Timeline for Does a book get lighter if you rearrange the letters?
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| Jul 4, 2022 at 3:54 | comment | added | user84158 | In the classical case the answer to your question would be no since macroscopic states are hard to compare as they are just jumbles of particles. In the quantum case, one could argue that the amount of information to encode a book into particle states would be less for certain configurations of letters than others. So you would need less particles and hence less mass. But that is a funny kind of "book" and not really the one I think you meant! | |
| Jul 4, 2022 at 3:03 | comment | added | Jackson Walters | Iām saying that the bits which eventually store the book consist of two states, 0 and 1, which are distinguishable, but copies of the 0 state are indistinguishable, as are copies of the 1 state. If the 1 state is, say, a voltage then there may just be a threshold above which you consider the state to be 1, even though two states might have slightly different voltages. This is classical, not quantum, information. An experiment would have to rule out mass-energy differences coming from mass-energy differences of the states themselves. | |
| Jul 2, 2022 at 22:09 | comment | added | user84158 | Well are you saying that the letters in the book are precisely the same as in atom-by-atom? Well in order to do that you might have to form the book through entangled particles. Therefore perhaps, yes, there would be less information in the book! But such entangled states on the scale of a book would be impossible to achieve. It is an interesting thought experiment though. | |
| Jul 2, 2022 at 3:04 | comment | added | Jackson Walters | The Kolmogorov complexity š¾(š„) for a string š„ does not depend on the person reading the string. Knowing that it's a telephone number does not reduce the complexity of the number. A book written in Chinese might appear "random" to one person, and a fascinating story to another. However, what is important are things like patterns and repetitions in the symbols, or if there is a way, a program, to generate the text which is considerably shorter than the text itself. | |
| Jul 1, 2022 at 23:12 | comment | added | user84158 | One person's random string of digits is another person's ordered telephone number. So how does the Universe know which is the one you define as "random"? | |
| Jul 1, 2022 at 19:28 | comment | added | Jackson Walters | Well, the definition of a random string is one with large Kolmogorov complexity, so incompressible with information content close to $N$, the number of bits in the string. The original book is a random string. The final book is a rearrangement of the bits so the string is maximally compressible. This is just trying to ask whether information has mass-energy, i.e. if the arrangement of matter itself has mass, beyond the mass of the matter being arranged. This should be experimentally testable - load up a big hard drive with a random string, weigh it, erase it, weigh it. Is there a difference? | |
| Jun 4, 2022 at 18:57 | history | answered | user84158 | CC BY-SA 4.0 |