# How confident are we that mass is not being lost in the universe?

After reading about the latest super-massive black hole in Nature 518, 512–515 (26 February 2015), I couldn't help but wonder if the accelerating expansion is a result of mass being lost.

My reasoning is as follows:

1. If the early universe had a particular (greater) mass than at present,
2. Then "space-time" could have had a "momentum" (determined by that mass) [1],
3. And that post-big-bang expansion was being retarded by existing mass [2],
4. But since then mass has been lost to the universe [3]
5. Which reduces the (retarding) due to gravity (less mass) [2]
6. Resulting in the "space-time" of the universe expanding faster [4]

I was never a cosmologist, so please point out which of my assumptions are provably invalid!

[2] I'm struggling to remember my undergrad physics - would two particles each with an initial velocity moving away from each other in a gravitational field (relatively) speed up if the gravitational field is reduced?

[3] Major assumption on my part!

[4] Maybe!

So I guess there are two questions here:

A. How confident are we that mass is not being lost in the universe?

and

B. Would such a mass-loss be able to explain the observed accelerating expansion?

• Hi first off I would say that the amount of mass-energy in the universe is believed to be conserved, constant through time. So although you can convert mass into energy, you still wind up with the amount of mass-energy in the universe always staying the same. What spacetime is made out off I have no idea, it depends on what hypothesis you believe in. It is just viewed as a place where things happen, like a stage before the actors appear.
– user74893
Mar 18, 2015 at 19:30
• Also it is generally accepted that we can only see a small piece of the universe, as the light from further parts has not yet reached us, so estimating how much mass there actually is in the universe is a difficult problem to put a value to.
– user74893
Mar 18, 2015 at 19:37
• You say And that post-big-bang expansion was being retarded by existing mass. The big bang is thought as containing all the mass and energy of the universe. All as energy at the start then some energy was converted to mass, as the temperature dropped. that would mean there was no other existing mass. It was all contained in the big bang. I know, it's impossible to get a mental picture of that, that why math is used so much, you spend more time working out equations than trying to visualise it in a commonsense way
– user74893
Mar 18, 2015 at 19:53
• These would have been good questions separately... While B is straight-forward to explain, A is certainly going to have an interesting answer. For one we can only describe what's in our light cone from the time of the big bang (the observable universe), whether there's an argument that mass has to be conserved in the observable universe rather than as a whole, or not, is intriguing Mar 18, 2015 at 21:42
• I made a fairly substantial edit. I thought the original question was quite discursive, and contained many sub-questions. If it's not an improvement, please feel free to revert it. Mar 18, 2015 at 22:52

You ask I'm struggling to remember my undergrad physics - would two particles each with an initial velocity moving away from each other in a gravitational field (relatively) speed up if the gravitational field is reduced?

To answer this part of your question, gravity only works in one way, pulling things together, never allowing them to move away from each other. If the gravity field was reduced, then they would still come together, just more slowly than before

• True, I misunderstood that. I should have read more carefully /: Mar 18, 2015 at 22:39
• hello, i made a substantial revision to the question that removed that sub-question. it might be reverted... Mar 18, 2015 at 22:57
• What I intended was this: If two particles are given a velocity away from each other (in a system with other masses distributed about), yes, their gravitational attraction will cause them to slow down, stop and eventually start moving toward each other (actually, the mass centre). However, in the mean time, if the "other" mass in the system is reduced, the rate of slowing down will decrease. So what will an observer measure? I realise that they will never see an increased velocity, unless there as another driving force that was unaffected by the mass loss. Mar 19, 2015 at 18:33
• @KevinM 2 main points that I would make, conservation of total mass-energy of any system is paramount (in the part of the universe know about at least), so the total of the particle's kinetic energy plus their potential energy always stays the same. Secondly, potential energy will always be minimised, given half a chance. e.g. an apple will always fall down if you hold it up and then let it go, so minimising it's potential energy (apologies if this is obvious to you). Best regards
– user74893
Mar 19, 2015 at 19:17
• >> How confident are we that mass is not being lost in the universe? << *

Mass (energy) can be lost in principle: if you convert mass to radiation (which you can, because mass and energy are equivalent), the radiation density dilutes with the growing scale factor to the 4th power because of the redshift, while mass density only dilutes with the scale factor to the third power (because volume is lenght³). So while the total mass provided by matter stays the same even when it thins out while the universe expands, the energy provided by radiation shrinks because the photons do not only get spread out like normal matter but also get their wavelengths increased and therefore their frequency reduced. Because not only mass is equivalent to energy, but also energy to frequency, energy (and therefore mass if you wanted to convert it back later) can be lost.

• I don't think you can use an argument of reduced density to say any energy (or mass in turn) is lost, because that would suggest individual photons (as a stand in for radiation) either disappear entirely or lose energy due to redshift (which is problematic). Mar 18, 2015 at 22:42
• but photons do loose energy while the universe expands, the photons which make up the 2.75 K CMB radiation once had a much higher temperature when the universe was smaller. they did not only dilute like normal matter, but also get stretched! Of course they never disappear completely, but the limit of the wavelength goes to infinity as the limit of the scale factor goes to infinity. So in the end you have the same amount of photons, but all redshifted and therefore carrying less energy. Mar 18, 2015 at 22:46
• Ok, I see what you're saying, but it's incorrect to directly compare the frequencies of photons from different reference frames. You can alter the redshift of CMB photons by moving towards or away from their source direction, but that doesn't change the energy for some other observer, so why should any other type of redshift change its energy? Mar 18, 2015 at 22:54
• the photons loose frequency relative to everyone sitting on a comoving coordinate (en.wikipedia.org/wiki/Comoving_distance), and from any direction. if you would accelerate to the front to cancel out the redshift in the front direction, the redshift from the back would increase even more than it would anyway. so there's no way around, because you can't accelerate in every direction at once. Mar 18, 2015 at 23:01
• ok, a better example - on the surface of a sufficiently massive object, the gravitational field can be 'tuned' (via the mass) to approximately compensate for the CMB redshift. in such a situation the energy is recovered no? Mar 18, 2015 at 23:32