# How is information conserved over time?

From what I've learned, information seems to be the knowledge of the past and it suggests that it is preserved by specific aspects of particles. But considering time isn't an issue, it suggests that the universe can be in a state effectively infinitely into the future, but the past still be preserved in that state. But if you consider that each aspect of space has a finite amount of aspects that constitute information, there can only be a finite number of possible combinations that can be used to code the past.

Effectively, where does the universe get the extra storage space to preserve information about the past as time goes on (At first I thought that the expanding universe allows for more values to be used for relative positional information but this posts says there is no minimum which wouldn't be the case if this was true)?

Information is conserved in a reversible, deterministic process because the original state of the system can be retrieved by reversing the flow of time (or, equivalently, by reversing the momenta of all the components of the system). This information (and, indeed, the whole history of the system) is stored in the state of the system at any point in time - indeed, it is the state of the system. There is no separate "storage" required.

Note, however, that just because information is conserved does not mean it is easily accessible, as it may be distributed across the state of the system. There may be no quicker or simpler way of determining the original state of the system other than running the whole system backwards.

In quantum mechanics the evolution of a quantum system through time in accordance with the Schrodinger equation is a reversible process and so conserves information. Whether wave function collapse leads to an actual loss of information or only an apparent loss depends on which interpretation of quantum mechanics you follow.

• Does this therefore mean that mathematically speaking, a base system is not the most efficient way of storing data?
– yolo
Jan 10, 2021 at 16:52
• @yolo I don't understand your question. You will have to explain what you mean by "efficient" and how you think information storage in physical systems is related to ways of representing numbers in mathematics. I suggest you post this as a separate question in math.stackexchange.com. Jan 10, 2021 at 17:01
• I mean consider the universe was stored in a universe. Theoretically; a single frame of the universe would give us information about every other state preceding it. That's akin to saving a dozen images in a single image file; all of equal storage space
– yolo
Mar 20, 2021 at 14:35