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Gravitational Time Dilation - Confused

  1. Apr 28, 2009 #1
    Hey everyone, recently I watched a discovery program about time travel. I understood time travel from the view point of traveling at/close to the speed of light, however, I am completely confused as to how time travel is possible using gravity.

    I know that it has to do with gravitational potential, but under that logic, one could say that as gravity increases, so does the speed at which objects fall, ergo, making them age slower. (Assuming that objects can fall at/close to the speed of light)

    I just don't understand the whole concept of Gravitational Time Dilation, can anyone please shed some light on it?
  2. jcsd
  3. Apr 28, 2009 #2


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    Welcome to PF!

    Hey valdar! Welcome to PF! :smile:
    It isn't! :wink:

    Using wormholes possibly, using gravity definitely not.
    Last edited: Apr 28, 2009
  4. Apr 28, 2009 #3
    First it should be made clear that the "time travel" when travelling at close to the speed of light is just the relative slowing of the moving clock relative to the clock of a stationary observer. There is no going backwards in time and murdering you grandparents or whatever else time travellers have the urge to do. There is no changeing the order of a sequence of events that have already happened (causalty). There is just differential ageing.

    Although the speed of a falling clock does have some influence on the slow down of the proper time of the falling clock it is not the crux of the matter. A perfectly stationary clock low down in a gravitational potential well, runs slow relative to clock higher up.

    Yes, they can. An object released from infinity aproaches the local speed of light as it aproaches the event horizon of a black hole. From the point of view of an observer higher up the velocity of the falling object (and the coordinate speed of light) aproaches zero as it aproaches the event horizon.

    There is a lot of ground to cover here and I have a feeling this is going to be a long thread. You can get started by googling the "equivalence principle".
  5. Apr 28, 2009 #4
    Thank you for replying. My biggest spheel is the following:

    but as they fell from the surface to the centre, they gained kinetic energy

    The vary same photons that ended up being "decelerated" while moving from the clock to the observers eye are "accelerated" when they move from a light source (lets say at the same distance as the observer themselves) to the clock.

    So if the distances are the same, the deceleration is equal to the acceleration, there shouldn't be any shifts. Where am I wrong?
  6. Apr 28, 2009 #5
    You would be right if the source of the photons in George's hole was a torch in the hand of the observer at the top of the hole. On the way down to the clock at the bottom of the hole they gain energy (higher frequency) and then after being reflected off the bottom clock they would lose the same amount of energy and arrive back at the top with the same frequency that they were emitted with. I think in George's example the clock is the source of the photons. (Imagine the hands painted with glow in the dark luminous paint)
  7. Apr 28, 2009 #6
    Sorry for the double post, but I --THINK-- I get it.

    Let's say you have a room. In that room you have a ball bouncing between the two walls. Every bounce is one second.

    You get two of the rooms. You put one room on earths surface, and another in the centre of the earth.

    For the room at the surface, the balls bounce is accelerated by gravity.
    For the room at the centre, the balls bounce is not accelerated by gravity.

    Observing the centre balls bounces from the surface, it will seem slower, and vice versa, is this about right?
  8. Apr 28, 2009 #7
    *thumbs up* except with light its not about physical acceleration but rather a path difference caused by curved space time. Also a freqency change (gravitational redshift). But it has much the same effect, in this example.
  9. Apr 28, 2009 #8
    It doesn't just seem slower, it IS slower. The slow down is not due to lack of being accelerated by gravity either. Imagine the balls are "super balls" that lose no energy with each bounce and they are bouncing from side to side horizonatally so that gravity has no direct influence on its bounce speed. A digital device counts each bounce of the balls. When one of the ball rooms is lowered to the centre of Earth and and brought slowly back to the surface again, the room that was at the centre would have counted less bounces, but both balls will be bouncing at the same speed when back together at the surface.
  10. Apr 28, 2009 #9
    Ok then there is another issue.

    Not being in a gravity field makes your internal clock run slower.THIS POINT IS WRONG. Being in the middle of a strong field makes your internal clock run slower
    Traveling at the speed of light makes your internal clock run slower.

    The faster you go the more you weigh, the more you weigh the more mass you have, making you, yourself have a gravitational field. But then how are you both able to have your internal clock run slow due to traveling fast, but at the same time, have it run fast by being the creating factor of a gravity field?
    Last edited: Apr 28, 2009
  11. Apr 28, 2009 #10


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    Um... it is the clock that is deep inside a gravitational field that runs more slowly.

    There's a great story on the web of a scientist-dad who took his kids on a camping trip up the mountains, along with some atomic clocks. See Clocks, Kids, and General Relativity on Mt Rainier. Just because I think the pictures are hilarious, here's a shot of plan A: backpack your atomic clock, compared with plan B: use the car and drive up a mountain.
    climb-5071a-1.jpg (<-- Plan A. Plan B -->) CIMG0566q.jpg
    They used plan B, and also left some clocks back home for the subsequent comparison.

    The clocks up the mountain run faster. By going up the mountain with his kids, this Dad got to spend an extra 22 nanoseconds with his kids that he'd have missed by staying home. As he says: It was the best extra 22 nanoseconds I've ever spent with the kids.

    Actually, the faster you go, the more energy you have ... as measured by someone who remains at rest! For you, in motion, there's no extra energy or extra gravity, involved.

    Cheers -- Sylas
  12. Apr 28, 2009 #11
    From an outside observer, you would be in the middle of a gravitational well, traveling at close to the speed of light then, right?

    If so, then that's what I was looking for.

    Wow the world is really subjective than I originally thought
  13. Apr 28, 2009 #12


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    Why do you say you'd be traveling at close to the speed of light? In the most common coordinate system to use for spherical bodies like planets (Schwarzschild coordinates), if you're at a constant distance from the center then your speed is zero.
  14. Apr 28, 2009 #13
    Sorry, let me explain that better, my original question was that as a mass accelerates, its weight increases, with an increase in weight there would be an increase in gravitational pull towards the object.

    Originally I had a mistake in my assumptions. Correctly, an object traveling very quickly would be both deep in a gravitational well (due to its own increase in mass, gravity) and it would have time pass by slower, and due to the fact that it is traveling close to the speed of light, it would also have time pass by slower.
  15. Apr 28, 2009 #14


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    I don't think so; the association of gravity and the additional energy of a moving object is not that simple. In fact, special relativity works all by itself in your example.

    If you have a clock on a massive object (large rest mass) which is moving (relative to you) at near to light speed, then there are two components in the time difference: the velocity part, that can be obtained with special relativity, and the gravitational part, for which you need general relativity.

    Indeed! It's worth mentioning, however, that rest mass is not subjective. It is an invariant.

    If you have two observers moving relative to each other at high speed, then their observations are symmetrical. From the perspective of either one, the other clock is slower.

    This symmetry is broken if one of the observers shifts their inertial frame, by changing velocity, and that's why there's no actual paradox with any of the travelling twins variations.

    In the case of gravitational time dilation, there's no symmetry between the observers. Each observer agrees that the clock in the kitchen is deeper into a gravitational field and running more slowly than the clock up on Mt Rainer. You can have observers on the mountain, and in the kitchen at home, in direct communication with each other, and agreeing without ambiguity that the kitchen clock runs slow.

    Cheers -- Sylas
  16. Apr 28, 2009 #15
    This was what I was trying to get at.

    Thank you :)
  17. Apr 28, 2009 #16
    From the information in this thread, I think the conceptualized spacetime material is actually drawn wrong.

    An "Empty" (objectless) area of space is has no gravity exerted upon it (minute, but very close to 0).
    The centre of any object in space (Excluding black holes) has no gravity exerted upon it either.

    If gravity is the culprit that bends the spacetime continuum, shouldn't it be equal between the core of an object, and empty space?

    see the attached picture - Please excuse my terrible MS paint skills

    Attached Files:

  18. Apr 28, 2009 #17


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    No, the conventional picture is the one that is more correct.

    You can show this by thinking of the gravitational blue shift of a light of a fixed reference frequency being shined down a deep hole to a detector at the center of the Earth.

    There is a blue shift observed when you shine the light down the height of the tower at Harvard. Put another way; the atomic clock at the top of the tower is running faster than the one at the bottom.

    Now imagine digging into the basement. Do you think there will be more, or less blueshift observed?

    There will be more blueshift observed, of course; and that's true because the light is moving deeper into the gravitational well. So it goes, all the way down to the center.

    This is getting back to being subjective again. A clock at the center of the Earth runs more slowly than one at the surface. You figure out how much more slowly NOT by measuring the gravitational acceleration in each location; but by considering a world line between the two locations... which involves moving deeper and deeper into a gravitational well.

    Cheers -- sylas
  19. Apr 28, 2009 #18
    From your example, there is a specific distance between the top and bottom of the tower. During that distance there is a specific amount of gravity excreted.
    If you dig into the basement, more gravity is excreted (due to increase in distance), increasing the blue shift.

    If you dig deep enough, gravity will become weaker and weaker, decreasing the -amount- that the blue shift happens by.

    It will still happen, it will still increase, but at a less and less value, which will be 0 at the centre then?

    Is that right?
    Last edited: Apr 28, 2009
  20. Apr 28, 2009 #19


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    Yes, I believe so. That is, the rate of change of blue shift goes to zero at the center of the Earth. But it's more and more blue shift all the way down.

    Inside a large hollow cavity at the center of the Earth, observers distributed around the cavity would all see their clocks running at the same rate, and they would all see the same difference between their clock, and a clock at the surface.

    Cheers -- sylas
  21. Apr 29, 2009 #20


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    Yes, there was a recent thread about this:
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