arXiv subjects
Publications and source records attributed to Florin Moldoveanu.
Recent quantum reconstruction projects demand pure unitary time evolution which seems to contradict the collapse postulate. Inspired by Zurek's environment assisted invariance idea, a natural unitary realization of wavefunction collapse is proposed using Grothendieck group construction for the tensor product commutative monoid.
Grid maps obtained from fused sensory information are nowadays among the most popular approaches for motion planning for autonomous driving cars. In this paper, we introduce Deep Grid Net (DGN), a deep learning (DL) system designed for understanding the context in which an autonomous car is driving. DGN incorporates a learned driving environment representation based on Occupancy Grids (OG) obtained from raw Lidar data and constructed on top of the Dempster-Shafer (DS) theory. The predicted driving context is further used for switching between different driving strategies implemented within EB robinos, Elektrobit's Autonomous Driving (AD) software platform. Based on genetic algorithms (GAs), we also propose a neuroevolutionary approach for learning the tuning hyperparameters of DGN. The performance of the proposed deep network has been evaluated against similar competing driving context estimation classifiers.
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell inequalities.
Products and tensor products are linked by a universal property. Imposing the invariance of the laws of Nature under tensor composition along with Leibniz identity determines quantum and classical mechanics algebraic structure through the interplay between products, coproducts, and the tensor product. Violations of Bell's inequalities distinguishes quantum from classical mechanics.
Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are relational, and (4) positivity (the ability to define a physical state). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.
Quantum and classical mechanics share a common algebraic formalism which is expressed naturally in the language of category theory. A third realization of this formalism is the so-called hyperbolic quantum mechanics where split-complex numbers replace the usual complex numbers. We introduce and explore the corresponding generalization of C*-algebras and prove that hyperbolic quantum mechanics is not a viable candidate for describing Nature. Quantum and classical mechanics are the only acceptable theories of Nature which are invariant under tensorial composition.
We show that EPR's criterion of reality leads to contradictions in quantum mechanics. When locality is assumed, an inequality involving only one particle is violated, while when parameter and outcome dependence are assumed, EPR-realism is shown to be not Lorentz invariant. Quantum mechanics is both non-local and non-realistic.
Four critical elementary mathematical mistakes in Joy Christian's counterexample to Bell's theorem are presented. Consequently, Joy Christian's hidden variable model cannot reproduce any quantum mechanics results and cannot be used as a counterexample to Bell's theorem. The mathematical investigation is followed by a short discussion about the possibility to construct other hidden variable theories. A tutorial section on relevant Clifford algebra topics was added at the end to help interested readers decide for themselves the validity of Joy's claims. Also an appendix section discusses recent developments.
The purpose of this contribution is to provide an introduction for a general physics audience to the recent results of Emile Grgin that unifies quantum mechanics and relativity into the same mathematical structure. This structure is the algebra of quantions, a non-division algebra that is the natural framework for electroweak theory on curved space-time. Similar with quaternions, quantions preserve the core features of associativity and complex conjugation while giving up the unnecessarily historically biased property of division. Lack of division makes possible structural unification with relativity (one cannot upgrade the linear Minkowski space to a division algebra due to null light-cone vectors) and demands an adjustment from Born's standard interpretation of the wave function in terms of probability currents. This paper is an overview to the theory of quantions, followed by discussions.
In a series of very interesting papers [1-7], Joy Christian constructed a counterexample to Bell's theorem. This counterexample does not have the same assumptions as the original Bell's theorem, and therefore it does not represent a genuine disproof in a strict mathematical sense. However, assuming the physical relevance of the new assumptions, the counterexample is shown to be a contextual hidden variable theory. If Bell's theorem's importance is to rule out contextual hidden variable theories obeying relativistic locality, then Joy Christian's counterexample achieves its aim. If however contextual hidden variables theories are not considered genuine physically theories and Bell's theorem's importance stems from its ability to be experimentally confirmed, then Joy Christian's counterexample does not diminish the importance of Bell's theorem. The implications of Joy Christian's counterexample are discussed in the context of information theory. Version 2 note: Subsequent analysis disproved the mathematical consistency of Joy Christian's model. This paper was based on the assumption of the mathematical validity of the model. Except for the addition of this note, the content of this paper was not modified in any other way.
Constructing the Theory of Everything (TOE) is an elusive goal of today's physics. Goedel's incompleteness theorem seems to forbid physics axiomatization, a necessary part of the TOE. The purpose of this contribution is to show how physics axiomatization can be achieved guided by a new heuristic rule. This will open up new roads into constructing the ultimate theory of everything. Three physical principles will be identified from the heuristic rule and they in turn will generate uniqueness results of various technical strengths regarding space, time, non-relativistic and relativistic quantum mechanics, electroweak symmetry and the dimensionality of space-time. The hope is that the strong force and the Standard Model axiomatizations are not too far out. Quantum gravity and cosmology are harder problems and maybe new approaches are needed. However, complete physics axiomatization seems to be an achievable goal, no longer part of philosophical discussions, but subject to rigorous mathematical proofs.
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.