A British clergyman who predicted black holes in 1783
bbc.com
bbc.com
> According to McCormmach, the existence of invisible stars was a relatively common idea among scientists of the time.
Talk about burying the lede. The life and times of Michell seem irrelevant here, when in fact many were calculating the idea of stars so heavy they would recapture their own light. And they were calculating this based on an incorrect principle of light-as-massive-particles. And these dark stars did not behave at all as black holes do according to modern theories.
So, black holes were not in fact predicted by British clergyman John Michell. This could have been an interesting article if it hadn't tried to force its deceptive headline.
I'm not saying there aren't similarities, but this ancient idea of invisible stars is a relatively simple thought experiment that only hints in the direction of black holes. For the most part, all the important properties of black holes were not predicted.
And strange moons circle through the skies,
Also there was too much discussion of his background before getting around to the topic at hand. A little detail might have been interesting, but it felt padded out.
According to the article, it seems that his contribution was calculating a body size/density which would, according to newtonian physics, disallow light from escaping its gravity. So while the idea of a dark star existed at the time, the especially prescient part was connecting this to gravity.
It would have been truly extraordinary if Michell had predicted _all_ of the relevant properties of black holes.
Every old theory was sort of right if you just ignore all the ways it was wrong and interpret it very liberally.
That's all you can really say: ancient Greek philosophy in no way resembled modern science, but that doesn't mean that we can't give the ones who got closer than others any credit.
I guess Archimedes was much closer to a craftsman, and Aristotle was more of what we'd call a liberal arts scholar. Reality puts a check on the flights of fancy of the craftsman.
See also the work of whoever build the Antikythera mechanism.
Some got closer by accident, not because they had the right methodology. Because of that I award them no points.
Likewise, Democritus correctly described matter as consisting of fundamental particles too small to see in 400 B.C., but verification wouldn't happen for over a millennium. Democritus still deserves credit for this observation.
One relevant excerpt:
“A phrase seems to have been humming in his ear like a tune one cannot get rid of; it crops up in his writings over and again: there is a force in the sun which moves the planet, there is a force in the sun, there is a force in the sun. And since there is a force in the sun, there must exist some beautifully simple relation between the planet’s distance from the sun and its speed. A light shines the brighter the nearer we are to its source, and the same must apply to the force of the sun: the closer the planet to it, the quicker it will move. This is his instinctive conviction, already expressed in the Mysterium Cosmographicum; but now, at last, he has succeeded in proving it.
In fact he has not. He has proved the inverse ratio of speed to distance only for the two extreme points of the orbit; and his extension of this ‘Law’ to the entire orbit was a patently incorrect generalization. Moreover, Kepler knew this, and admitted it at the end of the thirty-second chapter,18 before he became airborne; but immediately afterwards, he conveniently forgot it. This is the first of the critical mistakes which ‘as if by a miracle’ cancelled out, and led Kepler to the discovery of his Second Law. It looks as if his conscious, critical faculties were anaesthetized by the creative impulse, by his impatience to get to grips with the physical forces in the solar system.“
The more gravity, the larger the escape velocity.
But there's a maximum speed in the universe, the speed of light.
If a body has so much mass that the escape velocity is higher than the speed of light, you got a black hole.
Technically..
You certainly don't need to actually be moving at an escape velocity in order to move against the gravitational field of an object. Heck even on Earth it's not like rocket ships actually reach the escape velocity of Earth which is 11 km/s, they travel at less than half of that speed, let alone airplanes or helicopters which don't travel anywhere close to it.
An object that is able to sustain even 1 millimeter per year will be able to move arbitrarily far away from Earth, or Jupiter, or the Sun.
Black holes don't trap light because of escape velocity, and the fact that the Schwarzschild radius happens to be similar to a body's escape velocity is because both of them use the same fundamental principle in their derivation, not because the Schwarzschild radius is derived from the escape velocity.
Not sure what definition you’re using for ‘rocket ships’ - but obviously rockets that operate in earth and cislunar orbits don’t need to reach earth escape velocity. But interplanetary probes surely have to exceed the escape velocity, right?
Edit: ohhhh I think I see what you mean: you don’t have exceed escape velocity at earth’s surface. Sure. You can go to a higher altitude where escape velocity is lower and just exceed that.
Now for some reason when people talk about black holes existing because the escape velocity exceeds the speed of light, then it tricks people into thinking things they would never have otherwise thought, like in order to move away from an object you need to be moving at that object's escape velocity. Like somehow if you don't move away from an object at its escape velocity then you can't move away from that object at all.
Ignoring general relativity, if a black hole was nothing more than an object that had an escape velocity greater than the speed of light, then there's no reason why you couldn't enter the event horizon and then very slowly come back out, go back in, then sloooowly come back out, heck even come out and travel to an arbitrarily far galaxy and tell people about your adventure.
Escape velocity does not mean being unable to move away from an object, not for Earth and not for a black hole either. Escape velocity just means the velocity where no further propulsion or acceleration is needed to continue moving away from an object.
In general relativity, it's not simply that the escape velocity at the event horizon is equal to the speed of light, for if that were all there was to it, then simply bring some fuel with you to propel yourself away from the event horizon, feel free to do so at 1 cm an hour. In general relativity there are two perspectives, the perspective of the object entering the black hole where space-time curvature becomes so extreme that the spatial coordinate swaps places with the time coordinate in such a way that every future point is closer and closer to the singularity, and there is the perspective of an outside observer who sees an object getting closer to the event horizon undergo extreme time dilation and effectively freeze as their position perpetually smears itself across the entirety of the event horizon.
Light has no propulsion system, it doesn't make it out if the local escape velocity exceeds lightspeed even if there was no event horizon or other space warping effects involved.
You wouldn't even need a very significant velocity to escape the event horizon of a black hole if you had that velocity within a region close to the event horizon.
As I said, escape velocity is a good way to motivate the idea of a black hole, it serves a pedagogical purpose, but the story doesn't stop there and you quickly realize that in fact, the escape velocity itself has little to do with black holes. It just happens to share the same underlying principle that the calculation for the event horizon has.
and in case of black holes you need infinite energy to do that, in other cases the energy is finite
In mathematics one and the same theorem can have multiple derivations or proofs. WHile some proofs may be shorter, or more elegant, or rely on more widely understood theorems, they are still equally valid. Relying on fewer axioms is desirable though.
Physics is not practiced as pure mathematics. In physics there is always a tradeoff between simplicity and accuracy.
I have regularly observed different people using the same assumptions and arriving at the same resulst call each others derivation "wrong" simply because they dont like or perhaps understand each others derivation. Often just simple differences like the order of the steps, or derivations that are identical up to trivially regrouped factors in the quantities used, or one derivation working in the time domain while the other is in the frequency domain etc... It is surprising how hard people can argue while factually in agreement.
Returning to the simplicity and accuracy tradeoff. One might say there are islands where ideas quasicoherently match, where the accuracy over simplicity ratio peaks sufficiently. Without the intermediate islands no-one would be able to deduce a huge hop towards the truth. All the little islands along the way were important, even if they were flawed in hindsight.
Does the article state the clergyman derived general relativity? Or merely predicted celestial objects so heavy that light could not escape?
It is ironic that the distinction you make relies on special relativity, where frames of reference must be inertial, whereas merely considering gravitational forces requires the considerations of accelerating reference frames.
Konrad Zuse on the other hand ... not so many props thrown his way -- for obvious reasons, given the timing, but that doesn't have to continue.
One of his later systems was even proven to be Turing-complete! Pretty impressive for someone having absolutely no knowledge of what was happening elsewhere, like at Bletchley Park...