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Bell stated this theorem in his own words: “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.”

In other words, for us, nature is not local, because a local explanation is impossible.

If Bell’s theorem were refuted, we can no longer conclude that nature is non-local. Then, some conclusions can be drawn:
1. Measured values are not generated upon measurement, they already exist beforehand. Otherwise, a strong correlation between the outcomes of measurements at different sides would demand non-local effects.
2. The concept of superposition, which implies the simultaneous existence of incompatible physical states, is in question. If measured values exist beforehand, mutually exclusive values cannot exist simultaneously.
3. This supports Einstein's view of the meaning of the wave function as a description of an ensemble. Thus, quantum mechanics does not violate the principle of causality; at least for spin measurements.

As a consequence, the concept of a quantum computer also comes into question, as it relies upon the assumption that a quantum system bears simultaneous information about two mutually exclusive outcomes. If this assumption is no longer tenable, the diversity of the solution of a quantum computer is considerably restricted.

Are there other consequences?

Esail wrote:Bell stated this theorem in his own words: “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.”

In other words, for us, nature is not local, because a local explanation is impossible.

If Bell’s theorem were refuted, we can no longer conclude that nature is non-local. Then, some conclusions can be drawn:
1. Measured values are not generated upon measurement, they already exist beforehand. Otherwise, a strong correlation between the outcomes of measurements at different sides would demand non-local effects.
2. The concept of superposition, which implies the simultaneous existence of incompatible physical states, is in question. If measured values exist beforehand, mutually exclusive values cannot exist simultaneously.
3. This supports Einstein's view of the meaning of the wave function as a description of an ensemble. Thus, quantum mechanics does not violate the principle of causality; at least for spin measurements.

As a consequence, the concept of a quantum computer also comes into question, as it relies upon the assumption that a quantum system bears simultaneous information about two mutually exclusive outcomes. If this assumption is no longer tenable, the diversity of the solution of a quantum computer is considerably restricted.

Are there other consequences?

Indeed, there are many consequences.

I just wrote on another thread "[If Bell's theorem can be disproved using an explicit example being constructed by Fred Diether then] "I will publicly eat my hat, resign from the Royal Dutch Academy of Sciences, and retract 20 highly cited papers. All textbooks in quantum physics will have to be rewritten. A whole lot of mathematics and computer science will have to be rewritten too. Whoever does it, will be the toast of the town! Academia will be in turmoil, all the quantum computing start-ups will collapse. It will be possible to perform Shor's algorithm extremely fast on a *classical* computer and internet security will collapse. The stock markets will collapse. Civilisation might even break down completely".

You want the break down of civilization? Better keep quiet about this.

gill1109 wrote:It will be possible to perform Shor's algorithm extremely fast on a *classical* computer and internet security will collapse.

I don't think you need to be very concerned about that. If there are no simultaneous incompatible physical states, neither a quantum computer nor a normal supercomputer can benefit from the Shor's algorithm.

Esail wrote:

gill1109 wrote:It will be possible to perform Shor's algorithm extremely fast on a *classical* computer and internet security will collapse.

I don't think you need to be very concerned about that. If there are no simultaneous incompatible physical states, neither a quantum computer nor a normal supercomputer can benefit from the Shor's algorithm.

I am not concerned at all. But I have no idea at all what you mean.

I think it is clear that there *are* simultaneously incompatible physical states. The chair on which I am sitting could in principle be a meter away from me. In that case, I obviously wouldn't be sitting on it.

gill1109 wrote:But I have no idea at all what you mean.

If a Qubit is simultaneously in state "0" and state"1". That is what I mean is impossible if Bell were wrong.

Esail wrote:

gill1109 wrote:But I have no idea at all what you mean.

If a Qubit is simultaneously in state "0" and state"1". That is what I mean is impossible if Bell were wrong.

You may as well ask, how would the laws of physics change if pi were equal to 22/7.

We already have a successful hidden variables theory, which exactly reproduces the predictions of quantum mechanics. It’s called the de Broglie - Bohm pilot wave theory, dBB, or Bohmian mechanics. Since it reproduces QM predictions, Shor’s algorithm would still work as advertised. A qubit state which is superposition of 0 and 1 would actually be a statistical mixture of very many underlying states. The theory would be non-local. The different qubits would have instantaneous interactions with one another. The theory would depend on an absolute reference frame but still its predictions would be relativistically invariant.

gill1109 wrote: The different qubits would have instantaneous interactions with one another.

If Bell were wrong, there would be no need for spooky action at a distance to explain the quantum mechanical correlations. So there could be local models that do this. These would then have to take into account that the quantum world does not consist of distinguishable particles such as marbles, as Bell did, but that other laws prevail there. We know this from the Bose Einstein statistics, for example.

It is quite absurd that many scientists consider non-local interactions to be possible even though there is not the slightest clue as to how this might work.

Esail wrote:

gill1109 wrote: The different qubits would have instantaneous interactions with one another.

If Bell were wrong, there would be no need for spooky action at a distance to explain the quantum mechanical correlations. So there could be local models that do this. These would then have to take into account that the quantum world does not consist of distinguishable particles such as marbles, as Bell did, but that other laws prevail there. We know this from the Bose Einstein statistics, for example.
It is quite absurd that many scientists consider non-local interactions to be possible even though there is not the slightest clue as to how this might work.

I agree, quantum mechanics is quite absurd. However, Bell's theorem is a true theorem. If you disagree with me, please program your model, and win my 65 000 Euro challenge (and the Nobel prize)

gill1109 wrote:I agree, quantum mechanics is quite absurd. However, Bell's theorem is a true theorem. If you disagree with me, please program your model, and win my 65 000 Euro challenge (and the Nobel prize)

Please could you state what you understand Bell's"true" theorem to be? And it would help if you don't confuse Bell's theorem with a computer challenge.

In the other thread you cited Bell:

Can one find some functions (2) and some probability distribution π(µ) which reproduces the correlation (1)? Yes, many, but now we add the hypothesis of locality, that the setting b of a particular instrument has no effect on what happens, A, in a remote region, and likewise that a has no effect on B:
A(a, µ), B(b, µ). (3)
With these local forms, it is not possible to find functions A and B and a probability distribution π which give the correlation (1). This is the theorem.

If you agree that the above is Bell's theorem, then surely you know or should know that it is not true. You already know that it is possible to find local functions A(a, µ), B(b, µ) which reproduce the correlation (1), directly refuting Bell's "theorem".

minkwe wrote:

gill1109 wrote:I agree, quantum mechanics is quite absurd. However, Bell's theorem is a true theorem. If you disagree with me, please program your model, and win my 65 000 Euro challenge (and the Nobel prize)

Please could you state what you understand Bell's"true" theorem to be? And it would help if you don't confuse Bell's theorem with a computer challenge.

In the other thread you cited Bell:

Can one find some functions (2) and some probability distribution π(µ) which reproduces the correlation (1)? Yes, many, but now we add the hypothesis of locality, that the setting b of a particular instrument has no effect on what happens, A, in a remote region, and likewise that a has no effect on B:
A(a, µ), B(b, µ). (3)
With these local forms, it is not possible to find functions A and B and a probability distribution π which give the correlation (1). This is the theorem.

If you agree that the above is Bell's theorem, then surely you know or should know that it is not true. You already know that it is possible to find local functions A(a, µ), B(b, µ) which reproduce the correlation (1), directly refuting Bell's "theorem".

You are wasting your time. Gill has his brain stuck in Gill's theory that a local model has to correctly simulate an EPR experiment event by event.
.

minkwe wrote:
If you agree that the above is Bell's theorem, then surely you know or should know that it is not true. You already know that it is possible to find local functions A(a, µ), B(b, µ) which reproduce the correlation (1), directly refuting Bell's "theorem".

Please give an example of those "local functions A(a, µ), B(b, µ) which reproduce the correlation (1)"

Esail wrote:Please give an example of those "local functions A(a, µ), B(b, µ) which reproduce the correlation (1)"

You just need to violate measurement independence. An explicit sample is given in "Michel Feldmann. New loophole for the Einstein-Podolsky-Rosen paradox. Foundations of Physics Letters, 8(1):41-53, 1995."

Justo wrote:

Esail wrote:Please give an example of those "local functions A(a, µ), B(b, µ) which reproduce the correlation (1)"

You just need to violate measurement independence. An explicit sample is given in "Michel Feldmann. New loophole for the Einstein-Podolsky-Rosen paradox. Foundations of Physics Letters, 8(1):41-53, 1995."

This model implies stochastic coupling where the probability system depends on the choice of the arguments (polarizer setting) on both sides. It is so far refuted by EPR experiments over large distances (Weihs 1998)

Esail wrote:

Justo wrote:

Esail wrote:Please give an example of those "local functions A(a, µ), B(b, µ) which reproduce the correlation (1)"

You just need to violate measurement independence. An explicit sample is given in "Michel Feldmann. New loophole for the Einstein-Podolsky-Rosen paradox. Foundations of Physics Letters, 8(1):41-53, 1995."

This model implies stochastic coupling where the probability system depends on the choice of the arguments (polarizer setting) on both sides. It is so far refuted by EPR experiments over large distances (Weihs 1998)

I find your statement hard to believe. In particular, I think it would experimentally discard superdeterminism. Maybe I don't understand your statement.

Justo wrote:
I find your statement hard to believe. In particular, I think it would experimentally discard superdeterminism. Maybe I don't understand your statement.

Feldman claims a loophole which doesn't exist at all. The assumption that local functions A(a, µ), B(b, µ) can reproduce the correlation is theoretically wrong and experimentally falsified by many authors including Weihs. Insofar is Bell's derivation (1965) correct. In order to reproduce the correlations with hidden variables a different approach is necessary.

Esail wrote:

Justo wrote:
I find your statement hard to believe. In particular, I think it would experimentally discard superdeterminism. Maybe I don't understand your statement.

Feldman claims a loophole which doesn't exist at all. The assumption that local functions A(a, µ), B(b, µ) can reproduce the correlation is theoretically wrong and experimentally falsified by many authors including Weihs. Insofar is Bell's derivation (1965) correct. In order to reproduce the correlations with hidden variables a different approach is necessary.

A different approach is not necessary at all. Here is Joy's local model using quaternions.



And the result is....



The correlation result is exactly -a.b just like quantum mechanics predicts using a product calculation.
.

Fred, I think you are completely missing the point.

gill1109 wrote:Fred, I think you are completely missing the point.

What "point"? The point you can't seem to comprehend? Quite frankly, we don't care about your opinion or freakin' nonsense. That's the real "point". Yeah, that's the ticket!
Bell's theory is shot down. Get over it and move on. Thanks.

Justo wrote:

Esail wrote:Please give an example of those "local functions A(a, µ), B(b, µ) which reproduce the correlation (1)"

You just need to violate measurement independence. An explicit sample is given in "Michel Feldmann. New loophole for the Einstein-Podolsky-Rosen paradox. Foundations of Physics Letters, 8(1):41-53, 1995."

Indeed, that paper used the conspiracy loophole, but Feldmann's model is disproved by the results of the 2015 loophole-free experiments. Feldman's "conspiracy" needs time to be implemented, and in those new experiments there is not enough time.

https://www.researchgate.net/publication/225677089_New_loophole_for_the_Einstein-Podolsky-Rosen_paradox

gill1109 wrote:

Justo wrote:

Esail wrote:Please give an example of those "local functions A(a, µ), B(b, µ) which reproduce the correlation (1)"

You just need to violate measurement independence. An explicit sample is given in "Michel Feldmann. New loophole for the Einstein-Podolsky-Rosen paradox. Foundations of Physics Letters, 8(1):41-53, 1995."

Indeed, that paper used the conspiracy loophole, but Feldmann's model is disproved by the results of the 2015 loophole-free experiments. Feldman's "conspiracy" needs time to be implemented, and in those new experiments there is not enough time.

https://www.researchgate.net/publication/225677089_New_loophole_for_the_Einstein-Podolsky-Rosen_paradox

I don't know if those experiments can rule out "conspiracy". I used to think that needed time to take place but now I realized I was wrong.
I believe Zeilinger made Bell tests using light of distant quasar to rule out measurement dependence but I am not sure how that should be interpreted.