In Dirac theory the electron has a spin degree of freedom. The question is: Do electric and magnetic fields created by an electron in a given frame of reference depend on the electron spin? If yes, how?
I found the following cases: E'=E+-c sigma x B, and B'=B-+sigma x E/c, where sigma is the Pauli matrices, and +- for electron (positron) spin states. How does this sound? x: cross product and sigma is 3x3 Pauli matries
Of course electric and magnetic fields depend on its spins of electrons.
The magnetic field of any material is created by directed magnetic dipols which are created by single spins of single electrons. If every single electromagnetic dipol is directed in one direction then we speak from a magnet. If this is a f. i. permanent magnet then all spins are permanent directed in same direction by crystal - structures.
The magnetic field created by an electron in turn created the total magnetic moment of particle depend on the spin, who in turn shifted the spectrum of energy.
The electric field of a 'classical' charge does not depend on its spin. Only if the spin 'frequency' changes in time, an extra electric field appears during the change. Quantum spin, however, is the spin of a point particle without volume and radius. The reason physicists assumed particles are point like is to save special relativity, since the Zeeman effect in combination with the classical electron (with classical radius) could be explained only by assuming a superluminal rotational electron speed. A point particle cannot have a mechanical spin, so its "spin" is purely quantum mechanical, via matrices, a 4 component wave function, and 'Dirac algebra' (the math became very complicated and involved, which might be a sign of wrong assumptions). I think Woldemar Voigt made a false assumption about the TEM wave medium, see also http://www7b.biglobe.ne.jp/%7ekcy05t/spin.html
Dear Arbab,
The electric and magnetic fields are independent of the spin. Dirac's equation is related with the electric charge and spin, which related through the spinors (particle-antiparticle).
I don't understand the expressions that you have for the transformed fields
E'= E+ sigma x B
What do you mean by the product x? The three Pauli matrices are 2x2 while the electric and mangnetic field are vectors with three components. Notice that E and sigma x B ara also with very different physical units.
I hope this helps.
Dear Dr Arbab,
Regards. From engineering point of view, which is more macroscopic rather than microscopic, electric field is static rather than dynamic in contrast with magnetic field which is quite dynamic. The existence of a charge only indicates existence of electric field, irrespective of motion or particle being at rest. On the other hand, magnetic field rises due to motion of charge and vanishes when it comes to rest. However, physics and quantum mechanics experts may have a different prospective ... 😂
Dear Arbab,
The problem of units is solved because I didn't see that you put the veloctity of light c on the expressions for the electric and magnetic fields
E'= E+ c sigma x B
But notice that the other problems with the propducts remain unsolved and c has to be a vector for being treated properly as a velocity, instead of a constant (or scalar number).
I suppose that essential answer will be given in future investigations of electron's microscopic structure. At first, it is needed to concretize- what is "spin" for an elementary particle of some shape and internal structure. It should have clear mechanical definition.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Theoretical Physics