"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.
If you have a complicated qubit that collapses (by whatever mechanism) into a pure 1 or 0, you still have a qubit with a history in the world that is continuous. A complicated qubit doesn't carry any more information than the pure 1 or 0 in this particular sense.
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.)
I'd hazard to guess that "information" implies "not uniformly random", and "uniformly random" implies "no information". That the black hole ripples random implies that the input is in part "converted" to uniformly random and thus by the implications above that information is lost.
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 |+>.
Possibly - though decryption relies on other information held elsewhere (the keys), so I imagine within physics it then turns into a hidden variable problem.
You are right, there exists no such law in quantum mechanics.
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.
Here's a video that made me feel like I almost half-way understood one of the main underlying principles (AdS/CFT correspondence) https://www.youtube.com/watch?v=klpDHn8viX8
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.
"They found that at first, as the black hole gobbles up matter and gets bigger, its information content increases. But then, in its old age, as radiation starts spitting data back out, its information content decreases, diverging from Hawking’s description."
It doesn't, really, I guess they were trying to say that Hawking's predictions don't give us a clue what's going on with the information – if the black hole radiates like a black body it can't really push the information out through it.
For Hawking, radiation was steady and thermal (no data) until the black hole evaporates down to Planck scale, at which it would be impossible to release all the entropy, leading to the paradox of information loss.
What you quote is Don Page's view, that past the Page time, the black hole entropy starts to decrease.
I feel like articles like this quickly devolve into pseudo physics nonsense in attempting to explain such higher level, poorly understood, abstract ideas to laymen, as they're barely just skimming the surface of ideas that only really exist as high level math.
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.
Yes imagine it wasn't black holes but instead the quadratic formula. And you had to explain it with only analogies and absolutely no mathematical notation. I'm sure you could make some kind of explanation but it's not going to be very helpful to anyone.
You can think of it as information within other information within still other information...
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>)
I beg to differ on the proposition that you're a crackpot. That seems to me a perfectly mathematical way of thinking.
If you're a crackpot, it's because all mathematicians are.
So what? We have people believing in flat earth and fake moon landings, thinking vaccines are evil, homeopathy, following religions created by people giving video interviews.
There will be dummies willing to believe in anything. They should not matter how science is shaped.
Right, but does overly hand-wavy explanations representing itself as actual science help or hinder? If people conclude that "this is what science is like" then _no wonder_ we have the current informational problems.
If people will "believe anything" then isn't that an argument against, rather than for, giving them more of the same?
"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...
"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?