# Photon Mass?

Wei-Zhong He wzh at rio2.Berkeley.EDU
Sat Sep 10 23:31:03 EST 1994

```In article <34po4sINNmad at s-crim1.dl.ac.uk>,
R.G. Walters <mbrgw at s-crim1.dl.ac.uk> wrote:
>In article <sib-0809941303350001 at biomed-jww-245.biomed.brown.edu> sib at brown.edu (Sam Beale) writes:
>>In article <f_holleyg-080994084705 at holley.sfasu.edu>,
>>> Does a photon have mass or is it just an energy wave?
>>
>>No mass, all energy.  They travel at the speed of light.  This alone
>>disqualifies them from having mass.  Said another way, if they had mass
>>and travelled at the speed of light, they would have infinite energy.
>>Consult any physics book.
>
>But they DO have momentum.  Again, consult a physics book :-)
>
>Robin Walters.                      Robert Hill Institute, Sheffield UK.
>
>A fact is an opinion that everyone agrees with.
>

Well, somehow "No mass, all energy" is not a fact, because I can't agree
E = mc^2		............[1]
This implies that anything with energy should have mass, too.
For a photon, E=hv, where v is the frequency of light. Therefore, we have
m = hv/c^2		............[2]
To clear a bit of confusion, m is the relativity mass here. The kind of mass
that we can "weight" is refer to "mass at rest", m(0), in A Modern Physics
book. The relation between them is:
m(0)
m = ---------------	............[3]
sqrt{1-(u/c)^2}
where u is the velocity of the object.

As one can see now, the denominator in equation [3] is 0 in case of a photon,
because u is c. Fortunately, a photon has no mass at rest, i.e. m(0) = 0.
Therefore, equation [3] is still valid. Because a photon has mass as well as
speed, it carries momentum, too. Surely, it is
p = mc = hv/c

For any matter other than photon or phonon, m(0) is not 0. In that case, m
increases with u, so that one can never accelerate something, even as small
as an electron, to the speed of light.

In conclusion, it is right to say that a photon has no mass at rest. (There
wouldn't be a photon at rest, would it?).

Yours Sincerely,

Wei
-----
~{:NN0VR~}                     Department of Plant Biology
Wei-Zhong He                    University of California
Tel: (510) 643-5058             111, Koshland Hall (GPBB)
Fax: (510) 642-4995             Berkeley, CA 94720

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