Thread: relativistic mass, rest mass, invariant mass...

Could anyone please try to explain the differences to me?

I've been here: http://en.wikipedia.org/wiki/Mass_in_special_relativity but it hasn't really clicked with me. I'm having trouble finding a straight to the point comparison or description of them.

Any help would be great.

Originally Posted by someguy22

Could anyone please try to explain the differences to me?

I've been here: http://en.wikipedia.org/wiki/Mass_in_special_relativity but it hasn't really clicked with me. I'm having trouble finding a straight to the point comparison or description of them.

Any help would be great.

That Wiki article is correct, but is so pedantic that it is not very readable. They are trying to address a simple concept and at the same time address some misconceptions, the result -- they are clear as mud.

The simple answer is that in relativity there are two masses that are considered.

One is rest mass, aka invariant mass. Rest mass is simply the mass of the body measured in a reference frame that is at rest with respect to the body. The rest mass of the body is commonly denoted .

Then there is mass, aka relativiatic mass . It is usually denoted as . Mass is dependent on the reference frame in which it is measured. If mass is measured in a reference frame that is moving with velocity relative to the body then the mass is given by the usual equation from special relativity where . Einstein's energy equation then applies as usually written, where is the relativistic mass.

The Wiki articles advocate a different viewpoint, in which you deal only with the rest mass and drop the subscript and carry around. I think this can be very confusing. It appears that is has managed to confuse you, and that is quite understandable.

Thank you, correct me if I am wrong but this means that as you approach the speed of light your mass will approach infinity from the reference frame of an outside observer while staying constant in your own reference frame? Would this also mean that at speeds approaching the speed of light you have a significant gravitational field?

Originally Posted by someguy22

Thank you, correct me if I am wrong but this means that as you approach the speed of light your mass will approach infinity from the reference frame of an outside observer while staying constant in your own reference frame? Would this also mean that at speeds approaching the speed of light you have a significant gravitational field?

Yes and yes, from an appropriate reference frame. You need to a bit careful about the gravitational field as special relativity is not able to handle gravity. You need general relativity for that.

So if we can't handle gravity what are the usages of invariant and relativistic mass? The obvious one is using relativistic mass for because the energy will include a component of your kinetic energy, but what else is there?

Originally Posted by someguy22

So if we can't handle gravity what are the usages of invariant and relativistic mass? The obvious one is using relativistic mass for because the energy will include a component of your kinetic energy, but what else is there?

I said you can't handle gravity with special relativity.

General relativity is not only capable of handling gravity, it is the best theory of gravity that we have.

The mathematics of general relativity is much more complicated than is the case for special relativity. Special relativity can be handled with nothing more than some simple algebra. General relativity requires some sophisticated differential geometry. In general relativity you no longer have global coordinate systems, but have to work in the context of a differential manifold and local charts. Gravity is reflected by the curvature of space-time and the calculation of the curvature and the metric are difficult problems in tensor analysis, but the basic idea is that the distribution of matter and energy in the universe determine the curvature tensor for the space-time manifold. So enters the problem in a significant way since the curvature tensor is determined by all matter, all energy and even pressure.