On Sun, 11 May 2008, Jacques wrote:

Hi everybody,

I have a question which bothers me since long time and maybe with your help
I can find the answer at last. Since I heard the formule E=mc^2 for the
first time it struck me that there seems to be no logical relation between
the energy contained in a mass and the speed of light. I have no
difficulties to understand that the energy contained in a mass is equivalent
to that mass.

My problem is: what the hell has this to do with the speed of something else
(an electromagnetic wave). I cannot see the connection between them. These
two things: mass and energy on one side and the speed of light on the other
side seem too disparate to me to allow a logical link between them.

Starting from "E is proportional to m", there must be a unit conversion
constant with units of velocity^2. The unit chosen for mass doesn't
matter, since it affects the left-hand and right-hand sides of the
equation equally. What matters is then just our choice of units for
distance and time.

The speed "c" is special. In the framework of special relativity (is this
also true in general relativity?), it's the only speed that's the same in
all inertial reference frames. But c has the particular value that it has
due to our choice of units to measure time and space.

So, if some particular speed features in the conversion constant, it'll
either be some entirely random value, or c.

But, consider the inertia of electromagnetic waves. An EM wavepacket of
total energy E has momentum E/c (this is a general relationship for speeds
other than c for the inertia of energy moved as waves, whether acoustic,
elastic, or thermal waves, N. A. Umov, 1874 iirc). From this, one sees
E=mc^2 gives us the inertia of an EM wave. While this is not the modern
use of "m" in E=mc^2, where m is the rest mass, there is the older usage
of m as "relativistic mass". Especially when you get to photons, what is
the difference between EM waves and matter? Should there be a unified
description of at least some of the behaviour of matter and photons? If
so, then we must have E=mc^2.

I wonder, if someone can explain this connection. I wouldn't have been
surprised if the Joule (the unit for energy) had been established in
consequence of this formula, but I think both Joule, kg, m/s were already
existent before E=mc^2.

I learned from Wikipedia that James Joule died in 1889, thus before Einstein
discovered his famous formula, which I think happened in 1905.

These days, the modern joule is almost defined in terms of electromagnetic
radiation. Almost. Standards for units for time and distance are EM, mass
is not. But such standards aren't about logic or connectedness, but about
practical measurement.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/...,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html