The “equivalence” depends upon “rest mass”. A moving mass has inertial momentum, or a total energy of mc^2 + mv, so the solution is not so much that a photon has no mass, but has no inertial momentum but through E = pc does have an intrinsic momentum but always with the velocity c. There is no definition of momentum which doesn’t contain “m”. And as Edward2007 points out photons still exhibit boson like properties.

Whilst we are digesting that, you might also refresh your reading on the convergence of the photon gas calculations of Maxwell-Boltzman, Bose-Einstein and Fermi-Dirac. And then look up Wikipedia on the subject of J-Band radars and the cavity magnetron, and the resolution of pinhole cameras. This suggests that for microwaves the energy quantum, as defined by Planck's constant may have a wave width equal to the wave length ie a volume, and before you say “but…” there is an interesting calculation. The discovery of the CMBR shows that space is not empty. There is a continuous flux of radiation, defined by the “black body temperature”. Since this is a steady state we can ignore the velocity and the number of quanta in the volume at any instant is constant. If we consider a volume of space, say 1 cubic metre, and calculate how many quanta (of a wavelength diameter) will fit in that space, and apply The equation of state for an ideal gas, which is PV/NkT, where P = pressure, V=volume, k is the Boltzman constant, T is the temperature (Kelvin) and N is the number of molecules (in this case quanta) of the gas. So pressure P = NkT/V. Since kT = E, and since E = hf , (the number of quanta per second) the number of quanta in the volume at any instant is kT/f. This returns a constant value 6.626069x 10-34, recognisably “h”. The Pressure is therefore Nh/V. Similarly the density can be obtained from the number (N) quanta contained in the volume at the mass equivalent of h

So density = N x 7.37249577722913E-51/V. Now the speed of sound in a gas is √pressure/density. If you do that calculation for any wavelength you get the same very interesting number.

Graham