My equations for 4d Electromagnetism

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My equations for 4d Electromagnetism

Postby anderscolingustafson » Thu Oct 22, 2015 6:44 am

I decided to derive some equations for electromagnetism in 4d that assume an inverse square law.

4d Electromagnetism 3.png
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φE4 is the 4d electric flux which depends on the distance from the source of the electric flux. Q and q are for electric charge, ε0 is the electric constant, r is the distance, FB4=0 is basically saying that there are no magnetic monopoles although there would be no magnetic poles either, B4 is for 4d magnetic fields, μ0 is for the magnetic constant, FE4 is the force between two electric charges, FM4 is the force between two current carrying wire, I is for electric current, and L is the length of a current carrying wire.

I included magnetism because if special relativity still applies then a charge that is not moving relative to a current carrying wire will experience no force as the density of positive and negative charge will be the same, but a charge that is moving in the same or the opposite direction of the electric current relative to the wire will experience a force because from it's reference frame the some of the charge in the wire will have length contraction while the opposite charge in the wire will have length expansion so from its reference frame the wire has a greater density of one charge than the other. If the charge experiences a force from the wire in it's own reference frame it must experience a force in all reference frames and so from the reference frame of something that isn't moving relative to the wire the wire must have a magnetic field to account for the force between it and the moving charge when from it's reference frame the wire is neutral. While some of the equations that describe magnetism will be different in 4d so long as special relativity still applies there will be magnetism as magnetism is the result of combining special relativity with electricity. In 4d in order to understand magnetic fields it's best not to think of them in terms of field lines as that just tends to lead to confusion but instead it's best to think of them in terms of special relativity.

The "electric flux" is dependent on the distance as that is what would produce an inverse square law in 4d as the force between two charges is the electric flux of one of them multiplied by the charge of the other divided by 2pi2r3 and in order to produce an inverse square law an r in the denominator must cancel out with an r in the numerator.
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Re: My equations for 4d Electromagnetism

Postby anderscolingustafson » Fri Oct 23, 2015 6:41 am

If there are two objects that both have positive and negative charges and the negative charge of each has simple rotation and the negative charges both are spinning around the same dimensions and both have the same coordinates for the dimensions the negative charge is spinning around but different coordinates in the dimensions they are not spinning around then if the negative charge of each in the same direction they will experience a magnetic attraction while if the negative charge of each is spinning in opposite directions the objects will experience a magnetic repulsion. If the two objects have different coordinates for the dimensions the negative charges are spinning around around but the same coordinates for the dimensions the native charges are not spinning around then if the negative charges are spinning in the same direction the objects will experience a magnetic repulsion while if the negative charges of each are spinning in opposite directions they will experience a magnetic attraction.

If there are two objects in which the positive charge of each is not spinning but the negative charge of each has an isoclinic rotation then if the negative charges of each have the same type of isoclinic rotation the two objects will tend to experience both a magnetic attraction and a magnetic repulsion from each other so the effects their magnetic fields have on each other will tend to cancel. If the negative charges both have opposite types of isoclinic rotation from each other the effects of their magnetic fields will tend to add together meaning they will tend to attract or repel each other more strongly than objects in which the negative charges both have simple rotation.

In 4d if matter and anti matter both have opposite types of isoclinic rotation then that would mean that permanent magnets made of matter would be more strongly affected by permanent magnets made of anti-matter than permanent magnets made of matter if they are affected by permanent magnets made of matter at all. This would seem to indicate that while there would be a chirality for isoclinic rotation in 4d it would not define the difference between matter and anti-matter as both matter and anti-matter would each have both types of isoclinic meaning that the weak force or the equivalent of the weak force would not violate parity and so parity violation could not be a way for the 4d universe to favor matter over anti-matter.
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