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Re: [Phys-l] E=mc^2 because E=mc^2?

On 04/26/2007 05:46 PM, Fayngold, Moses wrote:

... let me derive E = mc^2 from the concept of spacetime,
....
to the mass-energy relationship:

E = mc^2 (6)

Note that this is much more general than just E0 = m0c^2 (7)
for the rest energy only.


Alas (6) is not one iota more general than
m^2 = E^2 - p^2
m^2 c^4 = E^2 - p^2 c^2

which is
-- what I wrote yesterday, and
-- which I and many many others have written on previous occasions, and
-- which is properly called the /spacetime/ approach to the task,
since it has a direct interpretation in terms of 4-vectors and the
geometry of spacetime.


John, if you are with Einstein, you must know that Einstein's celebrated equation is (6), rather than its truncated version (7).

This sort of appeal to authority just cracks me up. Even if it
were true, it would have negligible weight ... and there is no
reason to think it is true.

I recommended taking a modern (i.e. post-1908) approach to the
task. According to Oas and others, there is no evidence that
Einstein used a speed-dependent mass at any time after Minkowski's
celebrated 1908 paper, "Raum und Zeit".

More importantly, who cares? What if Einstein got it wrong?
Or, what if the field has progressed and evolved in the last
100 years? Would that be so terrible?

The idea of a speed-dependent mass is part and parcel of the
approach that uses rulers that can't be trusted and clocks that
can't be trusted ... an approach that predates any notion of
spacetime.

Next year is the 100th anniversary of spacetime. All the
students have heard of spacetime; it's well established as
part of pop culture. It gets mentioned in /Star Trek/ and
/Buffy/ and who-knows-where else. Isn't it about time we
taught folks what spacetime really is, and how to use it?



As for expanding the energy to first order to recover the
classical KE, the spacetime approach to doing that can be
found in many places including
http://www.av8n.com/physics/spacetime-momentum.htm#sec-ke

For more on the spacetime approach, using invariant rulers,
invariant clocks, and invariant mass, see
http://www.av8n.com/physics/odometer.pdf