Showing papers on "Special relativity (alternative formulations) published in 1972"

What is time

Abstract: Introduction 1. The Origin of Our Idea of Time 2. Time and Ourselves 3. Biological Clocks 4. The Measurement of Time 5. Time and Relativity 6. Time, Gravitation and the Universe 7. The Origin and Arrow of Time 8. The Significance of Time Appendix: Temporal Order in Special Relativity Bibliography Index

Poincaré's Rendiconti Paper On Relativity. Part II

Abstract: This is a continuation of the modernized presentation of Poincare's Rendiconti paper (begun in the November 1971 issue of this Journal). It covers Secs. 5–8 of that paper, dealing with its central theme, as indicated by its title, “On the dynamics of the electron,” the subject being of interest to both the historian of the classical theory of the electron and the historian of relativity.

Heisenberg equations of motion for spin-1/2 wave equation in general relativity

Abstract: The Heisenberg equations of motion for the spin-1/2 wave equation in general relativity are obtained by a covariant procedure. They are found to be similar to the equations of motion for a classical pole-dipole test-particle in general relativity. The identification is complete when the Heisenberg equations are taken to be satisfied by the respective expectation values.

The Twin Paradox in Special Relativity

Abstract: We resolve the twin paradox by calculating the relative ages of the twins first in the frame of the stationary twin and then in the frame of the accelerating twin. If we account for the effects of acceleration by keeping track of the instantaneous Lorentz frame of the accelerating twin, both calculations agree.

Symmetry in Einstein‐Maxwell Space‐Time

Abstract: By using the complex null tetrad as basis for the tangent space, a Killing vector field (``symmetry'') is introduced into the system of Einstein's equations with Maxwell's equations. The two bivectors Fμν and Kμ;ν (the associated Killing bivector) are assumed to have a principal null direction in common. Killing's equations, Maxwell's equations, and Einstein's equations are then written down for the case where this special direction is also a principal null geodesic for the Weyl conformal tensor. A certain analog of the Goldberg‐Sachs theorem is proved. The static cases, plus a sizeable class of the static algebraically special cases are examined, to wit: where the special direction is also shear‐free. In particular, all such algebraically special spaces must be Petrov Type D as a result of a coupling of the principal null directions for Fμν. This algebraically special metric is derived as an example of the static classes and is a static generalization of the Reissner‐Nordstrom metric.

The Lorentz Group: Axiomatics — Generalizations — Alternatives

Abstract: The 60th anniversary of Einstein’s Special Theory seems to be an appropriate occasion to ask ourselves the question: how do we look upon this theory today, in particular, do we still believe in (i) the truth of the two principles used by Einstein to establish the Lorentz group (LG), and (ii) the necessity of using them for this purpose.

A casuality group in finite space-time

Abstract: An axiomatic definition of the relativity group for a finite four-dimensional space-time is given. Causality is represented as a relation on space-time and the relativity group is defined to be the causal group, namely the group of all permutations of space-time which preserve the causal relation. This group is found to be linear (modulo translations) and to contain, along with transformations which are strictly analogous to the usual Poincare transformations, also transformations which interchange the inner with the outer part of light-cones. These transformations, which seem to set up a favourable framework for the introduction of tachyons, are possible in the real case only for a two-dimensional space-time and have to be introducedad hoc, while in the scheme which is proposed here they arise naturally. It is further found that in this model the analogue of the orthochronous relativity group of the conventional real case is trivial, since it contains no boosts.

On space-time, reference frames and the structure of relativity groups

Abstract: A general formulation of the notions of space-time, reference frame and relativistic invariance is given in essentially topological terms. Reference frames are axiomatized as C° mutually equivalent real four-dimensional C°-atlases of the set M denoting spacetime, and M is given the C°-manifold structure which is defined by these atlases. We attempt ti give an axiomatic characterization of the concept of equivalent frames by introducing the new structure of equiframe. In this way we can give a precise definition of space-time invariance group 2 of a physical theory formulated in terms of experiments of the yes-no type. It is shown that, under an obvious structural requirement and provided a suitable assumption is made on the spacetime domains of experiments, the group ~ can be realized isomorphically in a unique way onto a group ’* of homeomorphisms of the topological space M. We call ~ the relativity group of the theory. A physically acceptable topology on ~ is discussed. Lastly, the general formalism is applied to introduce in an axiomatic way the notion of inertial frame. It is shown that in a theory for which the equivalent frames are the inertial frames, the space-time invariance group is isomorphic either to the Poincaré group or to the inhomogeneous Galilei group. (*) On leave of absence from Istituto di Fisica dell’ Universita, Milano, Italy, A. v. Humboldt Fellow. Present address : Center for Particle Theory, the University of Texas at Austin, Austin, Texas 78712. 2 V. BERZI AND V. GORINI

Potentials of the typea n/rn, n>1, in collapsing systems in general relativity

Abstract: A nonl inear g e n e r a l i z a t i o n of Maxwel l ' s equat ions is cons t ruc t ed ; it leads to s ta t ic r e puls ive potent ia ls of the type a n / r n, n > 1. The c o r r e s p o n d i n g analog of the N o r d s t r S m R e i s s n e r m e t r i c is cons t ruc ted . It is shown that in c l a s s i c a l , i .e . , nonquantum, phys ics the f o r c e s , a n / r n+~, n > 1, do not lead to d i v e r g e n c e s of the s o u r c e s e l f ene rgy in ge ne ra l r e la t iv i ty . It is shown that if a co l laps ing s y s t e m pas se s th rough i ts g rav i t a t iona l r ad ius f o r m i n g a b lack hole the c l a s s i c a l f o r c e s a n / r n + I, n > 1, and a l so the e l e c t r o s t a t i c and g rav i t a t iona l f o r c e s , do not van ish in the e x t e r i o r space ; this r e s u l t con t r ad i c t s H a r t l e ' s r e s u l t [6] obtained for pa i r neut r ino f o r c e s ( ~ l / r S ) .

Introducing special relativity using simple geometry

Abstract: An outline is given of a simple geometrical exposition of the basic ideas of relativity which should lead to a sound grasp of these conceptions thus improving the student's understanding of the algebraic expressions and promoting confidence in their use.

Doppler frequency in interplanetary radar and general relativity

Abstract: The change of frequency of an interplanetary radar signal sent from the earth to another planet or to a space probe is worked out according to general relativity. The Schwarzschild spacetime is employed and its null geodesics control the motion of the signals. Exact Doppler frequency formulas are derived for one-way and two-way radar in terms of an arbitrary Schwarzschild radial coordinate. A reduction to the special relativity case is used to interpret the formulas in terms of the relative radial velocity of emitter and target. The general relativity corrections are worked out approximately for each of three possible Schwarzschild radial coordinates, and a numerical example is given. The amount of the correction is different according as one or the other of the Schwarzschild coordinates is identified with the radius vector deduced from classical celestial mechanics. The identification problem is discussed.