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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:
  22. Apr 29, 2009 #21
    Nope, it's wrong. Gravitational time dilation is not as closely connected to gravitational acceleration as you think and has more to do with gravitational potential. For example a clock at the centre of the Earth will be running slower than a clock at the centre of the Moon because the Earth has more mass and is in a deeper gravitational well. You can think of the rubber sheet analogy. A large bowling ball representing the Earth puts a deeper dent (gravitational well) in the rubber sheet than the dent made by a cricket ball representing the Moon. The gravitational acceleration at the centre of the Earth and at the centre of the Moon is the same (zero) but the clocks at the centres of the two bodies are NOT running at the same rate. The blue shift is increasing the deeper you go and the larger the mass of the body and does NOT go towards zero. If the body is sufficiently massive and its mass has collapsed towards a radius of 2GM/c^2 then a clock at the centre will stop (and the blue shift become infinite.) as the body becomes a black hole. That is the limiting case.

    <EDIT> I think I have misinterpreted your statement above. My statement above is more applicable to this earlier statement of yours:

    The time dilation at the core of an object is not equal to the time dilation of empty space.
    Last edited: Apr 29, 2009
  23. Apr 29, 2009 #22
    Look at it this way, if you have a stationary massive object in space with a tunnel (from one end to the other) in the middle of it, say a planet. As the light is traveling down the tunnel it is blue shifted until the centre of the object. From the centre of the object to the other side of the tunnel the light is red shifted, overall, there would be no shift, would there?

    See the attached image.

    2nd part. I understand that in the centre of the earth a clock would run slower than on the surface, how come?

    So then the speed of time is measured by how high or low we are on the spacetime continuum? relatively speaking of course.

    Attached Files:

  24. Apr 29, 2009 #23


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    That's correct. But remember, any "shift" is always dependent on an observer; not an absolute property of the light.

    You can only say the light coming out of the tunnel is "redshifted" as a comparison between what is observed in the center, and what is observed half way out.

    Because that's how massive objects bend spacetime.

    I don't think that's a meaningful statement, as phrased. "high and low on the spacetime continuum"?

    The passage of time is measured by clocks. A clock has a "world line", and "proper time" along a world line is what is measured by a clock with that world line. Relativity is the theory that allows you to infer what will be measured by a clock, given its world line.

    Cheers -- sylas
  25. Apr 29, 2009 #24
    In the above example, as drawn out in MS paint, how would you see the light shifted inside the planet? you see the light leave a source, travel into, and through the planet, and then out the other side..... what would you see happen? wouldnt you see both shifts

    wait.... in order for you to see both shifts that means that at every point in time during that line light is given off from that line which then travels towards you. wow. based on that youd see something completely different.

    That didn't work. Lets say that you are measuring the blue/red shifts of light. One measuring device is located at the beginning (before the blue shift) one in the middle (when the blue shift becomes red shift) and at the end (at the end of the red shift). In that case wouldnt you be able to "sense" the shifts using the measuring tools?

    Meaning, clocks only measure how high we are in the spacetime continuum, in other words if we are on a heavy object, or not. At a high point on the continuum clocks would run at a specific speed, at a low point they would run at another one, how far off am i?
  26. Apr 30, 2009 #25
    No single observer would be able to see the entire light path and all the shifts. You would require a series of observers arranged along the path. Imagine the test beam is wide and they have small detectors that can sample the beam without blocking it. Later they can compare measurements and compare them with what GR predicts. Using the calculations of GR they can predict what they would measure at some point they have not yet tested and then check if the prediction is correct. After predicting and checking that the equations are correct for several random points they can build up confidence in the predictions and determine what the frequency is at any point using only maths without requiring an infinite number of observers. Oh, and yes they would see both shifts.

    Yes, as above.

    continuum is a vague word. If you mean that at a high gravitational potential clocks run faster relative to clocks at a low gravitational potential... then yes.

    Science has very few answers for why the universe is the way it is or how it works the way it does (what mechanism). It can only tell you what you would expect to measure given certain parameters and offer some guiding principles learnt from observation and experience. One of those guiding principles in GR is the equivalence principle and another is the constant speed of light as measured locally.

    So we can not say WHY clocks in at a low gravitational potential run slower than clocks at higher gravitational potential anymore than we can state WHY objects fall from a high potential to a low potential. (not yet anyway without a complete gravitational theory of everything). There is some connection between the two observations and it might be possible to claim at some level that objects fall from a high gravitational potential to a lower gravitational potential because time runs slower at lower gravitational potential (or vice versa).

    When studying relativity you have to careful to note when you are talking about relative or coordinate or local or proper measurements. For example the statement that the speed of light is always constant is only true if you only mean the local speed of light. The statement that clocks run at different speeds is only true if you mean the relative rate rather than the proper rate. The proper rate of a clock is always one second per second but to claim that clocks do not run at different rates without making it clear that you specifically mean only proper clock rates is misleading just as it is misleading to claim the speed of light is always constant without making it clear you are only talking about the local speed of light. As you go deeper into a gravity well the relative speed of light gets slower, the relative speed of clocks gets slower and the relative length of rulers get shorter and the consequence of all that is that any observer always measures the local speed of light to be the same.

    Another surprise is that the frequency of a rising photon does not actually change! The observer higher up with the faster clock measures the frequency of the light as decreasing, merely because he is making the measurement with a faster clock! When you think about it, it makes sense. The energy of a photon is determined by its frequency. If its frequency was really getting lower then you have to ask where has all the missing energy gone? Objects usually shed energy by emitting photons, but photons do not shed energy by emitting more photons. Another mechanism used in Newtonian physics is that objects give up there energy to a gravitational field but in GR the gravitational field is not considered to store energy in the classical way. Therefore a rising or falling photon neither gains nor loses energy, but locally it appears to.
    Last edited: Apr 30, 2009
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