In 2007, John P. Lestone of Los Alamos National Laboratory, U.S.A., suggested a possible approach to calculating the value of the fine structure constant based upon a heuristic string theory. The electron, the muon, and the tau might each consist of a 2-sphere having precisely three vibrating superstrings. In his 2007 publication "Physics based calculation of the fine structure constant " J. P. Lestone suggested that "the photon emission and absorption area A of an electron is controlled by a length scale" where the length scale is near the Planck length.
"Physics based calculation of the fine structure constant" by J. P. Lestone, 2007
Lestone introduced physical hypotheses to calculate the fine structure constant:
(a) The photon emission and absorption area A on an electron is controlled by a length scale f.
(b) The electron has a corresponding effective mean temperature T and the relationship between T and f is the same as the relationship between the Planck temperature and the Planck length.
(c) The absorption across section A/4 should be associated with a corresponding stimulated emission cross section (A/4) * exp(-epsilon), where epsilon is the energy of the incident photon relative to the temperature of the system.
(d) When a photon is absorbed by an electron there is a probability of exp(-epsilon) that a stimulated emission occurs.
(e) An electron consists of a loop of string with its length moving on the 2-dimensional surface of a nearly spherical membrane with radius f.
(f) The string's length is n times the sphere's circumference and this length is long enough so that, in a short time interval, the string can cover most of the string's surface.
(g) The finite length of the string generates an uncertainty in the effective length of the particle, and this temperature uncertainty is related to the time it takes for a signal to travel the length of the string.
Is Lestone's work a promising approach to effective calculations in string theory? What might be some of the implications of Lestone's hypothesis? Renormalization in quantum electrodynamics deals with infinite integrals that arise in perturbation theory. Does Lestone's hypothesis have important implications for renormalization? I conjecture that, EVEN AFTER QUANTUM AVERAGING, Maxwell's equations might be false at the Planck scale, because Lestone's heuristic string theory might be empirically valid. Let ρ represent the electric charge density (charge per unit volume). I conjecture that, in equation (19b) on page 23 of Einstein's "The Meaning of Relativity" (5th edition), ρ should be replaced by the expression ρ/ (1 - (ρ^2 / (ρ(max))^2))^(1/2), where ρ(max) is the maximum of the absolute value of the electric charge density in the physical universe. Polchinski (2003) offered "two general principles of completeness: (1) In any theoretical framework that requires charge to be quantized, there will exist magnetic monopoles. (2) In any fully unified theory, for every gauge field there will exist electric and magnetic sources with the minimum relative Dirac quantum n = 1 (more precisely, the lattice of electric and magnetic charges is maximal)." Are Polchinski's two general principles likely to be correct if and only if nature is infinite?