Dimensions

[AntonioLao]

A field is completely determined by the existence of a vector potential and a scalar potential. The quanta of a vector potential are the charges of that field and the quanta of a scalar potential are the masses of that field. And the finiteness of charge and mass fixes the maximum number of fundamental particles. These charge and mass are the detectable things for experiments.

For the electromagnetic field, the symmetry is U(1).
For the electroweak field, the symmetry is SU(2).
For the QCD or strong color field, the symmetry is SU(3).

[Guille]

To everyone,

Antonio's last post made me think,

do forces have "dimensions"? are they "dimensional" by them selves? are their effects "dimensional"?

[AntonioLao]

gravity only attracts. if attractiveness is a dimension, then gravity is one dimensional.

electromagnetic force attracts as well as repels, then it is two dimensional: 1 for attraction and 1 for repulsion. These are analogous to degrees of freedom and are parts of directional properties of spacetime structures.

[Guille]

From your analogies, what dimensions do the electric and magnetic forces have? (separatelly)

[AntonioLao]

individually, the electric force is attractive as well as repulsive hence 2-dimension. The magnetic force is also attractive as well as repulsive hence also 2-dimension. The difference is that for electric charges, likes repel and unlikes attract, while for magnetic currents: currents flowing in the same direction attract but currents flowing in opposite direction repel.

[Guille]

individually, the electric force is attractive as well as repulsive hence 2-dimension. The magnetic force is also attractive as well as repulsive hence also 2-dimension. The difference is that for electric charges, likes repel and unlikes attract, while for magnetic currents: currents flowing in the same direction attract but currents flowing in opposite direction repel.

how can n dimensional things (forces) affect n+ (more than n dimensions) dimensional things (lie matter)?

[AntonioLao]

zero-dimensional object in motion gives 1D objects, 1D objects in motion give 2D objects, 2D objects in motion give 3D objects, 3D objects in motion give 4D objects, 4D objects give ..., I think you get the picture?

But in my research, all these motions are localized at the infinitesimal domain. If we can stopped the local motion of a 4D object such as an atom of hydrogen, we get pure 3D energy object (maybe a photon?). But no one can stopped the magnetic moment of a neutrino or an electron or a proton, etc. If we can freeze a photon, the result is 2D continuous space. If we can stopped the motion of 2D continuous space, the result is 1D quantized space. If we stopped the local motion of quantized space, we get back to the BB singularity.





Moderator note: Although this thread is rather old, I've closed it since there are lots of deleted posts resulting in the thread not reading correctly. Anyone wishing to carry on discussion of this topic may start a new thread in this forum ~neutralino