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

In summary, the conversation discusses the concept of center of momentum frames and how they relate to massless particles. It is explained that while massless particles do have momentum, they do not have a center of momentum frame due to their light-like four-momentum. This is in contrast to particles with mass, which can have a center of momentum frame. The concept of center of mass is also briefly mentioned, and it is noted that it is more complex in general relativity.
  • #1
consal
8
0
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...) :redface:
 
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  • #2
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
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
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
DaleSpam said:
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.

Oh right. Thanks!

edit

Wait, there is no massless particle that has time-like intervals?
 
  • #6
consal said:
Oh right. Thanks!

edit

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

No, all massless particles must move at c, and follow a light like path.
 
  • #7
Thanks again.
 

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

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

The concept of a "center of mass" or "center of gravity" is based on the idea that an object has a fixed position in space. However, in relativity, space and time are relative and interconnected, meaning that there is no absolute reference point to determine the position of an object. This makes it impossible to define a single point as the center of relativistic mass.

2. How does the theory of relativity explain the absence of a center of relativistic mass?

The theory of relativity states that the laws of physics are the same for all observers, regardless of their relative motion. This means that there is no preferred frame of reference in which the laws of physics apply. As a result, the concept of a fixed center of mass becomes meaningless in relativity.

3. Can we still apply the concept of a center of mass in relativistic systems?

While the concept of a center of mass cannot be applied in the same way in relativistic systems, it can still be used in certain cases. For example, the center of mass can be defined for a system of objects that are all moving at the same speed relative to each other. However, in general, the concept of a single, fixed center of mass is not applicable in relativity.

4. How is the concept of center of mass related to the concept of relativistic mass?

The concept of center of mass is related to relativistic mass in that both are based on the idea of a fixed position in space. However, relativistic mass takes into account the effects of motion on an object's mass, while the concept of center of mass does not. In relativity, an object's mass is not a fixed property, but rather depends on its relative motion and the observer's frame of reference.

5. Are there any practical implications of the absence of a center of relativistic mass?

Yes, there are practical implications of the absence of a center of relativistic mass. For example, in particle accelerators, the relativistic mass of particles increases as they approach the speed of light. This means that the center of mass of a system of particles can shift, making it difficult to predict the behavior of the system. This must be taken into account in the design and operation of these machines.

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