The correct answer is no one knows, but I’m going to make a wild, speculative, not fully-informed guess and suggest, possibly nothing. But first, a detour, to provide some context.
I came across an interview with very successful, multi-award-winning, Australian-Canadian actor, Pamela Rabe, who is best known (in Australia, at least) for her role in Wentworth (about a fictional female prison). She was interviewed by Benjamin Law in The Age Good Weekend magazine, a few weekends ago, where among many other questions, he asked, Is there a skill you wish you could acquire? She said there were so many, including singing better, speaking more languages and that she wished she was more patient. Many decades ago, I remember someone asking me a similar question, and I can still remember the answer: I said that I wish I was more intelligent, and I think that’s still true.
Some people might be surprised by this, and perhaps it’s a good thing I’m not, because I think I would be insufferable. Firstly, I’ve always found myself in the company of people who are much cleverer than me, right from when I started school, and right through my working life. The reason I wish I was more intelligent is that I’ve always been conscious of trying to understand things that are beyond my intellectual abilities. My aspirations don’t match my capabilities.
And this brings me to a discussion on black holes, which must, in some respects, represent the limits of what we know about the Universe and maybe what is even possible to know. Not surprisingly, Marcus du Sautoy spent quite a few pages discussing black holes in his excellent book, What We Cannot Know. But there is a short YouTube video by one of the world’s leading exponents on black holes, Kip Thorne, which provides a potted history. I also, not that long ago, read his excellent book, Black Holes and Time Warps; Einstein’s Outrageous Legacy (1994), which gives a very comprehensive history, in which he was not just an observer, but one of the actors.
It's worth watching the video because it highlights the role mathematics has played in physics, not only since Galileo, Kepler and Newton, but increasingly so in the 20th Century, following the twin revolutions of quantum mechanics and relativity theory. In fact, relativity theory predicted black holes, yet most scientists (including Einstein, initially) preferred to believe that they couldn’t exist; that Nature wouldn’t allow it.
We all suffer from these prejudices, including myself (and even Einstein). I discussed in a recent post how we create mathematical models in an attempt to explain things we observe. But more and more, in physics, we use mathematical models to explain things that we don’t observe, and black holes are the perfect example. If you watch the video interview with Thorne, this becomes obvious, because scientists were gradually won over by the mathematical arguments, before there was any incontrovertible physical evidence that they existed.
And since no one can observe what’s inside a black hole, we totally rely on mathematical models to give us a clue. Which brings me to the title of the post. The best known equation in reference to black holes in the Bekenstein-Hawking equation which give us the entropy of a black hole and predicts Hawking radiation. This is yet to be observed, but this is not surprising, as it’s virtually impossible. It’s simply not ‘hot’ enough to distinguish from the CMBR (cosmic microwave background radiation) which permeates the entire universe.
Here is the formula:
S(BH) = kA/4(lp)^2
Where S is the entropy of the black hole, A is the surface area of the sphere at the event horizon, and lp is the Planck length given by this formula:
√(Gh/2πc^3)
Where G is the gravitational constant, h is Planck’s constant and c is the constant for lightspeed.
Hawking liked the idea that it’s the only equation in physics to incorporate the 4 fundamental natural constants: k, G, h and c; in one formula.
So, once again, mathematics predicts something that’s never been observed, yet most scientists believe it to be true. This led to what was called the ‘information paradox’ that all information falling into a black hole would be lost, but what intrigues me is that if a black hole can, in principle, completely evaporate by converting all its mass into radiation, then it infers that the mass is not in fact lost – it must be still there, even if we can’t see it. This means, by inference, that it can’t have disappeared down a wormhole, which is one of the scenarios conjectured.
One of the mathematical models proposed is the 'holographic principle' for black holes, for which I’ll quote directly from Wikipedia, because it specifically references what I’ve already discussed.
The holographic principle was inspired by the Bekenstein bound of black hole thermodynamics, which conjectures that the maximum entropy in any region scales with the radius squared, rather than cubed as might be expected. In the case of a black hole, the insight was that the information content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon. The holographic principle resolves the black hole information paradox within the framework of string theory.
I know this is a long hop to make but what if the horizon not only contains the information but actually contains all the mass. In other words, what if everything is frozen at the event horizon because that’s where time ‘stops’. Most probably not true, and I don’t know enough to make a cogent argument. However, it would mean that the singularity predicted to exist at the centre of a black hole would not include its mass, but only spacetime.
Back in the 70s, I remember reading an article in Scientific American by a philosopher, who effectively argued that a black hole couldn’t exist. Now this was when their purported existence was mostly mathematical, and no one could unequivocally state that they existed physically. I admit I’m hazy about the details but, from what I can remember, he argued that it was self-referencing because it ‘swallowed itself’. Obviously, his argument was much more elaborate than that one-liner suggests. But I do remember thinking his argument flawed and I even wrote a letter to Scientific American challenging it. Basically, I think it’s a case of conflating the language used to describe a phenomenon with the physicality of it.
I only raise it now, because, as a philosopher, I’m just as ignorant of the subject as he was, so I could be completely wrong.
Addendum: I was of 2 minds whether to write this, but it kept bugging me -
wouldn't leave me alone, so I wrote it down. I've no idea how true it
might be, hence all the caveats and qualifications. It's absolutely at
the limit of what we can know at this point in time. As I've said
before, philosophy exists at the boundary of science and ignorance. It ultimately appealed to my aesthetics and belief in Nature’s aversion to perversity.