# Particles having nonzero rest mass can approach the speed of light

1. Dec 16, 2003

### Pabs

Particles having nonzero rest mass can approach, but not reach, the speed of light, since their mass would become infinite at that speed.

Can anyone expound upon this commencing with the very fundamental concepts (nonzero rest mass, mass, inertia, infinite mass etc.)?

2. Dec 16, 2003

### chroot

Staff Emeritus
Modern physicists would say that the particle's mass is always the same, and that it is its energy which becomes infinite at the speed of light.

Because energy and mass are quite directly related, however, a particle with more energy behaves, in the framework of Newton's laws, as if it had more mass.

Newton's laws are not correct except at low relative velocities, however -- so rather than modifying them by assuming an "increased mass," it makes more sense to simply not use them at high relative velocities. They are replaced by relativistic mechanics.

Nowadays, when someone says "mass," they mean "rest mass" or "invariant mass," which is a fundamental and unchanging characteristic of the object under scrutiny.

- Warren

3. Dec 16, 2003

### Pabs

Why would the mass of a particle become infinite at the speed of light? That was the essential intention of my questions.

4. Dec 16, 2003

### chroot

Staff Emeritus
No, the mass will always be the same. If the mass is non-zero, however, the energy will be infinite at the speed of light. (Kinetic energy depends on mass.)

- Warren

5. Dec 16, 2003

### DW

I agree, but with the exception that energy isn't divergent for massless particles which I'm sure you know and I would be careful about the following:

As mentioned in another thread the four vector law of motion for special relativity is four vector force equals mass times four vector acceleration
$$F^\mu = mA^\mu$$
where the mass m does not change with speed. The relation "in the framework of Newton's laws" that you are probably considering is the relation between ordinary force and coordinate acceleration. In that case the relativistic behavior can not be described simply by replacing mass with relativistic mass in
f = ma
either. To speed up a particle most effectively you want all the force in the direction of motion and when you do that the relation will be two orders of $$\gamma$$ too big to be relativistic mass.