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First, the inspiration for this question:

I just read that it takes one hour to send a picture from the New Horizons space probe, to Earth. It also takes around 5 hours for that picture to reach earth.

This means that there are about 4 pictures "floating" in space, somewhere between Pluto and earth.

This information is energy, and energy contributes to gravitation somewhere between Pluto and Earth at this moment.

Is this last assertion correct?

If so:

The sun outputs $10^{26} \text{ watt}$ of energy. It's been doing that for more than 4 billion years. In the observable universe, there are between $10^{22}$ and $10^{24}$ stars.

If the average star is similar to the sun, and we ignore energy that has been stored in planets, then up to $10^{(26 + 24)} = 10^{50} \text{ watt}$ of energy is being added to "empty space".

4 billion years is something like $10^{17}$ seconds (rounded down).

This means that there might be as much as $10^{(50+17)} = 10^{67} \text{ J}$ of energy, just moving about the universe.

Is this negligible?

The amount of energy is probably much higher than $10^{67}\rm\,J$, as I do not take into account light that was emitted more than 4 billion years ago. It also does not take into account stars beyond our observable universe.

I apologize for using very simplified estimates, but since the numbers are so big the errors become less important. I have naively used $E=mc^2$ to go from joules to kilograms. I get something like $10^9$ Milky Way masses.

Is this energy taken into account, when scientists say that the universe is expanding? I have a feeling that this energy would make it appear as if the universe is expanding faster.

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    $\begingroup$ It's not clear to me what you're asking. It seems to me you're enquiring about the Universe becoming lighter because of all that mass being converted to electromagnetic radiation and how that could influence the expansion of the Universe. Am I right? $\endgroup$ – Gert Oct 9 '15 at 1:15
  • $\begingroup$ @Gert No, I don't think it is possible for the universe as a system to become lighter - but I think that a substantial portion of the universes' energy is "in transit" in the form of radiation, and I am asking if this is taken into account when calculating the distance to other very distant objects. $\endgroup$ – frodeborli Oct 9 '15 at 9:20
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There absolutely is a contribution to the energy density of the universe due to radiation. It's small compared to baryonic matter, dark matter, or dark energy, and is mostly due to the cosmic microwave background (CMB) left over from the Big Bang. Sure, the CMB is faint here compared to the Sun, and faint within the Galaxy compared to the light from nearby stars; but the CMB fills the entire volume of intergalactic space more or less uniformly, while starlight from galaxies peters out like $1/r^2$ as you move into the void. Volume-averaged, the CMB wins.

The Particle Data Group quotes number densities \begin{align} n_\text{photon} &= \rm 410.7 \,cm^{-3} \\ n_\text{baryon} &= \rm 2.482\times10^{-7}\,cm^{-3} \end{align} for CMB photons and baryons — that is, there's about two baryons for every three billion photons. But baryons (protons and neutrons) each have a rest energy \begin{align} m_\text{baryon}c^2 &= 940\,\text{MeV} \end{align} while the CMB photons have energy \begin{align} E_\text{photon} &= k T_\text{CMB} = 86\, \frac{\mu\rm eV}{\rm K} \cdot 2.7\,\rm K \\ & = 230 \rm\,\mu eV. \end{align} This energy ratio $E_\text{baryon} / E_\text{photon} \approx 4\times 10^{12}$ counterbalances the number density ratio $n_\text{photon}/n_\text{baryon} = 6\times10^{-10}$, so that the energy density of the universe due to baryons is about 70 times larger than the energy density due to radiation. Since the baryons only make up about 5% of the energy density anyway, it's safe to leave the radiation density off in most discussions.

You've computed $10^9$ Milky Way masses' worth of stellar radiation emitted in the last third of the age of the Universe. If we guess there are about $10^{14}$ Milky Ways out there, my estimates give about $10^{12}$ Milky Ways worth of cosmic microwave background photons, which leaves plenty of room for your starlight to get lost in the noise.

So, your assertion is correct! Your arithmetic looks plausible! But the effect can be neglected.

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  • $\begingroup$ But just an elaboration: if - for example the universe was 10000 times brighter in the first quarter of it's life, then my number becomes 10^13. 10000 is just a quess, it might have been 10^10 times brighter the first 1 billion years. (this energy output is now "contained" inside black holes") And we're still ignoring half of the universe life time. Correct? But obviously, we can only speculate how bright the universe was in the beginning. $\endgroup$ – frodeborli Oct 9 '15 at 9:25
  • $\begingroup$ Could not "dark energy" = "background radiation"? $\endgroup$ – frodeborli Oct 9 '15 at 10:11
  • $\begingroup$ The early universe was "radiation dominated"; after it cooled it became "matter dominated"; currently it is "dark energy dominated." Dark energy has a different equation of state from the cosmic microwave background. $\endgroup$ – rob Oct 9 '15 at 23:17
  • $\begingroup$ Actually the photon number density is $$n_\text{photon} = 410\mathrm{\,cm}^{-3} \left( \frac{T}{2.723\rm\,K} \right)^3;$$ if you go back in time you're dealing with a smaller, hotter universe where the CMB is more important. The CMB was emitted when literally every atom in the universe went from ionized to neutral; radiation from photospheres will never compete. $\endgroup$ – rob Oct 9 '15 at 23:25
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Is this energy taken into account, when scientists say that the universe is expanding? 

Yes and no. Firstly, we see the universe is expanding rather directly, and try to figure out how many stars there are and how much they are putting out and use the different to figure out dark energy and dark matter. So when we estimate dark matter and dark energy, we take that energy into account.

But we'd pretty much how much the universe is expanding by just looking at it and measuring it rather directly.

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  • $\begingroup$ We only see that the universe is expanding based on red-shift. Between us, and the other star, there is a substantial amount of energy as photons. The amount of energy affecting light traveling from the distant star should be a function of the distance, and I'm just speculating that it would allow us to see greater red shift than if this energy was not there. The fact that the universe seem to be expanding at accelerating speeds seem counter intuitive (cosmological constant) and I believe somehow it could be collapsing, but appear to be expanding at the same time, confirming Einsteins blunder. $\endgroup$ – frodeborli Oct 9 '15 at 10:09
  • $\begingroup$ @frodeborli We don't know the universe is expanding. We make observations to infer the red shift and the distances and then get expanding universes as the only large scale isotropic and homogeneous models consistent with the large scale trends. There are epochs where the universe is radiation dominated and ones where it is matter dominated. But when we observe an expansion and then the amount of energy and matter we see doesn't match, we infer dark matter. $\endgroup$ – Timaeus Oct 9 '15 at 15:06
  • $\begingroup$ @frodeborli The dark energy is different, no amount of regular energy or matter could explain an accelerating expansion, so we just use the observed acceleration to infer dark energy. You seem to have all your inferences backwards. $\endgroup$ – Timaeus Oct 9 '15 at 15:06
  • $\begingroup$ I believe that energy in the form of radiation could make it appear as if the universe is expanding, while it actually is collapsing. I.e. the red shift does not come from expansion. $\endgroup$ – frodeborli Oct 10 '15 at 16:30
  • $\begingroup$ @frodeborli Don't believe that. Do the math instead. Make a mathematical model of a homogeneous isotropic spacetime with some radiation and some visible matter and some dark matter and some dark energy. You will notice that every model with zero dark energy has no accelerating expansion and that every model with only as much visible energy and visible matter we see is expanding faster than we see. No believing, instead we make models and compare with observation. It's science. $\endgroup$ – Timaeus Oct 10 '15 at 19:20

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