# Why can't there be a center of relativistic mass?

1. Jul 13, 2011

### consal

As the title. More specifically, with respect to the center of momentum frames massless particles don't have, why not if they still do have relativistic mass?

(Bracing for an easy answer to a stupid question...)

2. Jul 13, 2011

### PAllen

Welcome to physics forums.

Well, there is an issue understanding the question. Your title asks about center of mass, your words talk about center of momentum frame. These are closely related, but not the same, and you don't ask a specific question. The following might be helpful.

In special relativity, center of momentum frames are perfectly well defined and very useful (but they may not always exist, see below). Massless particles have momentum, and they definitely contribute to what is the center of momentum frame.

Are you questioning what is the center of momentum for a system of one massless particle? In this case, there is, indeed, none. More generally, a system of massless particles moving parallel has no center of momentum frame. Any other case does (even two photons at a slight angle to each other has a center of momentum frame).

As for center of mass, this concept is simple in special relativity, but complex in general relativity. I am not sure if there is any universally accepted definition in general relativity (several have been proposed, I don't know current consensus on them).

3. Jul 13, 2011

### consal

Well, yes, I'm mainly asking why a system of one massless particle cannot have a center of momentum frame if it has relativistic mass. What is inherent about invariable mass that it precludes the ability to have a center of momentum frame whereas relativistic mass cannot?

4. Jul 13, 2011

### Staff: Mentor

Hi consal, welcome to PF!

Since you are talking about the center of momentum frame I am going to assume that you know about four-vectors and the Minkowski norm. The four-momentum in the CoM frame is, by definition, timelike, and the four-momentum of a massless particle is, by definition, lightlike. There is no Lorentz transform which can transform a lightlike vector into a timelike one.

5. Jul 13, 2011

### consal

Oh right. Thanks!

edit

Wait, there is no massless particle that has time-like intervals?

6. Jul 13, 2011

### PAllen

No, all massless particles must move at c, and follow a light like path.

7. Jul 13, 2011

### consal

Thanks again.