Hi Jim, I found the quote in the FAQ:
https://www.physicsforums.com/showthread.php?t=506985
There was also an earlier (March 11, 2011) post by Ben Crowell which looks identical
https://www.physicsforums.com/showthread.php?p=3183075#post3183075
It's not entirely clear to me why Ben says the total mass-energy of the
observable universe cannot even be
defined.
Let's quote the whole paragraph, so as not to take it too much out of context:
"One can also estimate certain quantities such as the sum of the rest masses of all the hydrogen atoms in the observable universe, which is something like 10^54 kg. Such an estimate is not the same thing as the total mass-energy of the observable universe (which can't even be defined). It is not the mass-energy measured by any observer in any particular state of motion, and it is not conserved."
Personally I don't see why you can't define it. The "observable universe" is definable in a practical approximate way although its extent changes over time. I suppose it could be defined as the spherical region around an observer at CMB rest which encompasses all the material he can in principal have gotten some type of signal from, even if he doesn't yet have the technology to detect every type of signal.
We have a pretty good idea of the RADIUS (which is gradually increasing as time goes on--even discounting expansion, more and more material is actually or potentially "heard from" and gets included.)
If you know the concept of "comoving distance" (the proper or freezeframe distance at a definite modernday epoch e.g. Jan 1, 2010, so that expansion doesn't affect it) then you can say the comoving radius of the observable region is increasing (as light etc from more and more distant stuff comes in) and it is now roughly 46 billion ly.
We have a pretty good idea of the mass-energy DENSITY within this comoving radius of 46 Gly, centered at where Solar System currently is. (say from CMB stationary observer standpoint, which is often adopted in this kind of talk.)
So I personally don't see why the mass energy inside that sphere (say including ordinary+dark matter plus radiation) is not DEFINABLE.
But I think the important point the FAQ is making is that it is not CONSERVED. For two reasons:
1. the observable region is not a fixed region, as time goes on it comprises more and more stuff. So it would be crazy to expect energy to be conserved when you aren't even talking about the same region, from year to year.
Percentagewise the change is so tiny as to be ignored but still, it's not a fixed region.
2. even in a fixed region, with say some definite fixed comoving radius, you wouldn't expect total mass-energy to apply because the geometry is changing, distances are increasing over time. So the basic assumption of the energy conservation theorem (by Noether 1915) is not met. Expanding distance is especially hard on radiation because it affects a photon's wavelength. If you double a photon's wavelength, you cut its energy by half.
Google "energy not conserved in expanding universe" to get an essay by Sean Carroll which gives what I think is a fair balanced nontechnical discussion. Also check our own PF FAQ. And it's great if you find stuff that you don't think is clear or consistent for some reason and want to give feedback! I'll make a thread in case there's more from you or others.
extra info: google "Emmy Noether" She was 33 when she proved her conservation theorem. It explains why (in which circumstances, under which assumptions) quantities like energy, momentum, and rotational momentum are invariant.
http://en.wikipedia.org/wiki/Emmy_Noether
(gnarly technical account:
http://en.wikipedia.org/wiki/Noether's_theorem )
