Yes

 

Ahh the day I actually check in on the forums.

Simply put, your answer is wrong. You can't escape a black hole.
Solving for a variable is a piece of cake. However you are missing a crucial piece.
Your calculation would work for any distance outside of the event horizon. However, if you have a black hole of any mass, such as a solar mass (M☉), once you pass its event horizon, things get odd. Simply put, we don't know the laws of physics in this mysterious region of space. Thus we cannot draw a definite conclusion that the escape velocity would need to be that value.
We must remember some very important key features.
-The event horizon is not a kind of wall. The event horizon is the region where the escape velocity exceeds "c". Nothing in the universe can travel faster than "c", as it would gain infinite mass as it approached "c". Also, time dilation would affect your velocity relative to an observer, and you would never reach"c".
-A singularity is not an object, it is a point with no volume. Think of it as a point in one dimension. The singularity, which is a point, has no volume. however it has mass. How do you fit mass in no volume? Well, logically you would say it follows the divide by 0 error, however we say the density is infinite. Remember density=mass/volume.

You also must take a look at the quantum mechanical portion of this. Here lies many issues.
The reason we can't simply solve for some value within the event horizon is because of this. Once mass passes the event horizon and is spaghettified, it breaks up into elementary particles. Here, the concept of symmetry and super symmetry play a role. That is another topic. The man would now be many particles and information. Obviously, the value of m would change, which would skew the theoretical escape velocity. You also have issues with quantum mechanics, but I am not an expert in that field and would hate to give you a less than significant explanation of it.

Basically you can't apply classical equations to relativity scenarios. Mathematically and theoretically, that value is meaningless. Classically, it does, but black holes don't follow classical laws of physics within the event horizon.

I hope you find meaning in this comment. (A simple "yes" , mind you was the wrong answer, is just confusing the poor kid).^^

Also, I would advise against looking up the mathematics behind such events for now. If you must ask for confirmation of solving for a variable on a minecraft forum, I only worry what you may get yourself into looking at advanced calculus. You will only confuse yourself. However I do applaud you for coming out and learning stuff. Just take it step by step.

 

Do correct me if I'm wrong, but I believe the current understanding permits the possibility of particles travelling faster than the speed of light (neutrino's) However you cannot /accelerate/ an object past c.

Regardless a brilliant and, more importantly, simple explanation. Thank's for the read :)

 

That is indeed correct. The observation of neutrinos traveling faster than the speed of light is puzzling. However, neutrinos are one of many elementary particles which is part of the standard model and should not be confused with particles such as quarks and subatomic particles traveling faster than the speed of light. I haven't done much research in quantum/particle physics, so I could not provide a decent explanation behind that neutrino property. Also, there is need for more testing. The neutrino traveling faster than c isn't a universally accepted concept yet.
(Regarding the black hole, keep in mind that the neutrino was only measured to travel a few centimeters (if even) faster than c. Plus, neutrinos don't make up matter)

 

Well, technically speaking everyone is undergoing a degree of 'spaghettification' from some frame of reference. It certainly doesn't affect us in a day to day sense, but accelerating or decelerating does change our length and mass (from an inertial frame of reference)

 

spaghettification occurrs because the gravitational pull of your feet is much stronger than the gravitational pull on your head, and thus would "spaghettify" the person. And on a cosmological scale, 750 meters is more than a decent distance for anything to be spaghettified. 750 meters may seem like a long distance on earth, but on a larger scale like this it might as well not even exist. But the point is that everything is made up of particles, and those particles would be ripped away from the central mass. Quarks will not have the same gravitational pull of a 200 Lb man.

And no, you don't seem to understand. We don't know what would happen past the event horizon. Your calculations are false because of the simple fact that nobody knows what would happen past it. Past the event horizon, classical physics cannot be applied. Newton's gravitational equation cannot be applied. All classical physics is meaningless past the event horizon.

Basically just because you are having fun with calculations doesn't make it correct. Do not put your mindset into that, because it won't get you far in the physics field. If you apply quantum physics to classical physics "for fun", it doesn't make it true.

We live not on a (x,y,z) plane, but in a universe with spacetime. Real life calculations INSIDE OF A BLACK HOLE are too complicated to start off with. You should start off with more basic things.

You got the plane geometry math right, but the theoretical physics part wrong. And universal calculations with Einstein's equations? ...not yet.

 

Wut

 

@CosmOrigist teach me plz

 

Speaking of interesting particles with interesting behaviors, ever heard of the double slit theory? The gist of it is, electrons behave differently when being observed by a measuring device than when not being observed by a measuring device. Basically, they know we're watching them. (this doesn't imply they are intelligent beings or alive. It just implies that they were made to behave differently when observed, which is puzzling. )
http://highexistence.com/this-will-mindfuck-you-the-double-slit-experiment/

There are some things we may never be able to explain.

 

Neutrinos going faster than the speed of light has been throughly debunked. Quarks are also elementary particles in the standard model. Subatomic particles is a general term for hadrons, which is to say things made up or quarks. This is to say that neutrinos aren't completely different creatures from quarks. We know neutrinos travel slower than the speed of light because they experience change of "color" hence they experience time and hence have mass/travel less than the speed of light.

 

It all depends on the mass of the black hole. In more massive blackholes, people could easily cross the event horizon and get close to the singularity. In less massive blackholes, one would be spagehtified well before the event horizon. Also, this is going to sound weird, but you have to be careful with the concept of distance. Space inside and near the blackhole is curved like a funnel. So when you talk about distance, you could mean lateral distance from the edge of the funnel to the center or you could mean distance along the edge of funnel to the center, which will be longer. I might recommend you read Kip Thorne's book black holes and time warps. I have read it several times, and it will help answer your questions on black holes. If you have no physics background, the Feyman lectures on physics are classic introductions to the subject and many are easily accessible.

 

There is no way to know someone could cross the event horizon and live, or even cross in one piece.

 

It's a bit more complicated than that: Newton's gravitational law is a good approximation of gravity when the gravitational field is relatively weak, but as the gravitational field gets stronger, then the approximation is worse. Near the event horizon, Newton's law works horribly wrong, and you are forced to take into account General Relativity. Newton's gravitational law can be obtained as approximation of General Relativity under the conditions I specified.

Again: that formula is correct within a weak-gravitational-field environment, as it is a direct consequence of Newton's gravitational law. But under the extreme conditions near a black hole you can't just outright use: you need to take GR into account.

Actually, no. Let me elaborate.
Faster-than-c particles have been hypothesized theoretically, however for deep theoretical reasons they cannot interact with slower-than-c stuff. In absolutely no way. That means that:

1. we cannot measure them and prove their existence;
2. we cannot disprove their existence too;
3. they cannot have the slightest effect on us.

We have learned from history to be very wary of people saying weird things, feeling justified by the fact that "YOU CANNOT DISPRVE MA TEEOREE!!1!". That's a fundamental principle of Science known as falsificationism, which basically says "if something cannot be proven, disproven, or interacted with, why on Earth should we talk of such an irrelevant matter in the first place, when there's plenty of more serious stuff to understand in the, you know, real world?"
So, unless someone comes out with a theory of faster-than-c particles which:

1. do have an effect on the real world, and therefore can be interacted with somehow;
2. this theory is coherent with the currently most experimentally sound theories;
3. this theory can make predictions on measurements that have not been done yet;
4. last, but most important, the prediction of this new theory differ somehow from what we would have expected otherwise, thus allowing us to experimentally test the theory against the null hypothesis;

I was saying: unless all of this... faster-than-c particles are metaphisical objects, so you should probably call a priest and not a physicist.

"The horror! THE HORROR!" (cit.)
Every time I read something like this, I die a bit on the inside.
The very people from OPERA who made the "announcement" were extremely skeptic about their result. They were awkward, like: "We really tried very hard to find a mistake somewhere, really, there must be a mistake somewhere because this makes no sense at all, but we just couldn't find any, so, just to avoid conspiracy theorists to say that we hide the truth, here's what we saw. please, international scientific community, help us find the mistake as soon as possible please please"
A few months later, rather predictably, the mistake was found: https://en.wikipedia.org/wiki/OPERA_experiment#Time-of-flight_measurements
Did mainstream media say: "Sorry! The titles in red letters we published a few months ago were extremely exaggerated and actually more accurate measurements dismissed that anomaly"? NO WAY. Pictures of some not-so-famous chick suntanning at the shore gets more attention than a "sorry, we were wrong". Thank you, journalists, for spreading misinformation due to your own incompetence on what the scientific method is.

No, let's not mix length contraction with spaghettification: length contraction is a relativistic phenomenon (just Special Relativity, no need for General Relativity) which does not have any physical consequence, in the naive meaning of the world: you don't feel your length diminish, because it doesn't diminish in your frame of reference. It does in some other frame reference, but it's more of an artifact of the way we mathematically represent the world.
Spaghettification, on the other hand, is an extremely physical effect: you are really stretched, you feel a force pulling your head away from your feet. But we neither need to take into account Special Relativity nor General Relativity to explain that. Take Newton's formula: it gives you the force you feel, depending on your position. If you don't have where to hold on to, you fall freely and you feel weightless. But what if you are not a material point, but something with some length? Then, if you are aligned "vertically", the gravitational pull on your head is slightly lower than that felt by your feet: your feel will "try to go down" harder than your head. If you fall freely, the average force you will feel will still be zero (you will feel weightless, on average), however you will feel a force trying to elongate your body. It's called a tidal effect.
This is, by the way, the very reason why the Moon causes tides. But I want to clarify a common misunderstanding: it's not the Moon's gravitational net attraction to cause the tides! If it was that, then why do we have tides twice a day, one on the side of the Moon and one on the opposite side? The real cause of the tides is the difference of pull from the Moon on the two sides of the Earth (one facing the Moon, one on the opposite side). Earth's most mobile part are the oceans, but if Earth was all a giant blob of water it wouldn't be a sphere: it would be an ellipsoid (that is: an elongated sphere) oriented accordingly to the Moon's position.

I hope you are just trying to be more colorful. What really happens is... no, I'm not trying to explain this better than how the good old Richard P. Feynman did:
http://www.feynmanlectures.caltech.edu/III_01.html
And that's the least difficult part of Quantum Mechanics to understand, by the way: it makes perfect sense, once you are in the right framework and learn the math.

Technically, in our frame of reference, they never cross the event horizon, because their time (relatively to our time) slows down asymptotically to zero. So it's not that we cannot answer the question: the question is just unaskable

 

You refer to time as "zero". Are you implying that time does not continue and that it is halted or that the human perception of time no longer exists.

 

I'm saying that, if you are outside of the blackhole and you are far enough away, and you want to describe objectively the trajectory of a body free-falling towards the blackhole, then in your description it would never cross the event horizon.
Say, the universe is gonna last 175 pentazillions years? For that body to get through the event horizon, in your reference frame, it's going to take more. It's just never going to happen, in your reference frame.
I didn't say that time goes zero. I said that their time, relatively to your time (assuming you are far away), asymptotically slows down to zero. I was referring to the flow of time, to the difference in how their time flows relatively to your time. Over there, everything happens extremely slowly: the closer they are to the event horizon, the slower time flows, and therefore the slower they fall towards the event horizon. And asymptotically they never reach that point.

 

Ok here's an example. You know Zeno's paradox? Basically the paradox goes like this:

Now, if you take this literally, it's obvious bullshit: put your damn shoes and walk for 1km, problem solved.
But it can be an opportunity to reflect: why is the paradox false? It seems logical, but the outcome is contradicted by facts, therefore there must be some mistake in the logic of the paradox, though well hidden.
This is the mistake: yes, in order to travel 1km, you first have to travel 0.5km, and then 0.25 km, and then 0.125km, and then... etc. But even though you need to sum up an infinite amount of numbers, the result is not automatically infinite! In this case, indeed, 1/2 + 1/4 + 1/8 + 1/16 + .. = 1. So it actually takes a finite amount of time to travel from A to B.
Now, let's change things a bit: Imagine that, after you get to C, you decrease your speed to 1/2 of the speed you had before reaching C. And after you reach D, you decrease your speed to 1/2 of that, that is, 1/4 of your original speed. And so on. Now, the sum of all the distances you have to travel is still 1km; however it takes half an hour to travel the first 1/2 km; and then still half an hour to travel the next 1/4 km; and then still half an hour... etc. In our earlier example, it took half an hour + 1/4 of hour + 1/8 of hour +... at that totally amounted to 1 hour. In the latter, however, the closer you get to B, the slower you walk. And since it takes always half an hour for every checkpoint, and there are infinite checkpoints, you never reach B. You truly, never reach B, if you slow down that much.

Now. General Relativity is not this little example I just made up. But if we accept to oversimplify, then the first example is a crude way to represent what happens according to the frame reference of the falling man; while the latter represents what happens according to the frame reference of an external, far away observer (you, or us).

 

Well it's well known that gravity effects time. I just was confused as to what you were saying. Also, when you refer to space you say "free falling" as if space has a ground to fall to. The universe is most probably an ever-expanding sphere. There are no directions. Up, down, left, right, do not exist because there is no sky nor a ground. Similarly with a black hole. You can be hurtling towards a black hole, being pulled by its massive gravitational force, but unless you are referring to the black hole as down or bottom, free falling just isn't the term.