Entropy. There is a unique connection between time and the second law of thermodynamics. Entropy is the only quantity in physics that implies a progression - the arrow of time - that leads from now to then. As time passes, the 2nd Law states that the entropy of an isolated system never decreases. You could look at entropy as a kind of clock. The 2nd Law usually implies a loss of heat, or energy, in a system. You can't make a perpetual motion machine because of the 2nd Law. But perhaps, if you look at that wild idea of time slowing down - then entropy is more a measure of the time dilation than a loss of energy.
The implication is that the 2nd law pulls us through time. In Albert Einstein's theories of relativity, time dilation occurs when two observers are in relative uniform motion, one clock appears to move slower than the other. If we are changing relative position through time, the Lorentz transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik Lorentz. It reflects the surprising fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events.
Not such a huge leap to see time as the movement from one relativist point to the next! Hey, what's the probability of that? Continuous time evolution of an isolated system that obeys Schrödinger's equation (or Dirac's equation) involves the collapse of the wave function. Entropy, and the expansion of space, may be the relativistic expression of the 2nd Law.
