Does Time Slow Down Near a Black Hole?

[bioquest]

Does time slow down/stand still near a black hole? How much? Like, if you were on a spaceship close enough to a black hole would you not age for a long time because time would pass really slowly or would it just SEEM like time would be passing really slowly?

 

[CompuChip]

For you, nothing special would happen while you cross the event horizon and go to the center of the hole (as for the time passing, I mean -- you being pulled apart by immense gravity like a string of spaghetti is a completely different story).
But due to the gravitational forces light will escape from the vicinity of the hole just very slowly, and in fact slower and slower until the point where it cannot escape at all (the event horizon). Since the signals from closer to the horizon would take longer to reach an observer well away from the hole, and the signal from the event horizon would actually take infinitely long, such an observer would see you falling toward the event horizon infinitely without ever crossing it, and see you age more and more slowly.

 

[daniel_i_l]

But due to the gravitational forces light will escape from the vicinity of the hole just very slowly, and in fact slower and slower until the point where it cannot escape at all (the event horizon). Since the signals from closer to the horizon would take longer to reach an observer well away from the hole, and the signal from the event horizon would actually take infinitely long, such an observer would see you falling toward the event horizon infinitely without ever crossing it, and see you age more and more slowly.

Actually, no observer sees light going at less than c, but if light goes from close to a BH to an observer far away from the BH the far away observer will measure a lower frequency. As the source of the light gets closer and closer to the horizon of the BH the frequency that this observer measures gets lower and lower until the source gets to the horizon and then he measures 0 frequency - or in other words - no light at all.
The time dilation effects between an observer close to a BH and an observer far away from one have nothing to do with the the speed of signals between them. It has to due with the dependence of the ST metric on the distance from the BH.

 

[DaveC426913]

You do not have to cross the event horizon and get pulled into spaghetti to undergo time dilation. You could go into an orbit around the black hole or simply fly real close to the EH.

In an orbit around the BH you would experience nothing special (timewise at least, there would be some interesting tidal effects within your ship), but when you emerged from the gravitational field, you would find that more time had passed in the universe than you would have experienced personally. You would be younger than your twin brother.

Likewise, if your twin brother were observing you from a nearby planet, he would see you go into orbit and move about your ship slower than normal until you emerged.

 

[bioquest]

How much time would have passed in the universe than you would have experienced personally after emerging from the gravitational field? Could that time in that situation or different be something like hundreds of years/how long could it be?

 

[Chris Hillman]

Correcting some common misonceptions

Does time slow down/stand still near a black hole? How much?

• Of course not---that wouldn't even make sense. How could time "slow down"?
• This is a FAQ and also a common misconception. For a previous post by myself addressing this misconception, see [post=1181763]this post[/post].
• You are asking about a phenomenon known as "gravitational time dilation"; this term is standard but misleading.
• This effect can and should be understood as an effect of spacetime curvature: two initially parallel null geodesics diverge; when comparing proper times between emission and reception of wavefronts by two observers near a massive object, this can result in a red shift measured by the receiving observer when he receives signals from the sending observer.

Like, if you were on a spaceship close enough to a black hole would you not age for a long time because time would pass really slowly or would it just SEEM like time would be passing really slowly?

Of course none of your instruments would measure "time slowing down"; that wouldn't even make sense. Rather, if you sent time signals every second as measured by an ideal clock you carry to another observer in another spaceship which is farther away, then generally speaking (ignoring details about the how your spaceship and his are moving) he would receive the time signals redshifted and separated by more than one second as measured by his own ideal clock. Thus, to this second observer you would in a sense "appear" to be aging more slowly, but of course this wouldn't enable you to have a longer and richer life experience, all other things being equal!

You do not have to cross the event horizon and get pulled into spaghetti to undergo time dilation.

DaveC is speaking carelessly (or has a similar misconception). It is very important to understand that no one observer ever "undergoes time dilation" or "experiences time dilation" or even "measures time dilation". In both str and gtr "time dilation" always involves a pair of observers and is always heavily dependent on the details of the motion of both observers; in gtr, the geometry of spacetime itself is also crucial because as already explained this effects how signals propagate from one observer to another.

For you, nothing special would happen while you cross the event horizon and go to the center of the hole

No "center".

due to the gravitational forces light will escape from the vicinity of the hole just very slowly

This refers to coordinate speeds, which characterize our description of the situation rather than what is measured by a given observer. As measured by any observer, light always moves in a vacuum at unit speed (in geometric units in which c=G=1). Be aware that there are multiple operationally significant notions of "distance in the large" and thus "velocity in the large", even in flat spacetime. Failure to recognize invariably engenders needless confusion.

CompuChip is trying to express the same geometric picture in different words, in which two initially parallel radially outgoing null geodesics (modeling the world lines of "photons" emitted by a static observer near the hole, for example) will diverge due to spacetime curvature.

 

[pervect]

How much time would have passed in the universe than you would have experienced personally after emerging from the gravitational field? Could that time in that situation or different be something like hundreds of years/how long could it be?

A full answer to this question gets rather involved.

One can theoretically arrange a trajectory that passes close by a black hole such that one expreriences a short time following the trajectory, but a long time elapses in the universe outside the black hole.

However, one can also arrange such a trajectory without the black hole, simply by traveling near 'c'.

The black hole is different in that a stationary observer can experience this time dilation effect. But the stationary observer must accelerate to remain stationary if he gets close enough to the black hole for the so-called "gravitational time dilation" to be important. One can orbit a black hole if one doesn't get too close, but inside a certain radius, unpowered orbits are not possible, and one must thrust away from the black hole to avoid being drawn in. Really signficant time dilation occurs only inside this critical radius (called the photon sphere - at the critical radius, light itself has an orbit around the black hole, but nothing with rest mass can travel fast enough to achieve orbit because it must travel slower than light).

If you want to approach, but not cross, the event horizon of a black hole, and return, you will not be able to avoid this "slowdown" effect, so in that sense, time slows down near a black hole.

But such a close approach will inevitable also require crushingly large accelerations to avoid crossing the event horizon due to the fact that unpowered orbits do not exist.

Another common scenario is to imagine falling into a black hole, passing through the event horizon, and not returning. In this case, one does *NOT* see the history of the universe play itself out during the trip inward. (This is mentioned in several black hole FAQ's).

 

[bioquest]

accidentally posted twice

 

[bioquest]

One can theoretically arrange a trajectory that passes close by a black hole such that one expreriences a short time following the trajectory, but a long time elapses in the universe outside the black hole. However, one can also arrange such a trajectory without the black hole, simply by traveling near 'c'.

are you saying that...you would only age a little, but the rest of the universe could be like 200 years older than it was before you left? because you would age slowly? Or are you saying tha it would only feel like you were aging slower but you wouldn't really be?

 

[dibiz116]

are you saying that...you would only age a little, but the rest of the universe could be like 200 years older than it was before you left? because you would age slowly? Or are you saying tha it would only feel like you were aging slower but you wouldn't really be?

you wouldn't 'feel' like you were aging any slower or faster than usual, you would be aging normally (from your own perspective), but when you leave whatever situation is causing time dilation and returned to your original state in the universe, 200 years (or whatever amount of time) would have passed for the universe and only say, 2 years would have passed for you. time isn't going more or less slowly for either, more time just passed for the rest of the universe than the amount of time that passed for you.

but if something was observing you from this outside universe, you would appear to them to be aging slowly, just as if you could observe the universe from your position it would appear to be aging faster than normal, but in reality neither observer 'feels' like it is aging any slower or faster than usual.

 

[pervect]

One can theoretically arrange a trajectory that passes close by a black hole such that one expreriences a short time following the trajectory, but a long time elapses in the universe outside the black hole. However, one can also arrange such a trajectory without the black hole, simply by traveling near 'c'.

are you saying that...you would only age a little, but the rest of the universe could be like 200 years older than it was before you left? because you would age slowly? Or are you saying tha it would only feel like you were aging slower but you wouldn't really be?

I'm saying that if you had a twin, and you left from some place that was far away from the black hole and took a close pass by the black hole while your twin stayed home, you and your twin could compare ages when you returned from your trip.

When you returned, you would be young, and your twin would be old. This works just the way with a black hole as it does with the SR "twin paradox".

I'm also taking the viewpoint that you and your twin should only compare ages when you are both close to each other, i.e. "at the same place". This is due to something that's called "the relativity of simultaneity", which also important in SR.

 

[bioquest]

sorry double posted I don't know why it did that

 

[bioquest]

okay so

Where would you be able to go and have this happen? (Below) If one of the places this would happen was in/around a black hole, how close would you have to be to the black hole + other details? Also if you spent 2 years there might 200 years/how much time have passed in the rest of the universe?

you wouldn't 'feel' like you were aging any slower or faster than usual, you would be aging normally (from your own perspective), but when you leave whatever situation is causing time dilation and returned to your original state in the universe, 200 years (or whatever amount of time) would have passed for the universe and only say, 2 years would have passed for you.

and how much time would have passed in the universe at most do you think if you were in a place like that for 2 years where you would come and more time would have passed in the universe than for you?

Also would it be the more time spent there (2 years etc) the larger the amount of time dilation ie the larger the amount of difference would be in time passed between you and the rest of the universe?

 

[pervect]

I'm going to assume that you are looking for a large amount of time dilation.

The details are going to depend on the specific black hole you attempt to utilize. For this purpose, "bigger is better". I will utilize the black hole "Gargantua" from Kip Thorne's book, "Black Holes & Time warps". This book opens with several fictionalized accounts (using, however, very good physics) of exploring (or attempting to explore) various sizes of black holes. I would recommend the book to anyone interested in the topic of black holes. Gargantua, as you might guess, is one of the largest:

Fourty two years of starship time later, your ship deaccelerates into the vicinity of Gargantua, Overhead, you see the quasar 3c273 whit two brilliant blue jets squirting out of its center, below is the black abyss of Gargantua. Dropping into orbit around Gargantua and making your usual measurements, you confirm that its mass is, indeed, 15 trillion times that of the Sun, you see that it is spinning very slowly, and you compute from these data that the circumference of its horizon is 29 light-years. Here, at last, is a hole whose vicinity you can explore while experiencing bearably small tidal forces and rocket accelerations...

Skipping on a bit

In the final stage of your ship's descent Kares (the ships computer) blasts the rockets harder and harder to slow its fall. At last, the ship comes to a hovering rest at .0001 horizon circumferences, blasting with a 10-g acceleration to hold itself up against the hole's powerful gravitaional pull.

In this particular situation, one year of ships time will turn out to be equivalent to roughly 100 years of time far away from the black hole. To measure this, you measure the blue shift of infalling light. Thorne doesn't make a point of pointing out that this is the time dilation factor, but that's what it is:

Equally peculiarly, all the colors of all the stars and galaxies are wrong. A galaxy that you know is really green appears to be shimmering with soft x-rays. Gargantua's gravity, in pulling the galaxy's radiation downward to you, hs made the radiation more energeic by decreasing the wavelength from 5x10^-7 meters (greeen) to 5x10^-9 meters (x-ray).

To achieve a higher time dilation factor, you'll either need a bigger black hole (but Gargantua is already very large), or you'll be able to need to stand more than 10g's of acceleration (but that's already quite high).

One more point you might be interested in:

Everything in the starship is normal, absolutely the same as if the ship had been resting on the surface of a massive planet with 10-g surface gravity. If you did not lok outside the sptarship and see the bizarre spot overhead and the engulfing blackness all around, you would not know that you were very near the horizon of a black hole rather than on the surface of a planet - or you almost wouldn't know.

Thorne goes on to explain that with very sensitive instruments, you could detect the tidal force from the black hole.

 

[bioquest]

So...you could actually go to outer space, experience a year or so there (ie. only age a year, only experience a year, etc) and have 200 years or so pass by on earth? (I mean you can make comments clarifying the accuracy of the time difference...ie 3 years...100 years..etc)

 

[DaveC426913]

Yes. But there is no theoretical upper limit on the time dilation - it's asymptotic. It could be thousands or millions of years.

 

[bioquest]

So right now would we have the necessary knowledge to go up into space, near a black hole wherever, stay there, and come back to Earth 200 years or more later?

 

[pervect]

The exact amount of time dilation depends on the details, mainly how fast you go. See for instance

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html

This sort of time dilation is due only to velocity, and you can find the formula for it along with a calculator at:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html

Gravitational time dilation is also talked about with formulas at:

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

 

[DaveC426913]

So right now would we have the necessary knowledge to go up into space, near a black hole wherever, stay there, and come back to Earth 200 years or more later?

Apart from actually finding the right kind of BH and getting to it (neither of which is trivial), there's nothing technologically beyond us, no. The big trick is finding one that's large enough that you can get within the radius where time dilation has a noticeable effect without being so close that the tides tear your ship apart (the tides are more gentle around a larger BH).

 

[bioquest]

So are there any black holes that we know of currently that could be used for this purpose?

 

[DaveC426913]

So are there any black holes that we know of currently that could be used for this purpose?

Well, the closest BH is about 1600ly. We won't be going there any time in the next few centuries.

And we really don't know what size we need.

 

[bioquest]

How long does it take to get to something 1600ly away?

 

[Chris Hillman]

Hi, bioquest,

How long does it take to get to something 1600ly away?

Needless to say, the answer is heavily dependent upon the details of the kinematic history of your rocket ship (how hard it accelerates for such and such a period during the journey), the motion of the home object at time of departure, the motion of the destination object at the time of arrival, and so on.

Assuming the home and destination objects are both static wrt some inertial frame in Minkowski spacetime, then to obtain a "maximal twin paradox" resulting in a journey from home to some destination and back, you should imagine that your rocketship can somehow sustain 1 Earth gravity acceleration during the entire journey (turning around at the halfway point to begin to deccelerate, so that the rocket will again be static at the end of the journey). See http://www.math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html for details.

 

[bioquest]

What did you mean when you said this?

One can theoretically arrange a trajectory that passes close by a black hole such that one expreriences a short time following the trajectory, but a long time elapses in the universe outside the black hole. However, one can also arrange such a trajectory without the black hole, simply by traveling near 'c'.

So time dilation like this could be possible without a black hole? What did you mean by "c"?

 

[Chris Hillman]

Time elapses? Its a bit more complicated than that!

One can theoretically arrange a trajectory that passes close by a black hole such that one expreriences a short time following the trajectory, but a long time elapses in the universe outside the black hole.

[EDIT: I now see that bioquest might have been trying to quote Russ]

IMO that' s not a good way of thinking about it. "Time" does not elapse. Rather, a particular observer who carries an ideal clock will record proper time intervals between events on his world line. If these events involve reception of "signals" from elsewhere, he may be able to draw certain inferences about what has happened in some other region of spacetime (a region included in the absolute past of some appropriate event or events on his world line.)

 

[russ_watters]

So time dilation like this could be possible without a black hole? What did you mean by "c"?

C is the speed of light and time dilation also occurs at high speed. So rather than trying to go around the nearest black hole, you could just accelerate to close to the speed of light, then turn around and come back. When you got back, more time would have passed on Earth than for you on your ship.

 

[bioquest]

Whats the closest a spaceship can get to traveling at the speed of light?

 

[Chris Hillman]

Whats the closest a spaceship can get to traveling at the speed of light?

Arbitrarily close, as several posters have already pointed out. I stress again (sigh...) that velocity is always relative to another observer, usually an inertial observer. Did you yet look at the web page I cited above? All your questions are answered there.

 

[DaveC426913]

All you have to do to experience time dilation is have a rocketship with a nigh-bottomless fuel supply ... and a lot of patience.

You could fly the shuttle out from the solar system for a few months. After a few months of contstant accelreation (even the low acceleration of the shuttle's retros), you'll be traveling near the speed of light. Turn around and fly home. You will have expereinced less time than those on Earth. How much less time is dependent on how close you got to the speed of light and how long you were there.

There are calculators that will tell you how long a dilation will be exprienced for given input values. Google "relativistic calculator".

 

[Chris Hillman]

All you have to do to experience time dilation is have a rocketship with a nigh-bottomless fuel supply

I forgot to mention that the bottomless fuel supply is an extremely dubious aspect regarding any proposal to accelerate a spaceprobe to near the speed of light using a conventional rocket engine. Right now the best way to achieve reasonably large velocities relative to the solar system seems to be to use the major planets to achieve a "velocity boost", carefully aim at the nearest black hole, wait a few million years, and do the same thing upon arrival. (No, not a serious proposal with current technology!).

 

[Count Iblis]

C'mon, this is supposed to be the best theoretical physics forum on the entire internet. "Google relativistic calculator"

Let's work out the case of the photon rocket. Suppose in some frame the rocket is initially at rest in space. The four momentum is P1 = (M1,0). Then it burns anti-matter fuel and it's four momentum becomes P2= (M2 gamma, M2 gamma v). Conservation of four momentum:

P1 = P2 + Pf

where Pf is the total four momentum of the emitted photons and is thus of the form (E, -E). This means that:

Pf = P1 - P2

Square both sides and use that

Pf^2 = 0,

P1^2 = M1^2

P2^2 = M2^2

P1 dot P2 = gamma M1*M2

So we have:

0 = M1^2 + M2^2 - 2 gamma M1 M2 ----->

gamma = 1/2 [X + X^(-1)]

where X is the ratio of the final and initial mass

Note that if we use massive particles instead of photons Pf^2 would be strictly larger than zero and you would get a smaller gamma factor for the same initial/final mass ratio. So, the photon rocket is the best we can get.

Now, if we want to return to Earth we must put X= (M1/M2)^(1/4), where M1 is the initial mass of the rocket (which includes the fuel) and M2 the final mass. This is because we must accelerate to the gamma factor, and then change the direction of the velocity, which is equivalent to changing the velocity to zero and then back to the sama gamma factor but with the velocity in the opposite direction.

Then, when we reach Earth we must reduce the velocity to zero. If we want to travel at the same gamma factor during the trip, then the mass ratio's before and after the boosts must be the same each time, so X^4 = M1/M2


Now, we can play the following game. Suppose we have an anti-matter factory that produces anti-matter at a constant rate. We want to travel to some far away place, so we need a lot of antimatter. But, unfortunately, that takes a long time. An obvious strategy is to use some of the produced anti-matter to make small excursions. When we return form an excursion more time has passed in the frame of the factory, so we have a lot of anti-matter. If we do this right, we have more anti-matter than we would have had, had we stayed home despite using some for the excursion.

Now, if I remember correctly, it turns out that you can reduce the proper time you need to wait before you have the desired amnount of anti-matter be a factor of order Log(T/t), where T is the time needed to produce the anti-matter in the rest frame of the factory and t is the time needed to produce an amount of anti-matter equal to the mass of the rocket.

 

[DaveC426913]

I forgot to mention that the bottomless fuel supply is an extremely dubious aspect regarding any proposal to accelerate a spaceprobe to near the speed of light using a conventional rocket engine.

No, but planetary lasers are the next best thing.

 

[DaveC426913]

C'mon, this is supposed to be the best theoretical physics forum on the entire internet. "Google relativistic calculator"

You think the OP would rather have a half screen of calculation that leads to a single answer than be shown a tool where he can play to his heart's content?

 

[Count Iblis]

You think the OP would rather have a half screen of calculation that leads to a single answer than be shown a tool where he can play to his heart's content?

The relativistic calculators only give the formulae for the gamma factor as a function of velocity. Trivial stuff. And without knowledge of relativity you wouldn't be able to see that the gamma factor is simply 1/2 [X + X^(-1)] where X is the mass ratio before and after the burning of the anti-matter fuel. So, a 10^6 kg spacecraft carrying 10^6 kg antimatter fuel can reach a gamma factor of
(1/2)(2 + 1/2) = 1.25. And note that this formula was derived above in 13 (small) lines. The derivation was so simple that you can imagine doing it in your head without paper and pencil.

So, who needs the "relativistic calculator"

 

[bioquest]

I heard a theory that black holes exist on Earth, like really really tiny ones I read something about it being someone's theory when I read something about people contemplating making really really tiny black holes in a collider
um does anyone know about the theory about really small black holes already existing on Earth?