Showing papers on "Special relativity (alternative formulations) published in 1984"

The quaternion group and modern physics

Abstract: The paper shows how various physical covariance groups: SO(3), the Lorentz group, the general theory of relativity group, the Clifford algebra SU(2) and the conformal group can easily be related to the quaternion group. The quaternion calculus is introduced and several physical applications: crystallography the kinematics of rigid body motion, the Thomas precession the special theory of relatively, classical electromagnetism, the equation of motion of the general theory of relativity, and Dirac's relativistic wave equation are discussed.

Algebraic computing in general relativity.

Abstract: Algebraic Computing i.e. the use of computers to manipulate formulae, has been used in general relativity since about 1965. A very early example was the program GRAD ASSISTANT (Fletcher, 1965) that could calculate the Ricci tensor from a given not too complicated metric.

Revised Robertson's test theory of special relativity

Abstract: The only test theory used by workers in the field of testing special relativity to analyze the significance of their experiments is the proof by H. P. Robertson [Rev. Mod. Phys. 21, 378 (1949)] of the Lorentz transformations from the results of the experimental evidence. Some researchers would argue that the proof contains an unwarranted assumption disguised as a convention about synchronization procedures. Others would say that alternative conventions are possible. In the present paper, no convention is used, but the Lorentz transformations are still obtained using only the results of the experiments in Robertson's proof, namely the Michelson-Morley, Kennedy-Thorndike, and Ives-Stilwell experiments. Thus the revised proof is a valid test theory which is independent of any conventions, since one appeals only to the experimental evidence. The analysis of that evidence shows the directions in which efforts to test special relativity should go. Finally it is shown how the resulting test theory still has to be improved for consistency in the analysis of experiments with complicated experimental setups, how it can be simplified for expediency as to what should be tested, and how it should be completed for a missing step not considered by Robertson.

Massive from massless regular solutions in five-dimensional general relativity

Abstract: The regular multiwormhole solutions to the five-dimensional vacuum Einstein equations, previously obtained, are generalized to massive solutions, interpreted as systems of extended particles.

Four-dimensional symmetry from a broad viewpoint. IV: Covariant statistical mechanics with common time

Abstract: Pour vaincre certaines difficultes dans la generalisation relativiste de la mecanique statistique, on formule une mecanique statistique a 4 dimensions

Wave-particle duality and extended special relativity

Abstract: It is shown that the wave-particle duality implies the extension of special relativity to superluminal frames. The real one-dimensional superluminal Lorentz transformations are obtained as a special case of the Parker-Antippa transformations. Some interrelations between extended special relativity and the many-wave hypothesis are discussed.

The general theory of relativity: Why “It is probably the most beautiful of all existing theories”

Abstract: By common consent, the general theory of relativity has a special aesthetic appeal to those who have studied it. I have chosen to quote Landau and Lifschitz from their Classical Fields in the title of my talk since their magnificent series of volumes, encompassing the whole range of physics, gives to their assessment a special authenticity. Others besides Landau and Lifschitz have applied the epithet ‘beautiful to general relativity. Thus, Pauli, in his well-known article on ‘The Theory of Relativity’ in the Encyclopädie der Mathematischen Wissenschaftien (1921) has written

Einstein and special relativity: who wrote the added footnotes?

Abstract: = E1Rl2-E1RM0R+MlRl2 = «ElR-M By the condition of our experiment ElR > M and thus this expression is greater than o. Thus 2E2RE3R — 2ElRM0R = ((ElR — M0R)ly/2) 2 in this case but 2E2RE3R — 2E1RM0R = E\\R — E\\R—E\\R + M%R and must be greater than o and hence cos 0R > o and 0R < go\", because P2N = P3R # o. We have thus shown that in this procedurally defined, theory-neutral, experiment the predicted results when interpreted within the two paradigms give unambiguous and different results i.e. 8N = 90°, 6R < 90°. Thus a measurement of the angle between the velocities of the two outgoing objects will clearly distinguish between the two paradigms and the paradigms are commensurable. The fact that two paradigms are commensurable does not require a scientist to accept the one consistent with the experimental results, namely relativity. A clever classical physicist might very well accommodate the results by postulating new mechanical effects depending on motion through the ether. These two issues of commensurability and theory choice are often conflated, as exemplified in the statement by Barnes cited earlier, but it is useful to keep them separate and distinct.

Calorimetric test of special relativity

Abstract: Momentum-analyzed beams of 20 and $17.326 \frac{\mathrm{GeV}}{c}$ electrons with average currents of 4.23 and 4.55, and 9.48, 9.57, 14.4, and 15.66 \ensuremath{\mu}A, respectively, are predicted by special relativity to have average powers of 84.5 and 91, and 164.3, 165.8, 249.5, and 271.3 kW, respectively. This prediction is checked to 30% in a calorimetric experiment using the temperature rise in the cooling water of a high-energy beam dump at the Stanford Linear Accelerator Center. To our knowledge, this is the first macroscopic test specifically carried out to test this aspect of special relativity at these particle energies and power levels, although an earlier sequence of tests using copper as the heat absorber have been performed at this laboratory at lower power levels, and confirms the theory to higher accuracy.

Computational Relativity: Numerical and Algebraic Approaches Report of Workshop A4

Abstract: The current use of computers in general relativity was reviewed at GR10. Today several groups have working codes which can calculate the coupled general relativity/hydrodynamics equations in two spatial dimensions plus time. These codes are compared and a critical review is made of the areas needing improvement. The potential uses of numerical relativity are discussed. In some situations the gravitational field can be chosen to be an analytically known solution, and hydrodynamics can be done in that background field. Regge calculus is still in its infancy numerically, but interesting new work has been done. Algebraic computing is becoming a mature technology, with the emphasis moving toward making these powerful software tools available to those relativists without previous computer training.

On special relativity's second postulate

Abstract: On insiste sur le fait que l'hypothese que la vitesse de la lumiere est la meme dans tous les referentiels inertiels n'est pas une consequence immediate du principe de relativite

Relativity's most elaborate test

Abstract: A project to test the general theory of relativity is still going after a quarter of a century. The physics is such fun that the travelling may be better than the arrival.

Cosmology in General Relativity with Higher Derivatives

Abstract: The “standard” hot big bang model accounts for the expansion of the universe, the existence of the microwave background radiation, and the mass fraction of the light elements up to 4He. It does not naturally account for the high degree of isotropy and homogeneity of the universe in the large, nor for the existence of structure (galaxies, clusters) on smaller scales. Other problems, such as the lepton to baryon ratio, the preponderance of matter over antimatter, and the “coincidences” of dimensionless ratios of several fundamental physical and cosmological “constants,” also lie outside the “standard” model a t present. A solution of the large-scale homogeneity and isotropy problems, as well as the so-called flatness problem, has been proposed recently involving extreme supercooling during a phase transition associated with spontaneous symmetry breaking in grand unified theories (GUTs).’ This and related solutions are based on a direct application of the Einstein field equations for general relativity G, = -8*GT, Ag,. The new feature of such theories is due to the introduction of a cosmological constant A or stress tensor with p = p at high densities due to the GUTs. Such theories do not, however, alleviate the problem of the origin of galaxies. We propose a solution to both the largeand small-scale structure problems based on a modification of the left-hand side of the field equations.’ By starting with a gravitational field Lagrangian R + AR2 (where A is a new dimensional constant), we derive a new set of field equations, consistent with all current weak field gravitational tests, which modify the cosmological solutions to general relativity a t early times when the high-order terms predominate. Such solutions are without a particle horizon [with scale factor a( t ) a f as t 01. Therefore, large-scale fluctuations present a t an early epoch could in principle be damped. On the other hand, small-scale perturbations in both the density and metric tend to grow much more rapidly than in unmodified general relativity, easing the problem of the formation of galaxies later in the evolution of the universe.

Algebraic Programming in General Relativity and Cosmology

Abstract: Some algebraic programs, developed recently in the framework of a collaboration between two teams of physicists from Liege and Namur, are briefly described.

A note on elementary geometry and special relativity

Abstract: It is pointed out that the Minkowski space analogue of the well known theorem about the intersection of the heights of a triangle has a not too far-fetched physical interpretation.

Relativistic Stars with Anisotropic Pressure

Abstract: In this article we present various analytic solutions for anisotropic fluid spheres in general relativity.’ First we consider generalizations of t h e p = a p solution to the case where pressure is anisotropic and study the effects of anisotropy on the structure of neutron stars. Next we study radiating anisotropic fluid spheres and present three classes of analytic solutions. We also study slowly rotating anisotropic fluid spheres and present two analytic solutions corresponding to the nonradiating case. One of these solutions corresponds to uniform rotation, while the other corresponds to differential rotation. We also present differential equations to be solved for slowly rotating and radiating anisotropic fluids. Anisotropic pressure could be introduced by the existence of a solid core, by the presence of type-p superfluid, by the complexity of interactions, or by the existence of an external field. Recently it has been suggested that cooling of neutron stars might be accompanied by a phase transition from one anisotropic superfluid to another with significantly different properties.’ Besides these, an interesting way to generate anisotropic pressure is through the presence of two perfect fluids with the energymomentum tensor given as

Cosmological term in the general theory of relativity and localization of the de Sitter and Einstein groups

Abstract: The theory of a gauge gravitational field with localization of the de Sitter group is formulated. Starting from the tetradic components of the de Sitter universe, a relationship is established between the Riemannian metric and the de Sitter gauge field. It is shown that the general theory of relativity with the cosmological term is the simplest variant of the de Sitter gauge theory of gravitation, which transforms in the limit of an infinite radius of curvature of the de Sitter universe into the Poincare-invariant GTR without the cosmological term. A theory of a gauge gravitational field with localization of Einstein's group of motions of the uniform static universe (the Einstein group R × S0 (4)) is formulated in an analogous manner.