Uncovering the Mystery of Mass Gain in Special Relativity

[Ralphonsicus]

As objects approach the speed of light, according to Special Relativity, they gain mass. But when this happens, what does the mass come in the form of?

The first thing that comes to mind would be matter and antimatter. But if this is so, wouldn't they just annihilate, and do so in a fury as more matter and antimatter are added to the object?

 

[phinds]

It isn't really the MASS that increases, it is the mass-energy, and the increase comes from the energy expended in causing the acceleration.

 

[mathman]

The mass gain is what the observer sees resulting from the energy put into the particle to make it speed up. In the frame of the particle itself, the mass is unchanged.

 

[bossman27]

It doesn't "come from" anything. In my experience it's really not even all that common to talk about relativistic mass, we usually just write energy in terms of rest mass (which is invariant). It's a bit of a misleading concept anyway, because it implies (as you seem to have the impression) that it is related to some internal change in the object -- it's not.

It more or less comes from the fact that mass-energy (rest mass, that is) can be written $E_{0} = mc^{2}$

For a particle moving relative to an observer, the energy of the particle would be measured by the observer to be $E = \gamma mc^{2}$

Thus you can write $m_{rel} = \frac{E}{c^2} = \gamma m$, where $m$ is the rest mass, equating $E_{0}$ with $E$ but again, it's kind of an ambiguous and misleading concept.

 

[mfb]

The mass gain is what the observer sees resulting from the energy put into the particle to make it speed up.

That concept of a "relativistic mass" is not used any more in physics - it just remains in old textbooks and bad web pages.