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Space-time curvature

  1. Mar 1, 2005 #1
    I understand that the curvature is caused by the depression of a mass in the space-time surface. What I don't understand is what is causing this depression. For example, is it the bodie's resistance to the motion of the space-time surface? Or is it that the curvature is caused by the displaced volume of empty space (like a marble travelling through water)? Further, I don't understand how you can curve something that has no substance (ie. empty space).

    Also (this may sound dumb), assuming that the space-time surface is two-dimensional, can a body move parallel to this surface?
  2. jcsd
  3. Mar 2, 2005 #2


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    Mass causes the depression.
    None of these things.
    Like other things in physics (the "real" meaning of energy, what is "charge",...), it's just something you get used to.
    Not dumb! This is your only smart question. In a sense, pretending the situation is 2D, a planet moving in a circle around the sun is staying at one "level" on the surface and so is moving parallel to it.
  4. Mar 2, 2005 #3
    That's what I said
    Then what causes it?
    I don't understand
    someone else pretended, I just stole the idea :yuck:
  5. Mar 2, 2005 #4
    Unfortunately the popular picture of gravity being caused by a mass causing a depression in a space which behaves like a rubber sheet is, well how shall I put this, WRONG.

    The first problem is explaining why the mass causes the rubber sheet to depress. Well that's what you would expect to happen due to the weight of the mass. So you're explaining gravity in terms of gravity.

    The second problem is that the picture doesn't really describe the curvature of space-time near a mass. In the picture the curvature is in space, whereas in GR the time component of spacetime plays an important part.
  6. Mar 2, 2005 #5
    Do you mean, the depression cannot be caused by the weight of the mass because there is no external force causing it to weigh anything?

    Let me rephrase my initial inquiry: By what means does a mass cause a depression in space-time ? Or is there no direct answer?
  7. Mar 2, 2005 #6


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    I think you're taking the rubber sheet analogy too literally--you could just as easily imagine mass causing bumps as depressions, the curvature is all that matters. Matter/energy causes spacetime to curve, and moving objects in the absence of non-gravitational forces follow "geodesics" in curved spacetime. In a curved space, like the surface of the sphere or a rubber sheet, a geodesic is the shortest path between two points--on a sphere, this would always be a segment of the great circle that passes through the two points. But in curved spacetime, a geodesic is the path with the greatest proper time (the time as measured on a clock that follows that path between two points in spacetime).

    As for why matter/energy curves spacetime, and why objects follow geodesics through curved spacetime, that's just considered a fundamental law, like all fundamental laws it doesn't have any meta-explanation (maybe quantum gravity would explain it in terms of something more fundamental, but this would necessarily involve a new set of fundamental laws that themselves have no meta-explanation).
    Last edited: Mar 2, 2005
  8. Mar 2, 2005 #7
    thanks for the replies
  9. Mar 4, 2005 #8
    I don't understand your question. What is a "depression" ijn spacetime?

    If you're asking why mass causes spacetime curvature then the answer is that body knows why. They know how but not why.

  10. Mar 4, 2005 #9


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    The Greeks thought things fell because they had a natural place at the centre of the Earth, but they didn't know why they fell, that was a mystery.

    Newton explained why things fell by a gravitational force, but he didn't know why the force could act across millions of miles of empty space, that was a mystery.

    Einstein explained why gravitation acted across empty space by postulating that empty space itself was 'curved', but he didn't know why mass (and energy) curved space-time, that was a mystery.

    Is this a continuous progression so there always will be a mystery?

    Just a thought.

  11. Mar 4, 2005 #10
    Well, in order to establish convergence of a continuous progression of scientific advancements it is sufficient to show that the remaining mystery becomes negligible as time goes to infinity. :tongue2:

    The answer to the question "how does matter curve space time" is found by taking a more literal approach. Mass is spacetime in the same way that charge is the divergence of electric field. (taking the equal sign to be the is of identity)
  12. Mar 5, 2005 #11


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    One of the problems with the usual approach to geodesic deviation is that the time axis is finite. So, when you tell people to draw two great circles on a sphere, and that to look at how they approach each other and then go away and then approach each other again, is fine as far as it goes, but because one has to imagine that the time dimension is finite, it isn't really all that great an explanation.

    OTOH, asking people to imagine a sphere with an infintely long elastic bandage wrapped around the equator, so that the bandage passes over itself, and to imagine that one can draw lines on the elastic bandage from the start to the end, ignoring the fact that it covers itself up, and, oh yeah, the bandage is infintely thin, would seem to me to be likely to draw a lot of "huh"? "what is that guy talking about" "I dunno" sorts of responses.

    But, if one can somehow get around these minor little visualization problems :-), the infinitely long axis of the bandage can be considered to be the time axis, and the width of the bandage can be considered to be the space axis, for a 1-d space + a 1-d time (a 2-d space-time), and one can (hopefully, anyway), see that "straight lines" on the sphere, which are actually great circles, drawn on the bandage, will alternately approach each other and retreat from each other. Or maybe not, I suspect that the people who know this already can see this easily, with no trobule, and the ones who don't, still can't :-(.
  13. Mar 5, 2005 #12


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    But segments of great circles on a sphere are the shortest path through space on the sphere--if you want to add time, you need to consider the longest path through spacetime (the one with the greatest proper time), not the shortest. But we can't really intuitively visualize "length" in a space where the pythagorean theorem doesn't work locally anyway.
  14. Mar 5, 2005 #13


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    I never thought of it in that way, but you are right, even the elastic bandage model isn't perfect. The ultimate idea is to try and illustrate the geodesic deviation equation, though, which will apply to the more familiar Euclidean metric as well as to the Lorentzian metric used in GR.

    The intended point is that if you take a flat sheet of paper on the table, and you draw two lines through the same point, that the lines diverge indefinitely. If the paper is a space-time graph, two lines through the same point with different slopes represent the paths of particles with different velocities. Because they have different velocities, they move away from each other as time goes on, and never meet again.

    If you wrap the sheet of paper around a sphere, though, and you definine as "straight line" as being a great circle, you get a behavior that perfectly mimics gravitational attraction.

    Two straight lines through a point, representing a pair of particles with different velocities at the same point, move away from each other for a while, slow down, and then "turn back". They behave exactly as if they were on a flat sheet of paper, but attracting each other.
    Last edited: Mar 5, 2005
  15. Mar 6, 2005 #14
    First of all, I think you need to define what you mean by 'space-time curvature'. What exactly is this?
    In general relativity Einstein describes a gravitational field in terms of non-euclidean geometry. Thus, a body which 'orbits round' a body of mass is really following a straight line. This preserves the notion that all sorts of motion are equivalent and that there is no special frame of reference.
    How do you know a gravitational field exists in the first place; that a body B 'senses' another body A through a force of gravity?
    The simple answer is that B will display a rate of acceleration, this rate being determined by the mass density of A. But B can equally be at rest! From the perspective of B, it is the reference frame of A that is accelerating. Any force of gravity or change of motion vanishes with a different reference frame. It is important to remember this when describing gravity.

    If space-time curvature did not exist round a body of mass, a light-ray would not follow a straight line; it would expend more action than is necessary. So in a way the cause of gravity is kind of linked to the reason why everything follows a geodesic, especially light.
    Alas, anyone who claims to understand the reasons behind gravity are hopelessly misguided. It is a mystery WHY the 'force' exists, why the curvature of spacetime is manifested to certain observers, why inertial and gravitational forces are linked in such a way. Present physics can only explain how.
  16. Aug 16, 2011 #15
    What if mass actually IS the curvature? what if what we experience as mass, is actually areas of curvature in space-time? maybe mass does not cause the curvature, but areas of curvature in space-time manifest themselves as mass...

  17. Aug 16, 2011 #16
    Oh my god, maybe! ;)
    No, seriously, that's a nice approach! Maybe someone will come and disprove you with a certain formula though...
  18. Aug 16, 2011 #17


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    You have revived a 6 year old thread. This is not appreciated.

    Your approach is actually the gist of Einstein's lifelong search for a unified field theory. It never panned out. It is a beautiful idea (subjective opinion).
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