Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!houxm!vax135!cornell!uw-beaver!tektronix!hplabs!sri-unix!gwyn@BRL.ARPA From: gwyn@BRL.ARPA Newsgroups: net.physics Subject: Re: Questions about fundamental constants, gravity, electrons Message-ID: <496@sri-arpa.ARPA> Date: Wed, 14-Aug-85 09:45:25 EDT Article-I.D.: sri-arpa.496 Posted: Wed Aug 14 09:45:25 1985 Date-Received: Mon, 19-Aug-85 06:28:38 EDT Lines: 103 From: Doug Gwyn (VLD/VMB)(1) Change in values of "fundamental constants" over time. (2) Change in values of "fundamental constants" over the universe. These are related issues since space and time are interrelated. The real question is, what is meant by "fundamental constant"? If this means anything, it must mean a quantity whose numerical value is not arbitrary; otherwise it would be an accidental parameter of a specific configuration of the universe and thus would not be truly "fundamental". So what qualifies as a fundamental constant? At the current state of knowledge, there seem to be two categories of such constants. The first and simplest consists of pure (unitless) numbers, such as the fine-structure constant. The second consists of everything else believed to be intrinsic properties of the physical world. Such "constants" as the speed of light, density of water at STP, Planck's constant, and Newton's gravitational factor are not numerically constant at all, but depend on the units of measurement. However, to the extent that they measure something inherently real (as opposed to conventional), they qualify as fundamental physical constants. Because they are constrained by reality, their values are constrained to change in definite ways when the system of units is changed. By generalizing from this observation, one arrives at invariance groups and the tensor calculus. Now, because physics is more than (space-time) pointwise local, to compare events at one point of space-time with events at another, some "transport mechanism" is required to carry the quantities determined at one such event to another so that the two sets of quantities can be compared. Such a mechanism is known (the "affine connection" field), and Einstein's general theory of relativity is based on it. (Actually, the first formulation of general relativity did not use such a general viewpoint, but Levi-Civita, Weyl, and others developed the transport-mechanism viewpoint to such a degree that it is now the natural way to formulate relativistic field theory.) The full development of the purely affine theory leads to much more than just a theory of gravitation; I did a Master's thesis on this very subject. So, if physical quantities are going to vary over the space-time manifold, they're going to have to follow quite definite known rules of behavior. Of course, pure numerical (unitless) physical constants cannot vary from point to point if they measure something truly fundamental. Several famous theoreticians have gotten quite interested in deriving the values of such pure numbers. The names of Dirac and Eddington spring to mind in this connection. (3) How are the fundamental constants related? Well, the speed of light is just a conversion factor between space and time units, which were separate for historical reasons. Minkowski seems to have been the first to appreciate this point. The Newtonian gravitational constant relates units of energy (or mass) to those of space-time, according to the source-free formulation of general relativity. Various other presumably-fundamental constants can be combined to produce pure numbers; the "fine-structure" constant (roughly 1/137) is the most famous such pure number. It is not currently known whether such pure numbers measure local conditions or universal conditions; this is the same question as above. (4) Gravity as a "push" instead of a "pull". The best theory of gravitation (general relativity or its nonzero-torsion generalization) is not expressed in terms of attraction or repulsion. Therefore I find this question uninteresting. (5) Only one electron in the whole universe. This sounds like an idea attributed to Feynman and Wheeler. The idea is that a positron can be considered an electron going backward in time. If one thinks solely in terms of particle collisions in space-time, it becomes possible to propose that there is only one electron/positron trajectory zigzagging back and forth in time to produce all the electrons and positrons that we observe. The only real advantage to this theory is that it definitely accounts for the observation that all electrons have identical fundamental characteristics such as charge and rest mass. However, I am not at all fond of infinite-particle theories and think that a pure field theory is conceptually much cleaner (presumably, if the QCD type of theory is any good, it is exactly equivalent to a pure field theory -- if only we could magically perform all the Feynman integrals). The main drawback to a pure field theory is that it is not known to be able to explain quantization, but there are certainly some unexplored possibilities in that direction. (One of them is the question I asked some weeks back on this list, to which no one responded.)