I don't remember reading this before (in the Penrose obituary), that is that he discovered Hawking radiation when trying to prove that it didn't exist:
> Bekenstein realised this was key to the entropy problem. Every time a black hole swallows matter, its entropy appears to be lost, and at the same time, its event horizon grows. So, Bekenstein suggested, what if – to preserve the second law – the area of the horizon is itself a measure of entropy?
> Hawking immediately disliked the idea and was angry that his own work had been used in support of a concept so flawed. With entropy comes heat, but the black hole couldn’t be radiating heat – nothing can escape its pull of gravity. During a break from the lectures, Hawking got together with colleagues Brandon Carter, who also studied under Sciama, and James Bardeen, of the University of Washington, and confronted Bekenstein.
> The disagreement bothered Bekenstein. “These three were senior people. I was just out of my PhD. You worry whether you are just stupid and these guys know the truth,” he recalls.
> Back in Cambridge, Hawking set out to prove Bekenstein wrong. Instead, he discovered the precise form of the mathematical relationship between entropy and the black hole’s horizon. Rather than destroying the idea, he had confirmed it. It was Hawking’s greatest breakthrough.
> Black holes were a subject ripe for investigation in the early 1970s. Although Karl Schwarzschild had found such objects lurking in the equations of general relativity back in 1915, theoreticians viewed them as mere mathematical anomalies and were reluctant to believe they could actually exist.
Can someone recommend some books to learn these equations? I'm fascinated by the fact that an object can be found in an equation before it's observed.
I believe this falls out directly from the finite speed of light and fact that gravity would distort spacetime. You'd eventually end up with gravitational wells that light can't escape from.
That's a classical cartoon sketch of a black hole, it's not how they work in relativity. Black holes (specifically event horizons) are phenomena of space-time. They are regions where space-time is distorted in a way that leads to no space-time trajectories that leave the event horizon (in fact, all space-time trajectories that start within an event horizon inevitably have futures which go into the singularity). They incidentally trap light, but it's more accurate to say that they trap the future.
> They incidentally trap light, but it's more accurate to say that they trap the future.
That's an extraordinarily poetic way to put it, and not wrong. But I'd say that the black hole doesn't trap exactly the future, but rather prevents it from occurring. Due to time dilation the theoretical observer falling into the hole observes nothing special at event horizon and indeed time slows and asymptotically stops.
That observer is forever falling, forever seeing out, slower and slower.
Makes me wonder. Could you have a hollow black hole? I.e. some kind of large, spherical boundary for "all space-time trajectories", but left some space(time) in the interior free of large gravitational gradients - a space where stuff could live "normal time", forever isolated from the rest of the universe.
But where then does the gravity come from the BH? If all forces are transmitted by particles, where do the gravitons come from to pull things into the BH?
Slightly OT but since we are on HN I wanted to share my belief that coding turns from science to art when you start seeing possibilities in the algorithms that you didn't see before. Maybe a model that can best be described as an actual object when it adheres to the principles of quantum physics, for example.
Besides anti-matter that people already commented, the neutrino was kind of taken from an equation, the Higgs bosson was taken from an equation, the high mass quarks were also first predicted on equations.
The independence of the speed of light from the speed of the observer was predicted on an equation. The quantization of light was first predicted by an equation.
But there is the other side too. Tachions, for example were also predicted by a widely accepted equation. I guess it's more common for things predicted on equations to not exist than for them exist, but a lot of what we know came from theory.
> Bekenstein realised this was key to the entropy problem. Every time a black hole swallows matter, its entropy appears to be lost, and at the same time, its event horizon grows. So, Bekenstein suggested, what if – to preserve the second law – the area of the horizon is itself a measure of entropy?
> Hawking immediately disliked the idea and was angry that his own work had been used in support of a concept so flawed. With entropy comes heat, but the black hole couldn’t be radiating heat – nothing can escape its pull of gravity. During a break from the lectures, Hawking got together with colleagues Brandon Carter, who also studied under Sciama, and James Bardeen, of the University of Washington, and confronted Bekenstein.
> The disagreement bothered Bekenstein. “These three were senior people. I was just out of my PhD. You worry whether you are just stupid and these guys know the truth,” he recalls.
> Back in Cambridge, Hawking set out to prove Bekenstein wrong. Instead, he discovered the precise form of the mathematical relationship between entropy and the black hole’s horizon. Rather than destroying the idea, he had confirmed it. It was Hawking’s greatest breakthrough.