Can curved space explain magnetic force like it explains gravity?

[-Job-]

Isn't it possible to use the model of curved space, so effective in explaining gravity, to explain other forces, like the magnetic force? What are the biggest challenges with this approach?
Thanks for your time.

 

[vanesch]

I think the first one who tried this, were Kaluza and Klein:

http://en.wikipedia.org/wiki/Kaluza_Klein


The idea still lives on, in various variants.

 

[-Job-]

I was thinking that the interaction between the space-time curvatures induced by two objects could be relevant in explaining the forces between them, and that, in the case of the magnetic force, the curvatures of the two objects might come together to form a "valley" between them, both experiencing an acceleration towards the low point in that valley, if that makes any sense.

 

[selfAdjoint]

You have to allow for the funny "lop-sided" property of magnetism, expressed by the asymmetry of the vector curl in Maxwell's equations and by the "right hand rules" and "left hand rules" of the engineers. Your valley idea sounds too symmetrical.

 

[-Job-]

The general idea would be that objects might produce complex warping of space, as opposed to smooth curving of space. The interaction between these warpings producing high and low points which might influence the position of the objects, little by little.

 

[jtbell]

The general idea would be that objects might produce complex warping of space, as opposed to smooth curving of space.

What is "complex warping" as opposed to "smooth curving"?

 

[AlphaNumeric]

Non-differentiable, like a cusp, but in multiple dimensions perhaps? Though at such a point curvature goes to infinity, since it's undefined, so perhaps that's just a singularity (my mental image of 4d curvature, as you can imagine, not perfect ;)).

 

[-Job-]

I'm kind of abandoning this idea now because it would require that a mapping of the acceleration due to gravity with respect to the distance from the object that is producing the gravitational field to be non-symmetrical, like selfAdjoint mentioned. In fact for a magnet of some size, like a perfect sphere the size of a basketball, the gravitational field produced by that object would have to be non-symmetrical, meaning that if you were to orbit around that sphere always keeping the same distance d from that object, you'd experience slight variations in the gravitational force. That's what i meant as not-smooth, or complex. The visual interpretation would be, instead of the curved funnel shape of a ball weighing down on some cloth-like surface, that of an object weighing down on a non-cloth like surface, thus also causing outgoing ripples in that surface (a non smooth curving), not necessarily concentric, but fanning out from the center, or some other pattern, depending on the properties of the sphere. The idea would then be that depending on how the curvatures induced by two neighboring objects interact, valleys or peaks might be generated, a valley attracting the two objects, and a peak repulsing the two objects. I was just trying to avoid using extra dimensions, and work with what we already have to try to interpret magnetism.