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I am watching a course on quantum mechanics from Stanford university. Today I heard that the tutor said:
- Laws of physics are reversible,
- Information is never lost.
what does it mean exactly? And what is the relationship between these two statements?
Tell me some examples, please do not talk about processes in thermodynamics. thank you. :)
I know the lecture you are thinking of (I believe). In that lecture, the prof's statement that the laws of physics are reversible is grounded in what he explained, that each event is followed by a single event, such that:
Additionally, each event also only has one event prior to itself:
What follows from this is that the only acceptable sequence of events is:
In this case, the laws are reversible because, if in the original function, you could have event A, and know according to the laws that it would lead to event B, then C, you could reverse the laws, and given event C, know according to the reversed laws of physics that it would lead to event B, then A.
As for the lack of lost information, note that the universe he described is stroboscopic. In this case, each piece of 'information' is an event in the universe, and given that each event leads to another single event, the number of pieces of information is constant across time.
To understand what "Laws of Physics are reversible" means think of what the laws of Physics means. Usually, in this context, what we mean by the Laws of Physics is the laws (or say method) that one can use to predict what will be the outcome of a certain situation provided you have all the information about the situation at a given instant of time. Now, what would a reverse law mean? It would simply mean the method that one can use to figure out what would have been the initial situation at some past instant of time provided she has all the information about the current situation. Thus, by laws of Physics being reversible, we mean that the laws of Physics should have this property that they make the systems evolve in time in such a way that the reverse laws can be formulated.
Laws of Physics being reversible and the information about a system being conserved are very closely related and actually imply each other. What we mean by the information being conserved is that the information that a system has at a given instant of time should be sufficient to predict what will happen to the system in future as well as that what would have been the past of the system. This is called the conservation of information because such a scenario implies that the information that is contained in the system at one instant of time can (in principle) be read-off at any other instant of time. As you can realize, for the information to be conserved in this sense, both the laws (and their reverse) must exist and vice versa.
