If information doesn’t disappear, what happens to it when it’s carrier stops existing? For example, the hard drive is disintegrated or a brain decomposed. Does it return to being energy? If so, doesn’t it mean that it disappeared?
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It means that if you were to analyse absolutely everything left over, with perfect tools, and an inconceivably powerful supercomputer, it would *technically* be possible to reconstruct the destroyed hard drive or the decomposed brain.
You’d need to do things like gather every bit of light that touched the disintegrating hard drive, or every atom that went from the decmposing brain into the ecosystem, so it’s not *practically* possible; but physicists often care about things that aren’t practical because they’re interesting and/or because engineers have a habit of turning a physicist’s “this is cool but it’ll never matter” into new, previously impossible, technological innovations.
This is the distinction between macrostate and microstate.
Under many classical laws of physics, the information about microstate never lost: there is a one-to-one correspondence between each microstates at one point in time and microstates at some specific future time. The correspondence is not many-to-one, that is it is impossible for different microstate to result in the same microstate in the future. (relatedly, the correspondence is not one-to-many, this is known as determinism, we don’t gain information over time either)
The information about macrostate could be lost by transforming into information about microstate. This is what happen when the hard drive get disintegrated. Basically, this is the distinction between information that is practically accessible, and information that theoretically exist in the system.
The additional information that cannot be practically recovered, but still exists in the system, in measured in term of **entropy**. Entropy cannot decrease, and only increase.
The wording is that “information can’t be destroyed”, and it’s not referring to things like a memory or a list of email addresses, it’s referring to specifics in quantum mechanics.
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