What do physicists mean by information?
Every now and then I'll read a book by a scientist trying to explain a field or subfield or subproblem to laypeople like me (by Randall, Susskind, Greene, to name a few of the recent). I almost always like these books, but Sean Carroll's
From Eternity To Here is the first that's really clicked for me. I
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i: if something falls into a black whole it is destroyed (not simply transformed dispersed as if would be if it fell into a star), because right down to the smallest particles it passes irretrievably into a gravitational singularity
ii: in which case the "information" that is its basic waveform structure is destroyed
iii: except ii surely breaks the law of the conservation of information: the information that *is* the wave-form structure of the object has vanished irretrievably
iv: BUT black holes emit radiation [this was stephen hawking's proposal, i believe -- his great realisation and change of mind? it is a long time since i read "a brief history of time" tho it is in the other room
v: and moreover, they have this thing called (i think?) the light event horizon, where the light from objects that are falling into them remains held, unable to escape as a kind of image sphere AROUND a black hole
vi: and THIS is where the information that was the wave-form structure is forever held, as a permanent 2-dimensional holograph of the "last glimpse" as it were, of the destroyed 3-dimensional object
vii: which would be detailed enough in informational material, despite being "flat" as an image, for an observer with the correct tools and reading skills -- and presumably ability not to be dragged into the BH themselves -- to "read back" the 3-D wave-form detail from the this 2-D image (hence information is conserved)
[posts above has raised the issue that information in physics terms is not necessarily "communicable" -- as it must be for eg Claude Shannon -- bcz it doesn't require the presence of beings that can "read" the information <--- which is an interesting aspect of the problem, but not one that mathematicians and cosmologists spend much time on; they tend to operate as "under god's eye" communications theorists, even when militant aetheists; the information that is an object's waveform structure is deemed "objectively readable" even if no one is EVER going to be around who can actually read it] [for maths and physics this is a side-issue however: information in the social sense is very much NOT conversed, vast amounts is lost everyone someone dies -- the mathematical ideal is that, if the full picture of all waveforms could be retrieved, then ALL information, including the fleeting never-spoken thoughts of the long-dead, could be reconstituted, indeed the retrieval and the reconstitution would kind of be the same activity]
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even tho i believe that's being claimed is the totality of cosmic conservation and the totality of the cosmic conversation are IDENTICAL hah!
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I wouldn't say Hawking had a "great realisation and change of mind" so much as he was convinced that Maldacena's and Witten's ideas regarding the equivalence of anti de Sitter space and a 4-D gravity-free description effectively won the argument for 't Hooft and Susskind's side and so defeated his own idea that information is destroyed when a black hole evaporates. Susskind thought that Hawking dawdled at admitting defeat, whereas some others thought he conceded too soon, and that the issue is still open.
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