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Ok, fair enough point that invariant mass is going to be a nightmare to compute in this case, but my original point wasn't about which was easier to compute. I wanted to know when relativistic mass provides some unique benefit that other concepts don't cover.
Relativity theory gives a relationship predicting the increase of mass of relativistic moving particles, but no physical model has been given to describe the fundamental physical mechanism responsible for the formation of that additional mass.
As long as we speak of relativistic mass I can get it Pete. But it surprised me reading that Einstein defined the Electromagnetic field as 'matter', if I now got that right?
As we have EM fields all over I mean? Also, a magnetic field is frame dependent as I understands it, so where does that 'matter' go?
"We make a distinction hereafter between gravitational field and matter in this way, that we denote everything but the gravitational field as matter. Our use of the word therefore includes not only matter in the ordinary sense, but the electromagnetic field itself."But you are right there, although I think of it in terms of invariant mass as per definition unchanging in all frames of reference, one could easily define it such as invariant mass is a 'static description' of mass in that it do not contain any correction for temperature etc. One might say that the relativistic mass is a dynamical definition of mass perhaps?
And so also argue that the concept of relativistic mass is what best fits GR, whereas 'invariant proper mass' is a ideal definition, assuming some ideal state of eh, 'matter' As we normally call our invariant proper mass?
It's a very interesting point actually.
I must admit i should have read your question again prior to have posted Pete.
But is it possible that the main reason why QM and GR seem to be incompatible is because spacetime is not the cause but an effect?
I wish you a good health!
The funny thing Pete, is that I also found relativistic mass to be more appropriate once. Found myself questioning invariant mass in 2008 looking for it. I'm still not sure how to see invariant proper mass, although I would prefer to have some irreducible part being the same in any frame. But what I mean is that in GR and SpaceTime we exist in there is no such thing as a invariant mass. It changes and becomes a dynamic concept although you still may relate it to invariant proper mass. That's why I thought you might argue that relativistic mass was the more proper definition in GR.
Now this is just me wondering, and not directed to anyone in particular Pete