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# General Relativity

General Relativity

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Gravity: Gauge Field Last Updated on 2008-06-11 00:00:00 Apart from the ambiguous experimental evidence that gravitational radiation exists but its quantal effects are unmeasureable, what compelling theoretical evidence do we really have that gravity should be expressable as a field theory similar to QED, QCD and Electroweak theory which form the basis of the Standard Model? We have already seen how the graviton has an upper limit to its possible rest mass which is 100 trillion times lower than the photon itself. In addition to being massless, the graviton must have a spin assignment of 2 units so that the equation that defines its action looks like Einstein's equation for the gravitational field represented by a two-index field, $g_{\mu \nu}$. Steven Weinberg also proved an important theorem in 1964 which showed that spin-2 particles have to couple to all other particles and fields with a universal strength. So, even without a single clue... More »
Gravity: String Theory Last Updated on 2008-05-02 00:00:00 There was hardly any time to wrestle with the implications of these ideas before yet another revolution in thinking hit the theoretical fan. In 1982, John Schwartz and Michael Green announced 'Superstring Theory'. Henceforth, particles would not be thought of as point-like concentrations ofenergy, but as 1-D, vibrating 'strings' of energy.Particle world lines would be fattened from spaghetti-like, 1-D tracks in spacetime, to macaronni-like tubes, and with this new structure, all infinities would vanish without any need at allfor renormalization. The only problem is that: 1) Spacetime would have to have either 10 or 26 dimensions in order that the theory was self-consistent; and 2) the theory would naturally work only at energies near 1019 GeV. The lowest "mode" of string oscillation would yield particles withno rest mass at all. The next-highest mass range would be 1019 GeV. Throughout... More »
Gravity: Quantization ca. 1990 Last Updated on 2008-03-14 00:00:00 String theory does not do away with the need for some kind of background spacetime. The equations describing the movement of strings do so from the standpoint of a string moving in a flat, Minkowski space of up to 26-D. The 1-D strings trace-out 2-D surfaces. The geometry of these surfaces have a set of internal symmetries associated with them which allow the fields to appear as different kinds of particles. There are literally millions of different topologies for these compact spaces. The number of holes in these spaces, the so-called topological genus, may have something to do with the number of different kinds of lepton types; electron, muon, tauon. There may exist regions in the universe where these spaces have chosen slightly different ways to curl-up so that differences in the fundamental particle types mayexist in our universe. How do string theorists actually think... More »
Gravity: Renormalization Last Updated on 2008-03-13 00:00:00 By the late 1960's, the Canonical Quantum Gravity or 'Superspace Quantization' approach quickly bogged down in an ever-growing mathematical formalism inwhich the equations defining the quantum states of spacetime became too difficult to solve in general.   Covariant Quantum Gravity, on the other hand, with its reliance on concepts refined in the study of particle physics received several infusions of fresh blood during the 60's. Richard Feynman and Bryce DeWitt worked on systematically applying the techniquesof QED — the so-called perturbation series approach to gravity.This simply meant that they started with a very simple Feynmann diagram for, say, a photon emitting a single graviton, then two gravitons, then three etc. The contributions at each stage were added up to give the total strength of the process that involved a single photon interactingwith a cloud of virtual... More »
Gravity: Superspace Quantization Last Updated on 2008-03-13 00:00:00 By the 1960's several new attacks were launched on the theoretical underpinnings of the quantum gravity program by Arnowitt, Deser, Misner and Wheeler. The basic idea was simple: If you really want to find a quantum theory for gravity, you had better first find out just how the basic ideas of quantum mechanics and general relativity will have to be enlarged to include each other. In ordinary quantum field theory, each field is considered to be superimposed upon spacetime and is characterized by a particular quantum configuration. This configuration is indexed by a unique set of quantum numbers that represent the associated particle's spin, energy and angular momentum. This configuration  changes in a well-defined way as the system evolves subject to external influences such as absorbinga photon. Each state would be assigned a probability, and the evolution of the system would be... More »