All Submission Categories

Mathematical Description of the Oscillations of the Radius Difference Modulus at Symmetrical Orbital Points

Authors: Viktor Strohm
Comments: 11 Pages.

The provided materials demonstrate an empirical study (Figs. 1-12) identifying mysterious "envelope waves" through the analysis of distance differences at symmetrical points of planetary orbits. Additionally, a rigorous kinematic apparatus [2] has been developed to derive a force law applicable not only to closed ellipses but also to precessing orbits (rosettes).Using the kinematic apparatus from work [2], we can construct a mathematical description of the observed oscillations. The key idea is that the envelope wave in the graphs is a direct consequence of orbital precession, "decomposed" through an original methodology of symmetrical differences.
Category: Astrophysics

Horizons in a 3D Alternative and Symmetric Natario Warp Drive Vector Using the Adm-MTW-Alcubierre Formalism

Authors: Fernando Loup
Comments: 96 Pages. complements the developments in viXra:2509.0064

The Natario warp drive appeared for the first time in 2001.Although the idea of the warp dive as a spacetime distortion that allows a spaceship to travel faster than lightpredated the Natario work by 7 years Natario introduced in 2001 the new concept of a propulsion vector to define or to generate a warp drive spacetime.Natario defined a warp drive vector for constant speeds in Polar Coordinates but remember that a real warp drive must accelerate or de-accelerate in order to beaccepted as a physical valid model so it must possesses variable speeds.We developed the extension for a symmetric alternative warpdrive vector that encompasses variable speeds. Also Polar Coordinates uses only two dimensions and we know that a real spaceship is a 3D object inserted inside a 3D warp bubble that must be defined in real 3D Spherical Coordinates.In this work we present the alternative warp drive vector in 3D Spherical Coordinates for variable speeds.One the major drawbacks concerningwarp drives is the problem of the Horizons (causally disconnected portions of spacetime) in which an observer in the center of the bubble cannot signal nor control the front part of the bubble. The behavior of a photon sent to the front of the warp bubble in the case of the alternative warp drive with variable velocity and a lapse function is also one of the main purposes of this work. We present the behavior of a photon sent to the front of the bubblein the alternative warp drive in the 3+1 spacetimes with the lapse function using quadratic forms and the null-like geodesicsds^2=0 of General Relativity and theADM (Arnowitt-Dresner-Misner) formalism equations with the approach of MTW(Misner-Thorne-Wheeler) and Alcubierre.
Category: Relativity and Cosmology

A Complete Proof of the Rational Distance Problem for the Unit Square

Authors: Song Li
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper studies the following classical geometric problem: does there exist a point inside the unit square whose distances to all four vertices are rational? We first prove that if such a point exists, its coordinates must be rational. Through a scaling transformation, the original problem is equivalently reduced to a Diophantine problem involving an integer square with integer coordinates and integer distances. Based on the parity alignment of common legs, we discuss three cases and derive contradictions using the parameterization of primitive Pythagorean triples and parity analysis. Combined with known results for boundary cases, we prove that no such point exists inside the unit square.
Category: Number Theory

The Scholz Conjecture is True for 2^n-1 for Almost All N

Authors: Theophilus Agama
Comments: 9 Pages.

An addition chain of length h that leads to a number n is a sequence of positive integers s_0 = 1, s_1 = 2,. .. , s_h = n such that s_i = s_j + s_k (i > j ≥ k) for each 1 ≤ i ≤ h. A Brauer addition chain is the one where j = i − 1 for each 1 ≤ i ≤ h. Let l(·) and l* (·) denote the minimal length of an addition chain and the Brauer addition chain, respectively, that leads to an integer ·. Applying probabilistic methods to the iterated factor method, we show that l(2^n − 1) ≤ n − 1 + l(n) for almost all positive integers n as n −→ ∞.
Category: Number Theory

An Average Loneliness Gap of 1/n Can Allow a Minimum Loneliness Gap of 1/(2n)

Authors: Deepak Ponvel Chermakani
Comments: 6 Pages. 7 Theorems and 2 Algorithms

Consider n runners R0, R1, ... Rn-1, with distinct constant integer speeds S0, S1, ... Sn-1 respectively, where S0=0, running around the circumference of a circle of unit circumferential length from arbitrary starting points at time t=0. At time t, denote gi(t) be the minimum absolute distance along the circumference of Ri from R0. We first use aresult on prime numbers to obtain special cases of runners speeds, for which the Lonely Runner Conjecture (LRC) is true. We then develop an approach to the LRC that derives a time at which, some subset of the runners is placed at the extremities of arcs of sectors ensuring implicit separation from R0, while the remaining runners are directly separated from R0. We use this approach to show that in the general case for large n, there exists a time T at which, gi(T) > 1/(2n) for all integers i in [1,n-1], and (g1(T) + g2(T) + ... + gn-1(T))/(n-1) tends to 1/n.
Category: Number Theory

The Theory of Observational Relativity Serial Report 5: Is the Big Bang a Theory in Scientific Sense?

Authors: Xiaogang Ruan
Comments: 31 Pages.

The theory of Observational Relativity (OR), as a new theory of physics, reports its significant findings and new insights in the form of serial reports in F1000Research. Now, OR Serial Report 5 focuses on the Big Bang theory of modern cosmology. Human beings always believe that the universe was bestowed by the Creator: no matter time or space must have a starting point. So, cosmologists have invented the Big Bang model: the universe that human beings rely on for survival originated from a Big Bang 13.8 billion years ago. Einstein's theory of relativity is the most important theoretical basis of modern cosmology, and the invariance of light speed and the doctrine of spacetime curvature play important roles in the Big Bang theory. The Big Bang theory is not only a product of logical deduction and mathematical formulization, but also has empirical evidences such as cosmic expansion and cosmic microwave background radiation. However, the theory of OR has discovered that the speed of light is not really invariant, and spacetime is not really curved. From the broad perspective of the general observational agent, the theory of OR has clarified that Einstein's theory of relativity, including the special and the general, is that of optical observation adopting the optical agent, which has the observational locality, presenting us with only optical images of the physical world and not representing the objectively physical world. The doctrine of Big Bang, or even the entire modern cosmology, is only a mirage based on such optical images. Since the speed of light is not really invariant, the doctrine of spacetime curvature, the doctrine of cosmic expansion, and Einstein's theory of relativity, including the special and the general, cannot hold true. Can the Big Bang theory still hold up without Einstein's theory of relativity as the theoretical basis? Can the Big Bang theory still hold up without Hubble's doctrine of cosmic expansion as the empirical basis? This article has elucidated for readers from the perspectives of both science and philosophy that the doctrine of Big Bang is not only contrary to science but also contrary to philosophy.
Category: Relativity and Cosmology

Energy-Anti-energy,Matter-AnnihilatingMatter:FoundationalConceptReconstructionandTestableExperimentalSchemes

Authors: Jian Yang
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Based on respect for the classical physical conclusion that matter-antimatter annihilation produces photons, this paper redefines the logical boundaries of fundamental concepts such as energy-anti-energy and matter-annihilating matter. Itstrictly distinguishes between two types of physical processes: first, the traditional mass-energy conversion process when matter and antimatter meet, which leaves behind energy and photons; second, the field-configuration-annihilation process proposed herein, which after interaction completely returns to the quantum vacuum ground state, leaving no observablephysical remnants. This paper introduces two hypothetical physical entities — matter-annihilating matter and electron-annihilating electron—and clarifies their symmetric annihilation relationship. Based on the philosophy of binaryopposition and unity, a theoretical framework of Chaos Theory is constructed, proposing three core foundational rules with mathematical expressions. On this basis, two major directions are outlined: experiments feasible with current technology and research directions verifiable with future technology. A set of falsifiable scientific predictions is also proposed. All theoretical inferences are ultimately judged by physical experiments, providing a theoretical reference forfundamental physics and new physics beyond the Standard Model.
Category: Relativity and Cosmology

The Problem of Cosmological Constant Correlation Between Observation and QFT-Measurement as a Fixpoint-Description Spectral Self-Adjustment of the Cosmological Constant from Quantum Vacuum Structure

Authors: Holger A.W. Döring
Comments: 31 Pages.

Discussed is a trying to solve the obvious contradiction in discrepance between the measuring of cosmological constant (CC) from GRT-description and its calculated prediction in classical QFT.Either then the coupling of CC to theory is wrong or the physical and mathematical methods tocalculate CC by QFT in flat Minkowskispace-background are wrong. Tried is a fixpoint-method tocome to a calculated value of CC which better fits to observation. In this context the sum-rules for1-loop/2-loop in BSM-QFT are solved, three new scalarons ("Stooges") and two new heavyfermione ("Tweedles") are introduced to couple matter-field beyond SM to CC and to look atdiscrepances between measuring and calculation in a more consistent way.
Category: Quantum Gravity and String Theory

A Short Formula to Discover the Real Evolution of the Expansion of the Universe

Authors: Dino Bruniera
Comments: 4 Pages. In English and Italian (Note by viXra Admin: Please cite and list scientific references)

A short formula to find the real travel time of photons from Type Ia supernovae and, therefore, the real epoch relative to the scale factor of the expansion of the Universe, indicated by their redshift. This, thanks to the thousands of ob-servations of Type Ia supernovae of all epochs already available, would allow us to obtain a graph showing the real evolution of the expansion of the Universe.
Category: Relativity and Cosmology

For All Hyperoperations, 2^4 = 4^2 is The Only Whole Number Pair Exception to their Anticommutativity

Authors: Anthony Veglia
Comments: 7 Pages.

All higher-order hyperoperations beyond multiplication are anticommutative, featuring a pair of distinct input values being the base and the power, such as x^y. Using real whole numbers, other than the infinite trivial examples where x = y, it has been proven that 2^4 = 4^2 is the only exception to the anticommutativity property of the hyperoperation exponentiation. This proof shows that for all higher-order hyperoperations, including tetration, pentation, and beyond, thatsingular exception, H3(2, 4) = H3(4, 2), remains the sole example of "anti"-anticommutativityusing real whole number inputs.
Category: Number Theory

Eigenvalues of Transpose of a Matrix

Authors: Sanjeev Saxena
Comments: 1 Page.

A proof without using determinants is given to show that the eigenvalues of a square matrix A are the same as those of its transpose A^T. The proof only uses the fact that the row and column ranks of a matrix are same.
Category: Algebra

Turing-Unsimulability, and Instantaneous and Sustained Cosmic-Censorship-Falsity, for Einstein-Vacuum General Relativity

Authors: Warren D. Smith
Comments: 60 Pages.

(I) We construct instantaneous counterexamples to Penrose's "cosmic censorship conjecture" (CCC) in Einstein's vacuum field equations (EVFEs) in general relativity (GR).

(II) We also construct ones that persist for a positive timespan (e.g. 1 million years). More precisely, II demonstrates either (1) the existence of a solution of EVFEs – note, no matter is involved – for a million years, throughout which there are any desired arbitrary number (including infinity as a number") of "naked" point-singularities, or(2) Einstein solutions suddenly stop existing, or(3) solutions of Einstein that ought to be well described by Newton-law dynamics, are not, or(4) "stability" of Newton law solutions does not work the way everybody thought based both on many experiments and KAM/Nekhoroshev mathematical theory.

Consequently, if Penrose's CCC is physically valid,then the reason is not Einstein gravity alone – some other physics must play a crucial role. The construction for II shows as corollaries that GR can have everywhere non-analytic metrical solutions, maximally-refuting an unfortunately-widely-believed myth; and also indicates that naked singularities arise from generic initial data – at least with some people's notions of the word "generic" (but possibly not yours).

(III) We sketch a proof of the "Turing unsimulability" of EVFEs. More precisely, either (1) the metric of spacetime time-evolves during a finite timespan (e.g. 1 year) in a manner which no Turing machine can simulate to within arbitrary user-specified accuracy bound in any finite timespan, or (cases 2, 3 basically same as in II), or (4) "chaos lifetime" in Newtonian 3-body scenarios behaves very differently than everybody had thought based on extensive experiments. It probably should be possible to get rid of case (4) via a different, chaos-avoiding, proof technique based on more-explicitly defined motions with perturbation bounds devised with computer aid – I sketch how but do not actually do this. The argument also suggests that unsimulability happens with generic initial data, at least with some people's notions of the word "generic" (but possibly not yours). All these scenarios I, II, III involve finite and bounded total mass-energy.

Crucial to I-III is the fact that the EVFEs permit storing an infinitude of information in a compact finite-volume region using finite mass-energy; and furthermore (for III) an infinitude that's dynamically relevant, i.e. changing any single bit of that information will yield an easily-observable macroscopic consequence within a fixed timespan. That mathematical fact probably is unphysical, in which case the EVFEs are not the laws of gravity in our universe, but rather only an approximation to truer (e.g. "quantum gravity") laws.

I believe case 1 is the truth in both theorems II and III; cases 2-4 were added to handle my inability to prove case 1 fully rigorously.(Theorem I, however, is fully rigorous and does not need extra cases.) Key obstacles to rigor: Humankind presently is usually unable to prove eternal existence and uniqueness of solutions to the Einstein equations; and cannot prove or disprove (for any particular N≥3) that a positive-measure set of Newton N-body solutions can exhibit "eternal chaos." And although there has been progress on problems resembling "proving stability of the solar system" for Newton N-body problems (at least in a Nekhoroshev long-time-survival sense), that progress has not yet been good enough to handle N=∞. But regardless of which cases happen, I contend theorems I, II, III signify the failure of the EVFEs as an algorithmic theory of gravitational physics. Some lessons are drawn from that, e.g. everybody trying to combine standard model with GR whilekeeping the latter nonquantum, is misguided. Also includes(a) an introduction reviewing previous works in my "computational complexity status of physics" aka "Church's thesis meets physical law X" research programme;(b) a long survey of useful facts about Newtonian N-body problems, in some respects the best currently available, and highlighting the important open question of whether a positive-measure set of "eternal chaos" N-body solutions exist.
Category: Relativity and Cosmology

Some of the Biggest Problems for the Theory of Relativity

Authors: Lars Frølund Jensen
Comments: 4 Pages.

According to experts in special relativity, it is ‘mathematically self-consistent’, and therefore it should be impossible to demonstrate any inconsistency in the theory. Supposedly, only physical experiments have the possibility of disproving it! — However, I and other researchers have demonstrated several inconsistencies in both the special and general theory of relativity, and in this paper I will show examples that are so simple and clear that experts will easily be able to understand the arguments. So — unless they can demonstrate crucial errors in my argumentation — they will be able to realize that there are serious inconsistencies in the theory of relativity!
Category: Relativity and Cosmology

Pythagorean Theorem: an Alternative Formula

Authors: Muhammad Roy Asrori
Comments: 2 Pages.

In this note we give a formula for the pythagorean theorem.
Category: Number Theory

About Possibilities of Physical Unrealizability of Cosmological and Gravitational Singularities in General Relativity and in Relativistic Gravithermodynamics

Authors: Pavlo Danylchenko
Comments: 34 Pages.

The possibility to avoid physical realizability of cosmological singularity (singularity of Big Bang of the Universe) directly in the orthodoxal general theory of relativity (GR) and in its improved version — the relativistic gravithermodynamics (RGTD) is substantiated. This can take place in the case of counting of cosmological time in frame of reference of coordinates and time (FR) not comoving with matter, in which by the Weyl hypothesis galaxies of the expanding Universe are motionless. The absence of any limitations of the value of mass of astronomical body, which self-contracts in the comoving with expanding Universe FR (CFREU), when it has hollow topological form in the space of CFEU and mirror symmetry of its intrinsic space, is shown. Because of this symmetry, both external and internal boundary surfaces of body are observed as convex. At that, in the "turned inside out" internal part of the intrinsic space (in the Fuller-Wheeler lost antiworld) unlike external part, instead of the phenomenon of expansion phenomenon of contraction of "internal universe" is observed. And there is antimatter instead of matter in this internal part of the space. Inevitability of self-organization in physical vacuum of spiral-wave structural elements, which correspond to elementary quasiparticles, and universal electromagnetic nature of all non-fictive quasiparticles are substantiated. Ultrahigh luminosity of quasars and certain types of supernovas is caused by annihilation of matter and antimatter. It is proved that only in the case of the joint application in the Universe of a physically homogeneous exponential scale of unified gravithermodynamic time and a dynamic gravitational field, which ensure the invariance in space and time of the vacuum velocity of light and the Hubble constant, is it possible to ensure not only the general covariance of all physical laws, but also the gravitational-relativistic invariance of thermodynamic parameters and potentials of matter. Although the use in the Universe of a metrically homogeneous uniform scale of the proper time of matter and of a static gravitational field ensure the eternity of the existence of the Universe and the non-exceeding of the values of the false coordinate velocities of light of the GR by the radial velocities of distant galaxies, it does not ensure both the general covariance of all physical laws and the gravitational-relativistic invariance of thermodynamic parameters and potentials of matter.
Category: Relativity and Cosmology