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Can someone explain Gravitational Time dilation?

  1. Oct 17, 2009 #1
    I were trying to figure out the "logic" why gravitation (acceleration) causes time dilation.

    While at "velocity time dilation" its because (e.g) light in light clocks must travel longer distances.

    As seen on those pics:

    My problem is that material explaining "gravitation time dilation" is not much explaining. They rather say the effect is a fact, but doesn't bother to explain it same way as it's explained with velocity.

    So I were thinking and I created my little "theory" why is that, so pls try to confirm or deny that:

    1) look at the picture:
    http://docs.google.com/File?id=dctmvpzh_61fk6ww7gr_b [Broken]

    2) Part A
    There is a line which represents spacetime. Red dots show distance of 1 light year between the red dots. The yellow line inside a cube are my "light clocks". Meaning the yellow light will travel 1 light year to the red dot and 1 light year back to original middle red do.

    3) Part B
    As seen the "spacetime" is curved down, because there is an star which curve it.
    So that the spacetime is curved down and distance between red dots is stretched - because of gravitation. (like human would get stretched near black hole)

    And because this distance red-to-red is stratched, so it's not 1 light year anymore. Now it is let's say 1.5 light years. The same way the light years will be stretched and the yellow light will have to travel from middle red dot to the right red dot 1.5 light year, and same back. So the time will be 3 light years. So the time will be dilated.

    So is this my way of understanding right? That mass objects stretch the spacetime, and therefor the light (which travels same speed in all frames) will have to travel longer distance.(like it travels during object moving.)
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Oct 17, 2009 #2
    I have better picture now:

    http://docs.google.com/File?id=dctmvpzh_62cs97k54b_b [Broken]

    As visible on picture the full green line is a path of ship A - travelling thru spacetime with no gravitation influence.

    While second green light shows path of ship B - which travel thru space and then travel around the high mass star. Because of gravitation it will have to travel longer distance (down to star and up from star) as shown in red color line. Which will cause time dilation.

    Assume ship A has a light clock inside. And the light clock will measure 100 "cycles"
    While in ship B the cycles will grow at same rate as in the ship A. Untill ship B fly to gravitation influence of star. And now because ship B (ship B's light clocks) is flying thru spacetime stretched by gravitation - so the beam in light clocks will have to travel longer distances - showing time dilation (similar to longer distances cause by movement of ship or light clocks)

    a) Is this way of explanation correct?
    b) How many "cycles" will ship B's light clock measure? Less then 100, more then 100, exactly 100??
    Last edited by a moderator: May 4, 2017
  4. Oct 17, 2009 #3


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    That is not spacetime, just space. Without the time dimension in the diagram you cannot visualize gravitational time dilation.
    You idea is right, but you have to apply it to the time dimension:
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  5. Oct 17, 2009 #4
    Thank you for reply.

    I realized this sounds bad. It sounds like I think the time is slower because it will fly more kilometres thru the "gravitation well". I ment it as it will take longer distance for the light beam inside "light clocks" to make one "cycle" inside the clocks. (while the speed is always same)

    So this picture shows more accurately what I mean:
    http://docs.google.com/File?id=dctmvpzh_63f22c6wdf_b [Broken]

    The yellow thing is sun. The tiny lines is space. Whole picture is seen from the "top". So the space bends to the sun = the space between the lines far from sun have 10 cm, and near sun the space between the lines is bigger then 10 cm.

    The box with yellow V are those light clocks, where the yelow lines is light reflecting from bottom mirror to back to the top. So on the picture I assume that gravitation will cause stretch of space and the clocks itself, and the beam will take more time reflect from the mirror back to the top of clocks.

    I tried to add that time curve factor, so is this correct what I wrote upwards?
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  6. Oct 18, 2009 #5
    imagine a rocket starting at rest beside a long line of synchronized clocks one light sec apart. as the rocket accelerates at 1G the clocks become more and more out of synch from the rockets point of view. that means that the clocks are running at different rates from the rockets point of view. if you do the math you will see that there is a point behind the rocket where time stops from the point of view of the rocket.

    gravity = acceleration hence gravitational time dilation
  7. Oct 18, 2009 #6
    I know, I read this many times.
    The problem I have is why acceleration and gravitation cause time dilation. (I know it dilate time, I don't know why it dilate time - the "logic" of this effect is what I don't know)

    The logic at speed time dilation is simple - the light in "light clock" will have to travel longer path:
    http://upload.wikimedia.org/wikipedia/en/thumb/a/a5/Time-dilation-002.svg/800px-Time-dilation-002.svg.png [Broken]

    But I don't know what's the "logic" of the grav. time dilation.
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  8. Oct 18, 2009 #7


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    For a interesting visualisation of gravitational time dilation, check out
    http://arxiv.org/abs/gr-qc/0411060" [Broken]

    Max Tegmark uses the river model in his lectures.

    As Andrew Hamilton emphasizes, the river model can't be taken literally, but it's a good heuristic. Anything that is visualized in terms of the river model will match the predictions in terms of spacetime curvature.

    I think having several different models is better. It reminds me that none of the models can be taken literally; ultimately all models/visualizations are metaphors.

    Last edited by a moderator: May 4, 2017
  9. Oct 18, 2009 #8
    actually it has more to do with relativity of simultaneity. (this is what confuses all beginners). when the rocket is stationary all the clocks are synchronized. they tick simultaneously.

    look it up on wikipedia
  10. Oct 18, 2009 #9


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    I had some thoughts on how you could conclude gravitational time dilation geometrically using a light clock. Here is what I came up with:

    http://img38.imageshack.us/img38/2484/lightclocku.png [Broken]

    In an accelerated frame (left bottom) light doesn't move straight, so if the mirrors were parallel the beam would not hit the same point on the mirror (normal reflection). You could however manipulate the reflection so it does (adjusted reflection). Gravitational time dilation occurs in the accelerated frame (left bottom) because the length of the path varies with the position along the direction of acceleration.

    I'm not sure if all that is correct and happy about comments.
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  11. Oct 18, 2009 #10
    Thank you so much for the reply.
    I think it's correct. It sounds logic.

    But, this would mean the position of light clocks is also important .... while I have some sence that time dilation should be "general" - and not depending on position of clocks, let me explain:

    http://docs.google.com/File?id=dctmvpzh_64d5zr3jdg_b [Broken]

    On the left the black light beam is attracted enough by the black hole so that the light will actually never reach the second mirror.

    On the right side the light beam is just slowed down (or maybe only redshifted?) and in both cases will reach the second mirror.

    Problem is that B]it is not universal[/B]. It depends on the position of clocks - if they are layed horizontal the beam will not reach the mirror, while vertical the beam would be slowed down (or redshifted - I dont know).

    While motion time dilation is universal. No matter what position the clocks have - the beam always have to travel larger space - with unchanged speed, therefor time dilated.

    On other hand what you say is logic to me, but it's not "universal" and I have some kind of "feeling" it shouldn't matter on what position the clocks have.(just like the motion time dilation)

    a) as I wrote my "theory" or the way I try understand it - that gravitation stretches space and objects. Then no matter what position clocks are, the beam will travel longer path, with unchanged speed - therefor time dilated. - I have no idea whether it's correct or not.
    b) I also heard, that time dilation in accelerated frames is caused because the "process" will take more energy to happen. But the energy itself will not be increased - therefor processes will be time dilated - but this seems to me as something not probable.
    Last edited by a moderator: May 4, 2017
  12. Oct 18, 2009 #11
    no. the photon on the right will never reach the second mirror if it is released from a point which from the point of view of the second mirror is an event horizon.
  13. Oct 18, 2009 #12
    No no, I mean it as the light is released above event horizon, the "light clocks" are not in even horizon, both mirrors are slightly above it. (slightly = simply I assume the gravitation will be able to bend the light as in example on the left side.)
  14. Oct 18, 2009 #13
    no. the mirror thing isnt right. the only thing it could tell you is the rate at which a clock at that poist ticks. I gave a perfectly good explanation of gravitational time dilation below. it has to do with relativity of simultaneity from the point of view of an accelerating frame

  15. Oct 18, 2009 #14


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    Gravitational time dilation does in fact depend on the position of the clock. Basically you are comparing two clocks at rest to each other, but at different positions.

    But maybe by "position" you mean orientation? I think it will work as well if you rotate the clock by 90° it is just harder to visualize. The vertical clock above with infinitely extending mirrors is basically an infinite number of light clock placed along the direction of acceleration. But you need at least two clocks placed along the direction of acceleration to see gravitational time dilation. This is the spacetime diagram for two horizontal (beam parallel to acceleration direction) accelerating clocks.

    http://img195.imageshack.us/img195/7529/lightclocks.png [Broken]
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  16. Oct 19, 2009 #15
    Yes, you're right, I ment orientation - vertical & horizontal.

    The graph is amazing. It perfectly shows what I wanted to see. I worked with this when visualising the speed time dilation for me, and what you draw make sence to me.

    I can now imagine acceleration time dilation vertical or horizontal in spaceship accelerating, also horizontal clocks near some gravitation source. But it still makes me the problem of vertical clocks above the gravitation source. (as I showed in my last picture - on right side)

    I have already found out that light can't be slowed down by gravitation, it just undergo redshift, but its speed is constant. My problem now is to imagine that light will reach the vertical mirror slower, while its speed is constant.
  17. Oct 19, 2009 #16


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    This exactly what is shown here:

    http://img195.imageshack.us/img195/7529/lightclocks.png [Broken]

    Just rotate the whole picture. You have a clock at rest in a gravitational field. In relativity this clock is accelerated upwards. To see gravitational time dilation you need a second clock at rest to the first but a bit higher. To compare their rates easily the upper mirror of the lower clock is double sided and acts the lower mirror of the upper clock. Both signals are initially simultaneously emitted from the middle mirror, but they don't return at the same time, because the upper (right on the picture) clock is faster.

    This is tricky, since the speed of light in accelerated frames is only locally c. But the light clock has some spatial extend, so the average speed of the beam is not c:
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  18. Oct 19, 2009 #17


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    You can think of GR as just drawing the space-time of SR on an appropriate geometric surface.

    The actual surface you need is described in a paper by Marolf:

    See figure 12 for the surface.

    One of the difficulties here is that you have to be familiar with SR. The space-time diagrams you draw
    on the curved surface of figure 12 transform via the Lorentz transforms, they do not transform via the
    more familiar Galilean transforms. Another way of saying this - x^2 + (ct)^2 is not an invariant under a
    change of reference, rather (x^2) - (ct)^2 is.

    This doesn't explain WHY you have to do things way - there isn't really an explanation for "why" questions
    in science. All we can say is that if you do it in this manner, it seems to agree very well with experiment.
  19. Oct 22, 2009 #18
    Should we automatically assume that the light beam would hit the "clock" receptor in a relativistic c based frame of reference? The clock base is also moving forward at the speed of light and the photon could land behind it, especially if frame of reference "momentum" does not carry it forward. I know and understand all the mathematics that derives from this premise but I think it's flawed when applied to objects traveling near the speed of light, since lights top speed is independent of the frame of reference.
  20. Oct 22, 2009 #19


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    The clock cannot move at the the speed of light.
    Not if the clock moves inertially.
    Frames of reference don't have momentum
    Which premise? Galilean relativity? Or that all observes must agree if the photon stays in the clock, or not?
    "Traveling near the speed of light" relative to what? Some observer? Why schould the clock care that it is moving relative to some observer? What about the observer at rest to the clock? If he sees the photon stay in the clock, the moving observer must do so as well.
    This doesn't imply that the photon misses the mirror in one frame, and hits it in a different one. It just implies (together with Galilean relativity) that the clock ticks slower in a frame where it is moving.
  21. Oct 22, 2009 #20
    But the "clocks" slowdown is based on a pythagorean principle that doesn't apply at relativistic speeds.
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