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I Time in gravitational reference frame?

  1. Mar 16, 2016 #1
    Hi,
    so Newton said that gravity was like or equivalent to a force?

    When I learnt about SR we were talking about the passing of time as defined by a photon bouncing between two parallel mirrors. So when we're sitting our two parallel mirrors in a gravitational field, even though I suppose mathematically the experience of sitting in the field is like accelerating, the mirrors aren't actually moving. So why does the photon bouncing around in them see time change? If the mirrors aren't actually moving?

    Thanks
     
  2. jcsd
  3. Mar 16, 2016 #2
    Always provided that your reference frame is small enough, locally there will be no change whatsoever in the way time is measured and experienced; your light clock will continue to operate just as it always did, i.e. it will continue to measure exactly "one second per second". Time dilation becomes apparent only if you step outside your small local frame, and compare the light clock to some other reference clock which is in a different frame - you will then notice differences in the clock readings.

    Time dilation is not something that involves local "changes" of any kind, but rather it is a relationship between at least two reference frames in space-time. You can never experience time dilation by using a single, isolated clock. In essence, time dilation is a measure of how events are related in space-time, and that relationship is affected by the presence of sources of energy-momentum - that is an aspect of what we call gravity.
     
  4. Mar 16, 2016 #3

    A.T.

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    In non-inertial frames time passes at different rates depending on position, not just movement.
     
  5. Mar 16, 2016 #4

    Ibix

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    Newton described gravity as a force. It's not at all clear how light and gravity interact in a Newtonian picture. Einstein describes gravity in terms of curvature of spacetime.

    What do you mean by the mirrors "not actually moving"? According to a free-falling observer the mirrors (and the ground) are accelerating upwards. This is a particular case of a more general point - "not actually moving" is not a well defined concept, not even in Newtonian physics.

    You will not see any difference in operation of your light clock, whether you place it at the bottom of a mountain or the top. However, if you use a telescope to observe some other guy's clock at the top of the mountain from the bottom, you'll notice his clock ticking fast. You can interpret this as being because you are in an accelerating rocket, and are "catching up" with the other guy's clock (more precisely, compared to some inertial frame you were going faster at the second tick than the first) or because you are deeper in a gravitational field and are subject to time dilation due to the curvature of spacetime. But neither interpretation involves the photons in the light clock "seeing time change".
     
  6. Mar 17, 2016 #5
    Thanks for the replies!

    Ok so I'm floating in space (minding my own business as a non-interial frame of reference), then a planet with a photon clock on it falls towards me. As the planet is falling towards me the mirror face that is furthest from the planet's surface is moving away from the planet, towards me, so it will take longer for the photon to reach that top mirror? Thus, I see the planet's clock tick slower than the photonic-Fob watch chained to my pocket?
    So is that one ANALOGY for how it works, but the actual explanation is that the more distorted spacetime is from a large mass, the 'time' part of spacetime gets accelerated from the perspective of a non-enertial frame of reference?

    [Mentor's note: some personal theorizing in violation of the Physics Forums rules has been removed from this post]
     
    Last edited by a moderator: Mar 17, 2016
  7. Mar 17, 2016 #6

    Ibix

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    If you're floating in space then you're in an inertial frame. The simple test is: if I stand on a spring balance, does it say I weigh anything? If the answer is no, I'm free falling and in an inertial frame.

    That's a slightly different scenario from two clocks in a tower. But assuming you are only moving radially with respect to the Earth, yes. If you're moving tangentially as well, I think it depends on how deep in the field you and the other clock are (I think).

    I don't think analogy is the right word. "I'm in a rocket" and "I'm on the surface of a planet" are two competing hypotheses. Locally, both are equivalent. There's no way to tell the difference, whereas an analogy is an approximate description that's evocative rather than precise. If you start to look over a larger region you will notice that the apparent g-field is uniform or not, which will tell you whether you are in curved spacetime or not, and the "in a rocket" explanation is either falsified or not.

    I don't think that "the 'time' part of spacetime gets accelerated" makes any sense. How could you describe time being accelerated? What would you differentiate, and with respect to what?

    [Mentor's note: quotes of deleted text from a previous post have been removed]
     
    Last edited by a moderator: Mar 17, 2016
  8. Mar 17, 2016 #7

    PeterDonis

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    No, the analogy is not correct. Your analogy is with a light clock in flat spacetime, but your actual scenario is in curved spacetime (because of the presence of the planet). Flat spacetime and curved spacetime are not the same.

    You are also confusing inertial motion with accelerated motion. In the usual light clock scenario in flat spacetime, the light clock is moving inertially. In the usual equivalence principle scenario, the observer is accelerated--he feels weight. Locally he can't tell whether the weight he feels is because he is inside a rocket whose engine is accelerating it, or inside a room at rest on the surface of a planet, with the planet's surface pushing up on him. But neither of those cases is the same as moving inertially. Similar remarks would apply to a light clock sitting on the surface of a planet--you would have to analyze it as an accelerated light clock, not an inertial light clock.
     
  9. Mar 17, 2016 #8
    I'd just like a little clarity about the right terminology. Alfred is at rest in a train at a station. On his left Henry is in a train that suddenly accelerates forward with the result that he spills his coffee. Henry concludes that he is at rest in a gravitational field that results in the acceleration backwards of Alfred, along with his train and the platform. None of the passengers in Alfred's train spill their coffee because... they are in free fall, they are in an inertial frame?
     
  10. Mar 17, 2016 #9

    PeterDonis

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    Just to be clear, we are treating the station as floating somewhere out in space, so there is no Earth gravity involved. (Most thought experiments gloss over this, but for this one we need to make it explicit.) The station is in free fall, at rest in an inertial frame.

    Yes. And being at rest in a gravitational field, he feels acceleration, and can observe acceleration-related effects, such as spilling his coffee.

    That results in the coordinate acceleration backwards of Alfred, etc. But coordinate acceleration is not the same as proper acceleration, which is what Henry is experiencing. The term "acceleration" is often used sloppily, in a way that ignores this crucial distinction.

    Yes. And they can tell because they don't feel acceleration, whereas Henry does. The felt acceleration, or lack thereof, is an invariant, and doesn't change if we change frames, or if we introduce "gravitational fields" because we've chosen a non-inertial frame (such as Henry's frame when he spills his coffee).
     
  11. Mar 17, 2016 #10
    Thanks - that's very clear and helpful. I always thought setting these thought experiments on the earth confused things, but I like familiar territory.
     
  12. Mar 25, 2016 #11
    Its been so long that I'm looking over what I wrote almost as an impartial observer.
    Yeah I agree with you. I think what I was saying was: it's like time is a 'thing that happens' and when spacetime is warped, the time thing just does it's thing, but faster. However I agree, that time is only 'a thing' when relative to more than one reference frame, so yeah you're right.

    Also, For the life of me I can't remember what I wrote, do you remember what my 'personal theorising' was?

    So if I'm in a rocket accelerating at 9.8m/s/s, does that locally warp spacetime?

    could you please explain what inertial motion is? Is it just moving at a constant speed?
    and the difference between coordinate acceleration and proper acceleration?

    Thanks
     
  13. Mar 25, 2016 #12

    Ibix

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    It'd just get deleted again even if I could remember.

    No. In both cases you feel a "force of gravity" because the floor is pushing you out of your natural free-fall path. The curvature of spacetime is why you are falling into the floor when you're on a planet. In the rocket, you are falling into the floor because there's a rocket motor pushing the floor upwards. No spacetime curvature needed.


    Motion with no forces acting on you. So rockets off, no electromagnetic fields, not moving through a medium (remember gravity is not a force in relativity).

    Proper acceleration is something you measure with an accelerometer. Stand on a weighing scale. Do you weigh anything? If yes, you're undergoing proper acceleration.

    Coordinate acceleration is when the rate of change of your coordinates isn't constant. If I pick a coordinate system where x=0 here, x=1 is 1m away, x=2 is 1.5m away and x=3 is 1.75m away, then you walk along at constant speed (no proper acceleration - hold a weighing scale vertically in front of you and ask if it shows anything) then you get from x=1 to x=2 in less time than from x=0 to x=1. But this is just an artifact of the coordinate system, not anything real.

    That was obviously a contrived example. But non-trivial coordinate systems do arise in curved spacetime and it's important to distinguish between "my coordinate system isn't the best for what I want to measure" and "I am actually accelerating".
     
    Last edited: Mar 25, 2016
  14. Mar 25, 2016 #13

    PeterDonis

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    More precisely, the curvature of spacetime is why people all over the planet can be "falling into the floor", even though "into the floor" is a different direction in different parts of the planet. There's no way to reproduce that global effect in an accelerating rocket, no matter how large you make it.

    And just to add a clarification, this measurement is how we can tell, physically, whether or not something is moving inertially. If an accelerometer attached to an object reads zero, that object is moving inertially; if not, not.
     
  15. Mar 26, 2016 #14
    What if our planet were an (almost) infinite plane? Would the curvature of spacetime still be the reason why we are falling into the floor?
     
  16. Mar 26, 2016 #15
    Could you reproduce that global effect with millions of accelerating rockets, one for each person?
     
  17. Mar 26, 2016 #16

    Ibix

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    I'm told you can't make a uniform gravitational field. I think that this is because there are limits to material strength in relativity that you can't ignore and a disc bigger than a certain diameter will simply collapse under its own weight. So there's always curvature - even at the symmetry axis of such a disc there are non-zero second derivatives.

    Might be worth waiting for (e.g.) @PeterDonis to confirm that...
     
    Last edited: Mar 26, 2016
  18. Mar 26, 2016 #17

    Nugatory

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    It's more than that - a uniform gravitational field is not a vacuum solution of the Einstein field equations, you can't arrange matter in a way that produces a uniform field around it.
     
  19. Mar 26, 2016 #18

    Nugatory

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    You could reproduce the behavior in which dropped objects fall towards the floor of the ship they're in, no matter where on the sphere the ship is. However, objects at rest on the floors of different spaceships will move apart from one another, and this doesn't happen in the gravitational case - so still no global equivalence.
     
  20. Mar 26, 2016 #19

    Ibix

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    I was trying to work out why not. Symmetry suggests the good old infinite thin plane ought to produce a similarly symmetric field, but it would also have to have infinite extent in time too. I presume there's some reason why that doesn't work.
     
  21. Mar 26, 2016 #20

    PeterDonis

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    No, because the rockets would be accelerating in different directions and so they would move apart, whereas people all standing on the surface of the Earth are at rest relative to each other--they don't move apart.
     
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