What is the mass of all photons emitted in the universe?

[Louis Nardozi]

What is the mass of all photons emitted in the universe since the Big Bang?

 

[DrGreg]

What is the mass of all photons emitted in the universe since the Big Bang?

Zero

See our FAQ: Do Photons have Mass?

 

[DrStupid]

Zero

That's the mass of each individual photon, but I think the OP reather asks for the total mass of all photons.

 

[sophiecentaur]

Isn't n times Zero still zero?

 

[Kippiis]

Isn't n times Zero still zero?

It is.

 

[jim mcnamara]

Let's try this phys.org precis of a paper that estimated all of the starlight in the visible universe since "time zero":
https://phys.org/news/2018-11-scientists-starlight-universe.html

... according to the new measurement, the number of photons (particles of visible light) that escaped into space after being emitted by stars translates to 4x10⁸⁴

I think the OP wanted a big number. This tidbit fulfills that I believe.

 

[DrGreg]

That's the mass of each individual photon, but I think the OP reather asks for the total mass of all photons.

Isn't n times Zero still zero?

This actually raises all sorts of complications. The answer I gave in post #2 is really the answer to the question "What is the sum of all the the masses of photons emitted since the Big Bang?" But in relativity, the mass of a collection of particles is not necessarily equal to the sum of the masses of each particle. In special relativity, a collection of photons has a non-zero mass, unless all the photons travel in the same direction. In general relativity, the mass of a system isn't a well-defined concept. There are a number of different types of system mass, and some of them make sense only in special circumstances.

The original question asked about all photons emitted throughout the duration of the Universe, and they cannot be considered as a system of particles with a system mass, as photons are being created and destroyed all the time. Even if the question was changed to refer to all photons in existence now (whatever "now" is interpreted to mean), it still doesn't make much sense, I think, to talk about system mass as the photons don't form an isolated system: they are interacting with other particles.

So I think the best answer is $4 \times 10^{84} \times 0 = 0$.

 

[newjerseyrunner]

That's the mass of each individual photon, but I think the OP reather asks for the total mass of all photons.

So zero times infinity?Also, isn't the "number of anything in the universe" entirely non-sensical? If the universe is both homogenous and infinite (both of which we assume) then the total number of photons is infinity, and has been since the electroweak epoch. Before which the number was exactly zero.

 

[DrStupid]

So zero times infinity?

No, it isn't (not only in this special case). Better get the total energy E and the total momentum p of all potons and calculate the total mass according to E²=m²+p² (with c=1).

If the universe is both homogenous and infinite (both of which we assume) then the total number of photons is infinity, and has been since the electroweak epoch.

That's the trivial case. Reading "universe" as the visible universe is more challenging.

 

[Mark44]

So zero times infinity?

$10^{84}$ is a fairly large number, but it's still a finite number.

 

[Louis Nardozi]

I was looking for something along the lines of:

4*10⁸⁴*Percentage of photons still traveling in space (gotta be close to unity)* mass of photon traveling in space.
I wanted to see how it matched up to the amount of "dark matter" or "dark energy" in the universe.

 

[chasrob]

OTOH, a sharp upper limit on a photon's mass, 1.77 x 10^-54 kg, times 4 x 10⁸⁴, gives 7.107 x 10³⁰ kg. A few solar masses, eh?

 

[Vanadium 50]

I wanted to see how it matched up to the amount of "dark matter" or "dark energy" in the universe.

Then you don't need or want the additional complication of integrating over the entire universe. The photon density is enough to compare. It's something like 10^-5 of the total density.

 

[DrStupid]

4*10⁸⁴*Percentage of photons still traveling in space (gotta be close to unity)* mass of photon traveling in space. I wanted to see how it matched up to the amount of "dark matter" or "dark energy" in the universe.

It seems the term "photon" caused a lot of confusion. I think what you actually mean is the total radiation field.