Relativity and Magnetism

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Relativity and Magnetism

Postby anderscolingustafson » Thu Aug 20, 2015 4:58 pm

I found an interesting video on how electromagnets work

https://www.youtube.com/watch?v=1TKSfAkWWN0

From the reference frame of something that isn't moving relative to a wire with electricity flowing through it the density of positive and negative charges is equal and so there is no net electric charge. From the reference frame of something that has the same velocity as the current flowing through a wire the protons are moving and so the density of positive charge would be higher from that reference frame than it would relative to the wire while the electrons would not be moving and so the density of negative charge would be lower from that reference frame than it would relative to the wire so the wire would have a net positive electoral charge and so if it was also electrically charged it would experience a force from the wire. From the reference frame of something that isn't moving relative to the wire is electrically neutral but if something experiences a force in its own reference frame it must experience a force in all reference frames and so the wire with a moving current must have a magnetic field to account for the fact that it affects a moving charge.

This means that magnetism would work in basically the same way in any number of dimensions so long as relativity works in the same way. In any number of dimensions a moving current would produce a magnetic field because in any number of dimensions something that's moving will experience length contraction relative to something that's stationary. So in both 2d and 4d there would still be magnetic fields although magnetic fields would drop off with distance at different rates based on the number of dimensions. In any number of dimensions other than one a rotating charge would produce a magnetic field.

In two dimensions there would be two ways a charge could rotate that would be mirror images of each other and they would both produce magnetic fields that would be mirror images of each other. Two rotating charges of the same charge rotating in opposite ways would experience a magnetic attraction in 2d.

In 3d there is only one way that a rotating charge can rotate as any orientation of a rotating charge can be rotated to get to any other orientation. In 3d if there are two rotating like charges rotating in opposite directions and they both are next to each other they will experience a magnetic attraction and if there are two rotating like charges rotating in the same direction with their poles facing each other they will experience a magnetic attraction.

In 4d there is also only one way a rotating charge can have a simple rotation but a rotating charge could have a double rotation. There would be two basic ways that something could have an isoclinic rotation that would be mirror images of each other. A charge with an isoclinic rotation would be affected by the magnetic field of a charge with a simple rotation and it would be affected by a charge with an opposite rotation as both directions of the magnetic field would be attractive but it would experience either less of a magnetic force or no magnetic force from a charge with the same isoclinic rotation as if they were orientated in the same or opposite directions parts of them would have the same tangential velocity while others would have the opposite tangential velocity and so the attractive magnetic field of one direction would tend to cancel the repulsive magnetic field of the other directions.
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Re: Relativity and Magnetism

Postby granpa » Sat Aug 22, 2015 5:43 am

The only difference is that in 4d the magnetic field isnt a vector field. Its a bivector field.
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