|MadSci Network: Astronomy|
My initial response to this question was that the gravitational force from light (photons) would be extremely small because c^2 (as in E=mc^2) is so very, very large. However, I am not an expert on General Relativity, so I decided to talk to my colleuege, Dr. Ted Bunn about this, this is his response (edited a bit):
You're absolutely right: under most circumstances the mass-equivalent of the electromagnetic energy is very small, because c^2 is large. So, although electromagnetic energy does gravitate just like any other energy, it's usually negligible.
However, it has been measured in at least two cases I can think of:
1. Clever tests of the equivalence principle have shown that electromagnetic energy does gravitate. I'm not talking about light, but about electrostatic energy. (They're both energy stored in the electromagnetic field, of course.) [Moderator's Note: The "equivalence principle" is the foundation of general relativity; it states that the gravitational mass (the number that goes into the calculation of the gravitational force) of an object is the same as the inertial mass (the number that goes into Newton's second law, F=m*a).]
The idea is this: the electrostatic binding energy contributes a small part of the rest mass of various atoms and molecules. (People frequently realize that this is true for nuclear binding energy: it's why a helium-4 weighs less than 2 protons and 2 neutrons seperately. The same thing holds for electromagnetic binding energy, although the effect is much smaller.) If electromagnetic energy didn't gravitate, the equivalence principle would be violated, and material with different chemical compositions would fall at different rates (because the fraction of the rest mass contributed by electromagnetic energy is different for different materials).
This is a tiny effect, but people have gotten to be very good at testing the equivalence principle!
2. We believe that in the early Universe the energy of the photons dominated over the energy of matter. As you go back in time, and the temperature goes up, the energy density of photons rises faster than that of matter ((1+z)^4 instead of (1+z)^3, to be precise, where z is the redshift). So, even though photons contribute a tiny fraction of the energy density today, if you go back far enough, they must have dominated.
Although it's fairly indirect, this has been confirmed observationally: the calculations people do to get the abundances of light elements from big-bang nucleosynthesis are very sensitive to the expansion rate when nucleosynthesis was happening. If the Universe hadn't been radiation dominated at that time, the nucleosynthesis results would be much different.
I can't think of any other examples of times when the gravitation of electromagnetic energy is significant, although there may be some.
Hope that answers your question!
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