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How is time and space affected by the warps in General Relativity?

  1. Jan 11, 2008 #1
    From another post that was not directly about what warps in the space-time fabric do to space and time. So I had figure to make another post to keep things more in order then having the initial subject change direction instead of keep its original intention.

    But in the discussion in what the warps are someone had talked about what they do.

    and from the user CJames he had explained how time can be seen as slower or faster depending on where the gravitation pull was coming from.

    from what i gathered there is redshift and blueshift

    redshift being where what you see is delayed, for gravity (pulling it back) is making the light coming from a object to move slower when trying to reach the observer's eye.

    Blueshift is the just the opposite, light from a object seem to be faster when reaching the observer's eye because gravity is pulling it to the observer.

    Is this correct? If so it only states, time seems to change but doesn't truly change just the light coming from whats being view is delayed or accelerated making it SEEM slower or faster, but if correct can the definitions be expanded upon, so i could have a better understanding of the terms.

    But how is space change or warped?
    The user CJames explained it like this:

    "Now normally, if you draw one line, and then you draw two lines perpendicular to that line, you have two parallel lines. That's what happens in flat space. But what if I draw a line from the center of earth into outer space? And then what if i fire two laser beams perpendicular to that line? They will appear to curve toward the earth, due to the equivalence principle. But since the gravitational acceleration is stronger closer to the earth, the beam of light will bend more if it closer to the earth. As a result, even though both lines are perpendicular to the first one, they are NOT parallel lines! They are moving away from one another. This is not possible on a flat piece of paper. It is only possible in curved space. So space is warped."

    I understand what he is saying, but i dont see how this is warping space
    its bending the light not bending space.

    But he also adds:
    "Here is another way of looking at it. Like I said, the equivalence principle states that the force of gravity is actually an imaginary force, the same force we feel in an accelerating car. Therefore, while you sit in your chair, you are not actually sitting still. You are accelerating away from the center of the earth at 9.8 meters per second per second. And objects that are in free fall do not feel the force of gravity, they are weightless. So objects that are in free fall are not accelerating toward the surface of the earth. The surface of the earth is actually accelerating toward objects that are in free fall! And yet it is quite clear that the earth is not expanding. If the surface of the earth is not expanding, and yet it is accelerating away from the center of the earth, the only possible explanation is that time and space are warped in such a way that everything remains "at rest."

    I don't quite understand this. He is explaining gravity in terms of acceleration? And we are all being accelerated, thats equal to 1G, and the way we see it, it seems all at rest? How does this explain space being warped? Could you help clarify.
    Last edited: Jan 11, 2008
  2. jcsd
  3. Jan 11, 2008 #2
    I should first warn you as I did in the post you are quoting that I'm not familiar with the math of general relativity, just the concepts, so I can't give you the precise answer I'd like to, but let me see how close I can come.

    Remember the equivalence principle? If you are in an accelerating spaceship, a beam of light will appear to curve because the floor of the spaceship is accelerating toward the beam of light. But the beam of light is actually following a straight line. By the equivalence principle, the light in a gravitational field is doing the same thing. From the point of view of the light beam, it is actually traveling in a straight line (or more accurately, a geodesic). Think of the surface of the earth. Lines of longitude are parallel at the equator but meet at the north pole. This is possible because the earth is not flat, it is curved. Space has the same property in a gravitational field (although in the example I gave they were curved away from each other.)
  4. Jan 11, 2008 #3
    Now on to the second part

    I actually revisited this concept here just a few minutes ago


    To put it vaguely, how can the surface of the earth accelerate away from the center of the earth without expanding? Space and time have to be warped.

    Lets go into more detail. Think of two objects falling toward the earth (disregarding air resistance). One of them is below the other. You can see that as they fall, they will move away from one another, the lower one falling faster than the higher one.

    Now lets try to imagine a graph of the two object's falling. Let's make the horizontal axis time, and the vertical axis space (specifically, distance from the surface of the earth). Both objects will follow a parabolic curve with the vertex at the vertical axis, arcing down to the horizontal axis where it intersects at a specific time. Looking at the two lines, you will see that they diverge.

    Curved lines in a space-time graph represent acceleration. But typically, if something is accelerated you feel a phantom force, like the force you feel in an accelerating car. Objects in free fall don't feel this phantom force.

    General relativity applies the equivalence principle to this scenario. Now, we have to assume that the falling objects, in fact, are not accelerating. If that's true, we have to think of some way to plot this graph so that the lines representing the falling objects are not curved.

    Can you see how, if we were to bend this graph just right, as though it were made of rubber, we could do so in a way so that the lines representing the objects' trajectory wasn't curved? And furthermore, can you see how by doing this, you would actually curve the horizontal axis, so that it WAS curved? In this way, the horizontal axis, which represents the surface of the earth, is accelerating, while the objects in free fall are not.

    Also, consider the fact that if you draw two non-curved lines on this warped graph, they will be bent toward or away from each other, and the opposite. To draw two lines that are "parallel" in the sense that they stay the same distance from each other, they have to be curved lines. This means that for two objects to stay the same distance from each other in a gravitational field, they must be accelerating.

    If you're standing on the surface of the earth, you remain the same distance from the center of the earth. As a result, on our warped graph you would have to draw a curved line to describe your motion, which means you are accelerating away from the earth.

    I hope I didn't just get you more confused, but that's as detailed as I can get on the subject.
  5. Jan 11, 2008 #4
    Now since this light is seeming to bend to the one watching it from the floor of the acclerating space ship, they are saying it seems to bend because the space this light is traveling trough is curved do to gravity. If this is right, why can't we say the light is simply bending not the space its traveling through.
  6. Jan 11, 2008 #5

    It a way its confusing but it was only read once. Which i am sure if i look at it more closely i will not just get the jest of it, but it will help me understand it completely, but i ask, this description of the graph may be hard for me to imagine so i could replicate/draw it while you describe it, so i ask is there a base graph or series of graphs you could show has an example?
  7. Jan 11, 2008 #6
    I'm assuming you didn't see my second post yet, which I hope partially answers this question.

    The light on an accelerating spaceship isn't bending at all, and neither is the space. An actual warping of space and time only occurs in a true gravitational field. The equivalence principle doesn't state that space and time are always warped when the gravitational force is felt. It states that the gravitational force is equivalent to the force felt by an accelerating body.

    The point is, the light in an accelerating spaceship is NOT following a curved trajectory. Instead, the spaceship is accelerating toward the beam of light. If the two "forces" of gravity and acceleration are identical, this means that while a beam of light appears to curve in a gravitational field, it is really following a "straight" line (actually a geodesic). For two straight lines to become non-parallel if they were initially parallel, you need a (non-flat) warped space to work with, like the example of the longitude lines on the globe I gave earlier.
  8. Jan 11, 2008 #7


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    There is red-shift and blue-shift, but this explanation is wrong. It mixes up frequency due to gravity and that due to relative motion of the emitter and absorber.

    The gravitational case.
    Suppose you are on a platform 3 meters higher up than I am, and I throw a ball in the vertical direction for you to catch. When the ball reaches you it will be travelling slower than when it left my hand. It has lost kinetic energy, but gained potential energy from the gravitational field, because it is now further from the earths centre.

    Now if I shine a light up at you the light cannot slow down, because it never does, but it loses energy like the ball, by having a slightly lower frequency at your position, than it did in my position.

    This has been verified in the Pound-Rubka experiment.

    Relative motion case
    If light is shone from one inertial frame to another, there will be a real frquency shift observed, depending on the magnitude of the relatve velocity. This is a special relativistic effect and has nothing to do with gravity.

    Gravity is always seen as an acceleration, because the force is proportional to the mass for anything experiencing it.

    From F=ma, we can write a=F/m, and because there is always an m, the 'force' is actually an acceleration.

    To really understand curved space-time, you need advanced maths, so get cracking.
  9. Jan 11, 2008 #8

    I have been doing all my research on my freetime.
    I am 20 going to school for Visual Effects and motion graphics and math classes are need but i don't know if the level of math I would have to learn and understand is even accessible within the school, yet the very idea of me learning this math, makes me excited so that is enough to motivate me to teach myself if push comes to shove, but i will learn what i can from the school and go from there. But i am so glad to have gotten involved into all physicals because the instant interest lead to the interest, of literature, math, and ,the obvious, science. I would have never expected such interests to bloom from my accidental discovery of physics. This is why I laugh at that quote, 1 month ago I would have been disguised at the idea, now, intrigued and motivated.

    I guess the mystery makes some of us better people.
    Last edited: Jan 11, 2008
  10. Jan 11, 2008 #9
    Thankyou Mentz, I had meant to clarify that you're not traveling "faster" or "slower" compared to the beam of light, but I forgot in explaining everything else.

    I'm not a physicist, but is it correct to say that the relative motion case is completely separate from the gravitational case? I've never seen the math, but I guess I always assumed gravitational redshift/blueshift had something to do with extrapolating the special relativity effect from relative velocity to acceleration via some sort of derivative (or possibly integral, man my calculus is rusty). In other words, from the time the light was emitted to the time it is observed, there was a change in velocity, and I always figured that was what caused the redshift/blueshift. Was I wrong, or is that just another way of saying the same thing?

    Unfortunately, no, I don't know of any available visual representation of what I'm talking about. I've pieced together that explanation from various explanations I've heard from others and applying that to some rudimentary understanding of math. As far as I know it's about as close as you can get to the full mathematical explanation, but it's also possible I'm completely off on some of the concepts (nobody has contradicted me so far at least). I think if you read it over a few times though, and really think about it a LOT, you'll be able to see what I'm talking about.

    One possible source of confusion would be straight lines versus curved lines. This is a little confusing, because all lines are "curved" in a way when you are talking about warped space. As I mentioned in passing, I'm talking about geodesics. Geodesics are the analog to straight lines in warped space. It's the shortest distance between two points, but it's not entirely accurate to call it a straight line. (Okay, even that isn't COMPLETELY accurate, it's more like the shortest distance between all the points when you take the limit as the two points approach zero distance from one another but don't worry about that.) Basically, if you snap a rubber band against a globe, you get a geodesic. The longitudinal lines on the globe are geodesics. The latitudinal lines are not (except for the equator). So the latitudinal lines on the globe are analogous with the "curved" lines I was talking about in the previous example.

    The other thing is that, of course, my example involved one space dimension and one time dimension. The reality is that there are 3 space dimensions and 1 time dimension, which makes the graph impossible to visualize, although the concept is the same.
  11. Jan 11, 2008 #10


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    We could say that. But why it is bending? GR explains it this way: All free falling objects (including photons) move straight trough a curved space-time, so their paths appear bent. If you have problems to envision the curvature, you can think of curved space-time as areas of different refractive index. Light always bends towards the area of higher refractive index.

    I guess you mean: "If the surface of the earth is accelerated away from the earths center, how come the size of the earth stays constant?". Consider that acceleration in a certain direction, doesn't imply movement in that certain direction. In curved space-time you have to be accelerated, to keep a constant position in space. The best way to understand it is from pictures like in http://fy.chalmers.se/~rico/Theses/tesx.pdf". Jump to chapter 2 (2.6 "Forces and gravity" explains why an apple at rest needs an accelerating force upwards)
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  12. Jan 12, 2008 #11
    Thanks AT, this seems to be providing a visual example of what I was talking about (in much better detail), even though I've never seen it before. Very cool. It's going into my bookmarks, definitely.
  13. Jan 12, 2008 #12


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    Last edited by a moderator: Apr 23, 2017
  14. Jan 12, 2008 #13
    Very, VERY, cool. Thanyou much. Also in my bookmarks. Already.
  15. Jan 12, 2008 #14


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    In special relativity we describe a 'light beam' with wavenumber k moving in the x direction, by a four-vector u=(k, 1, 0, 0) ( signature -1,1,1,1). When it is boosted by a Lorentz transformation along the x-axis, the wavenumber is changed by the usual factor.
    That's the velocity dependent frequency shift in Minkowski ( no gravity) space.

    When gravity is present, there is a frequency shift which depends on the tt component of the metric at the transmitter and receiver. The equations are different.

    However in cosmological situations, the two are mixed when observing a distant galaxy, say.
  16. Jan 12, 2008 #15

    Yes, thinking of the frequency of the light beam as kinetic energy is probably the best way to go. But is it really inaccurate to say that the redshift/blueshift is due to acceleration? Think of the example of the accelerating spaceship. That takes place in flat spacetime. And doesn't the concept of kinetic energy being responsible for redshift carry over to special relativity anyway? The relative kinetic energy of a baseball is going to depend on your relative velocity. A beam of light always travels the same speed, but it's kinetic energy must similarly change, so it redshifts.

    As far as the equations being different, yes of course they would be. For one, the amount of acceleration changes with distance from the center of a gravitational body, while this is not the case in an accelerating spaceship.
  17. Jan 12, 2008 #16


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    The speed of light doesn't change, only its frequency. You can picture the oscillations of the light wave as pulses of a clock, just like different observers measure different clock rates based on their distance from a massive body, they also measure different frequencies of a light wave.
  18. Jan 12, 2008 #17


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    I'm not thinking of frequency as kinetic energy, except as an analogy to a layman. The formulae are all that counts. If you try to construct a model of the world based on simple mechanical analogies, it will break down at some point.

    You should be careful about attributing effects to 'space-curvature' as well. For all we know there's no such thing physically. There are other theories of gravity that do not use a metric.

    Anyhow, I've done all I can here.
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