# How do Einstein’s equations support mass gain in particle accelerators? [duplicate]

A charged particle that is accelerated through a particle accelerator like CERN undergoes this phenomenon: the particle gains more mass as it gets pushed to higher and higher speeds.

So Einstein's (most famous) equation is E=MC^2. If we're assuming the speed of light (or any EM wave) is constant, and the mass we put into this device is known at the time, the only thing that can change is energy input.

If more energy is put into the machine (with the effect of moving the particles within it at faster speeds), than the mass MUST increase right, since the speed of light is the absolute limit, a known quantity? The "C^2" part remains unchanged, and cannot be changed.

My question is, why is an increase in velocity of a particle the same as E, energy? So velocity is the same as energy is the same as mass? Is that right? We can consider all 3 of these things as equivalent: mass, energy, velocity?

## marked as duplicate by David Z♦Sep 20 '11 at 7:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• This is already covered by several questions on this site; the one linked above is just the first one I found. I also recommend looking at physics.stackexchange.com/q/2229, which explains why $E=mc^2$ does not apply to particles in an accelerator. (Also, just for emphasis: mass, energy, and velocity are not equivalent.) – David Z Sep 20 '11 at 7:21

## 1 Answer

The mass increase is not inferred from $E= m.c^2$, rather it comes form a different equation from his special relativity theory.

The formula is, $$M = M_0 . \gamma$$ where $$\gamma = 1/\sqrt{1-v^2/c^2}$$ and $v$ is velocity of particle and $c$ is speed of light. Since, high energy particle has high $v$, it mean that their mass increases considerably when approaching $c$, the speed of light.

You might notice that when $v$ equals $c$, the mass becomes undefined, another term for infinity. That's the reason why physicist say, any material particle can't reach speed of light.