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Comment by Maxatar | Hacker News Reader

The escape velocity is a nice pedagogical argument but it's completely incorrect and almost trivial to see why.

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.

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no sane mind would consider (then still hypothetical) light particles to carry propellant (functionally energetic fuel and reaction mass)

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.

> it's not like rocket ships actually reach the escape velocity of Earth

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.

No I really just mean the plain and simple scenario. Imagine you knew nothing about escape velocity or black holes, then you would not be confused at all by the idea that an object can move away from the Earth at any speed whatsoever, so long as its direction was away from the Earth. You don't need to move at Earth's escape velocity to move arbitrarily far away from the Earth. You could in principle travel all the way to the Andromeda galaxy without ever exceeding the Earth's escape velocity at any point.

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.

But you need some sort of propulsion system if you wish to escape while moving slower than local escape velocity. Rockets can do it because they have such a propulsion system. (Although in practice any ordinary rocket will normally exceed the escape velocity from the surface of the Earth. Due to Oberth you want to do your burn as close to the planet as possible and escape velocity from low orbit is only slightly less than from the surface. Since when you head out into interplanetary space you're normally going somewhere you're carrying extra velocity.)

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.

Make it out of what though? If all there is to consider is escape velocity, than light, or any object whatsoever, can absolutely escape the event horizon if it's moving at anything remotely close to the speed of light. Without propulsion it won't be able to travel to an arbitrarily far distance, but it can certainly escape the event horizon in any scenario other than if its initial velocity came from when the the object was at the center of mass.

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 note that he was looking at that--light might come up but not get away. The model is different but the results would look the same to an outside observer.

> An object that is able to sustain even 1 millimeter per year

and in case of black holes you need infinite energy to do that, in other cases the energy is finite

Right. In general relativity the fact that you can't escape a black hole isn't about velocity, it's about geometry. There's literally, physically, no path out.

But that is due to extreme curvature on account of the body’s mass. I think that John Michell was on the right path to discovering black holes, but the sciences known to him and his time weren’t sufficient for him to complete the thought.

these two concepts are distinguishable, since velocity ends up being about geometry.

Word salad.

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