# Are there more bosons or fermions in the universe?

The question is in the title: are there more bosons or fermions in the universe? Or is there the same number of bosons and fermions?

I think there is the same number but I don't know why exactly.

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I don't think you can quantify it: there are virtual particles as well making both numbers $\infty$. But I think the answer lies in how many photons are given off in a single fusion reaction in a typical star. –  Manishearth Mar 8 '12 at 11:14
Knowing the average star color and average energy per reaction; I guess it could be calculated. –  Manishearth Mar 8 '12 at 11:15
Hmm, there are a lot of neutrinos out there ... –  John Rennie Mar 8 '12 at 11:33
@JohnRennie aah yes we'd have to include those in our calculations. I could Google the data, but I'm no astrophysicist so I don't know how applicable the average values are(if they exist). –  Manishearth Mar 8 '12 at 12:04
Do you mean fundamental bosons and fermions, or can they be composite? For example, mesons are composite but photons are elementary. –  Phil H Mar 8 '12 at 12:08

Broadly fermions are associated with matter, and bosons are associated with exchange (force mediation), at least if we are considering elementary particles. A given matter particle will produce and absorb many many exchange particles in its lifetime, so we can guess that there are more bosons than fermions.

It is not, however, fixed. A photon can be converted to an electron/positron pair, which would reduce the number of bosons by 1 and increase the number of fermions by 2. So at different times and places, the balance will be different, including at different stages of the evolution of the universe.

Immediately after the Big Bang, it is theorised that the universe was so small and dense that only photons existed; any matter particles created would be immediately obliterated. However, as the universe cooled, matter particles could survive long enough to form structures, until we have the cooler universe we see today. Perhaps, if the universe survived long enough and expanded far enough, particles would be so far apart that they would experience very little force and the balance would be in favour of fermions. But unless something changes significantly, the structures of matter - atoms, nuclei, crystals - are all stable and involve continual exchange of bosonic particles to mediate the forces that maintain them.

Finally, remember that at quantum scales everything is probabilistic; we cannot say that a photon exists or not in the classical sense until we measure its effect, so there can be many virtual particles with some probability that we do not measure for every particle that we do. For some fairly involved discussion of it, see Quantum Electro-Dynamics, and the electron self-interaction problem. It involves all the possible paths of electrons interacting with themselves, and held up fundamental quantum field theory for quite a while.

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Neither the number of bosons nor the number of fermions notr their difference is conserved in nature. This means that these number change all the time.

Should they be equal by coincidence for some time, this would last only for a moment. Even such a coincidence would be extremely unlikely, given the huge number of particles in the universe.

Edit: I had added in the discussion to other answers that due to the infrared problem, the number of each kind of massless particles (in particular that of photons, but possibly also that of one species of neutrinos) is infinite.

This makes the answer to the question somewhat trivial: If there is a massless species of neutrinos (still a possibilty - we now only know that not all neutrinos are massless), the answer would be yes, though not for an interesting reason, as both numbers are countably infinite and hence equal. On the other hand, if all neutrinos are massive, the answer would be no, as there are then infinitely many bosons but only finitely many Fermions.

The real answer to the question is is that counting particles makes no sense; particle number is not a physically relevant observable, and tells nothing interesting about the universe. (Except perhaps an entry in the Guinness Book of Records - but isn't the universe extremal in every respect?)

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The question may be unanswerable because I'm pretty sure the number of photons is variable depending on your relativistic frame. At least that was an interesting observation that Feynman made, almost apologetically, in some of his early work; I'd have to look up the specific reference. (Hmm. Feynman's idea there would require variable-count photons to be generated in spin-cancelling pairs...)

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The number of soft photons in a scattering event is in fact infinite due to the infrared problem. Thus the question is, strictly speaking, meaningless. –  Arnold Neumaier Mar 8 '12 at 13:31