From: utzoo!decvax!harpo!seismo!hao!hplabs!sri-unix!KFL@MIT-MC
Newsgroups: net.physics
Title: Re:  Speed of light
Article-I.D.: sri-arpa.1356
Posted: Wed May 11 20:45:00 1983
Received: Thu May 19 02:15:28 1983

From:  Keith F. Lynch <KFL @ MIT-MC>

	From:     Doug Gwyn (VLD/VMB) <gwyn@Brl-Vld.ARPA>
	
	 		     ... the generalization of Euclidean distance
	after this "free-fall" transformation to an "inertial frame" would
	be:
	        ds^2 = (f dx)^2 + (e dy)^2 + (d dz)^2 - (c dt)^2 ,
	where (x,y,z,t) are local Cartesian 3-space coordinates and the
	time coordinate measured in arbitrary units.  People (not just
	theoretical physicists) are clever enough to use compatible units
	of distance for the three 3-space axis directions, so
	        f = e = d       by usual convention.
	In fact, theoreticians usually choose compatible units for time, so
	        f = e = d = c   by theoretical physics convention.

  You are saying that asking "what happens if c is changed" makes as much
sense as asking what happens if the ratio between vertical distance and
horizontal distance was changed?

	In this case, "ds" units are normal taken to be compatible also, so
	        f = e = d = c = 1       is the usual theoretical physics choice.
	In the case
	        f = e = d = 1   which assigns ds units compatible with distance,
	the speed of light is exactly c.  The theoreticians therefore have
	chosen units such that the speed of light is precisely 1.

  Ah yes.  If you let c (the speed of light), h-bar (Plank's constant),
and G (the gravitational constant) all equal 1, you have a perfectly
consistent and well defined system of units in which there are natural
units of time, distance, mass, etc.  One problem with doing it this way
(other than the practical problem that the value of G is not known to
very many places) is that it tempts people to assign all units a
dimensionality of unity, which greatly impairs one's ability to debug
physics equations.
	
	The reasons distance and
	time are hard to consider as "the same type of thing" lie in the
	opposite sign for the time coordinate in the diagonalized metric.

  Of course you are assuming that general relativity is the last word.
General relativity is built on special relativity, and special
relativity begins by assuming some of the things it is often used to
'prove'!  The only reason not to throw it out is that it manages to
predict the results of many experiments with pretty good accuracy.
There are almost certainly some very serious bugs in relativity, as was
demonstrated in Bell's theorem, which shows that general (and special!)
relitivity as it is generally understood is incompatible with quantum
mechanics as it is generally understood.
	
	The most natural generalization
	of general relativity, that is, the one making the fewest physical
	assumptions, leads directly to a cosmology with a natural distance
	unit.  Anyone who is really curious about this can drop me a note
	and I'll send out a copy of my thesis.

  Yes, I would like a copy please.
								...Keith