🚀 go-pugleaf

In article <6NOV199215292345@csa1.lbl.gov> sichase@csa1.lbl.gov 
(SCOTT I CHASE) writes:
|>The speed of light is a dimensional quantity, so it has the value that
|>it does only because we happen to use a certain set of units; I think,
|>then, that a better way to phrase the question is: why do we choose to
|>measure distances in centimeters and times in seconds?  
|
|Oh, come on.  That's just a dodge.  The speed of light is independent
|of the units you choose to measure it in.  If I take two light beams,
|and you measure the speed of light in cm/sec and I measure the
|speed of light in droobles/flimbat, the light from the two beams will
|still travel at the same speed.  Why *that* speed?

I think this touches on the interesting philosophical question of
"what is it that `a quantity' is?" What kind of "thing" is it that
"that speed" is?

I think what is being implied here is that all this talk about
"quantities" which have dimension is just a manner of speaking. The
claim is that whatever you can say about `quantities' must,
implicitly, mean something expressible solely in terms of
dimensionless ratios of quantities. Can we think of any fact which can
be stated about dimensioned quantities, which does not reduce in some
way to a claim about ratios of quantities?

For example, if I ask how long tall you are, the proposal is that the
only content which can be gathered from the question is to compare
your height to some reference length(s). A "length" is, essentially,
just defined by its ratios to the framework of all the other lengths
which we can talk about-- most especially to standardized ones. But,
if, for example, some bizarre change were to occur which affected only
the particular phenomenon which was used to define the standard,
leaving the ratios of most other quantities basically intact, then
we'd surely agree to change the standard, rather than regard all the
other quantities as having changed. (The old example was, "what if the
platinum bar in Paris were stretched".)

There is a natural gauge transformation here-- change of unit-- which
causes all the numbers to change, but the physical reality being
described stays the same. The things which are invariant under this
gauge are just the dimensionless ratios of quantities.

There are so many things which are intimately connected with the speed
of light that it is hard to imagine how we could make a model of a
counterfactual universe, in which the speed of light changes but the
overall framework of speeds remains roughly the same as in the real
world. One can write a story about it-- one of the Mr. Tompkins
stories e.g.-- but I'm not sure that there is a natural way of
modifying physical laws to fit the story.

From the standpoint of fundamental physics, it seems more natural to
invert the question, and treat c as the symbol we tack on to
quantities when we compare lengths with times, and define other speeds
in terms of it. (Isn't it now true that light of a given color travels
at a certain speed by definition, since both the meter and the second
are defined in terms of it?)

Massless particles follow paths which travel equally far in the space
direction as in the time direction! The question becomes why our
world-lines go at such a small slope v/c.

Keith Ramsay         "But I really think that frequent posters such as 
ramsay@unixg.ubc.ca  myself, Dale, Scott, McIrvin and others are not 
                     crackpots; we are simply loudmouths."