was shared from particle 2 to particle 1?
I mean you can setup a source of entangled particles and two very far detectors that would do measurements roughly at the same time on each particle in such a way that information traveling at the speed of light wouldn’t have time to travel the distance between both detectors.
You can then just gather roughly simultaneous measurements and at a later time join the datasets from both detectors to see what one measured vs the other for each pair.
If I understand correctly the current observations show that collapsing the state of one of the particle influences the other all the way at the other detector. Since there’s no hidden variables that predetermine the result of measurements while the result of the collapse is random, and the fact that particles still respect the correlation over any distance is why there seem to be a FTL communication between the particles.
Something has to be communicated between the particles for the influence to work FTL, but it also seem we cannot leverage this phenomenon to send “actual information” this way :/
edit: Important point with that experiment: once the particles have been observed, if you try the experiment a second time using the same particles, then you’ll get different results, this time in line with hidden variables because the particle’s state already collapsed.
I fully understand the concept of entanglement and the experiments you mention, but I’m still to understand what you mean when you say “something” is being transmitted between the particles.
As you say, this “something” cannot contain information, and it also cannot influence the particle physically, since there is no way to distinguish the physical state of the particle before and after it receives this “something”. So the signal contains nothing, and has no effect on physical reality. That sounds a lot like “nothing” rather than “something”.
I completely get the argument that somehow the two particles must agree on what result to give, but in the theory this is just a consequence of how entanglement and measurements work. No transmission required.
The message transferred between the particles supposedly FTL does contain information though. What I meant was that we cannot encode our own arbitrary information on top of it. The message has a physical effect on reality, without it the state we find the particles in cannot be respected.
Just reconsider this: If we agree that the result of a measurement is totally random (no hidden variable predetermining the result of the measurement) but that once we measure and know the state of one particle then we know with certainty the state of the other particle (entanglement): information about the collapse of the first measured particle was shared to the other so that it’s no longer random.
edit: If your argument is about “sharing information doesn’t imply transmission” then let’s stop here and leave this thread agreeing that “information was shared” :)
I have no opinions on what shape the information sharing takes. Nor am I interested in guessing.
The “message” does not have any local effect on reality - when you measure your particle, you have no way of figuring out if its partner was already measured elsewhere. The effect it does have is on the global state, maintaining the correlation that was encoded from the start.
If you write up the density matrix for the system before and after measurement of one of the particles, you can see that while the density matrix changes, it does not change in a way one can measure.
What I will concede is that before the first measurement the global state is |00>+|11>, afterwards it is |00> or |11>. This projection appears to happen instantaneously, no matter the distance, which is indeed faster than light.
But calling the wave function collapse a signal or a message or a transfer of information is misleading, I would say. In your example, we know that the initial state is |00>+|11>, and that the result of the first measurement is then, say, 1. Then no further information is required to know that the other measurement will result in 1. No messages required, no hidden variables, simply the process of elimination.
I would like to say that this is indeed a confusing subject, but that the math is clear, and that I am arguing what is my impression of the mainstream view in the field.
The 2022 nobel prize was given to experimentalists that observed the violation of Bell’s inequality.
https://en.m.wikipedia.org/wiki/Bell's_theorem https://en.m.wikipedia.org/wiki/Quantum_nonlocality
I’m genuinely not an expert but I get it to mean that there aren’t hidden variables created alongside the entangled particles.
That’s actually not quite accurate, although that is how it is commonly interpreted. The reason it is not accurate is because Bell’s theorem simply doesn’t show there is no hidden variables and indeed even Bell himself states very clearly what the theorem proves in the conclusion of his paper.
In other words, you can have hidden variables, but those hidden variables would not be Lorentz invariant. What is Lorentz invariance? Well, to be “invariant” basically means to be absolute, that is to say, unchanging based on reference frame. The term Lorentz here refers to Lorentz transformations under Minkowski space, i.e. the four-dimensional spacetime described by special relativity.
This implies you can actually have hidden variables under one of two conditions:
The first view is unpopular because special relativity is the basis of quantum field theory, and thus contradicting it would contradict with one of our best theories of nature. There has been some fringe research into figuring out ways to reformulate special relativity to make it compatible with invariant hidden variables,[3] but given quantum mechanics has been around for over a century and nobody has figured this out, I wouldn’t get your hopes up.
The second view is unpopular because it can be shown to violate a more subtle intuition we all tend to have, but is taken for granted so much I’m not sure if there’s even a name for it. The intuition is that not only should there be no mathematical contradictions within a single given reference frame so that an observer will never see the laws of physics break down, but that there should additionally be no contradictions when all possible reference frames are considered simultaneously.
It is not physically possible to observe all reference frames simulatenously, and thus one can argue that such an assumption should be abandoned because it is metaphysical and not something you can ever observe in practice.[4] Note that inconsistency between all reference frames considered simulatenously does not mean observers will disagree over the facts, because if one observer asks another for information about a measurement result, they are still acquiring information about that result from their reference frame, just indirectly, and thus they would never run into a disagreement in practice.
However, people still tend to find it too intuitive to abandon this notion of simultaneous consistency, so it remains unpopular and most physicists choose to just interpret quantum mechanics as if there are no hidden variables at all. #1 you can argue is enforced by the evidence, but #2 is more of a philosophical position, so ultimately the view that there are no hidden variables is not “proven” but proven if you accept certain philosophical assumptions.
There is actually a second way to restore local hidden variables which I did not go into detail here which is superdeterminism. Superdeterminism basically argues that if you did just have a theory which describes how particles behave now but a more holistic theory that includes the entire initial state of the universe going back to the Big Bang and tracing out how all particles evolved to the state they are now, you can place restrictions on how that system would develop that would such that it would always reproduce the correlations we see even with hidden variables that is indeed Lorentz invariant.
Although, the obvious problem is that it would never actually be possible to have such a theory, we cannot know the complete initial configuration of all particles in the universe, and so it’s not obvious how you would derive the correlations between particles beforehand. You would instead have to just assume they “know” how to be correlated already, which makes them equivalent to nonlocal hidden variable theories, and thus it is not entirely clear how they could be made Lorentz invariant. Not sure if anyone’s ever put forward a complete model in this framework either, same issue with nonlocal hidden variable theories.
Indeed. I’m not completely sure what point you are trying to make, but my point is not a hidden variable point. The states can be in a perfectly correlated superposition without any hidden variables, and still not “share anything” upon collapse into an eigenstate.
I will concede that it looks a lot like one particle somehow tells the other “hey, I just collapsed into the |1> state, so now you need to as well”, but at a closer look this seems to happen on its own without any such message being shared. In particular, while the collapse of one state causes the collapse of the other, there is no physical way to distinguish between a state that was collapsed due to entanglement, and one that wasn’t. At least not until you send a sub-FTL signal to explain what happened.
So if physically, the state of particle 1 before and after particle 2 was measured is indistinguishable, how can we say that “something” was shared from particle 2 to particle 1?
I mean you can setup a source of entangled particles and two very far detectors that would do measurements roughly at the same time on each particle in such a way that information traveling at the speed of light wouldn’t have time to travel the distance between both detectors.
You can then just gather roughly simultaneous measurements and at a later time join the datasets from both detectors to see what one measured vs the other for each pair.
If I understand correctly the current observations show that collapsing the state of one of the particle influences the other all the way at the other detector. Since there’s no hidden variables that predetermine the result of measurements while the result of the collapse is random, and the fact that particles still respect the correlation over any distance is why there seem to be a FTL communication between the particles.
Something has to be communicated between the particles for the influence to work FTL, but it also seem we cannot leverage this phenomenon to send “actual information” this way :/
edit: Important point with that experiment: once the particles have been observed, if you try the experiment a second time using the same particles, then you’ll get different results, this time in line with hidden variables because the particle’s state already collapsed.
I fully understand the concept of entanglement and the experiments you mention, but I’m still to understand what you mean when you say “something” is being transmitted between the particles.
As you say, this “something” cannot contain information, and it also cannot influence the particle physically, since there is no way to distinguish the physical state of the particle before and after it receives this “something”. So the signal contains nothing, and has no effect on physical reality. That sounds a lot like “nothing” rather than “something”.
I completely get the argument that somehow the two particles must agree on what result to give, but in the theory this is just a consequence of how entanglement and measurements work. No transmission required.
The message transferred between the particles supposedly FTL does contain information though. What I meant was that we cannot encode our own arbitrary information on top of it. The message has a physical effect on reality, without it the state we find the particles in cannot be respected.
Just reconsider this: If we agree that the result of a measurement is totally random (no hidden variable predetermining the result of the measurement) but that once we measure and know the state of one particle then we know with certainty the state of the other particle (entanglement): information about the collapse of the first measured particle was shared to the other so that it’s no longer random.
edit: If your argument is about “sharing information doesn’t imply transmission” then let’s stop here and leave this thread agreeing that “information was shared” :)
I have no opinions on what shape the information sharing takes. Nor am I interested in guessing.
The “message” does not have any local effect on reality - when you measure your particle, you have no way of figuring out if its partner was already measured elsewhere. The effect it does have is on the global state, maintaining the correlation that was encoded from the start.
If you write up the density matrix for the system before and after measurement of one of the particles, you can see that while the density matrix changes, it does not change in a way one can measure.
What I will concede is that before the first measurement the global state is |00>+|11>, afterwards it is |00> or |11>. This projection appears to happen instantaneously, no matter the distance, which is indeed faster than light.
But calling the wave function collapse a signal or a message or a transfer of information is misleading, I would say. In your example, we know that the initial state is |00>+|11>, and that the result of the first measurement is then, say, 1. Then no further information is required to know that the other measurement will result in 1. No messages required, no hidden variables, simply the process of elimination.
I would like to say that this is indeed a confusing subject, but that the math is clear, and that I am arguing what is my impression of the mainstream view in the field.