The black hole information paradox has been receiving some attention lately. This is the fact that information, that is any pattern of matter, that falls into a black hole is completely crushed as it approaches the singularity, losing whatever differentiation it might have had before. This has long been recognized as a problem, because in physics, information is supposed to be conserved.
Sabine Hossenfelder did a post on this issue a while back that I thought was pretty good. Interestingly, Hossenfelder explained the whole thing with nary a mention of “information” until the end. It’s all about deterministic processes and reversibility. It was one of the steps in my own realization that information is causation. But that left me interested in how this issue might eventually be resolved.
One solution that has historically been considered is that maybe all the information is preserved on the black hole’s event horizon. This is caused by the fact that, to an external observer, due to time dilation, an object never completely falls into a black hole, it just gets slower and slower as it approaches the event horizon.
As I understand it, a difficulty for this view is Hawking radiation, a very small amount of radiation that, due to quantum processes on the event horizon, manages to escape the black hole. Eventually that radiation leads the black hole to decay away. (“Eventually” for a respectable black hole might be something like 10100 years.) The problem is that, afterward, all that is left is an undifferentiated cloud of Hawking radiation in the universe, with no possibility, even in principle, of reconstructing what had fallen into the black hole throughout its history, again violating the conservation of information.
Recently, there was a Quanta article implying that maybe the information paradox has been solved. As I noted when I tweeted the article, it’s extremely interesting, but it seems like there are a lot of assumptions in the calculations, many of them non-trivial. And I’ve seen a number of physicists express skepticism that the paradox has really been solved, most recently Ethan Siegel at Starts with a Bang.
I have nothing intelligent to say on whether the paradox has been solved. That’ll have to be decided between theoretical physicists. But I do have a question, an extremely basic one, one that I’m hoping someone more familiar with the physics can answer. I’ve tried finding the answer in popular accounts of the paradox, but have come up empty so far.
As I noted above, any pattern of matter entering a black hole is crushed, right down to its sub-atomic components, as it approaches the singularity. (It does approach the singularity even if it remains smeared on the event horizon. One is true from the perspective of an observer falling in, the other from an external observer watching what happens. Relativity makes my head hurt.)
This crushing away of any differentiation leads to the black hole “no-hair theorem”, which basically says that a black hole, any black hole, can be fully described by its mass/energy, linear-momentum, angular-momentum, position, and electric charge. So black holes can’t be distinguished by what they consumed to acquire their size. A black hole that reached its size by consuming stars is indistinguishable from one that reached its size by consuming dark matter, except by the above attributes.
This seems to fit with the information paradox issue. Except that no account I’ve read talks about what effect the incoming information has on the attributes that are distinguishable. Suppose we have two books, each the same size and weight with the same number of pages, but with completely different text. A casual reading of the no-hair theorem, as well as the information paradox, might be that each book, if thrown into the black hole, should have exactly the same effect as the other.
But this doesn’t seem true to me. While the only difference between the books is the text, that is a difference, a physical difference. The difference amounts to where the atoms of ink are attached to the various pages. It seems like these different configurations of atoms should make a difference in the black hole’s attributes, an infinitesimally minute difference to be sure, but a difference just the same.
If so, if these differences result in changes in angular and linear momentum, however minor, changes that put the black hole at a different position at a different time than it otherwise might have been, then those seem like changes that affect the outside universe. The momentum, position, and path of the black hole make a difference in its gravitational effects, effects which propagate to the surrounding universe, altering the way the black hole affects surrounding stars, gas, or anything else.
If that’s true, then my questions is, why isn’t the lost information contained in all these perturbative effects as they propagate into the universe? Why do physicists even need to concern themselves with things smeared on the event horizon or the final nature of Hawking radiation?
I fully realize this is me not understanding something fundamental about what is happening. I’m just not clear on what it is. I’d be grateful for any ideas or references that would set me straight.