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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.)