arXiv:2109.03086

About the description of physical reality of Bell's experiment

Alejandro Andrés Hnilo

Published Sep 6, 2021• 1 citation

Abstract

A hidden variables model complying with the simplest form of Local Realism was recently introduced, which reproduces Quantum Mechanics' predictions for an even ideally perfect Bell's experiment. This is possible thanks to the use of a non-Boolean vector hidden variable. Yet, that model is as far as Quantum Mechanics from the goal of providing a complete description of physical reality in the EPR-sense. Such complete description includes the capacity to calculate, from the values taken by the hidden variables, the time values when particles are detected. This can be achieved by replacing Born's rule (which allow calculating only probabilities) with a deterministic condition for particle detection. The simplest choice is a threshold condition on the hidden variables. However, in order to test this choice, a new type of quantum (or wave, or non-Boolean) computer is necessary. This new type of quantum computer does not exist yet, not even in theory. In this paper, a classical (Boolean) computer code is presented which mimics the operation of that new type of quantum computer by using contextual instructions. These instructions take into account a consequence of the principle of superposition (which is a typical vector, i.e. non-Boolean, feature). Numerical results generated by the mimicking code are analyzed. They illustrate the features the hypothetical new type of quantum computer's output may have, and show how and why some intuitive assumptions about Bell's experiment fail.

DOI: 10.48550/arxiv.2109.03086

Related papers

Non-Boolean hidden variable model reproduces Quantum Mechanics’ predictions for Bell’s experiment.

Alejandro Andrés Hnilo

Abstract The experimentally verified violation of Bell’s inequalities apparently implies that at least one of two beliefs, which are accepted as true in almost all scientific practice, must be false. These beliefs are: that effects propagating at infinite velocity do not exist, and that natural phenomena occur independently of being observed. Giving up any one of these two beliefs (usually known together as Local Realism) is controversial. For many years, many theories have been proposed to reconcile the violation of Bell’s inequalities with Local Realism, but none has been fully successful. In this paper, it is recalled that Bell’s inequalities are equivalent to the conditions to decide the completeness of a theory according to Boolean logic. Therefore, any theory aimed to violate Bell’s inequalities must start by giving up Boolean logic. Two problems are therefore defined: the “soft” one is to explain the violation of Bell’s inequalities without violating (non-Boolean) Local Realism; the “hard” one is to predict the time values when single particles are detected, in such a way that the resulting number of coincidences violates Bell’s inequalities. A simple hidden variables model is introduced, which solves the “soft” problem even in an ideal setup. This is possible thanks to the use of vectors in real space as the hidden variables and the corresponding operation (projection), which do not hold to Boolean logic. This model reconciles the violation of Bell’s inequalities with Local Realism and should end a controversy that has lasted for decades. Regarding the “hard” problem, the introduced model is as incomplete as Quantum Mechanics is. It is claimed that solving the “hard” problem requires devising a new kind of quantum computer, which should be able to accept (non-Boolean) hidden variable values as input data and to replace the statistical Born’s rule of Quantum Mechanics with a deterministic threshold condition.

Aug 17, 20220 citations

Non-Boolean Hidden Variables model reproduces Quantum Mechanics' predictions for Bell's experiment

Alejandro Andrés Hnilo

The experimentally verified violation of Bell's inequalities apparently implies that at least one of two intuitive beliefs must be false: that effects propagating at infinite velocity do not exist, and that natural phenomena occur independently of being observed. Giving up any one of these two beliefs (usually known together as Local Realism) is controversial. Many theories have been proposed to reconcile the violation of Bell's inequalities with Local Realism, but none has been fully successful. In this paper, it is recalled that any theory aimed to violate Bell's inequalities must start by giving up Boolean logic. The problem is split in two: the "soft" problem is to explain the violation of Bell's inequalities within (non-Boolean) Local Realism. The "hard" problem is to predict the time values when single particles are detected. A simple hidden variables model is introduced, which solves the soft problem. This is possible thanks to the use of vectors as the hidden variables and the operation projection, which do not hold to Boolean logic. This model reconciles the violation of Bell's inequalities with Local Realism and should end decades of controversy. Regarding the hard problem, the introduced model is as incomplete as Quantum Mechanics is. It is argued that solving the hard problem involves devising a new kind of quantum computer, which should be able to accept (non-Boolean) hidden variables as input data and replace the statistical Born's rule with a deterministic threshold condition.

arXiv:2005.10367May 20, 20201 citation

What do we learn from computer simulations of Bell experiments?

Marian Kupczyński

Contrary to counterfactual definiteness quantum theory teaches us that measuring instruments are not passively reading predetermined values of physical observables. Counterfactual definiteness allows proving Bell inequalities. If the contextual character of quantum measurements is correctly taken into account the proofs of these inequalities may not be done. In recent computer simulations of idealized Bell experiment predetermined successive outcomes of measurements for each setting and predetermined time delays of their registrations are calculated. Time windows and time delays are used to select various samples. Correlations, estimated using these selected samples are consistent with the predictions of quantum theory and the time window dependence is similar to the dependence observed in some real experiments. It is an important example how correlations can be explained without evoking quantum non-locality. However by using a suitable post-selection one may prove anything. Since before the post-selection generated samples may not violate Bell inequalities as significantly as finite samples generated using quantum predictions thus one may not conclude that counterfactual definiteness is not able to distinguish classical from quantum physics. Moreover we show that for each choice of a time window there exists a contextual hidden variable probabilistic model consistent with the post-selection procedure used by the authors what explains why they are able to reproduce quantum predictions.

arXiv:1611.03444Nov 10, 20161 citation

A local hidden-variable model violating Bell's inequalities

A. Matzkin

A model for two entangled systems in an EPR setting is shown to reproduce the quantum-mechanical outcomes and expectation values. Each system is represented by a small sphere containing a point-like particle embedded in a field. A quantum state appears as an equivalence class of several possible particle-field configurations. Contrarily to Bell-type hidden variables models, the fields account for the non-commutative aspects of the measurements and deny the simultaneous reality of incompatible physical quantities, thereby allowing to escape EPR's completeness or locality dilemma.

Mar 29, 20072 citations

Locality Is Dead! Long Live Locality!

William Sulis

Several decades of theory and experiment into EPR correlations have led to the widely held belief that reality is non-local, in spite of the fact that this violates special relativity. To date, no experiment has shown a violation of special relativity, and EPR experiments do not demonstrate the existence of superluminal information exchange, merely correlations which violate certain inequalities. Every “loophole” in these hidden variable theories has been thought plugged. However, there is much confusion in the literature due to conflation of the terms ‘locality”, “realism”, “hidden variables”, “non-contextuality”. The presence of local hidden variables is thought to necessarily lead to a Kolmogorov probability structure (hence non-contextuality), but this is an assumption, one which is not true in general once context effects are taken into account. Treated as an observational theory, several authors have shown no incompatibility between quantum mechanics and locality, and that the Bell scenario is actually about whether reality is contextual. This paper proposes a descriptive theory by assuming a generated reality (following Whitehead’s Process Theory) which can violate the principle of continuity and possess non-Kolmogorov probability structure, and reproduce the results of non-relativistic quantum mechanics, while allowing only causally local information exchange, without hidden variables. A generated reality is thus compatible with both quantum mechanics and special relativity, reproducing all of the results expected from quantum mechanics while still maintaining causally local realism. This process model thus appears to be an ideal candidate for developing theories for the unification of quantum mechanics and general relativity.

Frontiers in PhysicsSep 15, 202015 citations

Quantum nonlocality: no, yes, how and why

Alejandro A. Hnilo

The problem of the existence of nonlocal effects in Quantum Mechanics is discussed. The problem is divided in two: the first ('soft') one is to explain the violation of Bell's inequalities as a statistical magnitude. This can be achieved by a simple model within non-Boolean Locality and Realism. This result shows that quantum non-Locality as a consequence of the statistical violation of Bell's inequalities is inexistent. The second ('hard') problem is to explain the violation as it is calculated from series of detection outcomes. L.Sica has demonstrated that, in order to violate Bell's inequalities, the series recorded at (say) Bob when the setting at station Alice is alfa, can be different from the series that would have been recorded at Bob if that setting had been alfa'instead. Therefore, non-Locality in the series of detection outcomes does exist. It cannot be experimentally verified because of its counterfactual nature, but is observed in computer simulations. An appropriate computer code is based on the simple model mentioned plus a contextual instruction. It explains 'how' (Sica's) non-Locality arises, and solves the hard problem. 'Why' the contextual instruction exists is explained by Hellwig and Kraus' postulate of covariant quantum state collapse. In consequence, (Sica's) non-Locality is not in contradiction with Relativity but, quite the opposite, it is implied by Relativistic covariance.

quant-pharXiv:2603.09000Mar 11, 20260 citations