Re: Time-reverse symmetry of the principle of relativity The question of the "arrow of time" and increasing entropy is not as clean cut as one might imagine. I think it it R.Penrose that pointed out that while a simple application of thermodymanis predicts the "heat death" of the universe where everything is cold and in thermal equilibrium, there is a paradox because the initial conditions of the universe just after the big bang is one of thermal equilibrium. This can be seen in the very small degree of thermal anisotropy in the CMB. THe situation for the entropy of the universe os a whole is complicatd by gravity. We know from Hawkings that the entropy of a gravitationally collapsed object (a black hole) is very high. This suggests that the expanding universe with reduction in mass energy density is an example of reducing gravitational entropy (the opposite of a black hole). So while the expansion of the universe represents increasing thermal entropy it represents reducing gravitational entropy at the same time. Many quantum cosmological models predict a "bouncing" universe that alternately collapses and expands again. That requires the total entropy of the universe to be constant over time as only constant entropy processes are reversible. That suggests that maybe thermal and gravitational entropy work in opposite directions and cancel each other out. It would be kinda cool it the total energy of the universe is always zero, the total charge of the universe is zero, the total linear and angular momentum is zero and the total entropy of the universe is always zero.