### Re: What is the relative mass of a particle at the velocity of light?

Date: Tue May 23 11:30:40 2000
Posted By: Samuel Silverstein, faculty, physics, Stockholm University
Area of science: Physics
ID: 958352803.Ph
Message:

William,

The concept of relativistic mass is rather dated, and has more or less died out in modern physics. As you know, its definition is

```              m
Mrel = ---------------
sqrt(1-v^2/c^2)
```
and many older textbooks treated it as a conserved quantity in collisions; that is to say, while "rest mass" is not conserved, relativistic mass is.

Notice that Mrel is just E divided by a factor of c^2. That means that whatever can be said about Mrel applies equally to E, so that instead of talking about "conservation of relativistic mass" we can just as well discuss the conservation of energy. Nowadays, only the rest mass m is used:

```      2     2       2
(mc^2)  =  E  - (cp)
```
Here, there is no denominator to give us an indeterminate answer. For massless particles, cp is simply equal to E, and m is zero.

The derivation of the properties of the force-carrying particles comes from gauge field theories, a topic that is far too deep to go into here. A good introductory textbook is "Introduction to Elementary Particles" by David Griffiths.

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