# Q & A: radiation mass density

Q:
I think this question has been asked on this website before, about the matter equivalent of the light in the universe, but I would like to put it in a more game like manner, a grosso modo way of calculating such a content.I will suppose I have my own universe with this properties, for simplicity:- it's 10 billion years old, so 10^11 years, roughly 3.1 * 10^17 seconds- it has 100 billion galaxies so 10^12- each galaxy has 100 billion stars so 10^12- each star is medium in size and just like our sun- the power output of the sun is 3.8 * 10^26 watts- the stars don't suffer from state changes due to the nuclear changes that normally occur...in this universe they stay the same ((_:=> the total energy output from their birth is about 12.4 * 10^67 joules and that dynamic mass is roughly 1.33 * 10^51 kg the mass of sun is roughly 2 * 10^30 kg so we get... some 10^21 solar masses equivalent which my universe released in an initially empty space.Once again, this is just a mathematical universe ((_: I would like to point out that by changing a little the time and energy output we can get higher values, which is significant because we are in this scenario 10^3 orders of magnitude below the actual numbers of suns. Making the universe bigger can actually reach to results like having more mass as light than as matter. Having different generations of stars (as the universe gets younger we should introduce a greater density of short living stars, but very large, which are far more energetic than the average sun). This reduces to a very simplistic reasoning and here I would to ask: If I have let's say a 9:1 ratio of light to matter it just means that in time, 90% of the available matter "converted" into energy?
- Stefanescu Marian (age 20)
Cluj Napoca, Romania
A:

Your calculation can be greatly simplified, reducing the number of places that errors can creep in, e.g. in converting 100 billion to exponential form.  Take one star and ask whether in its lifetime the radiation emitted has mass comparable to the star's mass. Take your power output of the Sun, 4*1026 W times the total lifetime of a star like that, around 1018 s, to get around 4*1044 J radiant energy. That's 4*1027 kg. As you say, that's a little more than 1/1000 of the Sun's mass. The point of doing the calculation this way is that you see right off that changing the number of stars doesn't change that ratio. It will come out different for different types of stars, but you'll still end up with most of the energy as star rest energy, not radiation.

In the long run as things clump into black holes and then (we believe) evaporate via Hawking radiation stars will turn into a thin radiation soup, but that's a much, much slower process.

Mike W.

(published on 04/20/2017)