# Particle creation, energy density and the Compton wavelength

• I
• jcap
In summary, the Compton wavelength of a particle is given by lambda = h / mc, and the energy density rho of a particle of mass m can be expressed as m^4 c^5 / h^3. The mass scale m in this expression indicates the level at which particles of mass m may spontaneously appear as the universe cools, but this does not necessarily mean it will occur. Pair creation becomes more likely with higher pressure, but it is not guaranteed to happen. If the pressure is low enough that m is less than the mass of any particle, massless particles such as photons may be produced with an energy equal to mc^2.

#### jcap

The Compton wavelength of a particle is given by
$$\lambda=\frac{h}{mc}.$$
One can construct an expression for the energy density ##\rho## of a particle of mass ##m## given by
$$\rho = \frac{mc^2}{\lambda^3}=\frac{m^4 c^5}{h^3}.$$
What is the physical significance of the mass scale ##m## in the above expression?

Does it mean that particles of mass ##m## will spontaneously appear when the energy density ##\rho## reaches the relevant level as the Universe cools?

Is the expression only correct for fermions as it assumes only one particle (or more correctly one particle/antiparticle pair) per ##\lambda^3## volume?

Once the energy density ##\rho## cools to a level such that ##m## is less than the mass of any particle would one then get massless particles such as photons spontaneously produced with an energy ##h\nu=mc^2## ?

jcap said:
Does it mean that particles of mass ##m## will spontaneously appear when the energy density ##\rho## reaches the relevant level as the Universe cools?
Things cannot spontaneously appear. There can be pair creation, and in general it gets more likely with higher pressure. It doesn't necessarily mean it has to happen. If we plug in 1 eV as an upper bound on neutrino masses we get 0.08 Pa, that is a good vacuum, with no process that would produce any relevant number of neutrinos if the pressure comes from air.