jcap
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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## ?
$$\lambda=\frac{h}{mc}.$$
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## ?