# I Bell's Theorem and Reality

#### kurt101

However, the resulting (super)deterministic quantum theories becomes (laughably ) untenable with these scenarios.
I am having trouble coming to the same conclusion, that the experiment you cited (https://arxiv.org/abs/1508.05949) invalidates any deterministic quantum theories. Do you also mean this to invalidate deterministic quantum theories that depend on FTL (spooky action at a distance)?

#### DrChinese

Science Advisor
Gold Member
I am having trouble coming to the same conclusion, that the experiment you cited (https://arxiv.org/abs/1508.05949) invalidates any deterministic quantum theories. Do you also mean this to invalidate deterministic quantum theories that depend on FTL (spooky action at a distance)?
I agree completely.

But there will probably be someone who holds to the superdeterministic explanation: that everything that occurs on Earth is part of the same conspiracy that makes QM look correct.

#### rubi

Science Advisor
I would absolutely dispute such characterization. No one can be sure that the Bell State measurement of 2 & 3 does not cause a change to 1 & 4.
I suppose I should make the mathematics a bit more clear:
The state of the system is $\left|\psi\right> = (\left|\psi_1\right>\otimes \left|\psi_2\right> - \left|\psi_2\right> \otimes \left|\psi_1\right>) \otimes (\left|\psi_3\right>\otimes \left|\psi_4\right> - \left|\psi_4\right> \otimes \left|\psi_3\right>)$. You can now do two things:
1. Compute the reduced density matrix in $\mathcal H_1 \otimes \mathcal H_4$ and call it $\rho_\text{no measurement}$.
2. Perform the Bell state measurement on particles 2 & 3. In that case, you get 4 orthogonal projectors $P_1,\ldots P_4$ and thus 4 states $\left|\xi_i\right> = P_i \left|\psi\right>$. Now you can compute the density matrix $\rho_\text{BSM} = \sum_i \left|\xi_i\right>\left<\xi_i\right|$ and again compute the reduced density matrix in $\mathcal H_1 \otimes \mathcal H_4$ and call it $\rho_\text{measurement}$.
Of course, you have to add all the normalization constants, which I omitted for brevity. You will find that mathematically $\rho_\text{no measurement} = \rho_\text{measurement}$. This shows that the Bell state measurement on particles 2 & 3 can not influence the physical state of the composite 1 & 4 system. Of course, this does not prevent us from performing entanglement swapping on the recorded data.

The experiment must be viewed as a total context, and identifying the causal agents when there is quantum nonlocality is not really possible. This is same kind of issue as you have with a quantum eraser. Does the eraser cause a non-local change?
I did view the experiment in the total context. The question is: Can the actions on particles 2 & 3 have a causal influence on the physical state of the 1 & 4 system? For this to be true, the state of the 1 & 4 system must change depending on what one does to the 2 & 3 system, but it doesn't. Yes, the situation is very analogous to the quantum eraser. It's also an effect of post-selection, which can be understood from standard quantum theory. The experiment says nothing about causality. It's just yet another indication that the predictions of quantum mechanics are correct.

#### DrChinese

Science Advisor
Gold Member
...The question is: Can the actions on particles 2 & 3 have a causal influence on the physical state of the 1 & 4 system? For this to be true, the state of the 1 & 4 system must change depending on what one does to the 2 & 3 system, but it doesn't. ... The experiment says nothing about causality. It's just yet another indication that the predictions of quantum mechanics are correct.
I agree with virtually everything you are saying. The part I think is unjustified is in bold (I added that emphasis). No one can really say. This is quantum nonlocality. There is no well-defined causal direction that we know of.

Yet to imply that post-selection means that everything evolves forward in time is tantamount to making a back-handed local realistic argument. And that I dispute. As far as anyone knows: measuring 2 & 3 as being in a Bell State does in fact project 1 & 4 non-locally into a fully entangled state. Or in the words of the second of the 2 papers I cited:

"A successful entanglement swapping procedure will result in photons 1 and 4 being entangled, although they never interacted with each other. This is done by performing a Bell-state measurement on particles 2 and 3, i.e. by projecting them on one of the four Bell states. Consequently, photons 1 and 4 will be projected onto the Bell state corresponding to the BSM outcome."

The mathematical language is not in question here. Just the interpretation... and clearly what I am saying is the same as the authors of the paper. And yet there are other acceptable causal interpretations too. But a local realistic one is NOT one of those.

#### Mentz114

Gold Member
I suppose I should make the mathematics a bit more clear:
The state of the system is $\left|\psi\right> = (\left|\psi_1\right>\otimes \left|\psi_2\right> - \left|\psi_2\right> \otimes \left|\psi_1\right>) \otimes (\left|\psi_3\right>\otimes \left|\psi_4\right> - \left|\psi_4\right> \otimes \left|\psi_3\right>)$. You can now do two things:
1. Compute the reduced density matrix in $\mathcal H_1 \otimes \mathcal H_4$ and call it $\rho_\text{no measurement}$.
2. Perform the Bell state measurement on particles 2 & 3. In that case, you get 4 orthogonal projectors $P_1,\ldots P_4$ and thus 4 states $\left|\xi_i\right> = P_i \left|\psi\right>$. Now you can compute the density matrix $\rho_\text{BSM} = \sum_i \left|\xi_i\right>\left<\xi_i\right|$ and again compute the reduced density matrix in $\mathcal H_1 \otimes \mathcal H_4$ and call it $\rho_\text{measurement}$.
Of course, you have to add all the normalization constants, which I omitted for brevity. You will find that mathematically $\rho_\text{no measurement} = \rho_\text{measurement}$. This shows that the Bell state measurement on particles 2 & 3 can not influence the physical state of the composite 1 & 4 system. Of course, this does not prevent us from performing entanglement swapping on the recorded data.

I did view the experiment in the total context. The question is: Can the actions on particles 2 & 3 have a causal influence on the physical state of the 1 & 4 system? For this to be true, the state of the 1 & 4 system must change depending on what one does to the 2 & 3 system, but it doesn't. Yes, the situation is very analogous to the quantum eraser. It's also an effect of post-selection, which can be understood from standard quantum theory. The experiment says nothing about causality. It's just yet another indication that the predictions of quantum mechanics are correct.
What about phase changes ? They are ignored in your analysis. Can the BSM affect amplitudes so that no probabilities change but a correlation is changed.

#### kurt101

I agree completely.
Sorry to be pedantic, but what do you mean by "I agree completely"? Are you saying that the experiment (https://arxiv.org/abs/1508.05949) invalidates deterministic quantum theories that depend on FTL (spooky action at a distance)?

#### rubi

Science Advisor
I agree with virtually everything you are saying. The part I think is unjustified is in bold (I added that emphasis). No one can really say. This is quantum nonlocality. There is no well-defined causal direction that we know of.

Yet to imply that post-selection means that everything evolves forward in time is tantamount to making a back-handed local realistic argument. And that I dispute. As far as anyone knows: measuring 2 & 3 as being in a Bell State does in fact project 1 & 4 non-locally into a fully entangled state. Or in the words of the second of the 2 papers I cited:

"A successful entanglement swapping procedure will result in photons 1 and 4 being entangled, although they never interacted with each other. This is done by performing a Bell-state measurement on particles 2 and 3, i.e. by projecting them on one of the four Bell states. Consequently, photons 1 and 4 will be projected onto the Bell state corresponding to the BSM outcome."

The mathematical language is not in question here. Just the interpretation... and clearly what I am saying is the same as the authors of the paper. And yet there are other acceptable causal interpretations too. But a local realistic one is NOT one of those.
Of course, I'm not disputing the fact that local realism is experimentally excluded. Maybe we just have a disagreement about definitions. The state of the composite system 1 & 4 is defined to be the density matrix that contains all information about the statistics of the composite system 1 & 4. And this density matrix is unaffected. However, the state of the composite 1 & 2 & 3 & 4 system is clearly affected by the measurement on particles 2 & 3. But in order to detect this change, one needs to perform measurements on the full system. Measurements on the 1 & 4 system can't detect a change of the global state. The state of the composite 1 & 4 system meets the mathematical criterion of an unentangled state, i.e. it is described by a separable density matrix, but the state of the composite 1 & 2 & 3 & 4 system becomes (even more) entangled through the BSM.

What about phase changes ? They are ignored in your analysis. Can the BSM affect amplitudes so that no probabilities change but a correlation is changed.
Phase changes are also included in the analysis. Everything is contained in the projectors $P_1,\ldots,P_4$, whose form is restricted by the commutation relations in such a way that the density matrix of the composite 1 & 4 system is unaffected.

#### stevendaryl

Staff Emeritus
Science Advisor
I'm not
Sorry to be pedantic, but what do you mean by "I agree completely"? Are you saying that the experiment (https://arxiv.org/abs/1508.05949) invalidates deterministic quantum theories that depend on FTL (spooky action at a distance)?
As far as I know, the nonlocal rule of thumb (I consider it too imprecise to count as an "interpretation") that measurement collapses the wave function is consistent with every quantum experiment performed so far.

#### stevendaryl

Staff Emeritus
Science Advisor
What about phase changes ? They are ignored in your analysis. Can the BSM affect amplitudes so that no probabilities change but a correlation is changed.
What do you mean by "correlation"? I thought correlation was defined in terms of probabilities. So if you don't change any probabilities, you don't change the correlation.

Do you mean changes of two-particle probabilities without changing single-particle probabilities?

#### DrChinese

Science Advisor
Gold Member
Sorry to be pedantic, but what do you mean by "I agree completely"? Are you saying that the experiment (https://arxiv.org/abs/1508.05949) invalidates deterministic quantum theories that depend on FTL (spooky action at a distance)?
No, just that local realistic ones are ruled out. At this point, it is "generally" agreed that nonlocal theories such as Bohmian Mechanics are viable.

#### DrChinese

Science Advisor
Gold Member
Of course, I'm not disputing the fact that local realism is experimentally excluded. Maybe we just have a disagreement about definitions. The state of the composite system 1 & 4 is defined to be the density matrix that contains all information about the statistics of the composite system 1 & 4. And this density matrix is unaffected. However, the state of the composite 1 & 2 & 3 & 4 system is clearly affected by the measurement on particles 2 & 3. But in order to detect this change, one needs to perform measurements on the full system. Measurements on the 1 & 4 system can't detect a change of the global state. The state of the composite 1 & 4 system meets the mathematical criterion of an unentangled state, i.e. it is described by a separable density matrix, but the state of the composite 1 & 2 & 3 & 4 system becomes (even more) entangled through the BSM.
I don't disagree really with any of this, and I don't think you disagree with the following:

We do the BSM on 2 & 3 and see we have an entangled pair in 1 & 4. 1 & 4 have never interacted on any local realistic basic. They did not have a common origin either, and no local causal agent ever impacted the pair. Clearly, if one were trying to explain their entanglement using some desperate form of local realism: about the only thing left is to say that these entangled particles were created on the same planet and everything on the planet shares a common light cone. Of course, that explanation fails in one critical manner: why aren't any and all pairs of particles - anywhere on Earth regardless of origin - also entangled? Why just these few special ones that had the successful BSM? That is, if the "Earth as common light cone" idea is to be considered? (Obviously, that idea seems ridiculous to me. )

I am relating the above scenario to the OP article, which is constructing its premise on a flawed concept: that all entanglement arises from a common entanglement source. It doesn't, as the experiments I cited indicate.

#### Mentz114

Gold Member
What do you mean by "correlation"? I thought correlation was defined in terms of probabilities. So if you don't change any probabilities, you don't change the correlation.

Do you mean changes of two-particle probabilities without changing single-particle probabilities?
I mean two particle correlations are not independent of phase. But I have to be satisfied with @rubi s answer. I'm struggling with the idea that the NV's can be entangled already before the interaction at C.

#### rubi

Science Advisor
We do the BSM on 2 & 3 and see we have an entangled pair in 1 & 4.
We need a clear definition of the terms here in order to agree or disagree. As I said, with the standard definition of the state of a (sub-)system that I have given (a state is defined to be a density matrix in the Hilbert space of the (sub-)system), the state of the 1 & 4 subsystem is separable (a quick calculation shows $\rho^{1,4}_\text{measurement} = \rho^{1,4}_\text{no measurement} = \left|\psi_1\right>\left<\psi_1\right|\otimes\left|\psi_4\right>\left<\psi_4\right|$), rather than entangled, while the state of the 1 & 2 & 3 & 4 system is entangled, i.e. non-separable.

1 & 4 have never interacted on any local realistic basic. They did not have a common origin either, and no local causal agent ever impacted the pair. Clearly, if one were trying to explain their entanglement using some desperate form of local realism: about the only thing left is to say that these entangled particles were created on the same planet and everything on the planet shares a common light cone. Of course, that explanation fails in one critical manner: why aren't any and all pairs of particles - anywhere on Earth regardless of origin - also entangled? Why just these few special ones that had the successful BSM? That is, if the "Earth as common light cone" idea is to be considered? (Obviously, that idea seems ridiculous to me. )
I agree with all of this.

#### kurt101

No, just that local realistic ones are ruled out. At this point, it is "generally" agreed that nonlocal theories such as Bohmian Mechanics are viable.
Thanks for the clarification! I think I am on the same page now.

#### kurt101

I mean two particle correlations are not independent of phase. But I have to be satisfied with @rubi s answer. I'm struggling with the idea that the NV's can be entangled already before the interaction at C.
I agree and maybe it is just my misunderstanding of the term entanglement, but I don't like saying that NV's can be entangled before the interaction at C.

#### DrChinese

Science Advisor
Gold Member
I mean two particle correlations are not independent of phase. But I have to be satisfied with @rubi s answer. I'm struggling with the idea that the NV's can be entangled already before the interaction at C.
Look at the photon entanglement experiments and it is clear that photons 1 & 4 can be entangled either before or after the Bell State Measurement of 2 & 3. Ordering of the measurements is not significant to the results in any way. You can interpret that in several different ways.

#### Mentz114

Gold Member
Look at the photon entanglement experiments and it is clear that photons 1 & 4 can be entangled either before or after the Bell State Measurement of 2 & 3. Ordering of the measurements is not significant to the results in any way. You can interpret that in several different ways.
I will interpret this by assuming that all the 'events' happen at the same time. As you say, ordering and precedence have no significance.

#### facenian

.....................
If an experiment like this were possible, then it would be a way to produce entangled particles that have no common past. That would seem to be an even simpler argument against local hidden variables than Bell's theorem--the correlations can't possibly be explained in terms of local hidden variables if they never met in the past to share that hidden variable.
Good. Then as I said, in some sense, it seems that Bell's inequality is almost unnecessary to demonstrate the impossibility of a local hidden-variables theory that could explain the correlations, since is there is no way for the entangled particles to acquire a common hidden variable.
Then I withdraw my previous suspicion about @DrChinese's assetions but I was right when I said that for these new tests hidden variables models are irrelevant rendering Bell's original arguments inaplicable

Last edited:

#### DrChinese

Science Advisor
Gold Member
but I was right when I said that for these new tests hidden variables models are irrelevant rendering Bell's original arguments inaplicable
You are looking at things in reverse. Bell tests are tests of local realism (local hidden vaiables). The local realistic boundary is usually expressed as a Bell inequality. These tests have that attribute too. Certain elements are 100% identical.

However, some of these tests have been constructed specifically to address issues that some groups of "die-hard" local realists have expressed. Most of these issues are unreasonable (for reasons I won't get into here), but scientists have found ways to address them anyway and rule those issues out. That way they are not lingering in the background. The experiment of Hanson et al is indeed a Bell test, as are the entanglement swapping tests I cited. The original Bell test did indeed conceive of a single common source of entangled pairs. But that should not be seen as a restriction. There are literally hundreds (if not thousands) of Bell tests that have been performed to demonstrate limits on local realistic theories.

For some reason, you have it in your head that Bell has said something that this test invalidates or seems to contradict. That is far from the case. First, Bell said many things. That does not mean they all are to be taken as of equal weight. Second, Bell died before many key discoveries in this area were made. Bell would have loved these experiments. He would have loved GHZ and PBR, as well as the entanglement swapping I cite. All of these shed light on entanglement and the nature of reality. Which was the entire purpose of the Bell program in the first place. Consider that Bell's Theorem was not the only "no-go" theorem he came up with. He worked on others in the 60's too, they too are groundbreaking even though less well known. Such as BKS:

https://en.wikipedia.org/wiki/Kochen–Specker_theorem
https://arxiv.org/abs/quant-ph/9709047

#### facenian

For some reason, you have it in your head that Bell has said something that this test invalidates or seems to contradict.
I did not mean that. What I said is that the cases considered by Bell and EPR do not apply to these new cases of entanglement. This in no way means that this new cases invalidate what Bell and EPR have said.

Last edited:

#### Aidyan

I'm sick of seeing these permanent and stubborn attempts trying to recover the anthropocentric classical determinism and local realism.

#### facenian

I'm sick of seeing these permanent and stubborn attempts trying to recover the anthropocentric classical determinism and local realism.
It seems that most arguments pretending to recover realism and locality by refuting Bell's theorem fall mainly in two categories:
1_ Those which are simply wrong from a logical and interpretacional point of view
2_ Those resorting to very implausible arguments such as superdermism

But, even worse, know I realize that there are new experiments that were not anticipated by Bell and Einstein that seem to contradict even more strikingly the notions of reality and locality and that can not be treated with the method used by Bell in his 1964 theorem. Am I correct on this? or I misunderstood the meaning of this new experiments that seem to test entangled particles which do not share a common past causal origin which could presumably be represented by a common hidden variable λ.

#### ueit

It seems that most arguments pretending to recover realism and locality by refuting Bell's theorem fall mainly in two categories:
1_ Those which are simply wrong from a logical and interpretacional point of view
2_ Those resorting to very implausible arguments such as superdermism
Why do you think superdeterminism is implausible? It is quite easy to reject Bell's statistical independence assumption by looking at any classical field theory, like Maxwell's theory or GR or fluid mechanics. Some superdeterministic proposals may be stupid but this does not mean anything for the concept itself.

#### mattt

It is not that Superdeterminism is "impossible", it is just that, it is so "ad hoc" that it really explains NOTHING (and of course it predicts nothing in general, so, it is mostly useless).

And yes, I know t'Hooft is working on a Superdeterminism model of Physics, but still.....

#### Boing3000

Gold Member
Why do you think superdeterminism is implausible?
I think the correct word would be "irrelevant". "Whatever happens ... happens" is not a useful statement in science. It maybe a valid logical one, but one that everybody that wants to make science will ignore ... by design.

### Want to reply to this thread?

"Bell's Theorem and Reality"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving