# The determination of mass dilation

1. Jun 8, 2012

### swampwiz

Mass dilation would of course be the relativistic mass (a term which really shouldn't be used.)

It seems none of the books or websites I have researched have explained this to my satisfaction, so I began thinking about this, and here is my derivation.

NOTE: IRF = Inertial Reference Frame

What do you all think? The key points are that the time used for the derivative is the proper time of the object, but the length is the observed length (which would be contracted) of the object - and that any force being applied to an object would be observe to be the same from any IRF - i.e., force is invariant.

Alternatively, if anyone knows of a very clear discussion somewhere, I'd be all ears & eyes!

2. Jun 8, 2012

### Staff: Mentor

What exactly do you need explained? "Relativistic mass" is just another word for "total energy". You appear to be asking why an object gains energy when it has work done on it by a force. Isn't that obvious?

If you are really asking what is the correct relativistic version of F = ma, see here:

http://en.wikipedia.org/wiki/List_of_relativistic_equations#Force

3. Jun 8, 2012

### swampwiz

No I am asking how the term for relativistic mass (or relativistic momentum, from which the relativistic mass can be derived) gets derived. The fact that energy is mass derives from the fact that there is this relativistic mass.

Yes, I know F = ma. It's the derivation of m that I am asking about.

4. Jun 8, 2012

### Muphrid

The use of "relativistic mass" has really fallen out of vogue of late. Nowadays, people tend to only use the invariant (rest) mass and use relativistic four-acceleration and four-momentum, and so on.

5. Jun 8, 2012

### Staff: Mentor

No, you have it backwards. Energy is the more fundamental concept; actually, 4-momentum is even more fundamental than that (since energy is just the time component of 4-momentum). The fact that "energy is mass" derives from the fact that energy has inertia; some people insist on viewing total energy as "relativistic mass" because of this, but that's a matter of interpretation, not "derivation". There's no "derivation" of relativistic mass beyond recognizing that it's just another name for the total energy.

But my point was that in relativity, F = ma is not correct, even if you interpret "m" as relativistic mass. The correct relativistic version of that equation is on the page I linked to, and it makes no mention of relativistic mass; the only "mass" involved is the rest mass.