5 ms·

Burn it to ash, collect info about the ash and reconstruct - no problem. But if you burn it in a way, that the only remains are "random thermal radiation" all t

by xaedes 4y ago

Burn it to ash, collect info about the ash and reconstruct - no problem. But if you burn it in a way, that the only remains are "random thermal radiation" all the information is lost and we have a serious paradox to resolve...

tsimionescu 4y ago
> But if you burn it in a way, that the only remains are "random thermal radiation" all the information is lost and we have a serious paradox to resolve... To quote the famous Spartan answer, If. That is, QM predicts this is impossible. Even if you threw the book into the Sun, you would (I must emphasize again in principle) be able to measure the radiation given off by the sun and at some point identify the words of the book.
- kgwgk 4y ago
  > according to QM, information is never lost (until you make a measurement > you would (I must emphasize again in principle) be able to measure the radiation given off by the sun and at some point identify the words of the book Does the “information” [1] survive measurements or not? [1] “Information? Whose information? Information about what?”
  - tsimionescu 4y ago
    > Does the “information” [1] survive measurements or not? My understanding is that it doesn't, but I believe that may depend on your interpretation of QM. Note also that "measurement" is pretty ill-defined. > “Information? Whose information? Information about what?” About the state of the system (the wavefunction). Basically in QM an isolated system cannot reach the same final state by more than one route; so, if you know what state it's in, you know exactly what route it took, what every previous state was. Maybe the problem is more clear if moving to computation from pure physics: In a classical computer, you can do something like "x = x & y; y = y & x". If you run this operation and find that x = 0 and y = 0, you can't know what values x and y had before, so that information was lost (ignoring other physical effects - if QM is right, the information is still retained, maybe radiated away by the processor or something). As such, in a quantum computer, this operation simply can't be performed. Instead, you have to use an ancillary bit, z, and some QC equivalent of the Toffoli gate [0]. Then you can compute something like {x, y, z} = {x, y, z XOR (x AND y)}; {y, x, z} = {y, x, z XOR (y AND x)}; if you get the result {0, 0, 1}, you can compute exactly what values x, y and z had initially. The same observations apply to physical interactions. [0] https://en.wikipedia.org/wiki/Toffoli_gate https://en.wikipedia.org/wiki/Toffoli_gate
    - kgwgk 4y ago
      Then you don’t think that it’s necessarily possible - even in principle - to identify the words in the book that you threw the into the Sun _measuring_ the radiation? > Basically in QM an isolated system cannot reach the same final state by more than one route; so, if you know what state it's in, you know exactly what route it took, what every previous state was. There is no way to know in what state is an isolated system - unless you know the state when you last interacted with it. You can “set” the state now and deduce the future evolution. You cannot “know” the state now and deduce the past evolution. If you think about the whole universe, the “state” that could be described by a “wavefunction” is not a state describing the observed universe. Not even the number of elementary particles would be defined. The physical relevance is unclear.
      - tsimionescu 4y ago
        > Then you don’t think that it’s necessarily possible - even in principle - to identify the words in the book that you threw the into the Sun _measuring_ the radiation? Well, this is why I said the measurement is problematic. It's perhaps not possible even in principle to actually measure it. But, in principle, the wave-function of the sun after you throw a book that has a coffee stain into it will be different from the wave-function of the sun after you throw the same book without the coffee stain. And that difference, in turn, could be detected through measurement, as it will affect the probabilities of a measurement of the sun. Of course, this means that you will actually have to throw a whole lot of books to be able to notice this statistical difference. > You cannot “know” the state now and deduce the past evolution. Well, because measurement collapses the state, you are right to some extent. But on the other hand, the measurement's result will be affected by anything that has ever happened to that system in a different way.
        kgwgk 4y ago
        > But, in principle, the wave-function of the sun after you throw a book that has a coffee stain into it will be different from the wave-function of the sun after you throw the same book without the coffee stain. That's different from saying that it can be measured in principle. And a having or not a coffee stain is different from the previous example. A coffee stain of a different shape would be closer. > And that difference, in turn, could be detected through measurement, as it will affect the probabilities of a measurement of the sun. I'm not sure how to interpret that. You just said that "It's perhaps not possible even in principle to actually measure it". [edit: maybe you mean that some kind of « statistical trace » remains, but we surely agree that’s very different from being able to identify the words in a particular book.] Anyway, the sun is not an isolated system so it cannot be described with a wave-function. The "wave-function of the universe" - if we assume that such a thing exists which evolves unitarily since the beginning of time - would contain the "information" about the universe in which you threw a book with a coffee stain and about the universe in which you threw a stainless book and about the universes in which there is no Sun to throw things into.

by xaedes 4y ago

tsimionescu 4y ago

> But if you burn it in a way, that the only remains are "random thermal radiation" all the information is lost and we have a serious paradox to resolve... To quote the famous Spartan answer, If. That is, QM predicts this is impossible. Even if you threw the book into the Sun, you would (I must emphasize again in principle) be able to measure the radiation given off by the sun and at some point identify the words of the book.

kgwgk 4y ago
> according to QM, information is never lost (until you make a measurement > you would (I must emphasize again in principle) be able to measure the radiation given off by the sun and at some point identify the words of the book Does the “information” [1] survive measurements or not? [1] “Information? Whose information? Information about what?”
- tsimionescu 4y ago
  > Does the “information” [1] survive measurements or not? My understanding is that it doesn't, but I believe that may depend on your interpretation of QM. Note also that "measurement" is pretty ill-defined. > “Information? Whose information? Information about what?” About the state of the system (the wavefunction). Basically in QM an isolated system cannot reach the same final state by more than one route; so, if you know what state it's in, you know exactly what route it took, what every previous state was. Maybe the problem is more clear if moving to computation from pure physics: In a classical computer, you can do something like "x = x & y; y = y & x". If you run this operation and find that x = 0 and y = 0, you can't know what values x and y had before, so that information was lost (ignoring other physical effects - if QM is right, the information is still retained, maybe radiated away by the processor or something). As such, in a quantum computer, this operation simply can't be performed. Instead, you have to use an ancillary bit, z, and some QC equivalent of the Toffoli gate [0]. Then you can compute something like {x, y, z} = {x, y, z XOR (x AND y)}; {y, x, z} = {y, x, z XOR (y AND x)}; if you get the result {0, 0, 1}, you can compute exactly what values x, y and z had initially. The same observations apply to physical interactions. [0] https://en.wikipedia.org/wiki/Toffoli_gate https://en.wikipedia.org/wiki/Toffoli_gate
  - kgwgk 4y ago
    Then you don’t think that it’s necessarily possible - even in principle - to identify the words in the book that you threw the into the Sun _measuring_ the radiation? > Basically in QM an isolated system cannot reach the same final state by more than one route; so, if you know what state it's in, you know exactly what route it took, what every previous state was. There is no way to know in what state is an isolated system - unless you know the state when you last interacted with it. You can “set” the state now and deduce the future evolution. You cannot “know” the state now and deduce the past evolution. If you think about the whole universe, the “state” that could be described by a “wavefunction” is not a state describing the observed universe. Not even the number of elementary particles would be defined. The physical relevance is unclear.
    - tsimionescu 4y ago
      > Then you don’t think that it’s necessarily possible - even in principle - to identify the words in the book that you threw the into the Sun _measuring_ the radiation? Well, this is why I said the measurement is problematic. It's perhaps not possible even in principle to actually measure it. But, in principle, the wave-function of the sun after you throw a book that has a coffee stain into it will be different from the wave-function of the sun after you throw the same book without the coffee stain. And that difference, in turn, could be detected through measurement, as it will affect the probabilities of a measurement of the sun. Of course, this means that you will actually have to throw a whole lot of books to be able to notice this statistical difference. > You cannot “know” the state now and deduce the past evolution. Well, because measurement collapses the state, you are right to some extent. But on the other hand, the measurement's result will be affected by anything that has ever happened to that system in a different way.
      - kgwgk 4y ago
        > But, in principle, the wave-function of the sun after you throw a book that has a coffee stain into it will be different from the wave-function of the sun after you throw the same book without the coffee stain. That's different from saying that it can be measured in principle. And a having or not a coffee stain is different from the previous example. A coffee stain of a different shape would be closer. > And that difference, in turn, could be detected through measurement, as it will affect the probabilities of a measurement of the sun. I'm not sure how to interpret that. You just said that "It's perhaps not possible even in principle to actually measure it". [edit: maybe you mean that some kind of « statistical trace » remains, but we surely agree that’s very different from being able to identify the words in a particular book.] Anyway, the sun is not an isolated system so it cannot be described with a wave-function. The "wave-function of the universe" - if we assume that such a thing exists which evolves unitarily since the beginning of time - would contain the "information" about the universe in which you threw a book with a coffee stain and about the universe in which you threw a stainless book and about the universes in which there is no Sun to throw things into.