Does Time Stop in a Black Hole?

[bananan]

since time slows down in a strong gravitational field, does time stop in a black hole?

and if it does stop what happens to motion implied by quantum mechanics?

 

[pervect]

If you hover near the event horizon, time slows down. However, it requires more and more acceleration to "maintain station".

To "maintain station" at the event horizon itself would require an infinite acceleration, thus it's not possible.

So it is not really possible to stop time.

The situation where an observer falls through the event horion looks a little bit like time stopping, but it isn't really. Time flows at a normal rate of 1 second per second for the falling observer. It is possible to compare two clocks directly when they are at rest, but when the clocks are moving with respect to each other, it becomes more difficult. This is the same sort of issue that comes up in the "twin paradox".

The situation where an observer falls through an event horzion is, as mentioned previously, by necessity a situation where the two clocks are moving with respect to each other, as it is not possible to "hold station" at the event horizon.

Quantum mechanics is totally irrelevant to the question, BTW.

 

[LURCH]

Time would theoreticaly stop at the singularity (at the center of the BH), but no observer could ever get there, so it could never be "observed" to have stopped.

I'm guessing that your question about "the motion implied by quantum mechanics" is a refference to indeterminacy, or the idea that all particles will allways have some nonzero momentum, yes? Well, that's one of the tricky questions about singularities to which we do not yet have an answer. We just don't know what happens when gravity becomes so strong that the curbature of spacetime becomes significant at the quantum scale.

One possible "loop hole" (and this part is just my own speculation) could be that QM only predicts that the location of a particle can never be known with exact precission. This would suggest that a quantum particle inside a singularity might become totally stationary, having zero momentum and one definite location, so long as that location can never be observed or measured. Which it certainly couldn't be if the particle is within the singularity, from whence no information can escape.

 

[J77]

What's that thing I've got in the back of my head where if you saw someone pass the event horizon, their image would stay at that point as you kept looking. If you looked away and back again, they would disappear?

Or am I thinking of some SF...

 

[DaveC426913]

The practical upshot, barring any inifinite acceleration to hover etc. is that, as the observer approached the event horizon, if he could still see the universe, he would see time speeding up. So much so that he would see stars grow old and die rapidly. The universe would age noticeably while he fell.

 

[MeJennifer]

To "maintain station" at the event horizon itself would require an infinite acceleration, thus it's not possible.

So are you saying that light (or even mass objects) cannot easily stay in orbit just above or at the event horizon?
If so, then I think that is incorrect.

It is only after passng the event horizon that no further orbits are stationary, they all get "sucked" into the singularity.

Time would theoreticaly stop at the singularity (at the center of the BH), but no observer could ever get there, so it could never be "observed" to have stopped.

In GR theory the time of the traveler from a reference frame at a distance from the black hole would stop already at the event horizon not at the singularity.
What happens to time in GR beyond the event horizon is simply a matter of interpretation.

 

[pervect]

The practical upshot, barring any inifinite acceleration to hover etc. is that, as the observer approached the event horizon, if he could still see the universe, he would see time speeding up. So much so that he would see stars grow old and die rapidly. The universe would age noticeably while he fell.

The observer approaching the event horizon CAN see the outside universe. The outside universe can't see him, but he can still see it. From the POV of the infalling observer, whehter or not light is blueshifted or redshifted will depend primarily on the direction he looks, and secondarily on his exact trajectory.

For instance, an observer falling into a black hole from at rest at infnity, looking backwards, sees everything redshifted by a factor of 2:1.

There's some discussion of this at http://casa.colorado.edu/~ajsh/singularity.html#redshift.map

and other places on the same website, which has a movie of what people see when they fall into a Schwarzschild black hole.

The observer falling into a Schwarzschild black hole does NOT see the entire history of the universe during his fall. This is for instance the answer to quiz question 5 on the same website:

http://origins.colorado.edu/~ajsh/singularity.html

look at the section "The schwarzschild bubble grows".

So there isn't any meaningful sense in which time stops.

 

[pervect]

So are you saying that light (or even mass objects) cannot easily stay in orbit just above or at the event horizon?
If so, then I think that is incorrect.

[edit]

This is fairly well known. The photon sphere, where light orbits a black hole, occurs at 1.5 times the Schwarzschild radius. Inside the photon sphere, closed orbits are impossible. One reason to see why is that the orbital velocity for such an orbiting object would have to be faster than light.

See the wikipedia website, for example
http://en.wikipedia.org/wiki/Photon_sphere

or google for photon sphere. Hamilton's website (the colorado.edu site I mentioned above) probably has this info on it somewhere.

To stay just above the event horizon, you have to hover on rockets. You cannot orbit there.

(If you want a text reference, this is also mentioned in Kip Thorne's excellent book on black holes "Black Holes and Time Warps: Einstein's outrageous legacy, BTW).

In GR theory the time of the traveler from a reference frame at a distance from the black hole would stop already at the event horizon not at the singularity.
What happens to time in GR beyond the event horizon is simply a matter of interpretation.

That's not exactly what happens. "Time stops", i.e. the metric coefficient for time goes to zero, at the event horizon in the Schwarzschild coordinate system. This is the coordinate system of a stationary observer. Stationary observers don't exist at the event horizon.

If you look as some other coordinate systems, such as the Painleve coordinate system representing an infalling observer, the metric coefficient for time does not go to zero at the event horizon. So the whole issue is about coordinates - it's not ultimately about physics at all. People tend to get confused a lot by taking coordinates too seriously (I've mentioned that in the past), this is just another example of coordinate generated confusion.

 

[MeJennifer]

If you look as some other coordinate systems, such as the Painleve coordinate system representing an infalling observer, the metric coefficient for time does not go to zero at the event horizon. So the whole issue is about coordinates - it's not ultimately about physics at all. People tend to get confused a lot by taking coordinates too seriously (I've mentioned that in the past), this is just another example of coordinate generated confusion.

Well talking about confusion, I was talking about:

In GR theory the time of the traveler from a reference frame at a distance from the black hole would stop already at the event horizon not at the singularity.
What happens to time in GR beyond the event horizon is simply a matter of interpretation.

Are you talking about the same thing or do you shift from an outside observer to an inside observer here?

 

[pervect]

It depends on exactly what you mean by time. Schwarzschild coordinate time stops at the event horizon, i.e. the metric coefficient g_00 goes to zero.

The proper time of an infalling object is finte, though. This proper time is computable by the outside observer, as well as directly observable by the infalling observer via a clock.

So when you say "time stops", it's a bit ambiguous. Coordinate time (specifically - Scwarzschild coordinate time) stops at the event horizon. Proper time doesn't. If you think of time as being coordinate time, then yes, the coordinate time stops. But this is a property of a particular cooordinate system, and as I remarked before, not of any particular physical significance, and coordinate systems do exist in which time does not stop at the horizon such as the Painleve coordinates.

"Proper time" exists for the outside observer just as it does for the infalling observer. The difference is that the outside observer has to calculate it, he can't directly measure it with a clock. The proper time for an object passing through the event horizon does not stop, even though the coordinate time does. This is true for a clock on the object itself, it's also true for the proper time that a distant observer would calculate.

 

[MeJennifer]

It depends on exactly what you mean by time. Schwarzschild coordinate time stops at the event horizon, i.e. the metric coefficient g_00 goes to zero.

The proper time of an infalling object is finte, though. This proper time is computable by the outside observer, as well as directly observable by the infalling observer via a clock.

So when you say "time stops", it's a bit ambiguous. Coordinate time (specifically - Scwarzschild coordinate time) stops at the event horizon. Proper time doesn't. If you think of time as being coordinate time, then yes, the coordinate time stops. But this is a property of a particular cooordinate system, and as I remarked before, not of any particular physical significance, and coordinate systems do exist in which time does not stop at the horizon such as the Painleve coordinates.

"Proper time" exists for the outside observer just as it does for the infalling observer. The difference is that the outside observer has to calculate it, he can't directly measure it with a clock. The proper time for an object passing through the event horizon does not stop, even though the coordinate time does. This is true for a clock on the object itself, it's also true for the proper time that a distant observer would calculate.

Looks like we are either in complete agreement or we are "beating around the bush" on this.

To me it is neither confusing nor a matter of coordinates.

In GR, consider observer O at a far and constant distance from a black hole B.
For O it appears that time runs increasingly slower for objects increasingly closer to the event horizon of B.
This is independent of O's choice in coordinate system.

Then, consider observer O' falling towards a black hole B.
For O' it appears that time runs increasingly faster for observer O the closer it gets to the event horizon.

This is independent of O's and O''s choice in coordinate system. This simply follows from the principle of relativity.

 

[pervect]

Looks like we are either in complete agreement or we are "beating around the bush" on this.

To me it is neither confusing nor a matter of coordinates.

In GR, consider observer O at a far and constant distance from a black hole B.
For O it appears that time runs increasingly slower for objects increasingly closer to the event horizon of B.
This is independent of O's choice in coordinate system.

This last part is where I disagree. The rate at which a clock at a separated location runs depends very much on the coordinate system one adopts, and how the comparison procedure is done.

There isn't any coordinate independent notion of "how fast" a distant clock is ticking, in general. One can talk about it in special cases, by commonly agreed on conventions, such as when there is a constant round-trip time for light. The twin paradox is an examle of why one can't compare the rate at which two clocks run in distant locations unambiguously. Each twin thinks the other's clock is running slowly. This is true even in SR, GR makes the comparion process even more non-intuitive.

 

[MeJennifer]

Ok, then let's use a simple example so you could prove your case.

Suppose that observer O, far removed from black hole B, measures the time dilation for traveler T who is well on his way to the event horizon. Traveler T, who had initially installed an ideal clock on the ship, sends a light pulse at say 100 times a second.

Now let say that O establishes at a certain point in his local time, by measuring the light pulses coming from T, that relative to his clock T's clock run's at 50%.

Then would we not conclude according to relativity that time for T slowed down by 50%?

Feel free to show that the numbers would be different if O would pick another coordinate system.

Don't you think it would be absurd to have a theory that claims to have any predictive power have a condition that the "correct" coordinate system has to be used to get the results as measured in reality, if there is no predefined procedure to pick such a "correct" coordinate system?