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Black Hole time dilation

  1. Feb 23, 2009 #1
    I was reading my astronomy text book 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...
  2. jcsd
  3. Feb 24, 2009 #2
    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.
  4. Feb 24, 2009 #3
    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.
  5. Feb 24, 2009 #4
    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?
  6. Feb 24, 2009 #5
    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)?
  7. Feb 24, 2009 #6
    Clocks are the only way we know to measure time. If clocks are running slow, it implies time that clock measures runs slow.
  8. Feb 24, 2009 #7
    I guess the clock is not the literal clock we buy from the store....I mean it is an idea clock without mechanical problem :)
  9. Feb 24, 2009 #8
    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.

    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.
    Last edited: Feb 24, 2009
  10. Feb 24, 2009 #9
    I think everyone is completely misinterpreting my question. So, lets 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?
  11. Feb 24, 2009 #10
    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!
    Last edited: Feb 24, 2009
  12. Feb 24, 2009 #11
    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.
  13. Feb 24, 2009 #12
    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.
  14. Feb 24, 2009 #13
    What velocity would matter have at the event horizon having free fallen essentially from infinity?
  15. Feb 24, 2009 #14
    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.
  16. Feb 24, 2009 #15
    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.
  17. Feb 24, 2009 #16
    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?
  18. Feb 24, 2009 #17
    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.
  19. Feb 24, 2009 #18
    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 ?
  20. Feb 24, 2009 #19
    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.
  21. Feb 24, 2009 #20
    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?
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