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From: rabid_fan on 1 May 2010 22:03
On Sat, 01 May 2010 16:17:31 -0700, BURT wrote:

> E = MC Squared
>
> Why is mass related by the square of light speed?

The relation is derived mathematically.

The kinetic energy of a particle, in a completely general
sense, is expressed by the integral with respect to time
of the following quantity:

F * v

where F is the force vector, v is the velocity vector,
and "*" represents the scalar product. (IOW it is a path
integral.)

The integral wrt time of F*v is the total energy required
to accelerate the particle from rest (at t0) to some final
velocity (at t1).

Using the standard methods of vector calculus (which I will
not reproduce), and with the substitution of relativistic mass,
the quantity can be re-expressed as:

F*v = c^2 * dm/dt

Integrating this quantity wrt time gives:

c^2 (m1 - m0), with m0 being the mass at t0 (i.e. rest mass)

So, a change in energy (delta E) is proportional to
a change in mass (delta m).

Experimentally, this is shown to apply to all forms of
energy.
From: Tom Roberts on 2 May 2010 11:40
BURT wrote:
> E = MC Squared
> Why is mass related by the square of light speed?

[Your "C" is normally notated in lower case, which I'll use.]

You got it wrong. In that equation c is not really the speed of light -- calling
it that is merely an accidental historical curiosity (see below).

In that equation, c is actually the invariant speed of the Lorentz transform,
and it is really just a units conversion factor, relating the unit of time to
the unit of distance. Historically we use seconds and meters, which happen to
make c be a very large number with units meters/second; most theoretical
physicists use units in which c=1 (and is unitless); that is, we use the same
unit for both time and distance (most commonly cm; for time, 29.9792458 cm = 1
nanosecond).

So in the above equation, c is merely converting the units between mass and
energy. If you look in the Particle Data Group publications, you'll see they
list the masses of particles in MeV, which is at base a unit of energy; clearly
they are using c=1 (this is standard in particle physics for units of mass,
momentum, and energy).

The reason c is also called the speed of light, and the reason that historical
curiosity occurred in the first place, is that light "just happens" to travel
with the invariant speed of the Lorentz transform. That is one of the more
remarkable facts about the world we inhabit, and its effect on theoretical
physics is profound.


Tom Roberts
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