The Particle Problem in the General Theory of Relativity

Abstract

The writers investigate the possibility of an atomistic theory of matter and electricity which, while excluding singularities of the field, makes use of no other variables than the g&"of the general relativity theory and the p"of the Maxwell theory. By the consideration of a simple example they are led to modify slightly the gravitational equations which then admit regular solutions for the static spherically symmetric case. These solutions involve the mathematical representation of physical space by a space of two identical sheets, a particle being represented by a "bridge" connecting these sheets. One is able to understand why no neutral particles of negative mass are to be found. The combined system of gravitational and electromagnetic equations are treated similarly and lead to a similar interpretation.The most natural elementary charged particle is found to be one of zero mass. The manyparticle system is expected to be represented by a regular solution of the field equations corresponding to a space of two identical sheets joined by many bridges. In this case, because of the absence of singularities, the field equations determine both the field and the motion of the particles. The many-particle problem, v;hich would decide the value of the theory, has not yet been treated.N spite of its great success in various fields, the -present theoretical physics is still far from being able to provide a unified foundation on which the theoretical treatment of all phenomena could be based. We have a general relativistic theory of macroscopic phenomena, which however has hitherto been unable to account for the atomic structure of matter and for quantum effects, and we have a quantum theory, which is able to account satisfactorily for a large number of atomic and quantum phenomena but which by its very nature is unsuited to the principle of relativity. Under these circumstances it does not seem superfluous to raise the question as to what extent the method of general relativity provides the possibility of accounting for atomic phenomena. It is to such a possibility that we wish to call attention in the present paper in spite of the fact that we are not yet able to decide whether this theory can account for quantum phenomena. The publication of this theoretical method is nevertheless justified, in our opinion, because it provides a clear procedure, characterized by a minimum of assumptions, the carrying out of which has no other diAiculties to overcome than those of a mathematical nature.The question with which we are concerned can be put as follows: Is an atomistic theory of matter and electri'city conceivable which, while excluding singularities in the field, makes use of no other field variables than those of the gravitational field (g"") and those of the electromagnetic field in the sense of Max&veil (vector potentials, p")?One would be inclined to answer this question in the negative in view of the fact that the Schwarzschild solution for the spherically symmetric static gravitational field and Reissner s extension of...

Lightlike Braneworlds in Anti-de Sitter Bulk Space-Times

“…5.15). The latter notion of the Einstein-Rosen "bridge" is not equivalent to the original Einstein-Rosen's formulation in the classic paper [55], where the spacetime manifold is static spherically symmetric consisting of two identical copies of the outer Schwarzschild space-time region (r > 2m) glued together along the horizon at r = 2m. Namely, the two regions in Kruskal-Szekeres space-time corresponding to the outer Schwarzschild space-time region (r > 2m) and labeled (I) and (III) in ref.…”

“…The crucial importance of LL-branes in wormhole physics is underscored by the role they are playing in the self-consistent contsruction of the famous EinsteinRosen "bridge" wormhole in its original formulation [55] -historically the first explicit wormhole solution. To this end let us make the following important remark.…”

“…Namely, the two regions in Kruskal-Szekeres space-time corresponding to the outer Schwarzschild space-time region (r > 2m) and labeled (I) and (III) in ref. [52] are generally disconnected and share only a two-sphere (the angular part) as a common border (U = 0,V = 0 in Kruskal-Szekeres coordinates), whereas in the original Einstein-Rosen "bridge" construction [55] the boundary between the two identical copies of the outer Schwarzschild space-time region (r > 2m) is their common horizon (r = 2m) -a three-dimensional lightlike hypersurface. In refs.…”

Proving the principle: Taking geodesic dynamics too seriously in Einstein's theory

“…17 This wavering was in response to a persistent challenge posed in his correspondence with Ludwik Silberstein (see (Havas, 1993) for a detailed review of this controversy) and only lasted for a period of months surrounding his publication of (Einstein and Rosen, 1935).…”

“…19 But for now it is worth noting that though their introduction of the singularity method is initially (1980). For discussion see (Pais, 2005, Howard, 1990, Earman and Eisenstaedt, 1999.17 This wavering was in response to a persistent challenge posed in his correspondence with Ludwik Silberstein (see (Havas, 1993) for a detailed review of this controversy) and only lasted for a period of months surrounding his publication of (Einstein and Rosen, 1935).18 See e.g. (Einstein et al, 1938, Einstein and Infeld, 1940 19 To avoid a tempting con ation, note that Einstein and Grommer's three ways are distinct from what I will below (in sections 2,3, and 4) classify as the three general families of deductions.…”