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Thread: Can gravity be geometrically shown as an extra dimension ?

  1. #1 Can gravity be geometrically shown as an extra dimension ? 
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    Relativity shows gravity as warped space-time according to Einstein;
    yet, Gunner Nordstrom may not have been totally wrong to theorize that
    that gravity could be geometrically shown as an extra dimension.
    The 3D planes X,Y, and Z are curved from flat euclidean space in a gravitational
    field : this is evidence of geometric motion in an extra dimension ... call it "G" .
    Therefore, you may move X,Y,Z, and G ... plus " Time " ... you may merge
    time/space together into a simple "G" for "gravity dimension" . This is saying
    that gravity is not a mere force, nor particle, but a motion through another dimension
    where matter/energy is drawn inwards ... since relativity says matter and energy are
    interchangeable the draw seems universal.
    P.S.
    The famous diagram of a bowling-ball on a rubber mat simply replaces gravity for Z " up-down" : really, you would have
    X,Y,Z and delta-X, delta-Y, and delta-Z ... which could be X,Y,Z, and G. Is this correct?
    Great analogy of dimensions in X, Y, Z coordinates :
    If a line is moving X and curves it needs some Y ;
    If a line is moving X , Y and curves it needs some Z ;
    If a line is moving X ,Y and Z and curves it needs some G .
    If you're going North, East, and Up , you're going 3-D ...
    If you're going North, East, Up , and " Curving Space/Time "
    you're going 4-D ( plus ) ...


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    Forum Freshman gottaBtold's Avatar
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    I am of the opinion (for now) that gravity could be shown to be coming from an “extra” dimension as an effect of creation.

    You stated: "Relativity shows gravity as warped space-time according to Einstein". Would it be more accurate to state it this way – gravity is a RESULT of warped space-time? The three-dimensional cannon ball on a two-dimensional rubber sheet is a bit misleading. It should show a cannon ball (mass) INSIDE a rubber sheet (space-time), thus distorting (warping) the rubber sheet (space-time) in all three dimensions.

    Some supposition - perhaps before the big-bang there was a two-dimensional “brane” which encountered a single-dimension “singularity”, whereupon the big-bang occurred, resulting in our three-dimensional space-time. This space-time is warped, necessarily, because of the way it was created – outward from the singularity in three dimensions. Like a diamond, space-time had “inclusions” (matter) inside it. The weak, strong and electromagnetic forces also came into being at creation time and we know how they act upon the “inclusions” inside space-time.

    Gravity could be representing the force coming from outside the three dimensions as a result of the big-bang shoving aside whatever it needed to shove aside to make room for our space-time and everything in it. Whatever that stuff was that was pushed aside wants to return to its original state, but since we’re here, all it can do is push back a little bit.


    Anyway - interesting subject and I look forward to hearing from some of the experts on this.


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    Einstein/Rosen embedding diagrams ( bowling ball on rubber sheet ) are not technically accurate as they represent a lower dimensional 'slice' ( or foliation as DrR likes to say ) of space/time. For the non-technical, mass/energy warps space/time, and the warped space/time tells mass/energy how it can move. For the more technically adept, Penrose diagrams are much more explanatory and accurate. For the most technically adept, you probably already understand the GR field equations and don't need diagrams to explain it.
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    Loop Quantum Gravity is similar to expressing gravity as a weave of the fabric of space to create something out of nothing ... as well as M theory ... and part of Gunner Nordstrom's concepts. In order to warp the three expanded dimensions you need a physical, geometric, dimension of gravity ... the 4'th ... and if you count time, the 5'th dimension ... not counting any compressed dimensions. Gravity would be a MOTION into a " pocket-dimension " ; ergo, a geometric movement out of flat Euclidean space ...
    besides time distortions.
    GRAVITY IS MOTION INTO A SUB-SPACE ! Is this logical ?
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    Yeah well, when loop quantum gravity or M-theory make a verifiable prediction, then they can be taken seriously and considered logical.

    Until then, just like string theory, they are an elegant mathematical theory in search of a universe to describe.
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    To make a long story short : don't you need another dimenison to warp 3D space/time ?
    If you don't simply say, " Yeah, time ..." , then gravity would be a dimension on its own.

    Graphs would need to be X,Y,Z, and G ( for gravity )...plus "whatever " depending on
    your standpoint for theoretical universe models ( Loop Quantum Gravity, M theory ...etc...)

    If you draw a line along X, you need to add Y to curve it , thus adding a dimension ...
    following this to 3D , you need to add a dimension to curve , or warp, space.
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    No, mathematically you do NOT need to embed a curve in an extra dimension.

    I know that, and I've fallen into that trap many times myself.
    Sometimes common sense can be a real 'ball-and-chain'.
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    Make and test for one prediction of your superunification theory. Then post like it was an accepted theory.
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    Needing to add a dimension to curve space seemed to make so much sense to me ; how can this be wrong? If you graph X and want to curve it you must add dimension Y ...etc... until X,Y,Z ( 3-D ) needs another dimension to curve. I'm sure you're right, but am a bit confused on the geometric details .
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    I think I see that the space in a gravitational field is distorted due to the space-time quantum density changing. Although the AETHER has been disproven, this seems to hint at a medium ( AETHER ) to space-time. I'm aware of the perpendicular mirror experiment disproving the AETHER; yet, so much of this insinuates a MEDIUM of space-time ( of course, quantized ).
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    You don't need y for x to curve. You only need it to visualize the curve on a Euclidean piece of paper.
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    Yes, gravity is an abnormality in space, due to the fact it warps space/time; furthermore, an extra dimension for the same reason.
    Yes, this is NOT the standard thought of modern physics ... but it makes sense to me.
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    Quote Originally Posted by ALM2study8 View Post
    Needing to add a dimension to curve space seemed to make so much sense to me ; how can this be wrong? If you graph X and want to curve it you must add dimension Y ...etc... until X,Y,Z ( 3-D ) needs another dimension to curve. I'm sure you're right, but am a bit confused on the geometric details .
    The problem is that you are still thinking in terms of Euclidean geometry. Our universe operates by the rules of non-Euclidean geometry. This is not really your fault, at the small scales at which we are used to and evolved dealing with, the universe behaves very closely to being Euclidean, so our thinking processes developed to deal with the world in this way. When we model Euclidean geometry as a plane transposed onto a surface curved through a 3rd dimension, it is just that, a model. It is a means to wrap our Euclidean-wired brains around non-Euclidean space. But this does not mean that non-Euclidean geometry needs that 3rd extra dimension. Non-Euclidean geometry just follows different rules. (parallel lines can meet or diverge, for example)
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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    In terms of models, perhaps space and time can be visualized effectively with the idea of a peice of flexible mirror, with the xy and z dimension represnted with height, width and the relfection in the mirror as the depth. Thus if the mirror is curved (the fourth dimension variable) it will distort the image in the mirror in another unperceived dimension to the observer who would only see a distorted image. Like a funhouse mirror. Have you ever noticed that if you hold something up to a curved mirror such as this the reflection will appear to accelerate when moved to the part that is curved, just as things accelerate when expereincing gravity?
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    ALM2study8,

    ......This is saying that gravity is not a mere force, nor particle, but a motion through another dimension where matter/energy is drawn inwards ...
    I should think there are two primary purposes for such a proposal. One might be to better understand gravity, and the other to better formulate it. Both, one would think, would involve some practical or proposed applications.

    General Relativity is functional within the solar system, and some other applications, seemingly the only use for a theory of maybe equal complication or of a new formulation would be in the dark matter or quantum realms? I do agree that another dimension G would seemingly add no more complication to observed reality than the idea of warped space does. But with this said, I think something simpler than GR like MOND-like formulations with logical justifications for all domains would be better than ideas and formulations of equal or more complication.

    Of course on an ongoing basis, whatever gravity formulation has the best verifiable predictions and appealing logic, will be the prevailing theory and formulations at that time. The same would seemingly apply to all formulas and understandings in physics and science in general.
    Last edited by forrest noble; April 18th, 2012 at 07:44 PM.
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    Quote Originally Posted by forrest noble View Post
    I think something simpler than GR like MOND-like formulations with logical justifications for all domains would be better than ideas and formulations of equal or more complication
    Actually, while the basic idea of MOND is straightforward, its mathematical formulation is definitely not. In its full form it is just as complicated as GR.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by forrest noble View Post
    I think something simpler than GR like MOND-like formulations with logical justifications for all domains would be better than ideas and formulations of equal or more complication
    Actually, while the basic idea of MOND is straightforward, its mathematical formulation is definitely not. In its full form it is just as complicated as GR.
    Milgram's MOND, my own and other MOND models that I know of, are vastly simpler than GR. GR involves 10 partial differential equations of Tensor Calculus. There are some variables that must be estimated in most cases, before even considering calculation. There are thought to be only a very few exact solutions in GR over its long history. On the other hand MOND does not propose warped space or Riemann geometry and calculations can sometimes involve just one equation. The most important consideration is that MOND does not compete with GR since only Newtonian gravity is used with dark matter at the galactic scale, to predict spiral galaxy rotation curves (stellar orbital velocities).

    Milgram's MOND, and most other generally known MOND models, are not thought to explain and calculate in all venues. It is thought to also require in such cases other explanations like dark matter, seemingly making it no better than Newtonian gravity with dark matter in such venues as galaxy clusters and the Lyman Alpha forest, for instance.

    Modified Newtonian dynamics - Wikipedia, the free encyclopedia
    Last edited by forrest noble; April 19th, 2012 at 11:20 AM.
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    Quote Originally Posted by forrest noble View Post
    Milgram's MOND, my own and other MOND models that I know of, are vastly simpler than GR. GR involves 10 partial differential equations of Tensor Calculus. There are some variables that must be estimated in most cases, before even considering calculation. There are thought to be only a very few exactly calculted answers in GR over its long history. On the other hand MOND does not propose warped space or Riemann geometry and calculations can sometimes involve just one equation. The most important consideration is that MOND does not compete with GR since only Newtonian gravity is used with dark matter at the galactic scale, to predict spiral galaxy rotation curves (stellar orbital velocities).

    Milgram's MOND, and most other generally known MOND models, are not thought to explain and calculate in all venues. It is thought to also require in such cases other explanations like dark matter, seemingly making it no better than Newtonian gravity in such venues as galaxy clusters and the Lyman Alpha forest, for instance.

    Modified Newtonian dynamics - Wikipedia, the free encyclopedia
    What you have referenced above is only the non-relativistic limit of the theory - obviously this is simple and straightforward. The full relativistically invariant formulation of this is called TVSG ( Tensor-Vector-Scalar Gravity ), and its mathematical formulation is just as complicated as GR - in fact I am finding this one a lot more confusing then the purely tensorial equations of GR :

    Tensor
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  20. #19  
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by forrest noble View Post
    Milgram's MOND, my own and other MOND models that I know of, are vastly simpler than GR. GR involves 10 partial differential equations of Tensor Calculus. There are some variables that must be estimated in most cases, before even considering calculation. There are thought to be only a very few exactly calculted answers in GR over its long history. On the other hand MOND does not propose warped space or Riemann geometry and calculations can sometimes involve just one equation. The most important consideration is that MOND does not compete with GR since only Newtonian gravity is used with dark matter at the galactic scale, to predict spiral galaxy rotation curves (stellar orbital velocities).

    Milgram's MOND, and most other generally known MOND models, are not thought to explain and calculate in all venues. It is thought to also require in such cases other explanations like dark matter, seemingly making it no better than Newtonian gravity in such venues as galaxy clusters and the Lyman Alpha forest, for instance.

    Modified Newtonian dynamics - Wikipedia, the free encyclopedia
    What you have referenced above is only the non-relativistic limit of the theory - obviously this is simple and straightforward. The full relativistically invariant formulation of this is called TVSG ( Tensor-Vector-Scalar Gravity ), and its mathematical formulation is just as complicated as GR - in fact I am finding this one a lot more confusing then the purely tensorial equations of GR :

    Tensor
    Tensor-vector-scalar gravity (TVSG) is just one version of MOND which granted is probably the most complicated. This model was developed by Jacob Bekenstein, intending for it to be what he called a relativistic generalization of Milgrom's MOND. Its equations have similarities to both Milgram's MOND and GR. It can supposedly make similar gravitational-lensing predictions to GR w/ dark matter, for instance, but also requires variable inputs which can be likened to the inclusions of dark matter variables to GR. This seemingly defeats the purpose of a MOND model in the first place which was/ is to eliminate the need for dark matter in its equations. The complications of TVSG, like GR, are also not needed concerning calculations of stellar rotation curves in spiral galaxies, which was the primary purpose for Milgrom's MOND and probably most other MOND formulations including mine.
    Last edited by forrest noble; April 20th, 2012 at 09:16 AM.
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    Quote Originally Posted by forrest noble View Post

    Tensor-vector-scalar gravity (TVSG) is just one version of MOND which granted is probably the most complicated. This model was developed by Jacob Bekenstein, intending for it to be what he called a relativistic generalization of Milgrom's MOND. Its equations have similarities to both Milgram's MOND and GR. It can supposedly make similar gravitational-lensing predictions to GR w/ dark matter, for instance, but also requires variable inputs which can be likened to the inclusions of dark matter variables to GR. This seemingly defeats the purpose of a MOND model in the first place which was/ is to eliminate the need for dark matter in its equations. The complications of TVSG, like GR, are also not needed concerning calculations of rotation characteristics of galaxies, which was the primary purpose for Milgrom's MOND and probably most other MOND formulations including mine.
    Remember that a complete theory of gravity must be able to correctly model all gravitational phenomena, not just galactic rotation curves. MOND is well able to explain the latter, but is not a relativistic theory, so will fail in the high energy domain. Only TVSG is a complete description, and to the best of my knowledge the only such model that makes correct predictions across all domains. This is analogous to the relationship between Newtonian Gravity and GR - the former is just a weak field approximation to the latter.
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