Re: How can photons be massless
From: Timo Nieminen (timo_at_physics.uq.edu.au)
Date: 07/14/04
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Date: Thu, 15 Jul 2004 09:14:29 +1000
On Thu, 14 Jul 2004, KOB0724 wrote:
> I recently read The Elegant Universe and
> it gave me a crash course in the theory of realativity. Now, maybe I
> missed a section or something but I can't understand how photons (and
> two of the other messenger particles, the gluons and the
> as-of-yet-not-found graviton) can be massless. Here is my reasoning:
> E=mc2, therfore anything with 0 mass would have 0 energy (thats just a
> standard application of algerbra.) But how can this be?
Simply that E = mc^2 is not actually correct - it's the low-speed limit of
the correct formula:
E = gamma m c^2
where gamma = ( 1 - v^2/c^2 ) ^ (-1/2), and m = rest mass (which is what
is meant by "mass of a particle")
A standard application of algebra gives 0 times infinity, which doesn't
give us any particular value. You can consider this to be why it is
possible for photons, all travelling at c, to have differing energies,
although all of them are the same type of particle.
Now, this means that if you know the energy of the photon, you know
(gamma m), and therefore you can calculate the momentum (equal to
gamma m v (and not m v), and the momentum is equal to E/c, leading to the
classical expression for radiation momentum flux, P/c.
There's a certain degree of confusion that results from some writers using
"m" to mean what other writers mean by "gamma m". The "m" in the former is
*not* what is meant by the "mass of a particle", the latter m is.
-- Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/ Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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