Hologram Within a Hologram Hints at Fate of Black Holes
nautil.us
nautil.us
"The problem is this: The laws of quantum mechanics insist that information about the past is never lost, including the record of whatever fell into a black hole. But Hawking’s calculation contradicted this. He applied both quantum mechanics and Albert Einstein’s theory of gravity to the space around a black hole and found that quantum jitters cause the black hole to emit radiation that’s perfectly random, carrying no information. " I always thought that amount of information about current description of it must be conserved. It's differet than history of the state evolution. IMO simplest QM experiment contradicts this statement: if you pass a linearly polarized filter on a rotated filter you get a random result. You can't infer original state. It's like mas conservation in box of eggs. If you shake it, the amount of eggs is the same, it's state is different and untrackable.
So in my understanding the blackhole was a perfect scrambler. It carries the same amount of information is distribution random. Or the number of bits must stay the same but their distribution changes. That might be slightly different from amount information definition in Shannon sense.
Was my understanding wrong all along?
At least that's how I'd interpret your paragraph.
You can have something that when observed appears to be uniformly random but can be transformed into something that is not. Consider a Hadamard transform applied to |+>.
But even if it would exist, then there would still be no justification for assuming that this law should still hold in a place as extreme as a black hole. A black hole is by its very nature a place where our current laws of physics are not defined.
The concern about black holes is that you toss a bunch of qubits (in the mass) in, and then there is a discontinuity; qubits with no particular relationship to anything that went in come off the surface as Hawking radiation. It isn't just that the qubits are really, really "scrambled"; thing getting too scrambled to put back into their original state in any feasible amount of work is a thing that happens all the time in the non-black-hole world anyhow. But there's still continuity, and the theoretical possibility of restoring the original state. The concern with black holes is that it isn't even theoretically possible to put together the original states. (It's going to be practically impossible either way.) There's a discontinuity in the qubits evolution, where they seem to entirely disappear from the universe at one place ("in" the black hole, for whatever exact definition of that ends up making sense; for this particular discussion, that's a complicated question!), and suddenly re-emerge with no relationship to any past state in the Hawking radiation. That discontinuity is the concern.
If I have this right.
(Stepping even further out of my comfort zone, I think part of the problem with this "discontinuity" is ultimately the same problems you learned about in calculus class with discontinuities in functions. Our understanding of QM is mostly expressed in differential equations. Those equations can't tell us about what happens if there are actually discontinuities in the world. In their own way they're as bad as the singularities that appear in relativity for black holes. It means "anything" could happen.)
re: "Following the discovery of this duality by Juan Maldacena"
Semi-unrelated: If you like articles like this, I bet you'll love that whole channel.
How does this differ from Hawkings conclusions?
What you quote is Don Page's view, that past the Page time, the black hole entropy starts to decrease.
Not necessarily a fault of the journalist, it's just that words really cannot capture the breadth of information or the inquisitive power of what the physicists derived without some understanding of the symbolic system involved.
Simple 2D example (for programmers) -- you have a binary string, which can be looked at as a series of 1's and 0's, or as a series of 8-bit bytes.
Well if we look at it as a series of bytes (think of that as the first "holographic" dimension, because the bytes don't really exist -- that is, all they really are is repeated groupings of 8-bits -- CPU's and programs and memory might work with data of that length and "see" them, but in essence, the string is is just 1's and 0's.
So that's the first "holographic" dimension... bytes. But now, inside of that string are substrings -- discrete runs of shorter information. Let's think of those substrings as "holographic" dimension 2.
From here, there could be even higher "holographic" dimensions, that is, let's say we observe only some substrings relative to a mathematical pattern, f(x).
Well, you can think of f(x) -- and the resulting data it produces as a result of reading specific substrings in a specific order -- as living in a higher dimension, a "higher dimensional" "observer", if you will...
Whenever you see the word "black hole" or "hologram" -- replace that with the word "information", and think about it from that perspective... usually there's something there...
(It's also equally-and-oppositely possible that I'm a crackpot and don't know what I'm talking about -- take this explanation with the proverbial grain of salt... <g>)
There will be dummies willing to believe in anything. They should not matter how science is shaped.
If people will "believe anything" then isn't that an argument against, rather than for, giving them more of the same?
Here's an example of a simple explanation that otherwise would require complex math https://youtu.be/ZcpwnozMh2U
"The problem is this: The laws of quantum mechanics insist that information about the past is never lost, including the record of whatever fell into a black hole. But Hawking’s calculation contradicted this. He applied both quantum mechanics and Albert Einstein’s theory of gravity to the space around a black hole and found that quantum jitters cause the black hole to emit radiation that’s perfectly random, carrying no information."
IF Hawking was wrong (remember, I said "if"), then the following identity would hold:
Radiation = Information
Also... There's an interesting philosophical question brought up by this... what is randonimity? How does one mathematically determine that something is random? Perhaps "random" is just a human word we use to explain/label a pattern that we as-of-yet don't understand... The history of mathematics is a history of patterns that were not understood at certain points in time, that became well understood at later points in time... So I ask the mathematical community: "define random". If "random" is just a series of numbers which have no apparent pattern, yet fall into a statistical distribution, then I'll bet that a future mathematician will show that the digits of Pi (or groupings thereof) to fall into the same statistical distribution as a "random" sequence of numbers... In other words, if this were proven, then if someone looked at Pi as that statistical distribution (without knowing anything else about Pi), they'd assert that the number series was random, when in fact it was not, that is, it was generated by an algorithm, the algorithm for Pi... which can be thought of as Information, whether you look at that information in algorithm form or outputted digits form...