An Interesting New Test of Realism

[DrChinese]

Check this out:

Violation of a temporal Bell inequality for single spins in solid by over 50 standard deviations, G. Waldherr, P. Neumann, S. F. Huelga, F. Jelezko, and J. Wrachtrup (2011)

"Quantum non-locality has been experimentally investigated by testing different forms of Bell's inequality, yet a loophole-free realization has not been achieved up to now. Much less explored are temporal Bell inequalities, which are not subject to the locality assumption, but impose a constrain on the system's time-correlations. In this paper, we report on the experimental violation of a temporal Bell's inequality using a nitrogen vacancy defect (NV) in diamond and provide a novel quantitative test of quantum coherence. We therefore present a new technique to initialize the electronic state of the NV with high fidelity, a necessary requirement for reliable quantum information processing and/or the implementation of protocols for quantum metrology."

This is a very interesting rendering of a Bell test, because in effect no locality assumption is required. That assumption is replaced by one called "stationarity", which is defined

"Stationarity": The conditional probability Qij(t1, t2) to find a system in state j at time t2, if it was in state i at time t1 only depends on the time difference t2 - t1.

By combining this stationarity assumption along with a standard Realism requirement, they get the following Temporal Bell Inequality (TBI):

Qii(0, 2t) - Qii^2(0, t) >= 0 (1)

Guess what, they get negative probabilities and violation of the TBI by over 50 standard deviations. This is a(nother) powerful indicator that Realism is not viable, as Stationary Realism is ruled out along with Local Realism. So either Realism is not viable, or BOTH Locality and Stationarity are ruled out.

-DrC

 

[lugita15]

So what would a violation of stationarity mean? What would the conditional probability depend on in that case?

 

[DrChinese]

So what would a violation of stationarity mean? What would the conditional probability depend on in that case?

Not sure I am the best person to answer that, but I will throw out the following: The question is ultimately equivalent to whether you can characterize the state of Schrodinger's cat before you open the box. It is undefined, in a superposition, etc. But it has no well-defined value. If you are a realist, it has a value at all times.

 

[lugita15]

The question is ultimately equivalent to whether you can characterize the state of Schrodinger's cat before you open the box. It is undefined, in a superposition, etc. But it has no well-defined value.

Isn't that by definition just the issue of realism in general, with or without "stationarity"? Where does this stuff about time enter the discussion?

 

[billschnieder]

Check this out:

Violation of a temporal Bell inequality for single spins in solid by over 50 standard deviations, G. Waldherr, P. Neumann, S. F. Huelga, F. Jelezko, and J. Wrachtrup (2011)
...

This is a very interesting rendering of a Bell test, because in effect no locality assumption is required. That assumption is replaced by one called "stationarity", which is defined

"Stationarity": The conditional probability Qij(t1, t2) to find a system in state j at time t2, if it was in state i at time t1 only depends on the time difference t2 - t1.

This paper was debunked in anticipation, almost 10 years ago:

Bell's inequality violation due to misidentification of spatially non-stationary random processes
Author: Louis Sica

Abstract
Correlations for the Bell gedankenexperiment are constructed using probabilities given by quantum mechanics, and non-local information. They satisfy Bell's inequality and exhibit spatial non-stationarity in angle. Correlations for three successive local spin measurements on one particle are computed as well. These correlations also exhibit non-stationarity, and satisfy the Bell inequality. In both cases, the mistaken assumption that the underlying process is wide-sense-stationary in angle results in violation of Bell's inequality. These results directly challenge the wide-spread belief that violation of Bell's inequality is a decisive test for non-locality.


Bell's inequality violation due to misidentification of spatially non-stationary random processes
Louis Sica. Journal of Modern Optics, 1362-3044, Volume 50, Issue 15, 2003, Pages 2465 – 2474
----

The connection between Bell's inequalities based on probabilities and those based on correlations
Author: Louis Sicaa

Abstract
Violation of Bell inequalities is widely regarded as a definitive test for non-locality. However, Bell correlational inequalities must always be satisfied by all jointly present, cross-correlated data. The correlations of variable pairs obtained in repeated runs are not cross-correlated in this way and are not required to satisfy the Bell inequality. In addition, by using information regarded as non-local, proper joint correlations may be computed among counterfactual and measured variables. These correlations satisfy the Bell inequality, but are spatially non-stationary in angle. By using a simple symmetry condition, such considerations may be extended to inequalities in probabilities. The latter may be derived directly from correlational inequalities developed by Clauser, Horne, Shimony and Holt (CHSH). Violation of either correlational or probabilistic Bell inequalities then implies that the Bell correlation cannot be accounted for by a stochastic process that is spatially stationary in angle coordinates. However, other processes may still be allowed.

The connection between Bell's inequalities based on probabilities and those based on correlations
Louis Sica, Journal of Modern Optics, 1362-3044, Volume 51, Issue 16, 2004, Pages 2461 – 2468

 

[zonde]

In this paper realism assumption is different than in EPR paper.
They say: "Reality": The state of any physical system is always well defined.
EPR definition: The state of physical system is well defined if you can predict outcome of measurement with certainty.

So it seems that what they are demonstrating is that result of next measurement depends from context of previous measurement (in this case rotation of nuclear spin state with RF pulses). So the context of measurements persists between measurements. This is exactly the thing that formulation of physical ensemble requires.

 

[Demystifier]

So either Realism is not viable, or BOTH Locality and Stationarity are ruled out.

Why one would assume stationarity in the first place? Anyway, it will probably not surprise anybody that Bohmian mechanics violates both locality and stationarity.

 

[DrChinese]

This paper was debunked in anticipation, almost 10 years ago:

Sica's paper is not clear on its definition of stationarity (not offering a definition at all). I would not consider it authoritative (or generally accepted) anyway.

 

[lugita15]

Why one would assume stationarity in the first place? Anyway, it will probably not surprise anybody that Bohmian mechanics violates both locality and stationarity.

So what do Bohmians think this conditional probability depends on, other than the time difference?

 

[DrChinese]

Why one would assume stationarity in the first place? Anyway, it will probably not surprise anybody that Bohmian mechanics violates both locality and stationarity.

It was required for the experiment. Of course, that does not make it a good assumption. It just proves that IF you assume it, Realism must be ruled out. So I might conclude that if you assume either locality OR stationarity, then Realism falls. If you reject both, as you do, then Realism may be retained. So I guess no surprise there.

 

[Demystifier]

So what do Bohmians think this conditional probability depends on, other than the time difference?

They don't think, they calculate it.
And the result of calculation is the same as with standard QM.

The point is that the behavior of relevant quantities in BM, just as in ordinary QM, depends on the wave function. So when the wave function has a nontrivial dependence on time, then one does not expect stationarity.