# Using mass of the observable Universe to estimate an energy equivalent

For quite some time now, physicists have been able to estimate the mass of the observable universe.

Reportedly it's around $10^{50} \:\mathrm{kg}$.

There is also general relativity, which states that $E=mc^2$.

If we can calculate the energy equivalent of the observable Universe, can we extend the same logic to the rest of it?

Let's leave electromagnetic radiation out of the picture for starters, since I know nothing about neither average photon density nor spectral distribution. Although if anyone does, please feel free to elaborate.

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Conservation of energy doesn't apply to cosmology. General relativity doesn't have a conserved scalar mass-energy that can be defined in all spacetimes.[MTW] There is no standard way to define the total energy of the universe (regardless of whether the universe is spatially finite or infinite). There is not even any standard way to define the total mass-energy of the observable universe. There is no standard way to say whether or not mass-energy is conserved during cosmological expansion.

The WP article you linked to discusses these points. You've picked a number out of the article without paying attention to the text surrounding that number, which says that the number doesn't really mean much and can't be extended in the way you suggest.

MTW: Misner, Thorne, and Wheeler, Gravitation, 1973. See p. 457.

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And you certainly can't apply the special-relativistic $E=mc^2$ to the entire universe. Special relativity doesn't work when you consider large enough volumes of spacetime that gravity becomes important. – Ted Bunn Jul 26 '11 at 17:07
@Ted Bunn: Does gravity change the amount of mass? – Jaanus Jul 26 '11 at 17:15
This question needs to be much more specific before it'll have a well-defined answer. What physical system are you imagining? How, operationally, do you wish to define "amount of mass"? – Ted Bunn Jul 26 '11 at 17:22
@Ted Bunn: You are right, it seems that I assumed the "common" interpretation of mass as a collection of particles. Apparently things work differently in general relativity. For a layman it is easy to forget that in physics one deals with models, not the perceptible reality models seek to describe. – Jaanus Jul 26 '11 at 17:38
@Jaanus: Dark energy certainly changes the total amount of mass. The density of dark energy does not change even as the universe expands, meaning that the total amount of dark energy increases. But if you interpret it as "total number of baryons", this is conserved, except perhaps in the very early universe, or by some as-yet unknown dynamics of dark matter. – Jerry Schirmer Mar 14 '12 at 5:37