Adam Brown: prediction

Transcript context

…Great question. There are actually two different perspectives you could take. One is the perspective of me watching you falling into the black hole. The other is the perspective of you falling into the black hole. Those two perspectives are consistent with each other but interestingly different, so maybe I should describe them both. First, let’s ask the question: what do I see as you fall into the black hole? This is how hard you need to fire your rocket to not fall into the black hole but you’re not going to do this. You’re just going to sit here a long, long way away from the black hole, turn off your rocket, and accept what comes. What comes is you’ll slowly accelerate towards the black hole, at a rate first given by the Newtonian formula and then, when you get close to the black hole, start picking up general relativity corrections to the Newtonian inverse-square law. What I will see as I watch you fall towards the black hole is that first you’ll go faster and faster and faster as you fall down the gravitational potential of the black hole. But then something strange will happen. You’ll stop going faster, and you’ll start going slower. The reason you’re going slower is that, as I watch you, you start to get gravitational time dilation as you fall down, and I start to see your clock running slow. The static formula doesn’t apply exactly since you’re moving, but the formula has the same effect, which is that as you get closer and closer to the black hole, your wristwatch starts running slower and slower and slower. In fact, if you do the appropriate integral, I never see you cross the event horizon. I just see you getting closer and closer to the event horizon, but slowing and slowing as you approach it. As I watch you—I’m presumably using light to watch you—that light gets more and more redshifted. The wavelength gets longer and longer, and the longer the wavelength of light, the harder it is to even really see you. You start getting delocalized by the wavelength of the light, and eventually I just stop seeing you entirely. There’s a final photon that you emit, and then you just fade to black, fade through red to black. I never see you cross the event horizon. This was noticed by people in the early days of general relativity and greatly confused them. They started to think that you would experience something funny yourself as you fell across the event horizon. That is not true. If I instead adopt your perspective, from your point of view, your clock isn’t running slow. It’s running at one second per second. If you look back at me, there’s some funny stuff going on to do with me running fast perhaps. But as far as you’re concerned, everything’s totally normal. You accelerate towards the black hole, getting faster and faster as you approach it. You just sail across the event horizon totally as normal. The event horizon is not a particularly violent place for you. ccelerate towards the black hole, getting faster and faster as you approach it. You just sail across the event horizon totally as normal. The event horizon is not a particularly violent place for you. You can calculate the tidal forces as you approach and then cross the event horizon. They’re not particularly big, or rather, for large black holes, they’re not particularly big. For a solar mass black hole, they would be pretty big and would be pretty painful. You’d find that your feet are being attracted to the black hole much more vigorously than your head is, because they’re closer, and you end up getting stretched. But if I take a big enough black hole, you wouldn’t notice anything funny happening whatsoever. The bigger the black hole, the smaller the tidal effects. If I took a black hole the mass of the galaxy, you’d be basically fine as you cross the event horizon. If I took an even bigger black hole than that, you could live out your entire life having crossed the event horizon, before you hit the singularity, which is fatal. When you cross the event horizon, you are doomed. You are doomed because once you cross the event horizon, you must proceed to the singularity. There’s no way you can fire a rocket to stop yourself hitting the singularity. You are doomed, but you are not dead. You are only for sure dead once you hit the singularity and get spaghettified, mangled by the tidal forces. But for a large enough black hole, you can be doomed and not even know it. The event horizon is really a not locally measurable quantity. It is a teleological fact. It says that once you have crossed the event horizon, you must proceed to the singularity. But it can take a long time to get there for a large enough black hole. In principle, for a black hole that was many light centuries across, you could live out your entire life. You could have descendants, all of whom live inside the black hole. Only once you really approach the singularity do the tidal forces get strong and kill you. As you were saying, GR explains or predicts a lot of phenomena. Some we think are correct, some we don’t know are correct. Why do we think black holes are correct but not wormholes?…

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