Physics Question

• For mary and her escape velocity question:
Suppose that you are standing on the surface of a planet. You throw a rock straight up into the air. Assuming you don’t throw it too hard, it will rise for a while, but eventually the acceleration due to the planet’s gravity will make it start to fall down again. If you threw the rock hard enough, though, you could make it escape the planet’s gravity entirely. It would keep on rising forever. The speed with which you need to throw the rock in order that it just barely escapes the planet’s gravity is called the “escape velocity.” As you would expect, the escape velocity depends on the mass of the planet: if the planet is extremely massive, then its gravity is very strong, and the escape velocity is high. A lighter planet would have a smaller escape velocity. The escape velocity also depends on how far you are from the planet’s center: the closer you are, the higher the escape velocity. The Earth’s escape velocity is 11.2 kilometers per second (about 25,000 m.p.h.), while the Moon’s is only 2.4 kilometers per second (about 5300 m.p.h.).

What happens when you get too close to the black hole:
Let’s suppose that you get into your spaceship and point it straight towards the million-solar-mass black hole in the center of our galaxy. (Actually, there’s some debate about whether our galaxy contains a central black hole, but let’s assume it does for the moment.) Starting from a long way away from the black hole, you just turn off your rockets and coast in. What happens?

At first, you don’t feel any gravitational forces at all. Since you’re in free fall, every part of your body and your spaceship is being pulled in the same way, and so you feel weightless. (This is exactly the same thing that happens to astronauts in Earth orbit: even though both astronauts and space shuttle are being pulled by the Earth’s gravity, they don’t feel any gravitational force because everything is being pulled in exactly the same way.) As you get closer and closer to the center of the hole, though, you start to feel “tidal” gravitational forces. Imagine that your feet are closer to the center than your head. The gravitational pull gets stronger as you get closer to the center of the hole, so your feet feel a stronger pull than your head does. As a result you feel “stretched.” (This force is called a tidal force because it is exactly like the forces that cause tides on earth.) These tidal forces get more and more intense as you get closer to the center, and eventually they will rip you apart.

For a very large black hole like the one you’re falling into, the tidal forces are not really noticeable until you get within about 600,000 kilometers of the center. Note that this is after you’ve crossed the horizon. If you were falling into a smaller black hole, say one that weighed as much as the Sun, tidal forces would start to make you quite uncomfortable when you were about 6000 kilometers away from the center, and you would have been torn apart by them long before you crossed the horizon. (That’s why we decided to let you jump into a big black hole instead of a small one: we wanted you to survive at least until you got inside.)

What do you see as you are falling in? Surprisingly, you don’t necessarily see anything particularly interesting. Images of faraway objects may be distorted in strange ways, since the black hole’s gravity bends light, but that’s about it. In particular, nothing special happens at the moment when you cross the horizon. Even after you’ve crossed the horizon, you can still see things on the outside: after all, the light from the things on the outside can still reach you. No one on the outside can see you, of course, since the light from you can’t escape past the horizon.

How long does the whole process take? Well, of course, it depends on how far away you start from. Let’s say you start at rest from a point whose distance from the singularity is ten times the black hole’s radius. Then for a million-solar-mass black hole, it takes you about 8 minutes to reach the horizon. Once you’ve gotten that far, it takes you only another seven seconds to hit the singularity. By the way, this time scales with the size of the black hole, so if you’d jumped into a smaller black hole, your time of death would be that much sooner.

Once you’ve crossed the horizon, in your remaining seven seconds, you might panic and start to fire your rockets in a desperate attempt to avoid the singularity. Unfortunately, it’s hopeless, since the singularity lies in your future, and there’s no way to avoid your future. In fact, the harder you fire your rockets, the sooner you hit the singularity. It’s best just to sit back and enjoy the ride.

• “For mary and her escape velocity question:
Suppose that you are standing on the surface of a planet. You throw a rock straight up into the air. Assuming you don’t throw it too hard, it will rise for a while, but eventually the acceleration due to the planet’s gravity will make it start to fall down again. If you threw the rock hard enough, though, you could make it escape the planet’s gravity entirely. It would keep on rising forever. The speed with which you need to throw the rock in order that it just barely escapes the planet’s gravity is called the “escape velocity.” As you would expect, the escape velocity depends on the mass of the planet: if the planet is extremely massive, then its gravity is very strong, and the escape velocity is high. A lighter planet would have a smaller escape velocity. The escape velocity also depends on how far you are from the planet’s center: the closer you are, the higher the escape velocity. The Earth’s escape velocity is 11.2 kilometers per second (about 25,000 m.p.h.), while the Moon’s is only 2.4 kilometers per second (about 5300 m.p.h.).”

yes, I know this. However, it is possible to “escape” from the gravity of an object without ever going close to the escape velocity. If you had enough power, and went 60, m.p.h. long enough, you could sail right through the solar system. What Baker’s point is that the energy expended to escape will be the same.

• OK but only if you were far enough away from the influence of any body that could tug to away from your course at that speed…

• It is all about the difference between potential energy and kinetic energy.

Potential energy = the distance one can fall = distance from your ship to the center of the earth/black hole Â Or to escape the earth or black hole, the distance from where you are to essentially infinity (since there is no known upper limit of distance to gravity waves).  Keep in mind that this distance is in gravity terms, most of the energy is real close to the earth/black hole.

Kinetic energy = the motion of your ship moving away from the center of the earth/black hole.

In order to escape the earth/black hole, you must apply enough kinetic energy (speed, velocity, motion…) to equal or exceed the potential energy (distance from effectively infinity to you…from the gravity standpoint). Â To better understand why the energy is the same regardless of whether it is done with a quick burst or with a slow push, simply look at the potential energy…the distance you have to move. Â It then is also apparent that the closer you get to the event horizon of a blackhole, the greater the potential energy becomes as you are deeper in the gravity well.

Outside the event horizon, this potential energy is small enough that the kinetic energy required to leave is possible to acheive, whether this is done in one quick burst of acceleration (escape velocity) or by a steady slow push. Â Once within the event horizon, the total kinetic energy required becomes equivalent to an escape velocity exceeding the speed of light. Â This is an infinite amount of energy which you can’t have and so you will become trapped.

• Nicely put. I had this weird idea of dropping a chain into a black hole and slowly pulling it out :) I guess the part that enters the hole would require infinite energy to get back out :(

• Thank you.

You are right that the part of the chain that enters the event horizon would then require infinite energy to get out.  So you would have to let go of the chain (otherwise you would get pulled in also :-o  ).

• Nicely put. I had this weird idea of dropping a chain into a black hole and slowly pulling it out :) I guess the part that enters the hole would require infinite energy to get back out :(

Looks like you’re thinking along these lines:

At the centre of the black hole, well inside the event horizon, general relativity predicts a singularity, a place where the curvature of spacetime becomes infinite and gravitational forces become infinitely strong. Spacetime inside the event horizon is peculiar in that the singularity is in every observer’s future, so all particles within the event horizon move inexorably towards it (Penrose and Hawking). This means that there is a conceptual inaccuracy in the nonrelativistic concept of a black hole as originally proposed by John Michell in 1783. In Michell’s theory, the escape velocity equals the speed of light, but it would still, for example, be theoretically possible to hoist an object out of a black hole using a rope. General relativity eliminates such loopholes, because once an object is inside the event horizon, its time-line contains an end-point to time itself, and no possible world-lines come back out through the event horizon.

• no possible world-lines come back out through the event horizon.

With the exceptions being the strange, unproven Hawking radiation, and whatever happens once this radiation causes the black hole to evaporate.  I wonder if it wouldn’t someday be possible to use this radiation to “see” beyond the event horizon.

• Yeah, that was just an exerpt from Wiki on Black Holes.

Thought Mary might be interested in John Michell, since I guess his theory had to do with the rope-chain thing.

I’m not familiar with it but still thought it was cool.

You should submit your own Wiki def, but instead call it “Baker Radiation”  :-D

• OK, just correcting what I think is an initial misunderstanding…

Escape Velocity means that, with a single initial burst of energy, that energy must be sufficient to accelerate the object to 17,000 mph to clear Earth’s gravity well.  Anything less, and the object falls back to Earth at some point.

Thus in a way, the initial concept is valid.  The Saturn V’s did not need to hit 17,000 mph to clear the Earth’s gravity well.  They just needed an amount of thrust (force) spread over time that, had it been released immediately, would have been able to accelerate the mass to 17,000 mph immediately.

Now, just outside the Event Horizon of a Black Hole, the escape velocity is a fraction under 186,000 mps (per SECOND).

Thus, to escape from JUST OUTSIDE the Event Horizon, you would need sufficent force applied over time to be equivalent to the force necessary that, if released immediately, would accelerate the object to a fraction under 186,000 mps.

Once you cross the Event Horizon, you need to be able to have enough thrust force to be equivalent to a one-time burst of the energy required to accelerat to greater than 186,000 mps.

The calculation for that force is infinite, since the amount of energy required to instantly translate an object to greater than 186,000 mps is infinite, based on Einstein.

An infinite amount of energy realease over time is an infinite amount of energy at ALL times.

Did that work for ya?

• DM, i doubt that a non-relativistic “concept” of a black hole makes a lot of sense. Using this 1783 thing as an early reference is not very useful. Even though Newtonian mechanics and the speed of light were known at that time, the problem would have been the “mass” of the light-particle, and i wonder why the idea was remembered after Maxwells equations postulated that light is a wave and not a particle.

Baker Street, there was a pretty famous bet, about whether information can escape the black hole / whether the Hawking Radiation carries information about what “fell into”  the hole when it evaporates again.
My own -personal- gut feeling is that information is physical and thus can be destroyed by decoherence. As some states are “immune” to several decoherence processes, information expressed in these states is more stable. Yet, i doubt that passing something through a singularity is a unitary process: We have no idea how the physics looks inside a black hole, so i wouldn’t have given in in the bet.

• From Wiki:

Not sure what is says, I didn’t have time to read the whole thing but it does have the equations and mentions energy.

http://en.wikipedia.org/wiki/Escape_velocity

I am not sure where Mary got the 17,000 mph.

Wiki gave a range of 7.1 to 11.2 km/s depending on your altitude.

7.1 km/s * 60 s/min * 60 min/hr * 3280 ft/km * mi/5280 ft = 15878.2 mph
11.2 km/s * 60 s/min * 60 min/hr * 3280 ft/km * mi/5280 ft = 25047.3 mph

The whole idea is at every speed, you will achieve a certain orbital distance away from the center of the earth.  Lose some of that orbital speed, and your orbit drops you closer.  Gain some speed and you can achieve a higher orbit.  Gain enough speed and you will break orbit altogether.

You can run some calcs based on the formulas on that site and then punch in an orbit distance = a few miles above the atmosphere to get the speed you need.

• @F_alk:

DM, i doubt that a non-relativistic “concept” of a black hole makes a lot of sense. Using this 1783 thing as an early reference is not very useful. Even though Newtonian mechanics and the speed of light were known at that time, the problem would have been the “mass” of the light-particle, and i wonder why the idea was remembered after Maxwells equations postulated that light is a wave and not a particle.

Baker Street, there was a pretty famous bet, about whether information can escape the black hole / whether the Hawking Radiation carries information about what "fell into"Â  the hole when it evaporates again.
My own -personal- gut feeling is that information is physical and thus can be destroyed by decoherence. As some states are “immune” to several decoherence processes, information expressed in these states is more stable. Yet, i doubt that passing something through a singularity is a unitary process: We have no idea how the physics looks inside a black hole, so i wouldn’t have given in in the bet.

Interesting stuff.  As the article says, Hawkings paper isn’t yet published (I don’t think it has been published yet) … but since he paid the debt, he believe the information isn’t lost.  This is stuff that is way over my head, but my gut feeling on the matter is that the information isn’t lost.  It will be interesting to see Hawkings paper once it is completed.

• The link at the bottom with the “hep” in there could be to a pre-print version of the paper (the address is the common pre-pront address). It is freely available if you are interested. I haven’t had a look into it though, so i can’t tell wether it is the preprint of the mentioned publication.

• My post also points out the following:

The Earth’s escape velocity is 11.2 kilometers per second (about 25,000 m.p.h.), while the Moon’s is only 2.4 kilometers per second (about 5300 m.p.h.).I dont think the other figure is correct ( 17,000)

• Thanks for noticing the pre-print version of the paper.  Its only 5 pages and surprisingly not too terribly difficult to follow.  From the article:

How does information get out of a black hole? My work with Hartle[8] showed the radiation could be thought of as
tunnelling out from inside the black hole. It was therefore not unreasonable to suppose that it could carry information
out of the black hole. This explains how a black hole can form and then give out the information about what is inside
it while remaining topologically trivial. There is no baby universe branching off, as I once thought. The information
remains firmly in our universe. Iâ€™m sorry to disappoint science fiction fans, but if information is preserved, there is
no possibility of using black holes to travel to other universes. If you jump into a black hole, your mass energy will
be returned to our universe but in a mangled form which contains the information about what you were like but in a
state where it can not be easily recognized. It is like burning an encyclopedia. Information is not lost, if one keeps the
smoke and the ashes. But it is difficult to read. In practice, it would be too difficult to re-build a macroscopic object
like an encyclopedia that fell inside a black hole from information in the radiation, but the information preserving
result is important for microscopic processes involving virtual black holes. If these had not been unitary, there would
have been observable effects, like the decay of baryons.

I gave John an encyclopedia of baseball, but maybe I should just have given him the ashes.

Falk wrote:

i doubt that passing something through a singularity is a unitary process

Hawking basically states this is a unitary process by what isn’t observed in other quantum effects…i.e. the decay of baryons.  I’m not sure if that is really proof or just a strong indication however.

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