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Felix M Lev

Publications and source records attributed to Felix M Lev.

6 recordsLinked to original sources
arXiv2024

Finite mathematics as the most general (fundamental) mathematics

The purpose of this paper is to explain at the simplest possible level why finite mathematics based on a finite ring of characteristic $p$ is more general (fundamental) than standard mathematics. The belief of most mathematicians and physicists that standard mathematics is the most fundamental arose for historical reasons. However, simple mathematical arguments show that standard mathematics (involving the concept of infinities) is a degenerate case of finite mathematics in the formal limit $p\to\infty$: standard mathematics arises from finite mathematics in the degenerate case when operations modulo a number are discarded. Quantum theory based on a finite ring of characteristic $p$ is more general than standard quantum theory because the latter is a degenerate case of the former in the formal limit $p\to\infty$.

physics.gen-ph↗
arXiv2023

The Concept of Dark Energy is not Based on the Principles of Physics: Cosmological Data Can be clearly Explained Without this Concept

The physics community has adopted the principle that when new experimental data appears, physicists should first try to explain it based on existing science. Only if all such attempts fail can new exotic explanations be brought in. However, in the case of cosmological acceleration, the opposite approach was taken: without serious attempts to explain this phenomenon from existing science, physicists attracted dark energy and other exotic concepts whose physical meaning is a mystery. As shown in our publications, the cosmological acceleration can be clearly explained without uncertainties. The derivation of this explanation requires significant technical efforts described in our publications. The purpose of this article published in the Proceedings of the 2nd International Conference on Gravitation, Astrophysics and Cosmology (April 16-17, 2026, Paris, France) is to explain our approach at the simplest possible level so that the basic ideas of our approach would be understandable to many physicists and astrophysicists.

physics.gen-ph↗
arXiv2019

Finite Mathematics, Finite Quantum Theory And A Conjecture On The Nature Of Time

We first give a rigorous mathematical proof that classical mathematics (involving such notions as infinitely small/large, continuity etc.) is a special degenerate case of finite one in the formal limit when the characteristic $p$ of the field or ring in finite mathematics goes to infinity. We consider a finite quantum theory (FQT) based on finite mathematics and prove that standard continuous quantum theory is a special case of FQT in the formal limit $p\to\infty$. The description of states in standard quantum theory contains a big redundancy of elements: the theory is based on real numbers while with any desired accuracy the states can be described by using only integers, i.e. rational and real numbers play only auxiliary role. Therefore, in FQT infinities cannot exist in principle, FQT is based on a more fundamental mathematics than standard quantum theory and the description of states in FQT is much more thrifty than in standard quantum theory. Space and time are purely classical notions and are not present in FQT at all. In the present paper we discuss how classical equations of motions arise as a consequence of the fact that $p$ changes, i.e. $p$ is the evolution parameter. It is shown that there exist scenarios when classical equations of motion for cosmological acceleration and gravity can be formulated exclusively in terms of quantum quantities without using space, time and standard semiclassical approximation.

physics.gen-ph↗
arXiv2017

Fundamental Quantal Paradox and its Resolution

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory. As a consequence, coordinate wave functions of photons emitted by stars have cosmic sizes. This results in a paradox because predictions of the theory contradict observations. The reason of the paradox and its resolution are discussed.

physics.gen-ph↗
arXiv2001

An integral version of Shor's factoring algorithm

We consider a version of Shor's quantum factoring algorithm such that the quantum Fourier transform is replaced by an extremely simple one where decomposition coefficients take only the values of $1,i,-1,-i$. In numerous calculations which have been carried out so far, our algorithm has been surprisingly stable and never failed. There are numerical indications that the probability of period finding given by the algorithm is a slowly decreasing function of the number to be factorized and is typically less than in Shor's algorithm. On the other hand, quantum computer (QC), capable of implementing our algorithm, will require a much less amount of resources and will be much less error-sensitive than standard QC. We also propose a modification of Coppersmith' Approximate Fast Fourier Transform. The numerical results show that the probability is signifacantly amplified even in the first post integral approximation. Our algorithm can be very useful at early stages of development of quantum computer.

quant-ph↗