# What is going on with star's energy?

The sun radiates $3.8 × 10^{26} J$ energy each second, this energy is absorbed by various celestial objects but most of it is reflected or emitted back in the space, similarly there must be energy pouring into empty space from various star systems, what is happening to all this energy ? In what form is it thriving if it is thriving ? Does it ultimately get absorbed by various objects ? Is it bringing some kind of change to the motion of galaxies etc ? Is there some sort of energy sink somewhere ( maybe getting sucked in by Black holes) ? Does it somehow combine and form new bodies via energy mass equivalence ? what is happening ?

Addendum : This maybe a on the edge of site's mainstream physics discussion policy, but till now all I understood was that no definitive proof of where the energy is going is available, @ John rennie says that due to red shift the wave's are losing energy, he says that energy density is tending to zero, but there is no account for this energy. At the same time, @Thriveth mathematically asserts that the universe is losing energy, I find it a bit of a controversial topic regarding energy conservation and can't shake off the idea that maybe this energy could account for dark energy/matter.

I add, millions of stars have died/ emptied their energy into the space since the beginning of time, by the logic of either answer, red shift or violation of energy conservation we can say that this energy is somewhere we can not account for, similarly we till now can't account reasons for dark matter/energy can't we explain both of these with each other ?

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–  John Rennie Jan 14 '14 at 17:53
I have read this article before too, but this explains why we do not see all the stars or a completely lit space, this does not explain the question of where the energy is going ! All I can understand from it is that the light from all the stars never reaches us, but still where does it reach to ? What finally happens ? –  Rijul Gupta Jan 14 '14 at 17:59
Well, "finally" hasn't happened yet... there's a lot of photons zipping around out there :-) –  Carl Witthoft Jan 14 '14 at 18:03
@Carl : I suppose extrapolations based on current observations can be made, maybe not proven but made all the same. –  Rijul Gupta Jan 14 '14 at 18:21
Space is big, really big. So most of the photons don't end up hitting anything –  Martin Beckett Jan 14 '14 at 18:34

There are two fates awaiting light emitted from stars.

Firstly light may be absorbed by various forms of matter. The majority of absorption will be by dust clouds since the disks of stars, planets etc cover a tiny fraction of the celestial sphere. This light heats the dust clouds and they in turn reradiate the energy as lower energy (e.g. infra-red) photons. So dust clouds, or any other form of light absorbing matter, only delay the transmission of light and lower its wavelength.

Secondly, all light eventually gets red shifted by the expansion of the universe - to zero energy/infinite wavelength given infinite time. Even light that is absorbed by matter is reradiated then subjected to the same cosmological red shifting.

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Doesn't the energy lost in red-shift lets say x J reappear as something else ? It must so as to facilitate conservatiob of energy, right ? –  Rijul Gupta Jan 14 '14 at 18:20
Once the dust cloud has reached equilibrium it radiates the same amount of EM that it absorbs. However it radiates at longer wavelengths. –  John Rennie Jan 14 '14 at 18:48
I completely agree, but as you say in your answer emission of zero energy waves would be taking place, where is the energy going ? –  Rijul Gupta Jan 14 '14 at 18:51
As the universe expands the energy of the light is spread over an increasing volume of space, so the energy density tends asymptotically to zero. –  John Rennie Jan 14 '14 at 19:20
Your assertions seems to be based on saying that the volume of universe/space is increasing much faster than the energg that is being poured into it, can you prove it ? And even if energy density tends to zero, it does not explain what is happening to it ? I also thought maybe that it is accelerating the expansion or has something to do with dark energy. –  Rijul Gupta Jan 14 '14 at 19:23

The, maybe somewhat surprising, answer is that it disappears.

When a photon is emitted, it travels a distance before it is then absorbed, re-emitted etc.; theoretically forever. However, while the photon is travelling the enormous distances of Space, it is redshifted due to cosmological expansion.

It is true what @John Rennie writes above, that this means that the photons' energy is "smeared" over a larger space and thus the energy density in general is decreasing. But that is not the whole story! This would be the case if we were talking about matter - same amount of matter in a larger volume means a correspondingly lower matter density, even though the amount of matter is unchanged. if $a$ is the scale factor of the Universe, matter density drops off as $\propto a^{-3}$, while a co-moving volume increases as $\propto a^3$. So, the density times the volume, which is the total amount of matter, goes as $\propto a^{-3}a^3=\text{const.}$

However, for photons it is different. On top of the "smearing" that matter also undergoes, photons lose their energy as $\propto a^{-1}$. So all in all, the energy density of photons drops off as $\propto a^{-4}$, while the volume of the Universe only grows as $\propto a^3$. The energy of photons goes as $\propto a^3a^{-4}=a^{-1}$ - it is not only the energy density that is dropping; the Universe is losing energy!

Again, this is surprising to most (including me when I learned it), but conservation of energy simply doesn't hold true globally in General Relativity. This enjoyable article by Tamara M. Davis explains it very nicely in a bit more detail than I can here (and she's also a lot smarter than I am).

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Davis' article actually argues that the Universe neither conserves nor loses energy - the total energy of thew Universe is simply undefined. And that if you look at it one way - the way I presented above - the Universe seems to lose energy, but you can also look at the cosmological redshift like a Doppler shift (mathematically equivalent), in which case the Universe does not lose any energy. But where Energy is not conserved, the question "what happens to the energy" is still not a well-defined one.

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Isn't it possible to consider this disappearing energy as the cause of dar matter/energy if we simple can't explain wherr this energy fs going and untill now haven't found particles responsible for dark matter/energy ? –  Rijul Gupta Jan 15 '14 at 10:18