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Thread: Deriving Gravimagnetic-Spin Relationships for the Angle Between two Spin-Vectors with a Magnetic Moment

  1. #1 Deriving Gravimagnetic-Spin Relationships for the Angle Between two Spin-Vectors with a Magnetic Moment 
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    I think my presentation was poor, going to rewrite it.


    Last edited by Geometrogenesis; February 23rd, 2012 at 08:19 AM.
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    .... and this


    Last edited by Geometrogenesis; February 23rd, 2012 at 08:22 AM.
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    ... I'll rewrite this too.
    Last edited by Geometrogenesis; February 23rd, 2012 at 08:22 AM.
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  5. #4  
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    Perhaps a few more interesting additions. It wasn't until a few moments ago, was I made aware that in the weak gravitational limit of the metric where is a small gravitational perturbation, that the Newtonian or (gravito-electromagnetic potential) is defined by http://arxiv.org/pdf/0912.2814v2.pdf . On page two, it proves that slowely moving matter fields (or a selective choice of particles no less) you can ignore second and higher terms in the source velocity. It results in a matrix for the perturbation which defines the field as a gravi-electric field.

    I am very tempted to get my pen and paper out and see if plugging in the respective matrices and new terms would bring some new insights. But I am in a bit of a rush; in mind, I took into consideration that eq. [10] is not just a gravimagnetic field equation, but if the on the left hand side of the equation (turning into an expression) is and if plugging their definition of the matrix into the equations somehow, would unify them as GEM equations.
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    ..... this will be changed...
    Last edited by Geometrogenesis; February 23rd, 2012 at 08:23 AM.
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    Motz has defined the gravitational charge of a particle as . This is a quantization condition which is obtained from a similar approach by noting a particle with a velocity is coupled to the gravimagnetic field by virtue of a cross product in the form



    This is actually fully discussed by Sciarma 1953MNRAS.113...34S Page 34 .
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  8. #7  
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    this in the next post.
    Last edited by Geometrogenesis; August 17th, 2013 at 01:53 PM.
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    [8],[7], [10],[15] are the equations of importance. Actually, [10] maybe understood in General Relativistic terms given as eq. [11].

    Eq. [11] is actually an important quantity describing the gravitomagnetic stress energy tensor related to the metric . The stress energy is proportional to the curvature of space. What I want to do is investigate this curvature as the presence of tiny distortions we know as ''particles''... in a simplified question, ''Are particles just tiny 'bits of' curvature?''

    Certainly on large scale effects, we can see noticable dynamics of massive objects deflecting light. Wherever mass is there is a proportional amount of curvature. In fact, the mass of a body is intrinsically related to the radius of curvature - this is a rule even for the miniscule. So, what we have are effectively particles which can be translated from an understanding of the geometry of the space which is, again the metric. Particles therefore can be seen like tiny ''knots'' in the fabric of spacetime, tiny knots manifested from a miniscule curvature.
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    th the appearance of the gravitomagnetic density, so the spin acts as a coupling in this case.
    Last edited by Geometrogenesis; August 17th, 2013 at 01:54 PM.
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  11. #10  
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    trinsic geometrical structure.
    Last edited by Geometrogenesis; August 17th, 2013 at 01:54 PM.
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  12. #11  
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    vitation does.
    Last edited by Geometrogenesis; August 17th, 2013 at 01:54 PM.
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    c moment along the x-axis.
    Last edited by Geometrogenesis; August 17th, 2013 at 01:55 PM.
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    qrt{G_{ij}} M[/tex]
    Last edited by Geometrogenesis; August 17th, 2013 at 01:54 PM.
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    ion integral.
    Last edited by Geometrogenesis; August 17th, 2013 at 01:55 PM.
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    and this bit too...
    Last edited by Geometrogenesis; February 24th, 2012 at 09:05 AM.
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    Thus this equation holds at the energy ranges for and above the graviton which can couple to the magnetic forces due to a spin-coupling on the metric.
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    itian it should be added/
    Last edited by Geometrogenesis; August 17th, 2013 at 01:55 PM.
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    Torsion fields are connected to idea's of twisting frame dragging, notions of spinning objects and Torque. In fact, the idea that somehow torsion is a real phenomena of nature should not be such a big surprise it is afterall a full representation of the Poincare Group. If torsion exists and particles physically rotate then you can bet they experience torsion as well, very small amounts of it.
    Last edited by Geometrogenesis; February 24th, 2012 at 09:07 AM.
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    The force then between two particles can be given as

    where

    is the unit vector. Perhaps as a little interesting snippet, if one concentrates on the right hand side and take the dot product of the unit

    vector with a Pauli Matrix (designed to account for a two-spin network), then square, you end up with



    Now, from our equation above, we can define a motion for a single particle. To do this, we require two more equations:



    which describes the motion of particle and for particle we have



    So how do you involve spin in these equations?

    Remember, particles and can be replaced by spin networks in an abstract sense, since there are -state amount of particles; in entropy-related equations, the -state amount of particles is defined by



    Where we clearly have and . These can take on new appearances, we usually denote with an uparrow-downarrow notation which describes a particle, for instance which is either in an up-state or a down-state of spin.

    These become the on-off nodes in Fotini Markoupoulou-Kalamari's graphity/geometrogenesis model.

    Now that we have defined the interaction as a force, we can now concentrate on new parameters such as the electric charge force between two particles and .

    If each particles is described by a charge then the equation describing the electric charge force between two particles is given as



    If there was a transactional interpretation dynamic here, the net force after the transaction would be

    Last edited by Geometrogenesis; February 23rd, 2012 at 04:07 PM.
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    Thus the force between two particles can be defined in terms of a gravimagnetic field



    And the charge of the masses themselves given by a force relationship



    Where we are summing over independant charges of a presumed Dirac particle with a mass and introducing the semi-metric officially.
    Last edited by Geometrogenesis; February 24th, 2012 at 03:40 AM.
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    The appearence of matter therefore satisfies



    This is the existing mass-charge of the field - the ''innate mass charge'' of a particle.
    Last edited by Geometrogenesis; February 25th, 2012 at 09:56 AM.
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    The Coriolis effect for a rotating shell of matter generates inside of itself a field called the Coriolis Force.
    It will be taken for now to assume that particles are not truely pointlike particles, that this seemed to have been the route we have taken because it was ''easier'' to deal with.
    It goes to say, even for a particle, there must be a small ''twisting effect'' of the gravitational field which could be deemed negligable by General Relativistic effects.
    As small as frame-dragging would be for particles, the idea of gravitomagnetic forces for a particle as a rotating sphere may have interesting relationships.
    For instance, gravitmagnetism allows bodies to exchange energy in the form of coupling external gravitomagnetic fields niether would they ever undergo a direct collision, though normally in QM we never tend to think of shoving two particle into the same location, in fact the more you try and do this the more energy you require.
    It seems that the more I read on this subject, there is some evidence that gravitomagnetic forces might be noticable around water molecules Gravitomagnetism . If this can be extended to particles, I wonder the true implications. In the work so far however, I have entertained the idea of treating mass like a quantization of charge. Charge is simply the coefficients of the Lie Algebra's on the theory.
    I want to see mass and charge as ''being the dimensions'' spoke about contained inside of a particle. I don't like the idea of thinking particle's as having no dimensions but still possessing charge and mass, especially since your usual standard definition of mass requires some volume to define the density of an object.
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    It has been comforting to come across a paper which seems to take the idea of a quantum Coriolis Field seriously. http://arxiv.org/ftp/arxiv/papers/1009/1009.3788.pdf The gravitomagnetic field (the Coriolis Field) I have been using has been of the form . In this paper, it gives it as force

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    The cross product form of the vecocity is actually discussed by Sciarma on the ''Origin of Matter'' including by Motz and gives rise to an angular momentum component in the motion of a particle which is of order



    The lowest state of quantization then is given by motz as



    Motz defined his cross product with the gravitational charge condition as



    where is the Coriolis Force Field.
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