Some days ago, I had come across an intriguing article about how our intuition about the forward direction of time or the celebrated arrow of time is linked with the theoretical predictions arising from fundamental and applied physical theory.
Consider a world full of objects obeying classical laws of mechanics. A little inspection would trivially show that the equations of motion are time reversible i.e. as far as the equations are considered, there is no preferred direction of time. This observation became a major worry for physicists with the advent of the second law of thermodynamics which stated that the entropy should always increase (thus giving a direction to time).
Though entropy was not a directly accessible experimental quantity, it had become obvious for a lame physicist to determine the positive direction of time. As trivial as the problem might sound in a common sensical way, consider that you are given a movie about a real life experiment and then you are asked to identify if the movie is played backwards or forwards. This question is certainly a non-trivial one (e.g. waves on water, where forward and reverse might look the same. I must mention that this strictly is not a very good example!) With the aid of the entropy law, the physicist will be quickly able to tell which is the positive direction!
This entropy law was a shocker to all the physicists and notably, since it hasn't been proved yet for a classical system, it is legitimate to believe that we will find instances where given a movie we exactly determine the arrow of time. In the realms of classical mechanics, though the law has not been proved, it's limitations are well known. E.g. a ball rolling on the floor does not indicate any direction of time. It is only when the system becomes macroscopic (A rolling ball, though is macroscopic in nature, here is modeled as a point particle for simplicity) that the entropy law is valid and it is the only case where we can with firmness determine the direction of time.
This brings me to the lecture I attended today, by one of the notable statistical physicists of our times. The main topic of the talk was violation of the second law of thermodynamics in systems which are neither microscopic nor macroscopic but lie on the boundary and give rise to interesting results. For concreteness, suppose we are given a movie about stretching a rubber band. By a movie, I mean every possible accessible detail about the experiment. It would be trivial to find out if the rubber band is being stretched or if it is being compressed based on our intuition. But when it comes to molecular level rubber bands, like RNA molecules. To put things in the lecturers own words, we only have a maximal likelihood of predicting if the RNA molecule is going forwards in time or backwards. To add more spice and mysticism to the story, the molecules itself doesn't know if it is going forward or backward in time. There is a probability associated with that :-)
On a more fundamental level, these issues have been resolved thanks to the asymmetry in the realms of quantum mechanical world, or the world which we live in. But nevertheless, for systems like the molecular rubber bands, which can still be treated classically for good reason, time might not know which direction is forward!