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Gravity ~ Acceleration ~ Centrifuge & GR

  1. Feb 1, 2010 #1
    Gravity & Acceleration are said to be fairly equivalent.
    This includes their respective effects on time dilation doesn't it?

    Is artificial gravity generated by centrifugal motion considered to be fairly equivalent to these?
     
  2. jcsd
  3. Feb 1, 2010 #2
    Hi.
    Artificial or natural doesn't matter with the time dilation effect of gravity.
    Regards.
     
  4. Feb 1, 2010 #3
    Thanks sweet.
    What happens if one of these effectively cancels out the same type or a different type?
    Does that have any effect on the time dilation due to GR?

    Examples of same type cancellation:
    1. If you are at the gravitational balance point between two planets (or planet & moon)?
    2. If you were at the centre of the Earth?

    Example of different type cancellation:
    2. If you were on a travelator (flat escalator) around the entire Earth diameter that was moving fast enough to make you weightless?
     
  5. Feb 1, 2010 #4

    A.T.

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    Clocks at rest in a rotating frame run at different rates along the radial direction. This is equivalent to gravitational-time-dilation.

    In the inertial non-rotating frame their desynchronization is blamed on their different speeds which cause different movement-time-dilation.
     
  6. Feb 1, 2010 #5
    Gravitational time dilation does not cancel out like gravitational force. The time dilation is more related to the gravitational potential than to the gravitational force. In the examples you gave:

    1. The gravitational time dilation at the balance point between two planets is greater than an infinity.

    2. The gravitational time dilation at the centre of the Earth is greater than an infinity and also greater than at the surface of the Earth. You can calculate this using the interior Schwarzschild solution.

    In a very rough visualisation, you can use the rubber sheet model. The depth of the depression of the rubber sheet is roughly proportional to the gravitational time dilation. If you have two masses on the rubber sheet, the sheet is depressed more between the two masses than at the far edges of the sheet.

    Note that I am considering the simplified case of a non rotating Earth. The rotation of the Earth effectively increases the time dilation factor at the surface. See comment below about combining gravitational time dilation and velocity time dilation.

    This is essentially the same situation as an orbiting satellite. The time dilation on the satellite is the product of time dilation due to the orbital velocity of the satellite and the gravitational time dilation due to the height of the satellite. In the case of low velocities and non extreme gravity as in the case of an Earth satellite this approximates to the sum of the gravitational and velocity time dilation factors.
     
  7. Feb 1, 2010 #6
    Thanks Kev.

    I thought the potential was represented by the slope and not the depth? Is that wrong?
    Just wondering because the slope of the balance point between the two planets has a gradient of 0?

    Infinity?

    Fair enough but I just need that clarification about if gravitational potential is represented by the slope or the depth?

    That's fine. I haven't included frame dragging or SR effects just to simplify it for me.

    I think I read that the GR time dilation is the major component of the time dilation with the SR time dilation only cancelling it a very tiny amount. That's cool. But I just want to understand the non-frame drag GR component a bit better first.

    Just as another example.
    If you had a centrifugal wheel spinning at 1G and you were in a gravity well near a planet at 1G also then at the 'bottom' of the rotation your net gravity would be 2G and at the top it would be 0G. At the bottom of rotation is your 'potential' going to be 2G or 1G still?

    Or, if it is depth related instead of slope related then does this mean that your potential between the 2 planets is the sum of the two opposite potentials at that point? Does this mean that instead of 0 time dilation that it is instead proportional to the sum of the opposite potentials. Or is only the greater potential used as the multiplier?
     
  8. Feb 1, 2010 #7
    In my crude understanding, "potential" and "potential gradient" are two different things. The potential gradient between the two planets is indeed zero, but it is the potential or depth that is important rather than the slope as far as gravitational time dilation is concerned.
    By infinity I was referring to a reference clock that is very far from any gravitational body. In the Schwarzschild metric the coordinate time of a clock "at infinity" is compared to the proper time of a local clock. The "infinity clock" runs at the maximum possible rate and is unaffected by any time dilation. Of course actually getting a clock to infinity is impractical and we can consider the limiting case of a clock very far from any gravitational sources, where the time dilation tends towards zero.
    OK, lets clarify the situation a little. Imagine you are far above the North pole and the Earth appears to be rotating anticlockwise. The vertical centrifugal wheel is at the equator. Now if the wheel is rotating clockwise (from your viewpoint above the North pole), the velocity of the wheel at the bottom of the rotation is adding to the velocity of the Earth's rotation so the increased effective velocity is increasing the velocity time dilation factor. The gravitational time dilation is simply what it would normally be at the surface of the Earth and is unaffected by how many g's are experienced by the clock on the wheel. If the wheel is rotating anticlockwise, its velocity at the bottom of the rotation is subtracting from the velocity of the Earth, so there is less velocity time dilation in this case. Note that the total time dilation is dependent on the direction the wheel is rotating in and independent of the number of g's experienced.

    To clarify further, consider a collection of different size wheels that all have the same rim velocity, but experience different g forces due to the different radii. All the clocks on the rims of all the wheels will run at the same rate as each other, independent of the g forces measured at the rims of the different wheels.
    If I recall correctly, the total gravitational potential between the two planets is simply the sum of the individual contributions from the two planets and these are not "opposite potentials" and do not cancel out.
     
  9. Feb 1, 2010 #8

    Janus

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    potential would be represented by the depth, local strength would be the slope.
    I believe he means at at infinity. Gravitational time dilation is measured with respect to an observer an infinite distance from the gravity source.
    it depends on the orbit.
    Neither, potential isn't measured in gs. Potential is related to how work it would take to lift the object to a different height in the field.
    Let's two centrifuges, They have different length arms, and spun such that a clock at the end experiences each feels 1g. The clock on the centrifuge on the longer arm will run slower, even though it feels the same g-force as the other clock. Or you could arrange it so that the speed of the ends of the arms are the same for each centrifuge. In this case both clocks will run at the same rate, even though one will feel a greater g0force than the other.
    One way to look at it would be to use the rubber sheet analogy. The planets make "dips" int he rubber sheet. Between the two dips is a shallow "trough". The depth of the trough at any point represents the potential.
     
  10. Feb 2, 2010 #9
    Thanks Kev & Janus.
    Just a question about yours Janus first because I just need clarification on your answer sorry just because it surprised me.
    If you were in 0g space (impossible I imagine but can approach hopefully) inside one of two spinning wheels and one wheel was bigger than the other but they spun with the same G force at the edge then would two equal masses - one on each wheel - weigh the same as each other on those different scales?
     
  11. Feb 2, 2010 #10

    Janus

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    Yes.
     
  12. Feb 2, 2010 #11
    Relating the above back to gravitational potential, are you saying with the above that:
    In case 1 (same g different speed) that it will take different forces to move the same weight an initial tiny identical distance in the same time to observers inside the separate wheels?
    In case 2 (different g same speed) that it will take the same force to move the same weight an initial tiny identical distance in the same time to observers inside the separate wheels?
    Am I interpreting it right or wrongly?
    Just to clarify, I'm talking about the internal wheel observers who don't see themselves as moving just that they are under gravity (albeit it is artificial).
    That clarification may be the difference but I'll just check with you.
     
  13. Feb 3, 2010 #12
    I'm also a little confused about this. For the example where you have two planets you are at the balance point between (or being in a bubble in the centre of the Earth) it takes no more effort to 'move' an object than it would if it were in 0g space.

    This is in contrast to the rubber sheet example which would suggest it would be harder to move the object at these points?

    Can someone help me with understanding the physical distinction?
     
  14. Feb 4, 2010 #13
    So is the amount of space time distortion at a point on the curve, that is due to GR, determined by the slope of the curve that its at or the depth of the point?
     
  15. Feb 4, 2010 #14

    Janus

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    No
    No
    With the the centrifuges, the potential is equal to the amount of total work needed to move the clock from the edge to the center of the centrifuge. This is what determines what the time dilation will be.
     
  16. Feb 4, 2010 #15

    Ich

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    In the rubber sheet example:

    The depth is the potential. Difference in potential = work per kg = difference in "clock rates".

    The slope is gravitational acceleration = gravitational force per kg = work per kg and m lift height. Has no effect on time dilatation (see "clock hypothesis").

    Spacetime distortion = curvature = tidal acceleration is the second derivation of depth. Has nothing to do with clock rates either.
     
  17. Feb 4, 2010 #16

    Janus

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    We are talking about the total effort needed to move the object from its point of equilibrium to a point far removed from either planet. Imagine you try and move an object from this position along a line perpendicular to the line joining the planets. The instant you start to move the object, the gravity of the planets will try to pull it back. The total amount of energy needed to lift the object from this "sweet spot" is the potential.

    For the hollow of the center of the Earth, it takes work to lift the object from the center to the surface, and then additional energy to lift it to an far distance above the Earth's surface. The far removed clock runs faster than the surface clock, and the surface clock runs faster than the clock at the center.
     
  18. Feb 4, 2010 #17
    Now I'm starting to understand it a bit better I think.
    For gravity wells it depends upon a point at infinity away because it is only at that point that the potential is 0 because it can be 'lifted' no further.
    Then you start running backwards from there and determine the work required to get something from the new measure from point to this original infinity point which has the potential of 0?
    Is that correct?
     
  19. Feb 4, 2010 #18

    Ich

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    You don't need that "potential of 0"; there's no need to define an "absolute clock rate", and it's not always possible. We're always talking about relative clock rates.
     
  20. Feb 4, 2010 #19
    Thanks Ich. Sure, I get that. No highest point measurable because it is at infinity. So things are instead measured relative to each other in terms of how deep they are in a space-time well where they are from that points respective infinity. You only need to get the difference between the highest object and the lowest object in space-time for GR purposes.

    I can't fathom the underlying physical mechanism that generates this 'instantaneous' relativity at a distance but I accept that it is the process by which time-space relativity is determined.
    As everyone is saying it is not weight based in any way, only relative depth based but it is a curiosity to me, I admit, as to how they 'simultaneously' conform to relative depths.
    The only physical medium we have is this 'space-time' which I have yet to come to grips with how it has this immaterial pervasive presence.
    Space-time is not made of any strange particles is it?
    It just is; isn't it?
     
  21. Feb 4, 2010 #20
    Someone on here a little while ago helped me to understand that instead of the 'trough' that you describe that you actually end up with something called a saddle ridge.
    That is that the two planets in the example that we are between have their low points shifted towards each other (hence why they move towards each other) but the low points don't combine to create a common trough. Instead a ridge remains between the two low points.

    If you add us we create our own little space time dimple. If we are at the balance point then we will sit at the bottom of our dimple and will cause the low gravity points of the two planets to shift a tiny little more towards the common centre; but still without combining.

    If we are more to one side of the balance than the other then our little dimple will be a little bit more towards the stronger side than us so we will move towards the stronger side because of this.

    But I have another question in relation to that.
    I assume you would measure our relative potential as being our height relative to the height of the planets in the overall space-time topology. So that actually makes our potential less than that of the planets. So for us at our point in-between the planets does that mean our clocks due to GR should actually be travelling faster?
     
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