# What's the deal with Relativistic Mass? [duplicate]

So I have taken a first course in Special Relativity and the Relativistic Mass is defined as: $$m = \frac{m_o}{\sqrt{1 - v^2/c^2}}.$$

Now, when this was introduced in the course, it was introduced as something profound and very important. Not only did it show why no particle can be accelerated to a speed equal or larger than c but it also was required for momentum to be conserved in SR.

So why is it then that I keep reading here on SE that this term is deprecated, obsolete, etc. ?

This also eventually led to the famous $E = mc^2$ so I gotta ask, does mass increase in a moving frame or does it not?

This is quite confusing!

## 1 Answer

...the Relativistic Mass is defined as...

is wrong. There is no relativistic mass. The mass is $m_0$ according to what its meaning is (namely, as coefficient appearing in the Lagrangian in correspondence of some terms) and does not change; rather, what changes is the way it enters the equations of motion, which in turn show an additional multiplicative coefficient.

The terminology comes from the fact that if you want to keep and maintain the equations of motion in the same form they are for non-relativistic classical mechanics you might interpret this new term all together as a new mass, but that leads most of the times to unfortunate conclusions also in other contexts. Moreover, the bare physical mass that you measure in laboratories will always be $m_0$.

The deal with the energy-mass relation is a different thing and it comes from the representation of the Hamiltonian when performing the Legendre transformation on the relativistic Lagrangian. A new term appears, which does not depend on the momentum of the particles and is therefore interpreted as rest energy contribution.

• @HelderVelez I will do a trivial edit and after that you can correct your vote. – anna v Sep 25 '15 at 16:00
• "There is no relativistic mass." That kind of fundamentalism has no place in science. Relativistic mass can be defined just fine as SilverSlash did. Whether it is more useful or more harmful is a different thing to decide and may not have unique answer valid for everybody. – Ján Lalinský Sep 25 '15 at 17:23
• I agree, but one cannot just keep reinventing the wheel over and over again. If two things are the same things, don't give them two different names. – gented Sep 25 '15 at 17:26