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Quantum mechanics by Jiri Soucek

The proof of the untruth of the counterfactual definiteness assumption in quantum mechanics, 2020

There were attempts to argument against the counterfactual definiteness assumption (CFD) in quant... more There were attempts to argument against the counterfactual definiteness assumption (CFD) in quantum mechanics while the most scientists accepted CFD. In fact, arguments are only arguments but not the proof. In this letter we give the correct and complete proof (using only empirical facts) of the untruth of CFD based on the recently obtained Strong Bell's theorem. Thus the often discussed question of the validity of CFD is definitely solved in the way that CFD is untruth in quantum mechanics.

The standard Bell's theorem states that quantum mechanics (QM) cannot be locally realistic. Here ... more The standard Bell's theorem states that quantum mechanics (QM) cannot be locally realistic. Here we prove the strong Bell's theorem which states that QM cannot be realistic. In the proof we use the Mermin's form of the Bell's theorem. Our result solves the old dilemma: non-locality or non-realism. Then we discuss the consequences of the strong Bell's theorem, e.g. that no Bell non-locality of QM exists and that quantum theory is local and non-realistic.

The standard Bell's theorem says that quantum mechanics (QM) cannot be locally realistic. Here we... more The standard Bell's theorem says that quantum mechanics (QM) cannot be locally realistic. Here we prove the strong Bell's theorem which says that QM cannot be realistic. In the proof we use the Mermin's form of the Bell's theorem. Our result solves the old dilemma: non-locality or non-realism. Then we discuss some consequences of the strong Bell's theorem, e.g. that no Bell non-locality of QM exists and that quantum theory is local and non-realistic. 2

A new model for quantum mechanics and the invalidity of no-go theorems, 2018

In this paper we define and study the new model for quantum mechanics (QM) – the hybrid epistemic... more In this paper we define and study the new model for quantum mechanics (QM) – the hybrid epistemic model. The new feature of this model consists in the fact that it does not contain the formal definition of the measurement process but the measurement process is one of possible processes inside of QM.
The hybrid-epistemic model of QM is based on two concepts: the quantum state of an ensemble and the properties of individual systems.
We show the local nature of EPR correlations in the hybrid-epistemic model of QM in all details.
We define precisely the epistemic and the ontic models of QM for the goal to prove that these three models give the same empirical predictions, i.e. that they are empirically equivalent.
We show that the no-go theorems (Bell’s theorem, the Leggett-Garg’s theorem and others theorems) cannot be proved in the hybrid-epistemic model of QM. This is one of the main results of this paper.
We shall consider the possible inconsistences of the ontic model of QM.
We introduce the property-epistemic model of QM which is the special simple case of the hybrid-epistemic model.
This study was published as a book ISBN 978-613-7-33070-8

In this Letter we give a completely general formulation of the argument that quantum mechanics (Q... more In this Letter we give a completely general formulation of the argument that quantum mechanics (QM) is invalid at short distances. The proof is based on the use of two reasonable " physical " hypotheses: (i) the particle structure of the Higgs' condensate, (ii) the origin of the randomness in quantum mechanics rests in the interaction with particles from the Higgs' condensate. In this short note we want to show that under certain quite general circumstances quantum mechanics (QM) must be invalid at short distances. In our argument we use two hypotheses:  The Higgs' condensate should be quantized and can be modeled as a set of infinite velocity tachyons  The origin of the randomness of QM is given by the interaction of a particle with tachyons from the Higgs' condensate. The quantization of the Higgs' condensate means the representation of the Higgs' condensate as a set of particles (i.e. as a set of bare Higgs' particles). Considering the form of the Higgs' Lagrangian we see that the bare Higgs' particles should be massive tachyons. In our model we shall use (for simplicity) infinite velocity tachyons. Each such tachyon is localized inside some three-dimensional hyper-plane IVT (τ) = {(x, t) | t=τ, x ∈ R 3 } where τ ∈ R 1 is a parameter. There are two possible forms of such tachyon: (1) the standard tachyon which trajectory as a line inside IVT(τ), (2) the non-local tachyon which trajectory is all IVT(τ) [1]. We shall consider both possibilities.

In this Letter we analyze the general nature of the recently obtained result saying that no-go th... more In this Letter we analyze the general nature of the recently obtained result saying that no-go theorems in quantum mechanics are not correctly proved. In [1] there was shown that the standard proof of the Bell's theorem [2] (and proofs of other no-go theorems) in quantum mechanics (QM) is not correct.

We present models in which the indeterministic feature of Quantum Mechanics is represented in the... more We present models in which the indeterministic feature of Quantum Mechanics is represented in the form of definite physical mechanisms. Our way is completely different from so-called hidden parameter models, namely, we start from a certain variant of QM - deterministic QM - which has most features similar to QM, but the evolution in this theory is deterministic. Then we introduce the subquantum medium composed of so-called space-like objects. The interaction of a deterministic QM-particle with this medium is represented by the random force, but it is the random force governed by the probability amplitude distribution. This is the quantum random force and it is very different from classical random force. This implies that in our models there are no Bell`s inequalities and that our models (depending on a certain parameter tau) can be arbitrarily close to QM. The parameter tau defines a relaxation time and on time intervals shorter than tau, the evolution violates Heisenberg`s uncertai...

We propose the experimental test of the uncertainty principle. From sub-quantum models it follows... more We propose the experimental test of the uncertainty principle. From sub-quantum models it follows that the uncertainty principle may be not true on short time intervals of the order of a picosecond. The positive result of this experiment would signify the limits of QM.

The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpre... more The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive number. The two-slit experiment, the mathematical formulation of the complex probability theory, the density matrix, Born's law and a possibility of hidden variables are discussed.

Journal of Physics A: Mathematical and General, 1981

The new approach to quaternion quantum mechanics is given. It is shown that such a theory describ... more The new approach to quaternion quantum mechanics is given. It is shown that such a theory describes tachyons and that the quantum theory of tachyons should be a quaternionic one. This theory needs fundamental changes in basic physical assumptions and in a sense it is complementary to known physics. An important analogy between the basic notions of quaternionic and complex quantum mechanics emerges from the new scheme. The consequences for the theory of quantum and classical tachyons seem to be very important.

Foundations of Physics Letters, 1989

Path integral expressions are given for the wave function and for the density matrix in a theory ... more Path integral expressions are given for the wave function and for the density matrix in a theory which describes state vector reduction. The magnitude of the contribution of each classical path to the propagator is not unity, as in ordinary quantum theory, but depends upon the path.

In this study we introduce and describe in details the hybrid-epistemic model for quantum mechani... more In this study we introduce and describe in details the hybrid-epistemic model for quantum mechanics. The main differences with respect to the standard model are following: (1) the measurement process is considered as an internal process inside quantum mechanics, i.e. it does not make a part of axioms and (2) the process of the observation of the state of the individual measuring system is introduced into axioms. The intrinsic measurement process is described in two variants (simplified and generalized). Our model contains hybrid, epistemic and hybrid-epistemic systems. Each hybrid system contains a unique orthogonal base composed from homogeneous (i.e. ontic) states. We show that in our model the measurement problem is consistently solvable. Our model represents the rational compromise between the Bohr's view (the ontic model) and the Einstein's view (the epistemic model).

We introduce a new concept of truth in empirical theories based on the experience in the study of... more We introduce a new concept of truth in empirical theories based on the experience in the study of quantum mechanics. In this concept a statement can be true, false or undecidable.

We prove that the Bell's theorem and the nonlocality of quantum mechanics are scientifically unfo... more We prove that the Bell's theorem and the nonlocality of quantum mechanics are scientifically unfounded statements.

Using a new concept of the truth in quantum mechanics we show that the individual superposition p... more Using a new concept of the truth in quantum mechanics we show that the individual superposition principle is scientifically unfounded.

In this article we consider four versions of quantum mechanics (QM), which form four di erent the... more In this article we consider four versions of quantum mechanics (QM), which form four di erent theories and which have the same experimental consequences (one of them is the standard QM). We consider six fundamental problems as criteria for the evaluation of these theories. The most successful is the
modified QM introduced in [1] and described in the axiomatic form in [2], which solves all six problems. The least successful is the standard QM, which does not solve any of considered problems. (It seems that the standard QM is unable to solve any of these problems.) Other two theories solve some of problems and did not solve some other problems. On the base of this result we recommend to abandon the standard QM and to accept the modified QM as the right QM, since both variants have the same experimental content and the differences rest
only in theoretical considerations.

t is argued that the lesson we should learn from Bell inequalities (BI) is not that Quantum Mecha... more t is argued that the lesson we should learn from Bell inequalities (BI) is not that Quantum Mechanics (QM) is nonlocal, but that QM contains an error which must be corrected.

In this note we shall show the relation between the locality of Quantum Mechanics and the meaning... more In this note we shall show the relation between the locality of Quantum Mechanics and the meaning of the quantum state.

In this note we show that in the modified quantum mechanics EPR correlations can be explained loc... more In this note we show that in the modified quantum mechanics EPR correlations can be explained locally. We show also that the claim on the quantum nonlocality is in the modified quantum mechanics false.

In this note we shall show that the proof of the nonlocality of Quantum Mechanics given in [1] co... more 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.

The proof of the untruth of the counterfactual definiteness assumption in quantum mechanics, 2020

A new model for quantum mechanics and the invalidity of no-go theorems, 2018

Journal of Physics A: Mathematical and General, 1981

Foundations of Physics Letters, 1989

Archive for Rational Mechanics and Analysis, 1989

In this paper we introduce some new classes of functions, among these a class of weak diffeomorph... more In this paper we introduce some new classes of functions, among these a class of weak diffeomorphisms. In these classes we prove by direct methods the existence of minimizers for several kinds of variational integrals. In particular, we prove the existence of one-to-one ...

Archive for Rational Mechanics and Analysis, 1974

Manuscripta Mathematica, 1989

We discuss the relaxed functional of the Dirichlet energy. We also prove partial regularity of mi... more We discuss the relaxed functional of the Dirichlet energy. We also prove partial regularity of minimizers and concentration of the gradient on singular lines.

Mathematische Nachrichten, 1973

Mathematische Annalen, 1985

Selecta Mathematica, 2004

In the last years there has been some interest in studying mappings in the fractional Sobolev spa... more In the last years there has been some interest in studying mappings in the fractional Sobolev space W 1/2 (Ω, S 1 ), see e.g., [3] [12] and the paper . Motivated by these papers, we characterize here in the framework of Cartesian currents, see , the class of weak limits of sequences of smooth mappings with values into S 1 with equibounded W 1/2 energies.

Cartesian Currents in the Calculus of Variations II, 1998

Czechoslovak Mathematical Journal

Časopis pro pěstování matematiky

$Research paper thumbnail of The particle model for the Higgs' condensate and the anomalous geometric diffraction$

The anomalous geometric diffraction in quantum mechanics and the time-like two slit experiment. T... more The anomalous geometric diffraction in quantum mechanics and the time-like two slit experiment. The dark energy hypothesis. The possible invalidity of quantum mechanics at short distances.

At first we identify the main error in the formulation of the concept of the weak solution to Nav... more At first we identify the main error in the formulation of the concept of the weak solution to Navier-Stokes (NS) equations which is the completely insufficient treatment of the incompressibility condition on the fluid (expressed in the standard way by div u = 0). The repair requires the complete reformulation of the NS problem. The basic concept must be the generalized motion (i.e. the generalized flow) which replaces the standard velocity field. Here we define the generalized flow on the bases of Geometric measure theory extended to the theory of Cartesian currents and weak diffeomorphisms (see [1], [2]). Then the key concept of the complete weak solution to the NS problem is defined and the two conjectures (the existence and the regularity ones) concerning the complete weak solutions are formulated. In two appendices many technical details are described (concerning e.g. Cartesian currents, homology conditions, weak diffeomorphisms, etc.). Our approach is based on the unification of the standard analysis of NS equations with the methods of Geometric measure theory and of the theory of Cartesian currents.

In [1] there was proved that quantum mechanics (QM) is non-realistic. In this paper we consider t... more In [1] there was proved that quantum mechanics (QM) is non-realistic. In this paper we consider the main consequences of this result. These are: the possible locality of QM ([2], [4]), the invalidity of most no-go theorems ([5]), the new meaning of the EPR paper, the new interpretation of Bell's theorems, the necessity of the fundamental reconsideration of the foundational research in QM. We have introduced and applied the concepts of an empty proof and an empty statement. 2

We prove that the Bell’s theorem and the nonlocality of quantum mechanics are scientifically unfo... more We prove that the Bell’s theorem and the nonlocality of quantum mechanics are scientifically unfounded statements.

viXra, 2015

It is argued that the lesson we should learn from Bell inequalities (BI) is not that Quantum Mech... more It is argued that the lesson we should learn from Bell inequalities (BI) is not that Quantum Mechanics (QM) is nonlocal, but that QM contains an error which must be corrected. 1

viXra, 2015

In this note we shall give the simple formulation of the local explanation of EPR correlations [1... more In this note we shall give the simple formulation of the local explanation of EPR correlations [1] based on [2]. We also show that Bell inequalities cannot be derived in the modified Quantum Mechanics (QM).

viXra, 2015

Lecture Notes in Mathematics, 1973

This work is subject to copyright. All rights are reserved, whether the whole or part of the mate... more This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher.

viXra, 2015

In the standard Quantum Mechanics there exists certain assumption (which I call the von Neuman ax... more In the standard Quantum Mechanics there exists certain assumption (which I call the von Neuman axiom) stating that an ensemble in the pure state is homogeneous. This means that all members of this ensemble are in the same individual state. In this note I am going to show that the von Neumann axiom is false. This also means that the standard interpretation of the wave function as the state of the individual system is in general false. In the ontic/epistemic terminology this means that the ontic interpretation of the wave function cannot be true. As a solution I propose the modified Quantum Mechanics which can be local.

viXra, 2015

viXra, 2017

In this study we introduce and describe in details the hybrid-epistemic model for quantum mechani... more In this study we introduce and describe in details the hybrid-epistemic model for quantum mechanics. The main differences with respect to the standard model are following: (1) the measurement process is considered as an internal process inside quantum mechanics, i.e. it does not make a part of axioms and (2) the process of the observation of the state of the individual measuring system is introduced into axioms. The intrinsic measurement process is described in two variants (simplified and generalized). Our model contains hybrid, epistemic and hybrid-epistemic systems. Each hybrid system contains a unique orthogonal base composed from homogeneous (i.e. ontic) states. We show that in our model the measurement problem is consistently solvable. Our model represents the rational compromise between the Bohr’s view (the ontic model) and the Einstein’s view (the epistemic model).

viXra, 2015

From the dichotomy "nonlocality vs non-realism" which is the consequence of Bell Inequa... more From the dichotomy "nonlocality vs non-realism" which is the consequence of Bell Inequalities (BI) we shall choose the non-realism. We shall present here the modified Quantum Mechanics (modQM) in the axiomatic form. ModQM was introduced in [5] and we shall show its non-realism in the description of an internal measurement process. ModQM allows the restoration of locality, since BI cannot be derived in it. In modQM it is possible to solve: the measurement problem, the collapse problem, the problem of a local model for EPR correlations (see[5]). ModQM is a unique explicit realization of non-realism in QM. ModQM should be preferred as an alternative to the standard QM mainly since it restores the locality.

viXra, 2014

In this paper we identify the superposition principle as a main source of problems in QM (measure... more 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 antisuperposition 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...

We prove that the Bell's theorem and the nonlocality of quantum mechanics are scientifically ... more We prove that the Bell's theorem and the nonlocality of quantum mechanics are scientifically unfounded statements.

$Research paper thumbnail of The particle model for the Higgs' condensate and the anomalous geometric diffraction$

viXra, 2015

We discuss the three options: the psi-ontic option, the psi-epistemic option and the novel psi-hy... more We discuss the three options: the psi-ontic option, the psi-epistemic option and the novel psi-hybrid option.

viXra, 2015

arXiv: Quantum Physics, 2010

In the paper the basic concepts of extended probability theory are introduced. The basic idea: th... more In the paper the basic concepts of extended probability theory are introduced. The basic idea: the concept of an event as a subset of \Omega is replaced with the concept of an event as a partition. The partition is any set of disjoint non-empty subsets of \Omega (i.e. partition=subset+its decomposition). Interpretation: elements inside certain part are indistinguishable, while elements from different parts are distinguishable. There are incompatible events, e.g {{e1},{e2}} and {{e1,e2}}. This is logical incompatibility analogical to the impossibility to have and simultaneously not to have the which-way information in the given experiment. The context is the maximal set of mutually compatible events. Each experiment has associated its context. In each context the extended probability is reduced to classical probability. Then the quadratic representation of events, partitions and probability measures is developed. At the end the central concept of quadratic probability spaces (which e...

$Research paper thumbnail of The particle model for the Higgs’ condensate: and the anomalous geometric diffraction$

In this paper we propose a particle model for the Higgs’ condensate: we propose that this condens... more In this paper we propose a particle model for the Higgs’ condensate: we propose that this condensate is the set of (infinite velocity) non-local tachyons. We show that then there exists the anomalous geometrical diffraction (which contradicts to quantum mechanics). We show that there exists a universal time constant which defines the limits of the validity of quantum mechanics. We propose an experiment testing the existence of the anomalous geometrical diffraction. We proposed the dark energy conjecture which enables to make an estimate of the time constant. We assume certain (“Feynman”) interaction between standard particle and the non-local tachyon. All this is related to the new (finite) form of the Feynman integral.

viXra, 2015

In this article we consider the variant of quantum mechanics (QM) which is based on the non-reali... more In this article we consider the variant of quantum mechanics (QM) which is based on the non-realism. There exists the theory of the modified QM introduced in [1] and [2] which is based on the non-realism, but it contains also other changes with respect to the standard QM (stQM). We introduce here the other non-realistic modification of QM (n-rQM) which contains the minimal changes with respect to stQM. The change consists in the replacement of the von Neumann`s axiom (ensembles which are in the pure state are homogeneous) by the anti-von Neumann`s axiom (any two different individual states must be orthogonal). This introduces the non-realism into n-rQM. We shall show that experimental consequences of n-rQM are the same as in stQM, but these two theories are substantially different. In n-rQM it is not possible to derive (using locality) the Bell inequalities. Thus n-rQM does not imply the non-locality (in contrast with stQM). Because of this the locality in n-rQM can be restored. The...