Can the laws of gravitation be extended to two energies? Is there a a force of attraction similar to gravity among two energies? (Excluding things like magnetic or electric attraction).
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3$\begingroup$ define "two energies" $\endgroup$– SecretCommented Aug 24, 2016 at 11:08
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$\begingroup$ Possible duplicates: physics.stackexchange.com/q/6197/2451 , physics.stackexchange.com/q/22876/2451 , physics.stackexchange.com/q/60020/2451 and links therein. $\endgroup$– Qmechanic ♦Commented Aug 28, 2016 at 7:21
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1$\begingroup$ Well, Hogwarts is much better in magic as in physics. Thus, also your question looks rather magical, as physical. :-) $\endgroup$– peterhCommented Aug 28, 2016 at 18:02
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Yes the laws of gravitation, more specifically general relativity, take energy into account, but we need to precise about what this means.
Suppose we are considering only matter. Then we would start with the matter distribution and calculate the curvature of spacetime. Having done this we can calculate how the curvature affects the motion of the matter i.e. the gravitational acceleration.
If we now include energy the first step is the same as with just matter. When we calculate the curvature of spacetime we use Einstein's equation:
$$ G_{\alpha\beta} = 8\pi T_{\alpha\beta} $$
where the left side $G_{\alpha\beta}$ is related to the curvature and the right side $T_{\alpha\beta}$ is the stress-energy tensor that describes the distribution of matter and energy. Note the and energy part. For example if we are caculating the curvature due to some distribution of matter we have to include the kinetic energies of the masses involved. In most cases the energies make an insignificant contribution, but they are in principle included in the calculation.
The second step is to calculate how the curvature affects the motion of the objects involved, and here we run into a problem because the term energy is ill defined. The only interpretation of this that makes sense is if the energy is an electromagnetic wave e.g. a light beam. In that case we can calculate how the motion of the light beam is affected by the spacetime curvature, and we call this gravitational lensing.
The last question would be if there is matter involved at all, for example if there are just two light beams. The answer is that the energy in the light beams does cause spacetime curvature and this does cause the light beams to curve. So in this sense the two energies do attract each other. However this is a rather subtle calculation. For example two parallel light beams travelling in the same direction do not attract each other but two parallel light beams travelling in opposite directions do attract. See Do two beams of light attract each other in general theory of relativity? for a discussion of this.
answered Aug 28, 2016 at 6:14