# Re: Constant 'c'?

Wed, 05 Nov 1997 13:15:29 -0500 (EST)

At 09:32 AM 11/5/97 -0500, George Murphy wrote:
>
>> I think I made it very clear in my previous posts that the constancy of the
>> speed of light is a fundamental feature of nature and has nothing to do with
>> what units we use in physics. The relation between calorie and joule is
>> precisely the same as the relation between inch and centimeter.
>
> Not exactly. People always knew that inches & centimeters were
>units for measuring the same physical quantity, length. Until the
>discovery of conservation of energy ~150 years ago, people didn't know
>that heat and mechanical work were different forms of the same thing,
>energy, & used different units for measuring them. What I'm arguing is
>that Minkowski's formulation of relativity in terms of space-time is
>analogous to the latter discovery, & thus that c is analogous to the
>mechanical equivalent of heat.

In the case of length and energy, the numerical constants, 2.54 and 4.184,
have no physical content and are only a historical curiosity. Note that one
is dealing only with energy or only with length. On the other hand, the
constant c is the speed of light in vacuum, a measurable quantity. By
defining the value of c to have an exact number, 299792458, one is only
defining the meter in terms of the unit of time, the second. But note that
we are dealing with two different quantities---space and time, albeit,
components of a 4-vector---which have different dimensions. If somewhere in
the universe, the velocity of light is different, then by using our
definition of the second and the meter, they would get a different length
for the meter. The numbers 2.54 and 4.184 are the same anywhere in the universe.

p.s. Perhaps we do need a referee to settle the issue.

>> For the same reason, Planck's E = h f and de Broglie's p =
>> h/ lambda are fundamental features of nature (or our understanding of nature
>> if you like) and not mere conversion factors. These findings of Planck and
>> de Broglie indicate the fundamental particle/wave duality of nature (or our
>> understanding of nature if you like).
> You point out here something that I've puzzled about. Of the 3
>basic constants c, G, & h (which can be combined to give "natural"
>Planck units for length, time, & mass), the first 2 can be seen as
>conversion factors: From special relativity, c converts space units to
>time units, & from general relativity G converts inertial mass units to
>gravitational mass units. But h can't be seen as such a conversion
>factor: Quantum theory (at least in versions I know) doesn't say that
>energy & frequency are really the same thing in different units. Any
>suggestions?
> George Murphy
>
>