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Cuved space kills me, help

  1. Oct 21, 2004 #1

    I am studying the theories of Relativity for almost 10 years now and it seems that I am lost. :cry:

    1. First, when space could be curved by an object, then I would like to ask, how could empty space be curved? And even if this empty space is curved, how could something be 'pulled' or fall to the centre? (as this curved space is empty?)

    2. If we have some curved object (say a plastic that's curved inside) out in space, where there's no gravity, then put a round object at the brink, would that object fall inside to the center of the curved plastic? And why?

    Answers could save me some 10 years.

  2. jcsd
  3. Oct 21, 2004 #2


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    The geometry of general relativity is non-euclidean. "Curved" is just an analogy or metaphor, a way of speaking. It helps some people to have the picture in their heads, but it bugs other people, like you.

    Non-euclidean geometries were discovered in the 19th century, some of them have "too many parallels" and in none of them do the angles of a triangle add up to exactly 180 degrees; it might be more, or less, but only Euclid has exactly equal. One of the things that happens in non-eucldean geometry is that if you have a little stick like a pencil, and you move it exactly parallel to itself in a circle, when it comes arounf full circle it will be pointing in a different direction than when it started. Now I know you're going to try this, but remember that "exactly", and know that the difference is very, very small. Even the most delicate experiment on earth couldn't prove that prediction. But there are other experiments that have shown general relativity to be a reliable theory.

    One of the geometric features is geodesics. A geodesic is a curved path, but one that is trying to be a straight as it can. If something is in free fall, so it's not being pushed this way or that, it follows a geodesic. So an orbit would be a geodesic, except I left out that this is all four dimensional, and time is part of it. The worldline of a falling object is the geodesic, and the geodesic of the earth around the sun is like a helix in the time direction.

    I hope this has helped. If you need more explaining, just ask.
    Last edited: Oct 21, 2004
  4. Nov 2, 2004 #3
    Let me make few things clear about curved space-time.

    1. Curving of space is not some thing miraculous, general theory of relativity just says there exists a frame of reference in which you can get rid from gravity.

    2. General theory of relativity predicts that light also interact with gravity, as a result it bends and moves along a curved path, but you can equally say that light always moves along stright line but the definition of stright line get changed in the presence of gravity (making stright line geodesic).

    3. Curving of space is not some thing absolute, it is just a matter of coordinate transformation.

    Last edited: Nov 2, 2004
  5. Nov 2, 2004 #4
    :devil: agreed, its only a way of visualizing space -time continuum
  6. Nov 2, 2004 #5

    To answer your first question:

    As far as I understand (and I have NOT studied relativity for 10 years – in fact, I have never studied it, so don’t trust me), “empty” spacetime is “curved” at cosmological distances… At which it isn’t actually empty. Let me try to make my latter opinion less confusing: Spacetime is curved by the presence of matter and energy. And the seemingly empty curved spacetime is also curved by the presence of matter and energy – matter and energy that are so far apart that the space between them appears to be empty. This is why the curvature is so diminutive. But not non-existent. The way I picture it is with the analogy of a very long rubber band stretched between two posts. If one was to, say, exert a tiny force on one end of the rubber band, the other end would be affected in a tiny way, despite the lack of directly applied force. But don’t trust me. = )

    To answer your second question:

    Nothing is actually “pulled into the centre”. That was Isaac Newton’s theory, and he admitted to his readers that he did not know exactly why this happened. Since relativistic spacetime is curved, the definition of a straight line changes. All objects that we perceive as “falling in” are actually trying to follow a straight path in spacetime, which is called a geodesic. A geodesic is the shortest distance between two points, which in Euclidean geometry would be a straight line. However, since spacetime is curved, the straight line is also distorted and curved.

    To answer your third question:

    No, the spherical object would not HAVE to fall into the plastic curve, even though it may (that’s just a chance of probability – without gravity, it is free to go wherever it pleases). This is because the fact that the plastic shape is curved doesn’t mean anything at all. It is simply a curved piece of plastic. Its gravitational attraction is far too weak to actually force the ball to fall towards it – and even if its gravitational attraction was much stronger, it would most likely cause the sphere to orbit it rather than fall into it. You are confused by the notion that objects fall in Einstein’s spacetime because it is curved – you think that objects will “fall into” anything that is curved. But as I had explained previously, they are simply following the closest thing to a straight line.

    I know it’s very very confusing, and I’m not very good at it myself (I’m in High School, so forgive my minute bank of knowledge), but I hope that I was somewhat able to help you out. Comment back with any questions and I’ll try to answer them if I can. = )

    - Alisa
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