That is true! However from the Maxwell theory together with the Lorentz transformation it follows that magnetic monopoles cannot exist. (Refer to the book of Rosser mentioned above).Experiment rules over mathematical proof
Is the reverse conclusion correct? That means if the electric charge is quantized then there must be magnetic monopoles?Dirac showed that if there was even one magnetic monopole in the universe, then electric charge would have to be quantized.
So what?Originally posted by Albrecht
If we would have magnetic monopoles in addition then we would have two independent causes of magnetism.
No, Maxwell's theory can be correct in regions free of magnetic charge, just as [nab].E=0 is true in regions free of electric charge.The Lorentz transformation fully explains the magnetic phenomena as given by Maxwell. If we now have an additional source of magnetism which would give an additional contribution to the magnetic field, the Maxwell equations can no longer be correct.
Is there in fact such a statement? Was it given by Maxwell?you are going to reproduce the "no monopoles" statement of the Maxwell theory
Can you please give us a reference to the corresponding paper of Dirac?Dirac produced an elegant generalized EM theory
Yes, it is [nab].B=0.Originally posted by Albrecht
Is there in fact such a statement? Was it given by Maxwell?
I don't have that reference, but the theory is nicely presented in section 1.4 of this book:Can you please give us a reference to the corresponding paper of Dirac?
The monopole will not disappear, because it is a permanent source of the B field, just as electric charges are permanent sources of the E field. In the Dirac theory, the B field can only disappear under Lorentz transformations if it arises from electric currents. Similarly, In the Dirac theory monopole currents can give rise to E fields that disappear under Lorentz transformations.Again my question: What is about the magnetic monopole which disappears when the observer is in an appropriate motion state. Can this happen?
Thanks for this reference to the EMFT book of Bo Thide.
It is an interesting intellectual exercise to build a complementary pairing of electricity and magnetism, in which the charge is called magnetic and the relativistic side effect is called electric.
It has very surprising logical consequences if we generalise this assumption of complementary charges.
We have to keep in mind that every polar force (so, assumably also the strong force) has it's own "magnetism", as relativity, which is the cause of magnetism, is valid for every force. Should we now assume that also in the case of the strong interaction there is not only this relativistic side effect, i.e. this related kind of a "magnetism" but that there are also monopoles of this related magnetism? If this is generalised, very force has to have besides it's original charge a kind of complementary charge corresponding to the magnetic monopole we are talking about.
Or do we have to assume that the electric force is special compared to the other forces? Do we know a reason why it should be that way?
On the other hand, do we know whether this "magnetic force" of the magnetic monopole, which would (if existing) be additional to the normal magnetic field, would interact with our existing electromagnetic world? Before we investigate this monopole charge by an experiment, we cannot know. To be serious we have initially to assume that it is some kind of a new "fifth force" if it should exist.