# Einstein equation $E=mc^2$: Does it mean an object without mass does not have energy?

Einstein equation $E=mc^2$ where $E$ is energy, $m$ mass, and $c$ the speed of light in vacuum. So does it mean objects without any mass does not posses energy for eg lights photons does not have mass but how can they posses energy

• This question (v2) seems spurred by a confusion between rest/invariant mass and relativistic mass. See e.g. this Phys.SE post, and a couple of paragraphs down on this Wikipedia page. – Qmechanic Nov 4 '13 at 15:25

The equation, properly understood is:

$$E = \gamma m c^2$$

where $m$ is the invariant mass (or the deprecated "rest mass").

Now, for a photon, the invariant mass is zero. But this does not imply that $E$ is zero since the Lorentz factor $\gamma \rightarrow \infty$ as the speed goes to c. Thus, this equation has an indeterminate form for a massless particle with speed c

However, from the relativistic energy momentum relation,

$$E^2 = (pc)^2 + (mc^2)^2$$

we see that, for a massless particle,

$$E = pc$$

Thus, the energy and momentum for a massless particle are proportional.

• Just a question bugging me here: in what literature is "rest mass" deprecated? – user34134 Nov 23 '13 at 2:59
• @GustavoColvero, for example, scitation.aip.org/content/aapt/journal/ajp/77/5/10.1119/… "The concept of relativistic mass, which increases with velocity, is not compatible with the standard language of relativity theory and impedes the understanding and learning of the theory by beginners. The same difficulty occurs with the term rest mass." – Alfred Centauri Nov 23 '13 at 3:10
• the troubling with relativistic mass I get. It's just that the part "The same difficulty occurs with the term rest mass" is kinda new to me. Thanks for the heads-up. – user34134 Nov 23 '13 at 3:40

$E^2 = (mc^2)^2 + (Pc)^2$ Where $P$ is the linear momentum of the particle. Therefore a particle can have Energy even if it does not have mass. In the case of photons, you don't have mass but you have momentum given by Broglie's relation $P=h/\lambda$.

The equation E = mc^2 is the conversion, not declaration, it told you that if you convert mass to energy, you will get energy, and if you convert energy to mass, you get mass

Photon is pure energy (it is particle) it can be converted to mass and it will be gone while itself have no mass