In this paper we identify the superposition principle as a main source of problems in QM (measurement, collapse, non-locality etc.). Here the superposition principle for individual systems is substituted by the anti-superposition principle: no non-trivial superposition of states is a possible individual state (for ensembles the superposition principle is true). The modified QM is based on the anti-superposition principle and on the new type of probability theory (Extended Probability Theory [1]), which allows the reversible Markov processes as models for QM. In the modified QM the measurement is a process inside of QM and the concept of an observation of the measuring system is defined. The outcome value is an attribute of the ensemble of measured systems. The collapse of the state is substituted by the Selection process. We show that the derivation of Bell’s inequalities is then impossible and thus QM remains a local theory. Our main results are: the locality of the modified QM, the local explanation of EPR correlations, the non-existence of the wave-particle duality, the solution of the measurement problem. We show that QM can be understood as a new type of the statistical mechanics of many-particle systems.
In this paper we identify the superposition principle as a main source of problems in QM (measurement, collapse, non-locality etc.). Here the superposition principle for individual systems is substituted by the anti-superposition principle: no non-trivial superposition of states is a possible individual state (for ensembles the superposition principle is true). The modified QM is based on the anti-superposition principle and on the new type of probability theory (Extended Probability Theory [1]), which allows the reversible Markov processes as models for QM. In the modified QM the measurement is a process inside of QM and the concept of an observation of the measuring system is defined. The outcome value is an attribute of the ensemble of measured systems. The collapse of the state is substituted by the Selection process. We show that the derivation of Bell’s inequalities is then impossible and thus QM remains a local theory. Our main results are: the locality of the modified QM, the local explanation of EPR correlations, the non-existence of the wave-particle duality, the solution of the measurement problem. We show that QM can be understood as a new type of the statistical mechanics of many-particle systems.
This paper demonstrates the capability to simulate EPR experiments in a realistic way (i.e. without transmission of information between the source and the detector) and confirms even more the Bell’s theorem, by demonstrating that effectively non-local variables are required to violate the Bell’s inequality. Unlike all EPR experiments, this modeling instead of simply noting the inadequacy of a local modeling proposes a new way of non-local idealization. These simulations work on spreadsheet by idealizing objects with a non-linear notion, the extended object. This allows to set up a new principle of locality (or non-locality) and a new meaning on the loopholes of EPR experiments. It sheds new light on several concepts of Quantum Mechanics (QM): the quantum states (would represent an equivalence class of many different indistinguishable objects seen as equivalent in terms of measurement), the wave function (would represent a probability on this equivalence class seen as a single set despite different probabilities of happening for the individual objects composing this equivalence class), the measurement (in our simulation, the measured object is not modified), the superposition of states (in our simulation, Schrödinger's cat is never both dead and alive). These simulations lead to several kinds of EPR experiments with violations of the Bell’s inequalities with values different from the QM, allow to realize entanglements with more than 2 objects (whatever the number of Alice and Bob) or even with more than 2 results (beyond the only “+1” or “-1” outputs). Many questions remain to be explored in the physics domain on quantum phenomena (teleportation, encryption, quantum computing, etc.…), but this theoretical approach also reveals the necessity of developing new non-linear tools in mathematics domain and seems to show that QM could finally be a limit case of a more fundamental nonlinear physics theory founded on these extended objects. This observation is strangely reminiscent of developments such as string theory.
This paper demonstrates the capability to simulate EPR experiments in a realistic way (i.e.without transmission of information between the source and the detector) and confirms even more the Bell's theorem, by demonstrating that effectively non-local variables are required to violate the Bell's inequality.Unlike all EPR experiments, this modeling instead of simply noting the inadequacy of a local modeling proposes a new way of non-local idealization.These simulations work on spreadsheet by idealizing objects with a non-linear notion, the extended object.This allows to set up a new principle of locality (or non-locality) and a new meaning on the loopholes of EPR experiments.It sheds new light on several concepts of Quantum Mechanics (QM): the quantum states (would represent an equivalence class of many different indistinguishable objects seen as equivalent in terms of measurement), the wave function (would represent a probability on this equivalence class seen as a single set despite different probabilities of happening for the individual objects composing this equivalence class), the measurement (in our simulation, the measured object is not modified), the superposition of states (in our simulation, Schrödinger's cat is never both dead and alive).These simulations lead to several kinds of EPR experiments with violations of the Bell's inequalities with values different from the QM, allow to realize entanglements with more than 2 objects (whatever the number of Alice and Bob) or even with more than 2 results (beyond the only "+1" or "-1" outputs).Many questions remain to be explored in the physics domain on quantum phenomena (teleportation, encryption, quantum computing, etc.), but this theoretical approach also reveals the necessity of developing new non-linear tools in mathematics domain and seems to show that QM could finally be a limit case of a more fundamental nonlinear physics theory founded on these How to cite this paper: Le Corre, S.
Abstract. In this note we shall show that the proof of the nonlocality of Quantum Mechanics given in [1] contains a gap. We also show that Bell inequalities cannot be derived in the modified QM. In the paper [1] there is a proof of the nonlocality of Quantum Mechanics (QM). In the proof of this statement the main step is the following implication: “from EPR correlations to the predetermination”. This means the following: “A deterministic hidden variable theory was one’s only hope, if one wanted to explain the predicted quantum correlations in a local way. ” ([1]. Page 2) – i.e. the nonlocality or the pre-determination. “The important thing was instead that the only way to explain the perfect correlations locally is to attribute outcome-determining properties to the individual particles. These properties, evidently, would vary randomly from one particle pair to the next, but would be fixed (in an appropriately correlated way) once and for all at the source for a given particle pair. ” ([1], page 2). This may be called the pre-determination. “ … such deterministic hidden variables are the only way to account locally for the
AbstractAn alternative interpretation of QM is presented. Hidden vari-ables prescribe the output of measurements for individual states ofthe ensemble, but a distribution of amplitudes of probability, insteadof a distribution of probabilities, is associated to them, as in orthodoxQM. Consequently, Bell’s type inequalities do not apply. In this in-terpretation, locality is restored in EPR experiments with entangledsubsystems, as the observable relative frequencies are obtained by theusual interference for sum of amplitudes, in complete parallelism withthe two slit experiment. The action reaction principle seems to be vio-lated in some QM measurements, and the existence of hidden variablescould solve this paradox too. In indirect measurements it remains ob-scure the way it could be restored. A version of the two slit experimentis proposed to search for the hidden reaction. Keywords: Alternative interpretations of QM, measurement problem, nonlocality, path integral formalism.PACS numbers: 03.65.Ca, 03.65.Ta, 03.65.Ud
It is shown that when properly analyzed using principles consistent with the
use of a Hilbert space to describe microscopic properties, quantum mechanics is
a local theory: one system cannot influence another system with which it does
not interact. Claims to the contrary based on quantum violations of Bell
inequalities are shown to be incorrect. A specific example traces a violation
of the CHSH Bell inequality in the case of a spin-3/2 particle to the
noncommutation of certain quantum operators in a situation where (non)locality
is not an issue. A consistent histories analysis of what quantum measurements
measure, in terms of quantum properties, is used to identify the basic problem
with derivations of Bell inequalities: the use of classical concepts (hidden
variables) rather than a probabilistic structure appropriate to the quantum
domain. A difficulty with the original Einstein-Podolsky-Rosen (EPR) argument
for the incompleteness of quantum mechanics is the use of a counterfactual
argument which is not valid if one assumes that Hilbert-space quantum mechanics
is complete; locality is not an issue. The quantum correlations that violate
Bell inequalities can be understood using local quantum common causes.
Wavefunction collapse and Schr\odinger steering are calculational procedures,
not physical processes. A general Principle of Einstein Locality rules out
nonlocal influences between noninteracting quantum systems. Some suggestions
are made for changes in terminology that could clarify discussions of quantum
foundations and be less confusing to students.
It has been claimed that quantum mechanics is a non-local theory, i.e., that the predictions of quantum mechanics are at odds with a conception of the world where all the interactions are mediated by local mechanisms. The cited reason is the violation of the Bell inequality in cases where measurements are performed on quantum systems of particles that have interacted in the past. Quantum mechanics predicts that the state of the particles in such a system are correlated, a result obtained from considering a thought-experiment often known as EPR. In this thesis, I will argue that the violation of the Bell inequality in EPR forces us to either accept that causes sometimes act both backwards and forwards in time, or give up some widely-held assumptions about causal relations or the role of causal explanations. First, I will present three principles regarding causality that I take be widely accepted. I will then present the background for the claim the quantum mechanics is a non-local theory, and discuss the implications of non-local causal influences in light of the Special Theory of Relativity. One argument against a causal explanation of the EPR-correlations will be discussed, and different models for the causal structure of EPR will be assessed. I will argue that a retrocausal model – models that include instances of retrocausation, where the direction of causation is the opposite of the direction of time – is the only viable option if we want to uphold the three principles presented in chapter 1. I will discuss the plausibility of rejecting one of these principles, and argue that at least one of the can be restricted in a way that still accounts for our commitment to it. Finally, I will assess the non-local models against the retrocausal models, and argue that a retrocausal model offers interpretational advantages over the non-local alternatives.