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General relativity question

  1. Nov 27, 2005 #1
    I am not sure that this is the best place for this but I have a question about general relativity. The standard view of gravity, under general relativity is a bowling ball on a tarpalleine (however that is spelt), distorting the tarpalleine, and causing any object on the tarpauline to fall down the incline towards it. Fair enough, but how litterally accurate is this view? Space is four dimensional, one of time, and three of space, so if we follow the bowling ball image the three dimensional space time matrix is distorted into another dimension, a fifth dimension, to produce gravity, or is gravity, under special relativity, an entirely three dimensional phenomona.
     
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  3. Nov 28, 2005 #2

    selfAdjoint

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    It is actually incorrect, in that it assumes an outside source of gravity to produce the curvature, whereas GR asserts that gravity IS the curvature. The only thing this model provides is a reduced dimension view of the curvature itself. If you can think of the curved sheet without the ball, and imagine the tracks of particles forced to move on the surface, you will get a better idea of what Einstein was talking about.
     
  4. Nov 28, 2005 #3
    You don't need the fifth dimension. You might be confusing parts of your three dimensional experience, with the parts of the four dimensions of GR.

    Think of it like this:
    You see 3D: x,y,z
    Plus a thing you called time (not a dimension) that tells you things ‘change or move’ within that 3D space.

    Now GR has 4D: A, B, C, D

    No one of your x, y, or z matches up with any one of the A, B, C, or D

    The presence mass causes ABCD to warp in specific ways to create the xyz you experience. Be careful not to expect to be able to tie coordinates in x to something like coordinates in A.
     
  5. Nov 28, 2005 #4
    We don't need any dimensions at all. Dimensions are only used to describe points in space, imaginary or not. You can most certainly use that concept of the 5th dimension (the one with the bowling ball...) to illustrate, and measure, the effects of gravity around massive objects. X and Y are every bit as irrational as that 5th dimension. Be careful how you apply logic to one thing that is irrational when doing so undoes something equally irrational that you use all the time. Machinists use X, Y and Z all the time, but X and Y only exist within the mind.
     
  6. Nov 28, 2005 #5
    It’s the 4D of GR that is “the one with the bowling ball...” not 5D.

    In these threads, we try to stick with facts and established theories here not (only exist within the mind) Metaphysics.
     
  7. Nov 28, 2005 #6
    For clarification, please explain how X and Y are fact, and not imaginary. It is my understanding that X is a straight line with no other characteristics other than it that stretches infinitely. It has no depth or height, so it can only be imagined. Y is the addition of shape to that line, or simply a bisect of X that can have a shape or stretch indefinitely, and also only resides within the imagination. Z adds depth, which gives it tangibility, with exception thrown to motion to actually allow for "touching" of it. This is not metaphysics, religion, zen, or any other type of philosophy, unless you consider physics to be philosphy. (which in most respects, it is...)

    Within GR, space-time does not mean tying two indifferent entities together. Space and time are two different entities, and would represent two different dimensions, if they were to be used to measure locations or motion. I suggest you revisit your textbooks for further clarification of what space-time is.

    Please understand that this is not intended to be confrontational or even argumentative. I only wish to further my understanding of the things unknown.
     
  8. Nov 28, 2005 #7

    selfAdjoint

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    This view of dimension has nothing to do with the way the word is used in physics, including relativity. A dimension is a degree of freedom of linear measurement, so you can orient your yardstick some particular way and measure length, orient it some other way and make another one, and make a third measurement in some third direction. And if no two of these are actually the same direction, then you find that all your measurements can be expressed as linear combinations of the three you chose, and this is what we mean by three dimensional. No mystical line, tangible or otherwise.

    If your friend has made his own three choices, then to express his measurements in your coordinate system (assuming he was using a matching yardstick to yours) you have to perform a mathematical rotation. When you do this you find that the square of the length he measured - sum of the squares of the lengths in his three directions - is the same as the squared length you measure - sum of the squares of the lengths in your three directions. So the rotations preserve this sum of squares; the squares themselves vary from coordinate system to rotated coordinate system, but their sum is invariant.
     
  9. Nov 28, 2005 #8
    Physical dimensions

    The physical dimensions are the parameters required to answer to the question where and when happened or will happen some event; for instance: When did Napoleon die? — On the 5 May 1821 at Saint Helena (15°56′ S 5°42′ W). They play a fundamental role in our perception of the world around us. According to Immanuel Kant, we actually do not perceive them but they form the frame in which we perceive events; they form the a priori background in which events are perceived.
    [edit]

    Spatial dimensions

    Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three. Moving down is the same as moving up a negative amount. Moving diagonally upward and forward is just as the name of the direction implies; i.e., moving in a linear combination of up and forward.
    [edit]

    Time

    Time is often referred to as the "fourth dimension". It is, in essence, one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that movement seems to occur at a fixed rate and in one direction.

    The equations used by physics to model reality often do not treat time in the same way that humans perceive it. In particular, the equations of classical mechanics are symmetric with respect to time, and equations of quantum mechanics are typically symmetric if both time and other quantities (such as charge and parity) are reversed. In these models, the perception of time flowing in one direction is an artifact of the laws of thermodynamics (we perceive time as flowing in the direction of increasing entropy).

    The most well-known treatment of time as a dimension is Einstein's theory of general relativity, which treats perceived space and time as parts of a four-dimensional manifold.


    (this was cut and pasted from Wikipedia. If you feel it is wrong, I encourage you to update it to reflect what more closely represents itself as correct.)
     
  10. Nov 28, 2005 #9

    I think that in the way I described it, I left the door open to misinterpretation. I worked as a machinist for a number of years, and I think I see the cartesian coordinate system from a slightly different perspective.
     
  11. Nov 28, 2005 #10
    Then why are you telling me to go read something?
    What part is your unknown?
    Are you clear on GR. – is it 4D or 5D for you?

    Do you understand “Background”?
    For GR is it ‘Dependent’ or ‘Independent’ for you?
    (you may need to do some reading here – try search threads)

    As you clarify those ideas from your readings, (not likely you’ve got to that part yet if you think GR is 5D) read what I said in my post, not what you imagine I said.

    Note that SR is 3D not 4D like GR, so they are different forms of relativity.
     
  12. Nov 28, 2005 #11

    JesseM

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    Both GR and SR are 4D, the difference is that SR deals only with flat 4D spacetime while GR deals with curved 4D spacetime (with the curvature related to the distribution of matter/energy).
     
  13. Nov 28, 2005 #12

    JesseM

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    The "rubber sheet" metaphor can be misleading--for one thing, it makes people think of objects being pulled "down" into depressions in the sheet, but really the orientation of the depression is irrelevant, you could just as easily imagine gravity creating humps in the sheet rather than depressions. All that's important is that the curvature of the surface determines the shortest path between two points, known as the "geodesic" path--for example, on the surface of a sphere, the shortest path between points is always a segment of the great circle (like lines of longitude, or the equator) that passes between those points. And even this is potentially misleading--on a curved 2D surface like a rubber sheet, a geodesic is the shortest path between two points on that 2D surface, but in general relativity, a geodesic is actually the path between two points in in curved 4D spacetime with the largest value of the "proper time" (time as measured by a clock that follows that path). And one other potentially misleading issue is the one you mention--to picture a curved 2D surface, we normally imagine it sitting in some higher 3D space, something that's known as an "embedding" of the curved surface in a higher-dimensional space. But mathematically there's no need to use a higher-dimensional embedding space, it is possible to describe curvature using purely intrinsic features that could be observed by a being confined to the surface (like whether the sum of angles of a triangle drawn on the surface is more, less, or equal to 180 degrees), and general relativity uses only such intrinsic features to describe what it means for space to be curved (see this page on differential geometry, the mathematical basis for general relativity, which talks about the difference between intrinsic and extrinsic descriptions of curvature).
     
  14. Nov 28, 2005 #13
    Under certain examples of GR, when applied to different examples of quantum mechanics calls out for 26 dimensions. I am not even slightly prepared to go into detail about that. All I was referring to, with regards to the "5d", was accounting for motion, which I only referred to it as 4d because most people associate it as such. If 4d represents space-time, how do you account for motion within this "warpage" of space-time? This warpage of space via mass is independent of motion, which is what I referred to as needing to separate time from this warpage.

    What I suggest to alleviate such confusion is to identify this warpage by using a distinct variable that describes the relationship of mass and the relative density of it versus space itself. By using this relationship, you can illustrate using the cartesian coordinate system exactly how much space is warped by mass. I am not a mathematician, and I am still trying to figure out exactly that formula. By seeing this concept as a variable, you can effectively use it to describe gravity associated with a singularity, providing you know it's density and volume. (not an easy thing to know...)

    When you account for time as being simply motion, you can easily understand 5 different spatial dimensions that you can illustrate pretty much all known locations, as well as forces.

    Or I am as my title suggests, crazy....
     
  15. Nov 28, 2005 #14
    I'll go for crazy.
    You need to get clear that motion in SR is covered in 3D. (time is not a D)
    Motion is covered in GR, including changing motion now, is 4D not 5D.
    Don't go into QM's Multi D's till you get that.
     
  16. Nov 28, 2005 #15
    Only when using frames of reference. By using frames of reference, you are in all essence stopping time for that being measured.

    This is an inherent problem with measuring time. Time is a constant, and stops for no one. With this we start getting into time dilation, and is certainly not for the meek to discuss.

    With this, I stop contributing to the thread because it has, in many respects, lost focus from what it was originally intended to do.
     
  17. Nov 28, 2005 #16

    JesseM

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    What do you mean that time is "not a dimension" in SR? What about the fact that time and space get mixed up in different observer's reference frames in SR, so that two events that take place in different places but at the same time in one frame will happen at different times in another frame? What about the fact that the coordinate-invariant spacetime interval between events depends on dt as well as dx, dy and dz, and it can be thought of as the analogue of distance in ordinary euclidean 3D space? What about the fact that in SR, the conservation of the energy-momentum 4-vector is more fundamental than conservation of energy or conservation of momentum individually?

    Since you are disagreeing with the definition used by the entire physics community here, can you provide your own novel definition of what it means for time to be a dimension, and why it should be considered a dimension in GR and not SR?
     
  18. Nov 28, 2005 #17

    StatusX

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    Spacetime is 4 dimensional because, roughly speaking, you need 4 coordinates to uniquely specify a point. In the same way, a sphere is 2-dimensional because a point is uniquely specified by its latitude and longitude. Now, the sphere has a metric which, in these coordinates, tells you the distance between two points seperated by some (infinitessimal) latitude and longitude. From this metric you get all you need to know about the sphere, and thinking about it in this abstract manner, you have a 2D, non-euclidean space. But you can embed the sphere in euclidean space in such a way that the distance between neighboring points as given by the metric is the same as the euclidean distance, ie, dx2+dy2+dz2. To do this, you need at least 3 dimensions.

    Likewise, for curved spacetime you need more than 4 dimensions if you want to embed the space in euclidean space in such a way as to preserve distances. Even then, since the metric is Minkowskian (ie, the distance can be negative if the points are timelike seperated), you can only look at spacelike slices, or use some artificial embedding that makes negative distances positve. It is a very abstract form of geometry.
     
  19. Nov 28, 2005 #18
    What you’re talking about in SR is simultaneity issues not 4D. As soon as you say 'spacetime' your talking about GR.

    Einstein abandoned SR in 1908 because he saw he couldn’t answer gravity or acceleration with it before most others in physics recognized that.
    Still took him 8 more years to come up with the new CONCEPT and math to use 4D with warping to solve the problem in the new GR.

    It’s only few in the scientific community think GR can be derived from the formulas of SR.
    IT CANNOT – I know I tried till I finally got it that SR and GR are two different CONCEPTS.
    Although, the principals of SR do apply in a GR world. Fundamentally SR is 3D and GR is 4D and are not the same thing. SR was complete within itself long before 4D was needed.

    Unfortunately quite a few people are still confused by not getting this clear.
    The other thing many get messed up on is thinking Einstein just added one dimension (time) to the existing three. He didn’t it’s not any part the three “we see” that warp. It’s the interrelation of the four that warp with each other that create the reality of the three “we see”, from each of our reference points. This is when you start getting into "background" issues.
     
  20. Nov 28, 2005 #19

    JesseM

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    Those "simultaneity issues" are part of what the term "spacetime" was invented to describe. Also, the fact that the invariant spacetime interval ds^2 = c^2*dt^2 - dx^2 - dy^2 - dz^2, which can be used to define the metric of flat spacetime, depends on the time coordinate is not a simultaneity issue.
    Not according to how every physicist in the world defines "spacetime". For example:

    http://en.wikipedia.org/wiki/Spacetime
    Or this:

    http://www.physics.nmt.edu/~raymond/classes/ph13xbook/node40.html
    Or this:

    http://www.einstein-online.info/en/navMeta/dictionary/s/
    This use of "space-time" accords with Einstein's own use of the word, see this section of a book by Einstein entitled "The Space-Time Continuum of the Special Theory of Relativity Considered as a Euclidean Continuum."

    So again, if you have your own definition of "spacetime", and of what it means for a theory to be 4D as opposed to 3D, then please provide it. If not, then probably the problem is just that you have misunderstood what physicists mean when they use these terms.
    I have never said that GR can be derived from SR, although once you know GR, you can derive SR as a special case of GR, and note that in arbitrarily small regions GR reduces to SR.

    However, this has nothing to do with the point about the proper use of "spacetime". GR does indeed involve some different concepts that aren't present in SR, but the basic idea of spacetime is not one of them (the idea that spacetime can be curved is, though).
    SR and GR are different, but the difference has nothing to do with one being 3D and one being 4D, at least not as any physicists would use these terms. So either you've made up your own terminology which disagrees with that used by all physicists, or you've just misunderstood what physicists mean by these terms.
     
  21. Nov 29, 2005 #20
    Mathematically “space-time” is not needed until you need to curve it. Using it on SR clouds the issue that SR is not 4D. SR can be handled with ‘classical’ thinking just fine. Physics didn’t leave the classical with SR, nor with QM first. It first went non-classical with GR, one of the reasons it was so hard to understand and accept.

    When “wikipedia” says “general relativity, an extension of special relativity” they are wrong. GR is a much bigger conceptual step than that.

    If you like, it’s my ‘opinion’ the phrase “space-time” should only be used where it’s needed or makes sense. That’s where it needs to curve, and that’s GR not SR. If you don’t want to accept the SR and GR are two different things – go ahead. Each to his own.

    See ya in another thread someday.
     
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