# Does infinite energy imply Infinite mass (and vice versa)?

If some kind of source was able to supply an infinite amount of energy, does that imply that it also must have an infinite mass? Is the contrary also true?

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Hello cipher. This is an imaginary question. Anyways, Have you taken $E=mc^2$ for that..? – Waffle's Crazy Peanut Oct 20 '12 at 13:49
Indeed i have. E=mc² is what actually made me ask this question – cipher Oct 20 '12 at 14:08
@CrazyBuddy While you grammatical and tag edits were very good, please do not completely change a title like that without firm evidence that you are on the right track. – dmckee Oct 20 '12 at 17:02
The conjecture here is trivially true, but uninteresting because it is non-physical. – dmckee Oct 20 '12 at 17:04

It is very dangerous to talk about infinity in physics, especially when talking special relativity.

To your question: Yes the object would need an infinite amount of mass. E.G. Take a battery that would have an finite amount of energy inside.

Then you would have

$M_{\text{Total mass of the battery}}=M_{0,(\text{the usual Mass of an uncharged battery})}+\frac{E_{\text{Amount of Energy the Battery can supply}}}{c^2}$

Now If you set $\lim E\rightarrow \infty$ of course $M_{\text{Total mass of the battery}}$ also diverges

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For a photon $E = |p|c$. When $p \rightarrow \infty$ its energy $E \rightarrow \infty$ but its mass continues being zero.

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It's rest mass remains zero. But it's gravitational interactions will continue to be dictated by mass-energy just as always. – Colin K Oct 20 '12 at 22:29
I dislike the term "rest mass"; specially for photons, which are never at rest. "Invariant mass" or simply "mass" are better terms. Gravitational interactions are given by the stress-energy-momentum tensor $T_{\mu\nu}$. Setting $m=0$ we obtain the form of the interaction for photons. – juanrga Oct 21 '12 at 11:01