Chiara and I were talking about physics last night, and wandered onto the topic of information leakage from black holes. It’s been a long, long time since I’ve had any conversations on the topic, or even really given it any thought.
I learned something curious a while ago from random readings I know not where: that the maximum amount of information that can be stored in a volume is related not to the volume, but the area that contains the volume. I found this really, really, really spooky. To be fair, it was presented in the context of being an argument in favor of us living in a holographic universe, and I seem to recall the article as being a wee bit provocational – intentionally making the surface area relationship seem like something we should all have a bit of an existential crisis over. I guess I fell for it.
Last night Chiara and I were talking about Hawking radiation and black holes; how information cannot be lost, even if it enters a black hole. Furthermore, the rate at which Hawking radiation is emitted from a black hole is (sort-of-obviously) going to be proportional to the surface area of the black hole. This is one of those ‘obvious’ things in physics that isn’t obvious at all, and there’s probably a two hundred page proof out there somewhere. So run with it, for now.
An aside, for clarification: information flux just refers to the rate of information crossing a two dimensional surface (though that surface might be a sphere – it’s still two dimensional). Information is what most of us would call mass, but more accurate. Photons have no rest mass, but they (can) encode information. Information is a form of order, and is subject to entropy; encoding information into an otherwise chaotic system requires energy, energy is equivalent to mass, butwhen we say ‘mass’ people think ‘thing I can hold in my hand’. So we talk about information flux instead of energy flux. At least that’s how I explain it to myself. I’m sure I am missing some important points, so don’t go quoting me to a real physicist or anything.
Anyway. We (somehow!) tied Hawking radiation back to the theory (whose? I forget) that information-flux is the ‘reason for’ the speed of light. That is to say, as a spacecraft approaches C, the amount of information about the universe crossing the spacecraft’s bow every second (pick either frame of reference) creates a ‘drag’ on the acceleration. This works both ways, of course; the cross section is a boundary in both directions. The rest of the universe is receiving information ‘about’ the spacecraft, and the spacecraft is receiving information ‘about’ the rest of the universe. I put ‘about’ in quotes, because the spacecraft is the information we’re discussing here.
It was a really exciting connection for me. For one thing, it blows away the silly notion that ‘the universe is probably a hologram because max information density is related to the surface area of a volume’. The universe might be a hologram, but relating those two things is (exactly) like saying that a bucket must be two dimensional because water flows in and out at a rate that’s proportional to its surface area, not its volume.
The conversation also made me realize something that I have ‘known’ for a long time, but never considered this way before: A ‘spaceship’ moving at nearly the speed of light is a black hole. All the same rules apply. Which makes a fun point: No matter how efficient your engine, as soon as you accelerate a craft past the point at which your spacecraft ‘obtains’ a Schwarzschild radius (which pops into place instantly, interestingly enough), you will no longer be able to accelerate further. Nor will you be able to decelerate without outside influence. Fun times! (Of course, thanks to the blue shifting of light as you accelerate, you would have melted your ship into oblivion long, long before your ship could achieve anything like this velocity).
With this hypothetical indestructible ship, one could accelerate until crossing this threshold and then use a gravitational assist to slow back down below the threshold. It’s certainly an interesting thought experiment. Way beyond me. It certainly isn’t something that can ever actually be done, at least not without technology that makes magic seem mundane.
Fun fun fun.
Another interesting question occurred to me while typing this up: If you accelerate a black hole, does its surface area increase? I suppose it must, since you’re technically increasing its mass.
The universe is truly insane.