Physics Question #3451

Sahm Atman, a 17 year old male from Berkeley, CA asks on May 18, 2006,

I understand why magnetism is a relativistic effect, "caused" by Lorenz contraction effectively increasing charge density. I have also read that in quantum mechanics there is an uncertainty relation between the electric field measurement and the magnetic field measurement, but I've never seen a good explanation of why this is the case. Presumably it's somehow an outgrowth of the basic position/momentum "uncertainty" (which I think I understand on the basis of the bandwidth theorem), but exactly how does the electric/magnetic field uncertainty follow? And is there an understandable connection between magnetism as a relativistic effect and the electric/magnetic field uncertainty relation?

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The answer

William George Unruh answered on May 19, 2006

Magnetism is not a relativistic effect. Magnetism is a separate entity although closely related to electricity. In fact in special relativity the electric field and the magnetic field are partially converted into each other when going to a moving frame. You can have a magnetic field without an electric field, and vice versa. These field are not tied to sources. They are entitities in their own right, just as the ripples on the surface of pond may be caused by throwing in a stone, but are not part of the stone-- they exist in their own right.

If you look at Maxwell's equations, the Magnetic field is related to the time derivative of the electric field. Ie, the Magnetic fields acts like the momentum of the electric field ( actually of the electric field potential). In quantum mechanics something and its momentum have an uncertainty relation with each other, and thus the electric and magnetic fields have an uncertainty relation with each other.

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