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At first I thought this an easy answer. Simply, no. Einsteins famous equation E=mc^2 shows us that energy and mass are directly proportional, so without mass, the value of E= 0. But after thinking some more it doesn't seem like such an easy answer. For example, light carries both energy and momentum in the form of photons, yet photons are said to be massless. How can they be massless when they carry energy and momentum? I'm still a little confused about the whole invariant/relativistic mass concept.

Also, vacuum energy is said to be an energy that exists in space even in the complete absence of matter. Again, how can this energy exist without matter?

So, to make things easy, I'd just like to know: Can energy exist without mass? And, if possible, could someone please explain the points stated above about the energy of massless photons and vacuum energy. Thanks.