Does time slow down when falling into a black hole?

[Sheneron]

I was reading my astronomy textbook and here is what it said about black hole time dilation.

"If we were to jump into a black hole... Our friends who stayed behind would see something different. They would see us falling more slowly as we came closer to the event horizon because, as explained by general relativity, clocks slow down in curved space-time. To them we would fall more and more slowly until we seemed hardly to move. Generations later, our descendants could focus their telescopes on us..."

So, because his time is slowing down as observed by a stationary observer does that mean his actual speed is slowing down? Thats what the book makes it sound like...

 

[z0rn dawg]

I was reading my astronomy textbook and here is what it said about black hole time dilation.

"If we were to jump into a black hole... Our friends who stayed behind would see something different. They would see us falling more slowly as we came closer to the event horizon because, as explained by general relativity, clocks slow down in curved space-time. To them we would fall more and more slowly until we seemed hardly to move. Generations later, our descendants could focus their telescopes on us..."

So, because his time is slowing down as observed by a stationary observer does that mean his actual speed is slowing down? Thats what the book makes it sound like...

No. The speed of light from the guy falling in would take more time to reach the observer (because of more gravity). It would appear as if he were falling slower, but he'd actually be falling in pretty fast. I think this is how it works.

 

[DaleSwanson]

Yes, gravity slows down time. It's important to remember that to any observer your own time will never seem slowed down, rather time outside the gravity well would seem sped up. If you fell into a black hole you wouldn't notice anything odd about your time, but the universe around you would seem to speed up, you could in theory watch the universe end. An outside observer would see a clock on your ship running slower and slower, and eventually stop. Neither speed of time is more real. Each is correct in its frame of reference.

 

[Sheneron]

Yes, gravity slows down time. It's important to remember that to any observer your own time will never seem slowed down, rather time outside the gravity well would seem sped up. If you fell into a black hole you wouldn't notice anything odd about your time, but the universe around you would seem to speed up, you could in theory watch the universe end. An outside observer would see a clock on your ship running slower and slower, and eventually stop. Neither speed of time is more real. Each is correct in its frame of reference.

Yes I understand that his time, as observed from a stationary observer would be slowing down and would become extremely slow as he approached the black hole. But, what about his speed? Just because his "clock" is running slower does that mean that his speed slows down? Or is it like z0rn Dawg said?

 

[ronald_dai]

Yes, gravity slows down time.

So during the beginning of the BIG BANG, the time should be very slow based on nowadays time reference from our Earth due to the extreme high density (the whole universe at one small zone which would be much denser than any black whole around today), right? Should we say this might explain why there could be two celestial objects stayed more than 4 bln LY away at 1.5 bln LY after the BIG BANG (if this 1.5 bln LY is completely calculated based on the uniform time passage)?

 

[Tac-Tics]

Yes I understand that his time, as observed from a stationary observer would be slowing down and would become extremely slow as he approached the black hole. But, what about his speed? Just because his "clock" is running slower does that mean that his speed slows down? Or is it like z0rn Dawg said?

Clocks are the only way we know to measure time. If clocks are running slow, it implies time that clock measures runs slow.

 

[ronald_dai]

Clocks are the only way we know to measure time. If clocks are running slow, it implies time that clock measures runs slow.

I guess the clock is not the literal clock we buy from the store...I mean it is an idea clock without mechanical problem :)

 

[DaleSwanson]

Yes I understand that his time, as observed from a stationary observer would be slowing down and would become extremely slow as he approached the black hole. But, what about his speed? Just because his "clock" is running slower does that mean that his speed slows down? Or is it like z0rn Dawg said?

He wouldn't think of his time as slowing down, rather he would see the rest of the universe speeding up. He would always see his clock as running at normal speed, but an outside clock would seem to be running fast. It's important to stress that the clocks wouldn't be wrong, they would always be right to observers in the same frame of reference as them. Not only would outside clocks run faster, but plants would grow faster, fusion in stars would happen faster, and everything else would actually be happening faster. Time itself would be moving faster.

So during the beginning of the BIG BANG, the time should be very slow based on nowadays time reference from our Earth due to the extreme high density (the whole universe at one small zone which would be much denser than any black whole around today), right? Should we say this might explain why there could be two celestial objects stayed more than 4 bln LY away at 1.5 bln LY after the BIG BANG (if this 1.5 bln LY is completely calculated based on the uniform time passage)?

There is no true speed at which time runs. If the entire universe was highly dense and caused time to slow down it would have to be measured by an observer outside of this high density. Since the whole universe would be high in gravity from the point of view of an observer inside the universe there would be no slow down of time.

 

[Sheneron]

I think everyone is completely misinterpreting my question. So, let's start over. I understand that he would see the universe speeding up and to him his clock would be ticking normally. That is not my question.

My question is... What is his speed? The book makes it sound like he would be visible forever because as his time slows down his physical speed would be slowing down? Is he still moving at near the speed of light or does his speed actually slow down as well?

 

[ronald_dai]

If the entire universe was highly dense and caused time to slow down it would have to be measured by an observer outside of this high density. Since the whole universe would be high in gravity from the point of view of an observer inside the universe there would be no slow down of time.

it sounded quite different when you said that the local time of the black hole was not change...if the local time of the black hole was not change then the local time of the BIG BANG should not change...but it should be extremely slow according to our time reference which is NOT the local of the BIG BANG, just like an observer outside the black hole would see the time inside the black hole is very slow!

 

[DaleSwanson]

I think everyone is completely misinterpreting my question. So, let's start over. I understand that he would see the universe speeding up and to him his clock would be ticking normally. That is not my question.

My question is... What is his speed? The book makes it sound like he would be visible forever because as his time slows down his physical speed would be slowing down? Is he still moving at near the speed of light or does his speed actually slow down as well?

Ah, speed as in velocity, sorry I misunderstood.

His velocity wouldn't be slowed down from his point of view. He would just fall into the black hole at whatever velocity he should be moving due to gravity and whatever velocity he had prior. An outside observer on the other hand would see his velocity slow down. Neither point of view is more true, it's all relative to your reference frame.

 

[Tac-Tics]

I think everyone is completely misinterpreting my question. So, let's start over. I understand that he would see the universe speeding up and to him his clock would be ticking normally. That is not my question.

My question is... What is his speed? The book makes it sound like he would be visible forever because as his time slows down his physical speed would be slowing down? Is he still moving at near the speed of light or does his speed actually slow down as well?

Ah. Interesting question.

An object falling into a black hole wouldn't be able to pass through the event horizon, so their velocity would have to approach zero asymptotically. I wish I knew the math a little better. Since the observer's velocity and time both slow down, it is the curvature of spacetime that accounts for the missing fraction of the 4-velocity.

The observer on the inside, of course, sees himself at rest, as all observers do. The even horizon is moving towards him at incredible speeds and it is accelerating towards him.

 

[skeptic2]

He would just fall into the black hole at whatever velocity he should be moving due to gravity and whatever velocity he had prior.

What velocity would matter have at the event horizon having free fallen essentially from infinity?

 

[DaleSwanson]

What velocity would matter have at the event horizon having free fallen essentially from infinity?

Hmm, I'm not certain I'll get everything right, but I think I can figure that out. Assume a size of 10 solar masses, that gives a Schwarzschild radius of 29534.3236 m. An object at that distance would have an GPE of -4.4937759 * 10¹⁶ m³ / s². This should mean if it fell from an infinite distance it should have an energy of 4.4937759 * 10¹⁶ joules (this is the part I'm really not certain on). Plugging that into the formula for speed from kinetic energy I get 299,792,458 m/s exactly, which is suspiciously familiar.

On reflection I seem to remember that the escape velocity at any point is the same as the velocity an object would have from an infinite free fall to that point. Which would have made all this calculations unnecessary.

 

[skeptic2]

This is the same answer I got. It seems on the surface that it objects can't fall into black holes for the same reason they can't escape - doing so means their velocity would exceed c.

 

[Sheneron]

So their velocity would indeed seemingly slow to 0 as observed by us. So does that mean that these particles which we accelerate to near the speed of light actually seem to move slower than what we shoot them out at?

 

[skeptic2]

So their velocity would indeed seemingly slow to 0 as observed by us.

Yes, they seemingly slow to 0 because not only is time dilated but space is contracted as well. The object is still traveling at 300 Mm/sec.

 

[v2kkim]

It is really mysterious. We (outside observer) will see many materials got frozen on the surface of the horizon of event, and theoretically we can detect them from their gravitational force from that frozen locations. But visual observation from outside observer will be practically impossible as time passes because of extreme red shift observed, but gravitational field should be just ok. Am I correct ?

 

[.:Endeavour:.]

I think everyone is completely misinterpreting my question. So, let's start over. I understand that he would see the universe speeding up and to him his clock would be ticking normally. That is not my question.

My question is... What is his speed? The book makes it sound like he would be visible forever because as his time slows down his physical speed would be slowing down? Is he still moving at near the speed of light or does his speed actually slow down as well?

Disregard what the book says because the exact answer to your question is something that is far from our reach. We only have pieces of the picture that in turn start to create the overall image of the black hole. Actually, objects don't fall in directly into the black hole, but instead it will spiral around it and then shoot out of the black hole at high speeds almost at the speed of light. I saw this documentary about black holes in NOVA, and they explained most of the physics surrounding a black hole.

An explanation might be that because very little light actually escapes from a black hole, the light that reaches out eyes might be the light from a different time. Its not time, but the light that reaches our eyes which isn't like the light emitted by a star or other body in space that we can see traveling at 299 792 458 m/s. Actually calculating the speed of a person falling in the black hole is hard to tell because the few light that escapes from a black hole can be from 1 second ago, one day ago, one year ago, one century ago, etc.. The person might be long gone, but you might still be seeing him falling in the black hole from the light that did escape.

The name of the documentary is called NOVA - Monster of the Milky Way if you want to watch it in Youtube.

 

[Sheneron]

So can anyone answer my second question?

The particles, say the ones they send around a collider, go near the speed of light from what I hear. So are those particles actually moving slower because their time is moving slower as seen from our stationary observation?

 

[.:Endeavour:.]

So you are saying that we see the particles moving at the speed of light where in reality they are moving slower because time is moving slower? Is that what your are asking.

 

[Sheneron]

Well I have heard that the particles are moving near the speed of light. But if they are going that fast than time must be moving slowly for them, so do we see them moving slowly(speed)?

 

[.:Endeavour:.]

I'm not sure how to answer it because we cannot actually see particles even more when they are moving near the speed of light. Is like the rotation of the Earth around its axes. We have a person jogging at a velocity of 470.11 m/s plus the rotation velocity of the Earth. The person looks like he is going as fast as a fighter jet, but when be subtract the rotation velocity of the Earth, which is 465.11 m/s or 1040.405 mph, the person is really going at 5 m/s.
Like I said on my first sentence, we cannot actually see the particles going at that speed because also they are too small to actually see them slowing down.

 

[DaleSwanson]

So can anyone answer my second question?

The particles, say the ones they send around a collider, go near the speed of light from what I hear. So are those particles actually moving slower because their time is moving slower as seen from our stationary observation?

If we send a particle at 0.99c then we measure it moving at 0.99c, not moving slow. If you had a clock on those particles and could observer it the clock would seem to be running slow. If you had a spaceship that could travel 0.99c and went for a trip when you got back more time would have passed on Earth than on your ship. This is called the Twin Paradox.
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html

 

[v2kkim]

If we send a particle at 0.99c then we measure it moving at 0.99c, not moving slow. If you had a clock on those particles and could observer it the clock would seem to be running slow. If you had a spaceship that could travel 0.99c and went for a trip when you got back more time would have passed on Earth than on your ship. This is called the Twin Paradox.
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html

DaleS, you are mostly right except one thing. We (outsider) will observe 'the 0.99c particle slow down near horizon of event'. The clock on the ship looks to slow down, means all motions slow down including ship movement when observed from far away.

 

[Sheneron]

So, if a person jumping into a black hole would seem to stop moving because he is moving so fast than the same would hold true of a particle moving really fast right?

So what you are saying is that if we shoot a particle out at 0.99c then we actually observe it moving slower than that? So then how do we know we really shot it out at 0.99c rather than just at a slower speed?

 

[Sheneron]

And then for the other side... If we shoot a particle at 0.99c and we see it moving at 0.99c then why does a person seem to slow down as he approaches a black hole?

 

[DaleSwanson]

I'm pretty sure v2kkim misunderstood that you were talking about a particle at 0.99c without any strong gravity (he mentions the event horizon). The particles at 0.99c would travel at 0.99c as measured by stationary observers. If you were observing from the particles point of view (on a ship at 0.99c), you would seem to be traveling much farther then you should be able to. The galaxy is 100,000 light years across but from your point of view you could cross it in much less time. This is because both time slows down and length contracts. You'd still measure light at c (as always).

This should help with the black hole part.
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

 

[Sheneron]

So the person jumping into the black hole doesn't actually move slower its just an optical effect?

 

[DaleSwanson]

No, gravity actually does slow the time down. I can't explain why in the faq he says that it's an optical effect, perhaps he means only not seeing you cross the event horizon is due to light not being able to escape.

Here's a link that I think does a better job of explaining it in layman's terms.

http://www.perimeterinstitute.ca/en/Outreach/Explore_Our_Universe/Why_Does_Gravity_Slow_Time?/

 

[.:Endeavour:.]

The astronaut, like in my post earlier, to actually know that the astronaut is slowing down is because of the little light that actually escapes from a black hole. That light can be last second ago to a century ago, or more. The astronaut might be already made it out of the black hole, but you are still seeing him falling into the black hole from the time that it takes light to reach the eyes of the observer. Is like seeing light traveling at the speed of sound or at 9 m/s while seeing a diver dive into the pool. The diver might be on the pool, but you are still seeing the diver falling in the pool.

 

[Sheneron]

Ok I know gravity slows the time down I get that. I really do. Everyone forget time for a second hah. My question this whole time is whether his actual velocity slows down along with the time, or whether he still travels at near the speed of light. Does it just seem like he is there forever(optical effect) or is he really there forever?

 

[v2kkim]

The gravity near black hole makes things complicated and interesting. And I am still trying to understand about it, but in general the following seems to be accepted: The far away person will observe the falling astronaut become slow and got frozen forever; but the astronaut will observe himself continuously moving to the center of BH. So, are you ready to accept two realities ?

Now, one interesting question is what the astronaut will observe while crossing event of horizon about the far away outside ?

 

[stevebd1]

Hello Sheneron

Here's a couple of equations from 'Exploring Black Holes' by Taylor & Wheeler (where $M=Gm/c^2$ and $c=1$)

velocity of a free-falling object as clocked by the shell observer (v=1 at event horizon)-

$$v_{shell}=\frac{dr_{shell}}{dt_{shell}}=-\sqrt{\frac{2M}{r}}$$

(minus square root because the expression describes a decreasing radius as the object falls toward the black hole outside the horizon)

where $dr_{shell}=dr/\sqrt(1-2M/r)$ and $dt_{shell}=dt\sqrt(1-2M/r)$

velocity as viewed from infinity (v=0 at event horizon)-

$$\frac{dr}{dt}=-\left(1-\frac{2M}{r}\right)\sqrt{\frac{2M}{r}}$$

which is derived from the energy equation $E/m=(1-2M/r)dt/d\tau=1$

 

[.:Endeavour:.]

Ok I know gravity slows the time down I get that. I really do. Everyone forget time for a second hah. My question this whole time is whether his actual velocity slows down along with the time, or whether he still travels at near the speed of light. Does it just seem like he is there forever(optical effect) or is he really there forever?

It might seem he is falling forever, but its because the light that you seeing been reflected the astronaut is light that actually escaped from the black hole, which as we know is very little. I think that excerpt that you posted about the observer looking at a continuous falling person, is because light doesn't easily escape a black holes surface. To actually know that he is slowing down, we cannot know. Black hole's gravity is massive on how compact the black hole is. So if a black hole is 2 miles across, it will have a massive gravity in contrast of a black hole that is 50 miles across. What I think, is that the astronaut will be accelerating until he eventually reaches the horizon, just like a free-falling object here on Earth accelerates do to the force of gravity.