  Special relativity allows massless particles to have states of different
integer (or half-integer) helicities that mix under boosts, much like the
spin-states of a massive particle. Such massless particles are known as
continuous spin particles (CSPs), a term coined by Wigner, and they are notable
for their infinite tower of spin polarizations. The mixing under boosts is
controlled by a spin-scale $\rho$ with units of momentum. Normally, we assume
$\rho=0$. The interactions of CSPs are known to satisfy certain simple
properties, one of which is that the $\rho \rightarrow 0$ limit generically
recovers familiar interactions of massless scalars, photons, or gravitons, with
all other polarizations decoupling in this limit. Thus, one can ask if the
photon of the Standard Model is a CSP at small but non-zero $\rho$. One concern
about this possibility -- originally raised by Wigner -- is that the infinite
tower of polarizations could pose problems for thermodynamics. To address this
question, we study the thermal evolution of a CSP photon gas coupled to
isothermal matter, across CSP helicity modes and phase space. We find that the
structure of the interactions dictated by Lorentz symmetry imply well behaved
thermodynamics. When the CSP photon's interactions to charged matter are turned
on, the primary $h=\pm 1$ helicity modes thermalize quickly, while the other
modes require increasingly long time-scales to thermalize, set by powers of
$T/\rho$. In familiar thermal systems, the CSP photon behaves like the QED
photon with small $\rho$- and time- dependent corrections to its effective
relativistic degrees of freedom. Sizable departures from familiar thermal
behavior arise at energy scales comparable to $\rho$ and could have testable
experimental consequences.
