kurzgesagt has a video about how, according to our understanding of physics, information cannot be destroyed. It’s in this video here: https://www.youtube.com/watch?v=yWO-cvGETRQ
They explained it as that if you have a piece of paper with writing on it, and you burned it, but then you collected every atom that once came from the paper, and measured their every property, you can perfectly recreate the paper and the writing, because apparently the atoms themselves retain the information about the paper. I’m curious about this concept, because to me, this sounds pretty unbelievable, because wouldn’t there be randomness that gets in the way of reconstructing the paper? Wouldn’t the information get lost in the noise at some point, and become too ambiguous or indistinguishable? Does this idea work for everything that can store information? For example, of you have a hard drive, which a file was overwritten, where does that information go? Are they still somehow stored away within the atoms of the hard drive? How would you, in theory, reconstruct it? Same questions with an SSD, if the cells containing electrons that make up the information in an SSD change states as they are overwritten, where does that information go? In the far far future, could forensics teams, in theory, use this principle to recover any data from any computer, regardless of what was done to it?
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Picture when playing billiards and someone does the initial “break” when they smash the cue ball into the triangle formation of the rest of the balls. If you took a snapshot a split second after the collision and also knew the exact velocities of all the balls, as well as their properties like mass, friction, elasticity, etc. it would be possible to take all that information and work backwards to determine the initial formation before the break happened, and even how hard the cue ball struck.
All of physical reality is like this, where if you have complete, god-like knowledge about every single factor of every single particle, you can work backwards to reconstruct the information.
So if you burn a page of a book, but you know the trajectory of every particle of smoke, every chemical change that occurred in the combustion of paper and ink into the resulting remains, every molecule of gas in the room that was creating the air currents, all with absolute knowledge, you could go backwards and reconstruct the page.
It’s not the carbon atoms themselves that remember they used to be a book, it’s that their state at any given point of time is the result of earlier conditions.
Edit: for your hard drive example. It seems like it wouldn’t work the same because the data is determined by the configurations of electrons and shuffling them around between rewrites would not leave the same type of information. But you have to think broader than that. When a hard drive rewrites it’s not happening in a closed system. There’s heat created, sound, radiation; all leaving the box of the hard drive into the external environment but leaving a trail nonetheless.
Practically we cannot do this, but conceptually, if you knew the exact state of every particle in the universe, you would have all the information.
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