Search

Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension ict, with the unit imaginary producing the correct spacetime distance x2-c2t2, and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary with the Clifford bivector i=e1e2 for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis e1 and e2. We find that with this model of planar spacetime, using a twodimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane. [ABSTRACT FROM AUTHOR]

The article discusses the spotlight theory of time. It explains the process involved in the formulation of the moving spotlight theory for it to harmonize with special relativity. It also notes the said theory of time as one version of the philosophical theories of time which appears to be incompatible with special relativity.

Equations of fully general relativistic radiation hydrodynamics in Kerr space–time are derived. While the interactions between matter and radiation are introduced in the comoving frame, the derivatives used when describing the global evolutions of both the matter and the radiation are given in the Boyer–Lindquist frame (BLF) which is a frame fixed to the coordinate describing the central black hole. Around a rotating black hole, both the matter and the radiation are influenced by the frame-dragging effects due to the black hole's rotation. As a fixed frame, we use the locally non-rotating reference frame (LNRF) which is one of the orthonormal frame. While the special relativistic effects such as beaming effects are introduced by the Lorentz transformation connecting the comoving frame and the LNRF, the general relativistic effects such as frame dragging and gravitational redshift are introduced by the tetrads connecting the LNRF and the BLF. [ABSTRACT FROM AUTHOR]

A conclusion drawn after a conference devoted (in 1995) to the “arrow of time” was the following: “Indeed, it seems not a very great exaggeration to say that the main problem with “the problem of the direction of time” is to figure out exactly what the problem is supposed to be !” What does that mean? That more than 130 years after the work of Ludwig Boltzmann on the interpretation of irreversibility of physical phenomena, and that one century after Einstein’s formulation of Special Relativity, we are still not sure what we mean when we talk of “time” or “arrow of time”. We shall try to show that one source of this difficulty is our tendency to confuse, at least verbally, time and becoming, i.e. the course of time and the arrow of time, two concepts that the formalisms of modern physics are careful to distinguish. [ABSTRACT FROM AUTHOR]

"Real Time Relativity" is a computer program that lets users move at relativistic speeds through a simulated world populated with planets, clocks, and buildings. The counterintuitive and spectacular optical effects of relativity are prominent, while systematic exploration of the simulation allows the user to discover relativistic effects such as length contraction and the relativity of simultaneity. We report on the physics and technology underpinning the simulation, and our experience using it for teaching special relativity to first year students. [ABSTRACT FROM AUTHOR]

In special relativity, a pair of clocks synchronized in their own reference frame are not synchronized in another. How do two clocks, initially synchronized and at rest in the laboratory frame, fall out of sync as their speed relative to the lab gradually increases? The answer lies in general-relativistic time dilation. The path to the answer sheds light on the thread-between-spaceships paradox (also called the Bell spaceship paradox), on the twin paradox, and on the character of length contraction. [ABSTRACT FROM AUTHOR]

It is shown in this article how it is possible to calculate so-called special relativistic phenomena maintaining classical conceptions of relativity, using the substantiated conception that the velocity of electromagnetic radiation is determined by the minimum energy principle. In this context the characteristics of time and space get a different interpretation than that of relativistic physics. [ABSTRACT FROM AUTHOR]

A central observer at Greenwich builds in real time a diachronic representation of 4-D(t) space-time by assigning two distinct times to a given remote event, such as a meteorite impact on Mars: (1) diachronic time read on his Greenwich clock (GMT) at observation time, and (2) synchronic or local Einstein time as directly seen from Greenwich on the Mars clock. In a spherical coordinate system the Greenwich diachronic observer uses local Einstein time relative to diachronic time as a radial coordinate, leaving the role of the fourth coordinate to diachronic time. In a 4-D(t) conceptual framework the same diachronic time applies integrally to all directly observed local Einstein times, thus implying an infinite diachronic speed for incoming light. In the 4-D(t) conceptual framework the detection of a photon is considered to be an instantaneous transfer of energy and momentum across the time gap between emitter and receiver. The Lorentz transformation can be obtained by requiring that history updated now and here be the same for another observer flying by. Some results are (1) the conventional (synchronic) speed of light c is identified with the flow of time, (2) the twin paradox is resolved in a twin-symmetric fashion, and (3) a new solution for the Einstein-Podolsky-Rosen paradox maintains harmony between special relativity and quantum mechanics. The diachronic approach presents the pedagogical advantage of using a single diagram to display space-time relationships of events in two coordinate systems in relative motion. [ABSTRACT FROM AUTHOR]

This paper shows that the properties of space-time that constitutes the background of the theory of special relativity, namely its dimensionality, the correct partition of dimensions between one time-type and three space-type dimensions and the Minkowski metrics, may emerge from a set of completely interacting binary units structured by a noise defined in a Landau-type free energy of Fliggs fields and by gauge symmetries, in particular those related to the permutation group of four objects. [ABSTRACT FROM AUTHOR]

I examine the issue of persistence over time in thecontext of the special theory of relativity (SR). Thefour-dimensional ontology of perduring objects isclearly favored by SR. But it is a different questionif and to what extent this ontology is required, andthe rival endurantist ontology ruled out, by thistheory. In addressing this question, I take theessential idea of endurantism, that objects are whollypresent at single moments of time, and argue that itcommits one to unacceptable conclusions regardingcoexistence, in the context of SR. I then propose anddiscuss a plausible account of coexistence forperduring objects, which is free of these defects. This leaves the endurantist room for some maneuvers. I consider them and show that they do not really helpthe endurantist out. She can accommodate the notionof coexistence in the relativistic framework only atthe cost of renouncing central endurantist intuitions. [ABSTRACT FROM AUTHOR]