Why is the relativistic mass a rejected concept?

[PAllen]

I don't have a direct comment off the top of my head. But the funny thing is that we know that in some exact solutions, the "mass" measured at infinity is certainly not the relativistic mass (eg. http://books.google.com/books?id=qhDFuWbLlgQC&source=gbs_navlinks_s, p259).

Nice that that book page was available on google. The explanation given is that the difference is the self gravitational binding energy. Well, duh, that is excluded by the assumptions of MTW section 19.1. This particular derivation is very general as to e.g. relative speed of the elements contributing to T, but explicitly excludes significant self gravitation. Thus, it says, you can't use it for a star.

 

[atyy]

Ok, here's a thought - does the invariant mass include potential energy?

 

[PAllen]

Ok, here's a thought - does the invariant mass include potential energy?

No.

My transform argument to show the irrelevance of relativistic mass for a rapidly moving body covers any 'isolated body' however structured or massive (concluding that only center of momentum mass / energy *contributes* to coordinate independent features of curvature). However, invariant mass is useful only assuming no E/M, and no significant self gravitation. It is just norm of the sum of the component 4-momenta.

Now, I did find that a true total 4-momentum vector can be defined for any isolated body, in AF spacetime, in GR (no exceptions apparently; proof due to Moller). However, I have no idea under what conditions the norm of this vector could be taken to be an active gravitational mass. I have an intuition that, since such a total 4-momentum must take account of E/M and gravitational self-energy, it's norm might meaningful as a gravitational mass under some conditions - but then, if it were that simple, it would be well known result. So maybe it just doesn't work at that level of generality.

 

[atyy]

I think one reason for not requiring coordinate invariance is that we are talking about phi, which has no meaning. In Newtonian physics, only grad(phi) has meaning. If you change reference frames, you change the kinetic energy of everything by a constant, which doesn't affect grad(phi).

 

[Drakkith]

A fast moving object will length contract. Its density will increase If its density is given by its invariant mass divided by volume. Will it turn into a black hole?

No. It is not length contracting in its own frame. The density of the object is not increasing.

 

[PAllen]

No. It is not length contracting in its own frame. The density of the object is not increasing.

I hope you realize that was a joke, poking at my insistence that if only we stop using relativistic mass, newbie questions about fast moving objects will turn into black holes will go away. Atyy certainly doesn't believe that a black hole would form. Getting the joke, and the point, I responded, "no that's a black pancake, not a black hole".

 

[Drakkith]

I hope you realize that was a joke, poking at my insistence that if only we stop using relativistic mass, newbie questions about fast moving objects will turn into black holes will go away. Atyy certainly doesn't believe that a black hole would form. Getting the joke, and the point, I responded, "no that's a black pancake, not a black hole".

It makes so much sense now!

I guess that's what I get for not reading the whole thread lol.