# Does matter become energy at the speed of light?

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## Solution 1

Your question is so confused that it's hard to give a meaningful answer...

if matter were to travel the speed of light, would it become energy?

Anything that has a rest mass $m_0$ has an energy associated with that mass of $E=m_0 c^2$. If this mass is also moving with some momentum $p$, it has a kinetic energy associated with the motion. The total energy (including both kinetic- and rest-energy) of the moving mass is: $$E=\sqrt{m_0^2 c^4+p^2c^2}\;.$$

Given the relativistic definition of momentum, $p=m_0 v \frac{1}{\sqrt{1-v^2/c^2}}$, where v is the velocity, the expression for energy can be re-written as: $$E=m_0c^2\frac{1}{\sqrt{1-v^2/c^2}};.$$ So, clearly, no massive body or particle can travel at the speed of light, because the energy of that body or particle would be infinite...

## Solution 2

At hyperrelativistic speeds, a massive object has the bulk of its energy in kenetic form so the invariant mass is small residue. It acts like a very low mass particle at meerly relativistic speeds, or a almost massless neutrino at any speed.

A 7Tev proton is travelling at $0.999999991c$ and its mass is only contributing on the order of one one hundredth of a percent to that total.

It acts more like a massless particle: adding more energy does not make it go (usfully or noticably) faster, but adds to its momemtum and shortens its wavelength. The fact that it has energy even when all the momentum is removed is a tiny correction, rather than the most significant thing about it.

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### CuriousWebDeveloper

Updated on March 08, 2020

According to modern physics, we can't push matter to the speed of light. It would slow down (relative to its environment). But theoretically, if matter were to travel the speed of light, would it become energy?

It seems to me that $E = mc^2$ could be rearranged to prove that it would.

If so, what kind of energy would it become, and do we know what that transition would look like?

Would the transition be instant, or is there some kind of transitional state between matter and energy?

• JDługosz over 8 years
"If it could" means changing the rules, so an answer is whatever your changed rules would have. It does make sense to look at what happens as velocity gets arbitrarily closer to c, which I explored in my Answer.
• Alfred Centauri over 8 years
It's important to appreciate that there are (an infinity of) inertial reference frames in which CuriousWebDeveloper is moving arbitrarily close to the speed of light; in these reference frames, you have arbitrarily large kinetic energy. But, none of this has any effect on you because you are always at rest with respect to yourself. This holds for other forms of matter too.