- Published 2004

Albert Einstein showed that Newton’s law, one of the most basic laws in physics, is a special case of the solutions of the classical field equations of his general theory of relativity. Specifically, g00 = 1 + 2ΦN ⇒ ∇ΦN = 4πGNρ from R αγ − 1 2gαγR = −8πGNT , etc., where he have now introduced the familiar metric of space-time gμν , the Newtonian potential ΦN , Newton’s constant GN , the mass density ρ, the contracted Riemann tensor R , and the appropriate energy momentum tensor T . There have been several successful tests of Einstein’s theory in classical physics [1–3]. Heisenberg and Schroedinger, following Bohr, formulated a quantum mechanics that has explained, in the Standard Model(SM) [4], all established experimentally accessible quantum phenomena except the quantum treatment of Newton’s law. Indeed, even with tremendous progress in quantum field theory, superstrings [5, 6], loop quantum gravity [7], etc., no satisfactory treatment of the quantum mechanics of Newton’s law is known to be correct phenomenologically. Here, we apply a new approach [8] to quantum gravitational phenomena, building on previous work by Feynman [9,10] to get a minimal union of Bohr’s and Einstein’s ideas. There are four approaches [11] to the attendant bad UV behavior of quantum gravity (QG): extended theories of gravitation such as supersymmetric theories superstrings and loop quantum gravity; resummation, a new version of which we discuss presently; composite gravitons; and, asymptotic safety – fixed point theory, recently pursued with success in Refs. [12,13]. Our approach allows us to make contact with both the extended theory approach and the asymptotic safety approach. Our new approach , resummed quantum gravity, is based on well-tested YFS [14, 15] methods. We first review Feynman’s formulation of Einstein’s theory in Sect. 2. We present resummed QG in Sect. 3. In Sect. 4 we discuss Newton’s law. In Sect. 5 we discuss the black hole physics, some of which is related to Hawking radiation [16].

@inproceedings{Ward2004MassiveEP,
title={Massive Elementary Particles and Black Holes in Resummed Quantum Gravity},
author={Bennie F. L. Ward},
year={2004}
}