While that's the common understanding, general relativity tells us that the spacetime curvature is dictated by the stress-energy tensor, which is accounts for all different types of mass and energy. For example, if you have a crystal at very low temperature it will gravitate less than the same crystal at a high temperature (though for familiar materials it is a VERY slight effect).
Oh wow TIL. So, say a neutron star has stronger gravity than given by its mass alone, due to its energy density? What fraction of gravitational force are we talking roughly for such an object?
Edit: Do photons have gravity even though they are massless?
Edit2: Is that why gravity can bend photons?
GRT suddenly makes a bit more sense to me if the answer to these are 2x yes, so thank you!
The issue is the speed of light is so big. So, you need a LOT of energy in order to source gravity comparably to just a little bit of mass (essentially, because E=mc^2 -- or perhaps phrased more clearly in this case, m = E/c^2).
Even Newtonian Gravity can bend light classically, by Galilean relativity. But, weirdly, it essentially hinges on the fact that the the mass m of the photon cancels from m*a = GmM/r^2. Of course, that is really the equivalence principle---the acceleration of all things under gravity's influence is the same.
Whether or not light is a source of Newtonian gravity... I'm not sure. It's a tricky question because m=0. I want to say no because the "equal and opposite" forces should both be 0, even though one of them effects an acceleration on the other. I should emphasize that I'm not sure!
In Einsteinian gravity, the paths of photons (and indeed all things) are bent because spacetime itself is curved.
Classical electromagnetic static fields and waves certainly have an energy density that can source gravity, and individual photons do too. But their energy is on the order of hbar. So you're talking a source of gravity like hbar/c^2. THIS IS REALLY TINY unless the photon's frequency is ENORMOUS.
To me, the speed of light is actually really slow - meaning, if you think classically you assume c infinite (at which point, as far as I understand, relativity theory essentially behaves like classical physics).
Learning that information travels way slower than the universe expands is quite unnerving. Similarly, learning that earth's fate could be determined already since hundreds of thousands of years through a hypernova directed at it - that we'll only know about when it hits us and wipes out our atmosphere. Well... light speed is far too slow for my taste ;).
Edit: It still doesn't answer my first question though: If you have something really energy dense like a neutron star - what fraction of gravity does energy make out then? 1E-3? 1E-10? 1/2? I'd find that interesting to know. According to wiki, neutron stars fall in temperature within years of creation from up to 1E12 K to 1E6 K. Six orders of magnitude. Depending on how much this decreases gravity I could imagine this effect alone influencing stellar orbits (I assume that a supernova would still allow other stars in a multi star system to continue existing). Has such a thing ever been measured?
Sorry.. there's just a whole can of worms opened about this in my head right now. Need to find an astro physicist to shake down :D.
Watch that youtube link in my sibling comment first, but I actually wanted to take a crack at an answer. What's the change in mass, ∆m, as the star cools? We'll assume the mass of the neutron star is 1.5 solar masses.
E = mc^2
∆m = ∆E/c^2
So really, what's ∆E? A hyper hand-wavy estimate:
∆E = Q = mc∆T (c being specific heat)
Specific heat by mass is really hard to predict, but by moles it is fairly constant, well within an order of magnitude. So we'll discuss mass in moles.
m = neutron star moles
m = (mass of neutron star / mass of neutron) / Avogadro's #
m = 2.9580163e33 mol
c = 24 J / (mol * K)
∆T = 1e12 K - 1e6 K
Substituting that back into the original, as a neutron star cools:
∆m = 7.0991681e45 J / c^2 = 7.89888982e28 kg
Which is like 2.6% of the mass of the original star, so a pretty solid chunk. But that number is pulled out of my ass—I am not a physicist.
But there are even more weird effects going on, due to the warping of gravity the mass of neutron stars can be up to 20% less than you'd expect based on its baryonic (neutron) constituents (questions 4 and 7):
About your last equation, wouldn't J/m^2/s^2 come out as kg? 7.9E2 would be very low then, no?
I wonder how much energy is stored electromagnetically and through nuclear forces though. These things are supposed to have extremely strong EM fields and I imagine every piled up nucleus like a little atomic spring that has been depressed as much as possible. Wouldn't most of the stored energy be in there?
