Why isn't tomorrow like yesterday? Having grown up in a world of growth and decay - of directed change - most people might consider this question a little odd. After all, a movie taken of just about any large-scale natural process has a clear direction of time - if the movie is played backwards, seedlings dwindle into seeds and water jumps up a waterfall. However, this macroscopic "arrow of time" is due to the randomising effects of the very large number of atoms involved. The underlying laws of classical physics (CP) have no arrow of time. Run a movie of the frictionless pulleys and massless springs of our A-level physics books backwards and they look fine.
The macroscopic arrow of time arises because a situation is spectacularly unlikely to arise where all the molecules in a river happen to be flowing with just the right directions and speeds to collide and bounce up just as a waterfall appears. Hence a river won't flow backwards.
We can therefore conclude that tomorrow isn't like yesterday because of this macroscopic arrow of time. However, we also need the fundamental laws of physics to have an arrow of time. The reason is related to one of the great mysteries of current science - why is the Universe made of matter rather than anti-matter? Anti-matter is extremely rare in our universe, in fact so rare that when Paul Dirac formulated his theory of the electron in 1928 and found solutions that looked like positively-charged electrons, he didn't know what they might be (as normal electrons always have a negative charge). He was still groping for an answer in 1932, when Carl Anderson found positively-charged electrons in cosmic rays, and the penny dropped that the Dirac Equation implies that for every particle there is an equal and opposite anti-particle. Of course (as viewers of Star Trek are aware), if the two should meet, they will annihilate into radiation (with unfortunate consequences for anyone standing nearby).
What Star Trek never told you, however, is that the same thing works the other way - radiation can turn into matter and anti-matter (that is, the same reaction, but with time running the other way). In fact, the matter in the universe today was born in just this way, congealed out of the blazing radiation of the Big Bang. But if the laws of physics are the same for anti-matter and matter, the exact same amounts of matter and anti-matter would have been created, and we would not be here.