[Chabs]

Outside observers never see the material cross the horizon, ever. That's why it's called a horizon, you'll never reach it (from the pov of an outside observer).

Growth-wise, you have to keep in mind that the black hole doesn't grow when matter crosses the horizon, but when the matter gets close enough to the horizon that mass of black hole + mass of new matter creates a blackhole of a larger radius that encompasses that matter.

[takk309]

Would this be one way that information would not be destroyed, at least from the reference frame of the outside observer?

[ncallaway]

By my understanding of the theory, yes (according to some unproven theories). The information can be imprinted on the surface of a black hole (and, later are dissipated by imprinting on Hawking Radiation).

This is also the principle that led to our theoretical understanding that the maximum amount of information that can be contained in a volume is bounded by the _surface area_ of the volume. This is the Holopgraphic Principle: https://en.wikipedia.org/wiki/Holographic_principle.

There's a great PBS Space Time youtube video on this concept, which explains it far better and more accurately that I ever could: https://www.youtube.com/watch?v=9XkHBmE-N34

[takk309]

Thanks for the great reply.

[0898]

Question if you don't mind. This "information being destroyed" thing. What do they mean by information? Isn't information a human construct? How is the universe supposed to know what information is?

[russdill]

Our theories of physics are time reversible. If you play a movie of an egg breaking backwards, it's a perfectly physically possible thing. It's just super unlikely. If you had perfect knowledge of the state of the egg, you could simulate it backwards to get the egg.

If information can be destroyed, physics are no longer reversible. Playing things in reverse would give you events that occur for no reason. This is hugely important not just for particle physics, but also thermodynamics.

[knodi123]

A fun way to imagine it is with Maxwell's Demon.

https://en.wikipedia.org/wiki/Maxwell%27s_demon

That is an example of one way in which information can be exchanged for work.

[smogcutter]

This is me being dense, but I don't see the connection to parent's question. Is it that the demon uses information (the speed of the particles?) to perform work (decrease entropy)? But also not really, bc that would violate the 2nd law of thermodynamics? I understood parent's question to be what the heck does "information" mean in this context to begin with. My question too, because I'm pretty sure I've got the wrong answer myself.

[Chabs]

Information as actual physical property (as opposed to a human construct) is basically the only way we found to solve Maxwell's demon seemingly reducing entropy.

Specifically, the entropy within the box gets converted into information inside the demon's "head", which eventually gets radiated away as entropy outside the box. This way, the box's entropy falls, but the entropy of universe as a whole is raised (or at least maintained).

[ComputerGuru]

https://en.m.wikipedia.org/wiki/Physical_information

See especially the section on entropy.

[Chabs]

Long answer short: Information has to be a fundamental conserved property of the universe for the second law of thermodynamics to work under some thought experiments.

[takk309]

From my limited understanding information is meant to mean the characteristics of a given particle; the waveform, spin, etc.

[codethief]

There're different levels of making this statement precise. Here's one:

Physics is a deterministic theory, even at a quantum level where we call determinism unitarity. (Leaving the measurement problem & collapse of the wave function aside for a moment.)

Determinism means, we can start with one state of a given physical system and basically hit the "fast forward" or "backward" button to see what the state was like in the past and what other state it's going to evolve to in the future. This assignment of future states to past or current states and vice versa is unique and one-to-one, hence deterministic:

past -> future

A --------> X

B --------> Y

where the arrows indicate evolution in time.

This is what allows us to make predictions for the future outcome of experiments or draw conclusions from experimental results in the first place.

Now, the problem with black holes and in particular their evaporation through Hawking radiation is that Hawking radiation does not in any known way depend on what once fell into the black hole but, instead, just on the black hole's total mass. So let's say you start with two different mass distributions A, B of the same mass M and each collapses and forms a black hole BH of mass M. You could argue that the original matter is still somewhere inside the black hole, so the black hole's internal state still depends on the past matter distribution and we should indicate this by talking about black hole BH_A and black hole BH_B. So we have:

A -> BH_A

B -> BH_B

Then Hawking radiation sets in and both black holes vanish eventually and give way to a state of Hawking radition H:

A -> BH_A -> H

B -> BH_B -> H

As mentioned before, the Hawking state H really only depends on the mass M of the black hole, so since both BH_A and BH_B had the same mass, we will also get the same final Hawking state H. As you can see, the mapping {past events -> future events} is no longer one-to-one: From H alone you cannot draw any conclusions about the original state anymore. (Was it A or B?)

This is (one half of) what is meant when people say that information is lost (about the original state).

The other half is that a classical (eternal) black hole state is a so-called pure state from the point of quantum mechanics: There is never any doubt about its precise state. It is always perfectly described by only its mass (and angular momentum and charge)[1]. Hawking radiation, however, is not such a state once the black hole has fully evaporated. Instead, at that point it is a so-called mixed quantum state meaning that it could be any of a whole "mix" of states. We can only give a probability distribution for what the state is in reality; in Hawking's case it's a perfectly thermal distribution. (Side remark: I should point out that such a mixed state is not the same thing as a superposition in quantum mechanics! In particular, the probability distribution here is not related to any wave function.)

Anyway, what this means is that we have now evolved from a black hole state BH, that was precisely known, to another state about which nothing can be said anymore outside of the probability distribution:

BH -> Hawking_1 or Hawking_2 or Hawking_3 or …?

This constitutes a loss of predictability.

TL;DR To sum up, there are two aspects: The loss of information and the loss of predictability. Both are just the two sides of the same medal: The breakdown of determinism.

[1] https://en.wikipedia.org/wiki/No-hair_theorem

[0898]

Thanks for this answer. Appreciate it.

[doombolt]

How would you ever observe black hole to grow/accreate matter then?

[qubex]

Infalling matter or radiation becomes ‘simply’ infinitely red-shifted (on account of the slowed time), and hence undetectable to an external observer — and is hence indistinguishable from the bulk of the prior-existing “black hole proper”.

[mcbits]

Conversely, a particle on the surface of an object compressed to near its Schwarzschild radius should experience an extreme blue shift and time contraction. Imagine absorbing in one instant a billion years of microwave background radiation blue shifted to gamma and beyond. How could the near-black-hole hang onto it?

[Already__Taken]

Inside of a black hole doesn't hang on to anything. There is simply no longer a direction that points out.

[qubex]

Yeah... basically looking backwards from the perspective of an infalling particle one would experience the full blast of the Big Bang as it occurred ‘originally’.

[doombolt]

Yes, it is indistinguishable. But it seems that actual black hole is more like a hollow crust in this setting and not a point of mass.

[pitaj]

You can indirectly measure it's mass, charge, and angular momentum.