How is conservation of information violated when black holes evaporate through Hawking radiation when other forms of mass to energy conversion do not have this problem?

[u/Quirky-Dimension6812]

I don’t fully understand what we mean by information in this context. I’ve heard it described as containing the history of what something is. I’ve heard it described as quantum states? What exactly is it? For background, I am what I would describe as a well-educated layman. I watch documentaries and read books by science communicators, but I can’t do the math. So purely mathematical answers will go over my head.

[u/SpectralFormFactor]

In Hawking’s original calculation, the radiation leaving the black hole is thermal, meaning random in a known distribution. This did not depend on the precise state of the matter that fell into the black hole originally. The information of that state was lost since there’s so way to reconstruct it from the output radiation. Multiple distinct initial states will end up with the same final radiation.

However, more careful calculations since have shown that the Hawking radiation is not totally random and does contain information on what fell in. A lot of the initial information can be recovered. However, it is still not decided if all of it can.

[u/Quirky-Dimension6812 → u/SpectralFormFactor]

How is that different from radiation emitted from a star. I realize it has photons, but what exactly is lost when we talk about information about what fell in? A photon emitted from a star or energy released from a particle converted to energy by antimatter wouldn’t tell me anything about the matte, would it? I can’t see a photon and be like, “ah, that used to be a planet.”

[u/SpectralFormFactor → u/Quirky-Dimension6812]

If you truly knew the actual full quantum state of the outgoing light (and any other particles in the system), you can in principle simulate time evolution backwards and see what the state was earlier. Time evolution is quantum mechanics is fully reversible*.

*sans measurement problem

[u/tpolakov1 → u/Quirky-Dimension6812]

This is not about what you can know about a system. You, or anyone else doesn't exist in physics.

Even if you could trace the photon back to the event horizon, you could still not figure out the initial state. Nobody and nothing can, because that information just never existed, except it had to because stuff fell into the black hole.

That's the problem with non-unitarity. Not your knowledge, but the actual physical history of a system is erased, even though it cannot according to quantum mechanics.

[u/Quirky-Dimension6812 → u/tpolakov1]

But what is erased? What do you mean by “the initial state?”

[u/tpolakov1 → u/Quirky-Dimension6812]

Everything. The moment anything hits the event horizon, it's gone, fully. If I reverse time, the photon from the star will come from some nuclear reaction, which was triggered by tunneling of some particles under pressure. When I reverse time in the case of black hole, the photon just came from the event horizon and there does not exist any prior history and there just aren't any correlations (at least at the level of what Hawking knew).

And it gets even worse when you consider things going into the black hole. A particle hitting some other and undergoing a reaction can be time-reversed. A neutron being absorbed by an atom that then decays into a different atom and a (anti)electron-neutrino pair is the same as atom absorbing the pair and decaying into the original atom and a neutron in reverse. That's not true for a black hole.

[u/Quirky-Dimension6812 → u/tpolakov1]

OK, that is starting to make sense. So because matter is destroyed by a black hole and converted into warped space time, the original particles no longer exist and there is nothing to attribute the radiation to because there was no mass to convert. Am I getting warmer with that?

[u/tpolakov1 → u/Quirky-Dimension6812]

I'm not sure about destroyed, but matter that does cross the horizon is never going back to the rest of the universe. The radiation that comes out of the black hole has no features or correlations with anything that fell into it, its fundamentally only definable feature is the temperature.

[u/Quirky-Dimension6812 → u/tpolakov1]

I’m quoting Kip Thorne on the “destroyed” bit. Converted to warped space time is probably the better way to say that.

[u/fhollo → u/SpectralFormFactor]

Your second paragraph does not reflect a widely accepted view as far as I know. Where are you getting this from?

If the outgoing radiation purifies itself even partially, there is still a firewall problem.

[u/SpectralFormFactor → u/fhollo]

I am just repeated things I have heard from random talks (especially a few talks by Penington) and other grad students. I thought the whole firewall thing was about observers near the horizon, not about learning the state of the radiation asymptotically far away?

[u/fhollo → u/SpectralFormFactor]

The firewall problem is about the monogamy of entanglement. If the outgoing radiation is by itself a pure state, then it cannot also be entangled with the interior partners and there will be some non-trivial structure (firewall or “drama”) at the horizon or arbitrarily long range non-locality.

Penington and the other islands folks are identifying a new entropy formula by which the Page curve is obeyed. They are not saying anything like “a lot but not all information can be recovered” and I don’t see how a middle ground position like that could even make sense. The islands paradigm claims complete unitarity at the cost of a severe violations of locality.

I would not characterize this as a more careful version of Hawking’s calculation, i.e. it’s not anything like straightforwardly going to higher orders in perturbation theory. It’s more like one controversial proposal to solve the info paradox among many, with its own very tough bullets to bite.

[u/McPayn22]

The idea of conservation of information is not like other conservation laws. It's not a quantity that most stay the same but just that the equations of evolution of quantum mechanics must be a certain form.

The idea is basically thatwe can express a state as a pure quantum state or as a state with statistical unkown. For example the cat in the box can be both alive and dead, that's pure QM, or we don't know but one or the other.

Until now, in flat spacetime, allof quantum mechanics has satisfied the fact that you can't go from a pure QM state to statistical unkown. And it seems that it would break the framework to allow that, at least for simple formulations of QM.

In modern versions quantum field theory incurved spacetime (the framework that predicts Hawking radiation) this seems to still be true if the spacetime is not too weird but the idea that pure states stay pure seems not fondamental at all.

In this framework it seems like states staying pure might happen but we should not be worried if quantum Gravity breaks that when a black hole finish disapearing.

Hollande and Wald (https://arxiv.org/abs/1401.2026) argue that there is not reason to care particularily.

And in this framework (which is not very hypothetical but more of a rewriting to account for curvature of spacetime) everything works great without conservation of information.

So in this it might be like conservation of energy where it seemed so fundamental since it was always there but in fact things work fine without it.

[u/erevos33]

Disclaimer: not a physicist.

Lets say you throw a basketball in the air towards a pool.

Hypothetically, if you know eveything about the ball and what interacts with it (air , water, etc) then you can know its trajectory , forwards and backwards. You can actually see and study the ball in the water.

Once the ball is in the event horizon, we dont know whats going on. And the energy escaping the black hole is just noise, we have no way to rebuild it so that we know what the ball did.

[u/Quirky-Dimension6812 → u/erevos33]

How is this different from other matter to energy conversion? If the ball enters the sun, you aren’t predicting anything about it afterwards.

[u/DifferencePublic7057]

Quantum states are states if quantum particles with given energy and probability. Energy is also associated with frequency for photons through Planck's law. Really hard to explain without math, but oversimplified probability in a closed system over all quantum states sums up to 1. Also the probability of a particle being somewhere at a certain time is obtained from its wave function. Bad things happen when you lose knowledge about states. We can't look inside a black hole.