  Time reversal symmetry and magnetoelastic correlations are probed by means of
high-resolution volume dilatometry in URu2Si2 at cryogenic temperatures and
magnetic fields more than enough to suppress the hidden order state at H_HO(T =
0.66 K) approximately 35 T. We report a significant crystal lattice volume
expansion at and above H_HO(T), and even above T_HO, possibly a consequence of
field-induced f-electron localization, and hysteresis at some high field phase
boundaries that confirm volume involvement. We investigate in detail the
magnetostriction and magnetization as the temperature is reduced over two
decades from 50 K where the system is paramagnetic, to 0.5 K in the realms of
the hidden order state. We find a dominant quadratic-in-field dependence delta
L/L proportional to H^2, a result consistent with a state that is symmetric
under time reversal. The data shows, however, an incipient yet unmistakable
asymptotic approach to linear (delta L/L proportional to 1-H/H_0) for 15 T < H
< H_HO(0.66 K) approximately 35 T at the lowest temperatures. We discuss these
results in the framework of a Ginzburg-Landau formalism that proposes a complex
order parameter for the HO to model the (H,T,p) phase diagram.
