Relativity, Causality and the ‘Substratum’

Light from a distant γ-ray burst backs up a key prediction of Albert Einstein's theory of relativity — that photon speed is the same regardless of energy. But it might set the stage for evolution of the theory. Observations of the distant and short γ-ray burst GRB 090510 with the Fermi Gamma-ray Space Telescope have provided an opportunity to test a central prediction of Einstein's special theory of relativity — the Lorentz invariance. This holds that all observers measure exactly the same speed of light in a vacuum, independent of photon energy. A key test of the violation of Lorentz invariance is a possible variation of photon speed with energy. Accumulated over cosmological light-travel times, even a tiny variation in photon speed should become observable — as for instance sharp features in the light curve of a γ-ray burst. No evidence for the violation of Lorentz invariance was found in the GRB 090510 spectrum, at least down to a limit of the Planck length divided by 1.2. This argues against quantum-gravity theories where the quantum nature of space–time linearly alters the speed of light with photon energy.

The magneto-ionic theory for drifting plasma at large drift velocities is discussed by using Einstein's special theory of relativity and the Lorentz transformation, for the case where the drift velocity, the static magnetic field, and the electromagnetic wave propagation are all in the same longitudinal direction. It is shown that the algebraic equation thus found for the refractive index is identical with the one found previously in the first-order approximation for small drift velocities.

A Lorentz transformation of signature $(m,n)$, $m,n \in {\mathbb N}$, is a pseudo-rotation in a pseudo-Euclidean space of signature $(m,n)$. Accordingly, the Lorentz transformation of signature $(1,3)$ is the common Lorentz transformation of special relativity theory. It is known that entangled particles involve Lorentz symmetry violation. Hence, the aim of this article is to expose and illustrate the symmetry groups of systems of entangled particles uncovered in [44] It turns out that the Lorentz transformations of signature $(m,n)$ form the symmetry group by which systems of $m$ $n$-dimensional entangled particles can be understood, just as the common Lorentz group of signature $(1,3)$ forms the symmetry group by which Einstein's special theory of relativity can be understood. Consequently, it is useful to extend special relativity theory by incorporating Lorentz transformation groups of signature $(m,3)$ for all $m\geq 2$. The resulting extended special relativity theory, then, provides not only the symmetry group of the $(1+3)$-dimensional spacetime of particles, but also the symmetry group of the $(m+3)$-dimensional spacetime of systems of $m$ entangled three-dimensional particles, for each $m\geq 2$.

Albert Einstein's Special Theory of Relativity, or Special Relativity for short, came into being in 1905 in a paper with the unassuming title of “On the electrodynamics of moving bodies.” As the title suggests, Special Relativity is a theory of “moving bodies,” that is: motion. In particular, it is a theory of how motion is perceived differently by different observers. Since motion is the process in which an object's location in space changes with time , any theory of motion is also a theory of space and time . Therefore, Special Relativity can be said to be a theory of how space and time are perceived differently by different observers. The “electrodynamics” part of the paper title refers to the fact that the theory has something to do with light , which is an electromagnetic wave. As we will learn in this book, the speed of light in vacuum, which we will call c , plays a very special role in the theory of relativity. Einstein (1879-1955) was not the first to construct a successful theory of motion. Building upon pioneering work by Galileo Galilei (1564-1642), Sir Isaac Newton (1642-1727) had constructed theories of motion and gravity which were spelled out in his famous book Philosophiae Naturalis Principia Mathematica , which is so famous that when people say the Principia , it is understood that they are referring to Newton's book.

Science sets itself apart from other paths to truth by recognizing that even its greate practitioners sometimes err.

It is known that entangled particles involve Lorentz symmetry violation. Hence, we pay attention to Lorentz transformations of signature $(m,n)$ for all positive integers $m$ and $n$. We show that these form the symmetry groups by which systems of $m$ entangled $n$-dimensional particles can be understood, just as the common Lorentz group of signature $(1,3)$ forms the symmetry group by which Einstein's special theory of relativity is understood. A novel, unified parametric realization of the Lorentz transformations of any signature $(m,n)$ shakes down the underlying matrix algebra into elegant and transparent results.

The purpose of the present study is to develop a counterpart of the special relativity theory that is consistent with the existence of a preferred frame but, like the standard relativity theory, is based on the relativity principle and the universality of the (two-way) speed of light. The synthesis of such seemingly incompatible concepts as the existence of preferred frame and the relativity principle is possible at the expense of the freedom in assigning the one-way speeds of light that exists in special relativity. In the framework developed, a degree of anisotropy of the one-way speed acquires meaning of a characteristic of the really existing anisotropy caused by motion of an inertial frame relative to the preferred frame. The anisotropic special relativity kinematics is developed based on the symmetry principles: 1) Space-time transformations between inertial frames leave the equation of anisotropic light propagation invariant and 2) a set of the transformations possesses a group structure. The Lie group theory apparatus is applied to define groups of transformations between inertial frames. Applying the transformations to the problem of calculating the CMB temperature distribution yields a relation in which the angular dependence coincides with that obtained on the basis of the standard relativity theory but the mean temperature is corrected by the terms second order in the observer velocity.

Einstein assumed the “principle of relativity” when constructing the special theory of relativity (STR). He claimed that all inertial frames are equivalent, and that it is impossible to discriminate between inertial frames. However, among the coordinate systems regarded by Einstein as inertial frames, there are some in which light propagates isotropically, and some in which light propagates anisotropically. A method has been found which discriminates between these. This paper discusses the “triplet thought experiment” in which accelerated motion is eliminated from the famous twin paradox thought experiment of the STR. Here the inertial frames regarded as equivalent by the STR are identified as “classically stationary frames SCl” and “classically moving frames (S'Cl) ” First, an observer M in frame performs the triplet thought experiment, and it is confirmed that the delay in time which elapses in the moving frame agrees with the predictions of the STR. Next, an observer in rocket A (S'Cl) performs the triplet thought experiment, and observes the same time delay. Before starting movement at constant velocity, rocket A experiences accelerated motion. The coordinate system of rocket A cannot be regarded physically as a stationary frame. Even so, observer A observes the delay predicted by the STR. If it can be accepted that frames SCl are included in inertial frames, then the problem of the twin paradox will no longer be a paradox.

High-energy collisions, scatterings and most decays are, for the most part, relativistic quantum processes. It is therefore imperative to recall relativistic kinematics and the basic rules of tensor calculus; see Appendix B.2 for a more complete introduction. However, this chapter neither replaces nor competes with complete treatments of the special theory of relativity such as the illustrative but perfectly detailed text [512] or the first and original text [566]. Instead, the purpose of this chapter is to provide an introduction and the results that will be useful in following the subsequent material. 3.1 The Lorentz transformations and tensors When describing physical processes, one necessarily uses a mathematical apparatus such as a (reference) coordinate system – equipped with a specific and appropriate collection of coordinates. The choice of any one such coordinate system is arbitrary and should not affect the characteristics of the natural laws. The basic idea (oft cited as one of the two postulates) of Einstein's theory of relativity is that the change in the choice of the coordinate system and corresponding coordinates used to describe spacetime must not change the meaning of natural laws – and so must not have any measurable, i.e., observable consequences. Digression 3.1 Chapter 5 will show that the so-called gauge principle is simply the generalization of this relativity to the spaces of so-called internal degrees of freedom (also a type of coordinates), such as the phase of the complex wave-function of any charged particle. In the special theory of relativity , this idea of relativity is limited to so-called inertial (coordinate) systems, which are usually defined as coordinate systems that differ from each other only in moving one with respect to the other with a constant relative velocity. However, against all intentions, this “definition” does not exclude, for example, a pair of coordinate systems that co-rotate about the same axis with the same angular velocity, but move with a constant relative velocity along the co-rotating axis.

The theory of special and general relativity causes a “schizophrenic” dilemma in physics. It undeniably provides mathematically correct values, but it is undeniably epistemologically wrong in many respects. Including the relativistic explanation of the gravitational “time dilation” and the curvature of light beams at the surfaces of large masses, the author demonstrates the illogical character of relativistic physics. When one thinks the relativistic explanations of gravitational time dilatation and of the curvature of light rays by masses through to the end, they lead to absurd and contradictory logical conclusions.

As one of the most influential experiments on the development of modern macroscopic theory from Newtonian mechanics to Einstein's special theory of relativity, the phenomenon of light dragging in a moving medium has been discussed and observed extensively in different types of systems. To have a significant dragging effect, the long duration of light travelling in the medium is preferred. Here we demonstrate a light-dragging experiment in an electromagnetically induced transparent cold atomic ensemble and enhance the dragging effect by at least three orders of magnitude compared with the previous experiments. With a large enhancement of the dragging effect, we realize an atom-based velocimeter that has a sensitivity two orders of magnitude higher than the velocity width of the atomic medium used. Such a demonstration could pave the way for motional sensing using the collective state of atoms in a room temperature vapour cell or solid state material.

Relativistic Flight Mechanics and Space Travel is about the fascinating prospect of future human space travel. Its purpose is to demonstrate that such ventures may not be as difficult as one might believe and are certainly not impossible. The foundations for relativistic flight mechanics are provided in a clear and instructive manner by using well established principles which are used to explore space flight possibilities within and beyond our galaxy. The main substance of the book begins with a background review of Einstein's Special Theory of Relativity as it pertains to relativistic flight mechanics and space travel. The book explores the dynamics and kinematics of relativistic space flight from the point of view of the astronauts in the spacecraft and compares these with those observed by earth's scientists and engineers-differences that are quite surprising. A quasi historical treatment leads quite naturally into the central subject areas of the book where attention is focused n various issues not ordinarily covered by such treatment. To accomplish this, numerous simple thought experiments are used to bring rather complicated subject matter down to a level easily understood by most readers with an engineering or science background. The primary subjects regarding photon rocketry and space travel are covered in some depth and include a flight plan together with numerous calculations represented in graphical form. A geometric treatment of relativistic effects by using Minkowski diagrams is included for completeness. The book concludes with brief discussions of other prospective, even exotic, transport systems for relativistic space travel. A glossary and simple end-of-chapter problems with answers enhance the learning process.

While the Lorentz group serves as the basic language for Einstein's special theory of relativity, it is turning out to be the basic mathematical instrument in optical sciences, particularly in ray optics and polarization optics. The beam transfer matrix, commonly called the $ABCD$ matrix, is shown to be a two-by-two representation of the Lorentz group applicable to the three-dimensional space-time consisting of two space and one time dimensions. The Jones matrix applicable to polarization states turns out to be the two-by-two representations of the Lorentz group applicable to the four-dimensional space-time consisting of three space and one time dimensions. The four-by-four Mueller matrix applicable to the Stokes parameters as well as the Poincare sphere are both shown to be the representations of the Lorentz group.

A scientist claims that the classic formula for the force exerted by electric and magnetic fields—the so-called Lorentz force—clashes with Einstein's special theory of relativity.

It was shown [1] that, in a Friedmann universe considered as an expanding ensemble of fundamental particles and whose 3-space is Euclidean, the propagation of light and its associated wavelength(s) partake in the expansion of the universe. In consequence, a light-signal emitted from any source will reach and pass every fundamental particle in its path at the same speed, c, despite the systematic mutual recession of any pair of such particles. This result, derived from the Robertson-Walker metric, is in full accord with all local physical experience of light transmission and with the requirements o f Einstein's Special Theory of Relativity. It is shown here that the same result also applies to any curved-space Friedmann universe.