Past, Future... what is really the difference?

This is a blog about the fundamentals of physics and intriguing questions. Because I´m from Brazil I usually write in portuguese. This project is growing fast, however, and it is incredible how thing spread rapidly in the internet. So I will start to write in english ocasionally so that a larger number of persons will be able to follow my questioning. Right now I´m on the middle of my final exams period in the university, so I don´t have too much time to think before posting. I´ll be able to elaborate a lot more soon. In this post I will just share a question that give physicists a lot of headaches.

You might have heard someday that physics claims to be the science that tries to explain the whole universe. One could wonder that such a project is utopic...that thousands and thousands of books would be necessary to explain something as complex as the universe. But, by the fundamental pratice of experimentation, one can find out that there is a lot of regularity in the behaviour of things in space and time. It is an experimental fact that some laws apply in general and always. And by observing things closely, it is surprising to see that the complexity is not contained in the laws, but elsewhere. Stars, planets, atoms and even you are physical system that obey a few (very simple) laws. So how can we observe so much complexity anyway?

The main reason for that is that the fundamental laws apply to elementary particles ( or superstrings, or anything else) that are very small compared to us as conscious beings. Those elementary ''bricks'' of matter exist in an amazing huge number. By huge number I mean millions of millions of millions of... When they interact with each other (obeying very simple laws) complex behaviour start to appear. Stars start to burn, planets are formed and you born. But, ultimately, those complex systems are always big as regarding to their number of elementary ''bricks'' ( there is also chaos theory, but lets forget that for a second).

And in fact, stastical mechanics is a branch of physics that prove that macroscopic and complex phenomena is the result of the behaviour of a large ensemble of atoms, molecules, or anything else obeying very simple laws. So, in summary, complexity arises from simplicity plus a big number of systems, and this can be very well understood. Physicists and engineers develop new materials, for example, using this kind of reasoning.

However, one beautiful piece of this link between macroscopic complexity and microscopic simplicity remains unexplained. The difference between past and future.

Recall Newton´s second law, F=ma. In the past this was considered one of those fundamental simple laws that I just mentioned. All matter, they thought, was made of elementary bricks they called atoms, that obeyed this simple law. Our current picture has evolved a lot since them, but the following arguments are still valid. So let´s assume that newton´s second law is true. By looking at F=ma, we can see that this equation is symmetric in time! (If you have studied calculus, the aceleration is d²x/dt² and by exchaging t´=-t, it is straightfoward that d²x/dt²=d²x/d(t')².)

This means that if instead of measuring time with a normal clock, we choose to use one that runs backwards, there´s no way we can state wheter this clock is the foward or  the reversed one.Said in another way, if you observe two successive states of a physical system, F=ma states that you can never tell what was the cause and what was the consequence. Modern refinements of Newton´s law (quantum theory and relativity) won´t help us in this issue, for they also state that there´s no difference between past and future. So, apparently, the meaning of time for the fundamental bricks of the universe is something quite different to what we would expect!

Now, it is reasonable that when 10²³ atoms interact together the resulting behaviour could be complex. But how could the assymetry between past and future that we observe  ever be recovered  if the fundamental laws that the bricks of nature obey don´t distinguish past and future at all??

This question, know as the ''arrow of time problem'' remains unsolved. Any ideas?