Special Relativity Research Articles

Cosmological consequences of the Lorentz and Doppler transformations

The common opinion that the Lorentz transformation distorts the Minkowski spacetime arises from a mathematically incorrect neglect of its non-diagonal terms. When the non-diagonal Lorentz transformation is properly treated, the time dilation and the space distortion disappear. Consequently, the Lorentz metric produced by the Lorentz transformation is identical to the Minkowski metric. The spacetime distortion in moving inertial frames is properly described by the so-called Doppler metric produced by the Doppler transformation. This transformation assumes the existence of a preferred frame and depicts the Doppler shift of light for a moving light source and/or observer. The Doppler metric is Lorentz invariant and leaves the Maxwell’s equations unchanged from their form in the Minkowski spacetime. Moreover, the Doppler metric is experimentally confirmed because it yields the null result in the Michelson–Morley experiment and other interferometric experiments. The suitability of the Doppler metric for describing light properties in Special and General Relativity is supported by recent cosmological observations of the cosmic microwave background.

Local versus Global Time in Early Relativity Theory.

In his groundbreaking 1905 paper on special relativity, Einstein distinguished between local and global time in inertial systems, introducing his famous definition of distant simultaneity to give physical content to the notion of global time. Over the following decade, Einstein attempted to generalize this analysis of relativistic time to include accelerated frames of reference, which, according to the principle of equivalence, should also account for time in the presence of gravity. Characteristically, Einstein's methodology during this period focused on simple, intuitively accessible physical situations, exhibiting a high degree of symmetry. However, in the final general theory of relativity, the a priori existence of such global symmetries cannot be assumed. Despite this, Einstein repeated some of his early reasoning patterns even in his 1916 review paper on general relativity and in later writings. Modern commentators have criticized these arguments as confused, invalid, and inconsistent. Here, we defend Einstein in the specific context of his use of global time and his derivations of the gravitational redshift formula. We argue that a detailed examination of Einstein's early work clarifies his later reasoning and demonstrates its consistency and validity.

Relational Quantum Mechanics and Contextuality

This paper discusses the question of stable facts in relational quantum mechanics (RQM). I examine how the approach to quantum logic in the consistent histories formalism can be used to clarify what infomation about a system can be shared between different observers. I suggest that the mathematical framework for Consistent Histories can and should be incorporated into RQM, whilst being clear on the interpretational differences between the two approaches. Finally I briefly discuss two related issues: the similarities and differences between special relativity and RQM and the recent Cross-Perspectival Links modification to RQM.

Loop special relativity: Kaluza-Klein area metric as a line element for stringy events

Loop special relativity: Kaluza-Klein area metric as a line element for stringy events

Neutrinos, light, matter, and the unification of gravitational and nuclear forces

Neutrinos, light, matter, and the unification of gravitational and nuclear forces The discovery of neutrinos and the measurement of their masses are significant events in the history of science. The Rotating Lepton Model provides a useful basis for understanding particles and nuclear reactions, highlighting the importance of Special Relativity, Gravity, and Quantum Mechanics in our universe. Professor Constantinos G. Vayenas explains. The discovery of neutrinos by Pauli some 90 years ago and the measurement of their masses by Kajita and McDonald (1) some 20 years ago constitute significant developments in the history of science. The recent (2023) (2) detection of neutrino production during the proton-proton collision experiments at CERN confirms the basic assumption of the Rotating Lepton Model (RLM) (2020), (3) i.e. that protons and neutrons comprise rotating neutrino triads, the former with a central positron. This implies that all matter in our Universe, including electromagnetic radiation, (4) comprises only five elementary particles: The three neutrinos (ν1, ν2, and ν3), the electron, and the positron. It also implies that two forces (gravity and electromagnetism) suffice for describing the interactions between these five particles and the concomitant production of all other composite particles, such as hadrons and bosons.

The geometry of the constant gravitational field

The complete title of this paper should be “The geometry of the constant gravitational field or how to switch from the mechanical Lagrangian to a geometric Lagrangian” and in this abstract we sketch why. To begin with, let us say that Einstein managed to integrate the constant gravitational field in the special theory of relativity, obtaining a metric whose geodesics are locally parabolas. The existence of a similar metric deduced from the considerations of Newtonian mechanics is somehow obstructed by the Lagrangian involved in the description of the constant gravitational field. Therefore, we need to explain how the mechanical Lagrangian above which is not suitable for a metric description of the constant gravitational field can be switched into a geometrical Lagrangian having the same geodesics and suitable for the metric description of the constant gravitational field. The geometric method found by us is related to a parabolic type of transformations. A consequence of the previous method can be applied for the study of bending of light rays in a constant gravitational field.

The local validity of special relativity from a scale-relative perspective

The local validity of special relativity from a scale-relative perspective

Zeptosecond‐Scale Single‐Photon Gyroscope

AbstractThis work presents an all‐fiber telecom‐range optical gyroscope employing a spontaneous parametric down conversion crystal to produce ultra‐low intensity thermal light by tracing‐out one of the heralded photons. The prototype exhibits a detection limit on photon delay measurements of 249 zs over a 72 s averaging time and 26 zs in differential delay measurements at s averaging. The detection scheme proves to be the most resource‐efficient possible, saturating of the Cramér–Rao bound. These results are groundbreaking in the context of low‐photon regime quantum metrology, paving the way to novel experimental configurations to bridge quantum optics with special or general relativity.

Pythagorean triples using the relativistic velocity addition formula

In the special theory of relativity, there is an unusual formula for addition of velocities. We will use this formula to generate Pythagorean triples. We define a Pythagorean triple in the usual manner as a triple of positive integers (a, b, c) such that a2 + b2 = c2. The numbers a and b are called legs, and c is called the hypotenuse. Later, we will allow b to take on the value of any integer. A primitive Pythagorean triple is a Pythagorean triple for which a, b and c are relatively prime.

Revisiting the Matter of Time Dilation in Special Relativity

There are different interpretations of the Lorentz transformations of the Special Theory of Relativity (SR) concerning the relative rates of two clocks that are moving at constant relative rectilinear velocity (Einstein’s definition of conditions necessary for SR). [It is common to talk in terms of how one observer “views” another clock that is moving at constant velocity relative to them. This carries an implication of visual observation. That is a limitation avoided in this contribution by the use of “as determined”, without specifying the means employed, but wherever “as viewed” does occur, it is to be considered as “as determined”]. One opinion, which is the settled opinion among physicists, holds that the clocks are “actually” going at different rates. Another opinion holds that it is merely a matter of how observers determine the clocks’ rates to be related, with the clocks in fact going at the same rate. The differences in these interpretations are resolved analytically. Five arguments are presented [excluding an inference from the first postulate]. The clocks are determined to have the same rates, i.e. there is no “time dilation” under SR conditions. The related opinion – that the clocks are going at the same rate, but are determined by observers to be going at different rates - is seen to be consistent. Experimental reports, which directly conclude that the clocks are going at different rates, are shown to be seriously flawed, or to not even comply with Einstein’s definition of SR

Relativistic Consistency of Nonlocal Quantum Correlations.

What guarantees the "peaceful coexistence" of quantum nonlocality and special relativity? The tension arises because entanglement leads to locally inexplicable correlations between distant events that have no absolute temporal order in relativistic spacetime. This paper identifies a relativistic consistency condition that is weaker than Bell locality but stronger than the no-signaling condition meant to exclude superluminal communication. While justifications for the no-signaling condition often rely on anthropocentric arguments, relativistic consistency is simply the requirement that joint outcome distributions for spacelike separated measurements (or measurement-like processes) must be independent of their temporal order. This is necessary to obtain consistent statistical predictions across different Lorentz frames. We first consider ideal quantum measurements, derive the relevant consistency condition on the level of probability distributions, and show that it implies no-signaling (but not vice versa). We then extend the results to general quantum operations and derive corresponding operator conditions. This will allow us to clarify the relationships between relativistic consistency, no-signaling, and local commutativity. We argue that relativistic consistency is the basic physical principle that ensures the compatibility of quantum statistics and relativistic spacetime structure, while no-signaling and local commutativity can be justified on this basis.

Application of the Pythagorean Theorem as a Quick Solution in Solving Relativistic Momentum Problems

The Pythagorean theorem is a fundamental concept in mathematics that is often used to solve various geometric problems. In physics studies, especially in relativistic momentum analysis, the application of this theorem can be a fast and effective solution. This article explores the application of the Pythagorean theorem in the context of relativistic momentum, where the speed and energy of objects approach the speed of light. By exploiting the quadratic relationship between the components of the relativistic momentum and energy vectors, the Pythagorean theorem allows for simpler and more efficient calculations. This research identifies the relationship between the Pythagorean theorem equation and the relativistic momentum equation through several steps. The first step involves calculating the Pythagorean theorem equation. The second step is to calculate Einstein's special relativity equations. The final step is to analyze the relationship between the two equations. In this case, the relativistic and Pythagorean momentum equations have similarities and one of the formulas can be used.

Bell inequality violation in relativity theory

A violation of Bell local realism inequalities in Clauser–Horne–Shimony–Holt form has been discovered in a relativistic Gedankenexperiment. This means that there are no definite joint probabilities and this finds a classical explanation in the structure of special relativity. The discovered nonlocality is weaker than Albert Einstein’s quantum ‘spooky action at a distance’, and its presence suggests certain parallels between special relativity and quantum mechanics.

Unruh effect using Doppler shift method in DSR framework

We study the Unruh effect in doubly special relativity (DSR) framework by generalising the Doppler-shift method to DSR. For both the scalar and Dirac particles, we observe a deviation in the power spectrum of Unruh radiation from the standard Bose–Einstein and Fermi–Dirac distributions, respectively, due to the presence of the frame independent length scale of DSR. We further show that this deviation results in the modification of Unruh temperature which then depends non-linearly on the proper acceleration in DSR.

PORTABLE MUON TELESCOPE FOR COSMIC RAY MONITORING

A portable muon telescope for monitoring of cosmic rays has been developed, based on GM counters shielded with lead adsorbers. The triple coincidence mode of operation results in a relatively good spatial resolution allowing to measure the cosmic ray flux, its east-west anomaly and also to detect the consequences of the special theory of relativity. The apparatus is suitable for long term observations of the cosmic ray flux and due to its simple and robust construction can also be used also for educational purposes.

Duality between the Maxwell-Chern-Simons and self-dual models in very special relativity

This work investigates the classical and quantum duality between the SIM(1)-Maxwell-Chern-Simons (MCS) model and its self-dual counterpart. Initially, we focus on free-field cases to establish equivalence through two distinct approaches: comparing the equations of motion and utilizing the master Lagrangian method. In both instances, the classical correspondence between the self-dual and MCS dual fields undergoes modifications due to very special relativity (VSR). Specifically, the duality is established when the associated VSR-mass parameters are identical, and the dual field is introduced through a non-local VSR correction. Furthermore, we analyze the duality when the self-dual model is minimally coupled to fermions. As a result, we demonstrate that Thirring-like interactions, corrected for non-local VSR contributions, are included in the MCS model. Additionally, we establish the quantum equivalence of the models by performing a functional integration of the fields and comparing the resulting effective Lagrangians.

Theoretical Analysis of Moving Galaxies in the Large Scale Structure of SpaceTime

In this paper we will make further theoretical analysis for the validity of the accelerating universe based on General Relativity and three new problems of the standard model of the universe are presented from different perspectives. The first part, analyzed the explosion mechanism of the cosmic initial singularity and put forward a different view from the rest. It’s virtually impossible to start with a giant explosion, the big bang by now cosmologists had refined the idea. The second part devised a new model of the twin paradox. It’s one in which people have been consider to include both special and general relativity in the calculations to expose the counterintuitive weirdness of relativity theory. It seems to has a curious coincidence with the cat-a feline in a locked box that is both dead and alive until the box is opened-was a thought experiment devised by physicist Schr ö dinger. In part three the author makes determination on the cosmological deceleration parameter q0 by using mathematical derivation, and based on which to construct a thought experiment on cosmological redshift. It is needed to make a static model of the universe that both conforms to the Copernican principle and satisfies Hubble’s law and it’s possible to make us a fresh perspective and thought process.

Integrated transmission expansion planning incorporating fault current limiting devices and thyristor-controlled series compensation using meta-heuristic optimization techniques

Transmission expansion planning (TEP) is a vital process of ensuring power systems' reliable and efficient operation. The optimization of TEP is a complex challenge, necessitating the application of mathematical programming techniques and meta-heuristics. However, selecting the right optimization algorithm is crucial, as each algorithm has its strengths and limitations. Therefore, testing new optimization algorithms is essential to enhance the toolbox of methods. This paper presents a comprehensive study on the application of ten recent meta-heuristic algorithms for solving the TEP problem across three distinct power networks varying in scale. The ten meta-heuristic algorithms considered in this study include Sinh Cosh Optimizer, Walrus Optimizer, Snow Geese Algorithm, Triangulation Topology Aggregation Optimizer, Electric Eel Foraging Optimization, Kepler Optimization Algorithm (KOA), Dung Beetle Optimizer, Sea-Horse Optimizer, Special Relativity Search, and White Shark Optimizer (WSO). Three TEP models incorporating fault current limiters and thyristor-controlled series compensation devices are utilized to evaluate the performance of the meta-heuristic algorithms, each representing a different scale and complexity level. Factors such as convergence speed, solution quality, and scalability are considered in evaluating the algorithms’ performance. The results demonstrated that KOA achieved the best performance across all tested systems in terms of solution quality. KOA’s average value was 6.8% lower than the second-best algorithm in some case studies. Additionally, the results indicated that WSO required approximately 2–3 times less time than the other algorithms. However, despite WSO’s rapid convergence, its average solution value was comparatively higher than that of some other algorithms. In TEP, prioritizing solution quality is paramount over algorithm speed.

Impulsive coupled systems with regular and singular ϕ-Laplacians and generalized jump conditions

This work contains sufficient conditions for the solvability of a third-order coupled system with two differential equations involving different Laplacians, fully discontinuous nonlinearities, two-point boundary conditions, and two sets of impulsive effects. The first existing result is obtained from Schauder’s fixed point theorem, and the second one provides also the localization of a solution via the lower and upper solutions technique.We point out that it is the first time that impulsive coupled systems with strongly nonlinear fully differential equations and generalized impulse effects are considered simultaneously. Moreover, the singular case is applied to a special relativity model in classical electrodynamics.

Understanding Lorentz Utilizing Galilei: The Emergence of a Friendly Extended Special Relativity Theory that Admits Relativistic Multi-Particle Entanglement

Special relativity theory stems from the Lorentz transformation of signature (1,3). The incorporation into special relativity of the Lorentz transformations of signature (m,n) for all m,n∈ℕ (n = 3 in physical applications) enriches the theory. The resulting enriched special relativity is a friendly extended special relativity that admits multi-particle entanglement, as demanded by relativistic quantum mechanics. The Lorentz transformation of signature (m,n) admits a novel physical interpretation induced by the intuitively clear interpretation of the Galilei transformation of signature (m,n) for all m,n > 1. In this sense we understand Lorentz utilizing Galilei in m temporal and n spatial dimensions, resulting in the emergence of multi-particle entanglement that the enriched special theory of relativity admits. Remarkably, it turns out that, for any m,n∈ℕ, the group of Lorentz transformations of signature (m,n) is the symmetry group that underlies any multi-particle system that consists of m n - dimensional entangled particles.