information - Is there really time reversibility in physics?

First, how i got to the question. I was randomly looking at this page: http://en.wikipedia.org/wiki/Langton%27s_ant

describing some sort of cellular automaton.

Here is the path of this automaton after more then 10000 steps:

You can clearly see that after some time ant gets stuck in the loop (actually its a highway) and will be going on it forever.

Here comes the problem with many faces:

If we turn back time and start ant from one of the loop(highway) points we will never get to the original messy part, so obviously this computation is not time reversible since there is no way out of the loop! :) (But there should be ! :D)

Another thing is that information is also not time reversible - since if at some point in computation operation DELETE is used to erase all the previous data there is no way to get that data back.

Ok. So far so good. Lets take this question one step further. How is that so? They always told us laws of physics are time reversible and so on.

My intuitive answer is following. We can say that in the universe there are so called LAWS (physics and so on) and OPERATIONS. What is the difference?

LAWS do not change the objects on which they are operating and hence probably are time reversible.

OPERATIONS on the other hand can change objects, their number in the system and hence are not time reversible (if I delete some files there is no algorithm how to restore them again)

I understand its very close to the idea and interpretation of information.

So when they show us movie backwards and we think time got reversed its actually false! Yes you can reverse the motion of the people and objects, but you can not reverse speach for example since there is no logical connection between phrases being said. Here we can see how the content of the movie (life) is actually twofold - time revesible part (geometry in the poorest sense) and informational part (speech, computations and so on).

From all above it seems that the universe overall is NOT time reversible, and there is no way to go back in time! :) Or is there?