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Curvature of Time?

  1. Jan 3, 2007 #1
    We can all see what curvature of space looks like, just by throwing a ball and watching it follow the natural geodesic.

    But what does curvature of time look like?

    How do we experience it?

    We typically experience the passage of time in what seems to be a forward linear manner. The forward part seems to be due to how our nervous system works, thus giving a chronological bias towards causality in our perception.

    But if we can see how gravity curves space, then how do we percieve how it affects time?
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  3. Jan 3, 2007 #2


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    Time dilation.

  4. Jan 3, 2007 #3
    But Time Dilation isn't supposed to happen unless we approach some significant fraction of the speed of light. Meanwhile, we can observe the curvature of space even when standing totally still, can't we?

    Are we saying that acceleration towards the speed of light is similar to an object undergoing freefall, whereby it moves according to the natural geodesic curve of space? So then "time dilation" or curvature of time, becomes apparent or manifest to us due to lightspeed being a reference frame analogous to freefall?

    Due to the constraints of our nervous system, we tend to perceive T as an ordinal axis, compared to X,Y,Z where we have full degrees of freedom along each axis.
    So when we don't have full freedom on the T-axis, and can only experience it in a "forward time" direction, then we can only experience this time dilation as a deviation or discrepancy in the passage of time.

    If Time could move backwards, we could experience gravity as a repulsive force, and then presumably would we similarly experience the curvature of time as "time contraction" instead of time dilation?
    Last edited: Jan 3, 2007
  5. Jan 3, 2007 #4
    No that involves the curvature of both space and time.
  6. Jan 3, 2007 #5


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    No. Time dilation happens anytime there's gravity, and anytime any two things are moving in relation to one another. You're experiencing a kind of time dilation right now by sitting in the Earth's gravitational well. When you fly in an airplane, you're experiencing another kind of time dilation.

    The magnitude of these time dilations is very small by human standards, so you don't really notice it. It is observable with atomic clocks, however.

    The force keeping your butt in the chair is, in fact, a result of the curvature of space. You might need to consider that you cannot have curvature in space without curvature in time.

    No, objects that are accelerated do not follow geodesics.

    Light speed is not a frame of reference. A reference frame is nothing more than a coordinate system, generally chosen so that some observer is at its origin.

    Every technical term you used here (ordinal, degree of freedom) is used incorrectly, so I have no idea what you're trying to say.

    If you change all positive charges to negative charges, flip all movements as in a mirror image, and then reverse time, you might be surprised -- nothing changes. Things keep on doing what they were doing before. The physical laws are invariant until these transformations, collectively called CPT (charge, parity, and time). Thus, the "direction" of time is an arbitrary choice, at least in the way that the physical laws operate.

    Something like that. The physical laws would not be the same if you only reversed time, so the physics would actually be completely different. I'd have to think about it a bit to explicitly figure out all the consequences.

    - Warren
  7. Jan 3, 2007 #6


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    Gravitational time dilation can be experienced even when "sitting still". Time dilation happens anytime one is near a large mass, not only when one is moving.

    The following quote may be of some help. It's excerpted from


    How does this relate to gravitational time dilation? Attempt to form a square in space-time, by moving 1 meter up, 1 second into the future, 1 meter south, 1 second into the past.

    You don't wind up at your starting point in space-time, because (to oversimplify a bit) clocks at different altitudes don't tick at the same rate due to gravitational time dilation.

    This is very similar to the way that one does not wind up at one's starting place by starting at the equator on the Earth, going 1 meter north, 1 meter east, 1 meter south, and 1 meter west. The reason is the same - curvature.
    Last edited: Jan 4, 2007
  8. Jan 4, 2007 #7


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    In Riemann geometry, a 1-dimesional curve or a 1-dimensional manifold cannot be curved. Thus, time as a 1-dimensional entity cannot be curved either. What can be curved is space or spacetime.
  9. Jan 4, 2007 #8
    Note that relativity works with pseudo-Riemannian manifolds.
    Most of the rules are the same but for instance in a pseudo-Riemannian manifold the arc length between two points can be longer than the length of any geodesic between them.
  10. Jan 4, 2007 #9

    This is true, however an object following a geodesic path may appear to be accelerating in some respect due to the curvature of space-time. e.g. the bending of light around the sun can be interpreted as the light accelerating towards the sun. If we throw a ball it ends up on a geodesic, yet it appears to accelerate towards the Earth etc..
  11. Jan 4, 2007 #10
    If this geodesic doesn't minimise the arc length, then how is it defined? A path that parallel transports its tangent vector into itself? I was under the impression that these definitions are identical... not sure where that came from though...

    According to wikipedia the definition of a geodesic on a (psuedo-)Riemannian manifold is "Just as in a standard metric space, a geodesic on a (pseudo-)Riemannian manifold M is defined as a curve γ(t) minimizes the length of the curve."

    Wikipedia can be wrong though (the grammar in the above quote is, at the least!)
  12. Jan 4, 2007 #11


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    Chroot's comment refers to the observer-independent spacetime 4-acceleration rather an observer-dependent spatial 3-acceleration [familiar to Galilean/Newtonian kinematics].
    Last edited: Jan 4, 2007
  13. Jan 4, 2007 #12


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    because of gravity, clocks in sattalites go faster than clocks on earth - this is taken into account in GPS systems.
  14. Jan 5, 2007 #13


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    What I said above about Riemannian geometry is true also for the pseudo-Riemannian geometry. Your observation on the arc length above does not imply that a curve may be curved. The pseudo-Riemann curvature of a 1-dimensional curve is zero.
  15. Jan 5, 2007 #14
    I always like the use of imaginary numbers here to explain the time axis of the graph.

    I imagine a graph with an (x,y,z,t) axis. You can use whatever you like to represent the fourth axis, but imaginary numbers are an already oft used axis so it makes sense to use it in discussion about time and space curvature. In this context I can equally equate a curve in space with a curve in time prvided I've set the graph up correctly. I was thinking about this with relation to time after looking into complex numbers, couldn't you call this time I thought? And a friend said yes someones already done it, seems obvious.

    there's the much more simple representation with minowski diagrams. But if I want to get at least an intuitive grasp of 4D space-time I think about it something like that.
  16. Jan 5, 2007 #15
    This is also called a Wick rotation.
    But while a Wick rotation works in flat space-time it does not so in curved space-time. Which is one of the current problems in the development of a quantum theory of gravity.
  17. Jan 5, 2007 #16
    Yeah it's only a way of dealing with it in your head(intuitively) I assume you mean that the bend caused by the magnitude of the vector and the relation to time doesn't match up with Gravity and it's relation because of the warping of space itself. Interesting.

    Just think of gravities bend in space and time in the same way as you would the relation to c, and time. Even though one cannot be mapped in a relation to the other, one is a direct consequence of the other. I'm sure there are better analogies.
    Last edited: Jan 5, 2007
  18. Jan 5, 2007 #17
    I never really took physics but I think that the direction of gravity (like other fields) would stay the same regardless of whether you go backwards or forward in time. For example:

    If someone threw a ball upward, it would decelerate until it reached the apex and then accelerate downward until it hit the ground. If you filmed the event and played it backwards, you will see the ball jump from the ground at a given velocity and decelerate until it reached the apex and then accelerate downward until it landed in the person's hand. In either case, the acceleration is downward. When I use the terms 'accelerate' and 'decelerate', I am referring to the apparent behavior of the ball as it travels along the geodesic.
    However, I believe that what I said above still holds true from the standpoint of Einstein's field equations. The time component of spacetime curvature (if I'm not mistaken) is expressed as a function of -dt^2 (or dt^2 depending on convention). Which means the sign (+ or -) should not affect the equations.

    Also, the only law that I can think of that reverses with time reversal is the second law of thermodynamics.

    It's been 23 years since I tested out of physics at college so please be patient with me if I am dead wrong.
  19. Jan 6, 2007 #18
    To get the effect of moving backward in time, on curvature; substitute with "-t" in equations instead of "t" in the Curvatur Tensor. To get the effect of moving backward in time, on gravity; substitute with "-t" in equations instead of "t" in the final free fall equations.

    Wonna add, curvature in GR, is a 4-dimensional concept. It simply means, that transformations from certain frame to another are flat (i.e. roughly speaking; not so simple as SR's). So, I agree with your point of view grant9076 in checking the equations like this. But ........ you have a very good mathematical engineer! .. Are you a mathematician or an engineer?

    Schwartz VANDSLIRE.
  20. Jan 6, 2007 #19
    Thanks but actually, I'm a pilot by trade. Although I did well when I got my bachelors in engineering, it has been a couple of decades and I really haven't thought about that stuff until I first visited this site a few months ago. So, I cannot consider myself to be either.

    However, although testing out of physics never gave me the opportunity to study relativity in detail, it always seemed to make perfect sense. Personally, I think that it is only a matter of time before some genius out there unifies Einstein's theory with quantum mechanics.
    Last edited by a moderator: Jan 6, 2007
  21. Jan 6, 2007 #20
    In addition to the above thought experiment, another unsophisticated thought experiment that I did as a teenager that cemented my belief in general relativity was the following:

    If a particle with negative mass was in a gravitational field, it would sense it as repulsion. However, because it has negative mass, it will react opposite to the force and 'accelerate' downward just like a particle with positive mass. I reasoned at the time that if the reaction to gravity is the same for a negative mass as it is for a positive mass, then it must be true for every mass in between including zero mass. Based on these 2 thought experiments, I concluded that whether something has positive mass, negative mass or no mass, whether it travels forward or backward in time, if it exists, it has to react to gravity in exactly the same way.

    I saw no other option but to conclude that gravity is a distortion of spacetime and that Einstein was fundamentally right. These thought experiments made the concept more intuitively obvious to me than any article or book that I have read on the subject prior or since.
    Last edited by a moderator: Jan 6, 2007
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