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Reading the book called "The great design particles fields and creation" one finds the following paragraph

In a universe like ours, constructed of electrically charged elements, magnetism and the magnetic field can be considered a relativistic consequence of the electric field. If the speed of light were infinite, or if all charges moved very slowly, there would be no magnetic field and no magnetism. But in the universe we live in, where the speed of light is finite and electrical charges do move, magnetic fields accompany electric fields. The other vector fields associated with weak and strong nuclear forces have similar magnetic counterparts that derive from relativistic effects

Questions

  • Does gravity have such a counter part?

  • if not why, if yes what is it called?

  • The book does not explain why such a speed limit produces magnetic fields, can some one explain?

Qmechanic
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Thulashitharan D
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    It may interest you https://en.wikipedia.org/wiki/Gravitoelectromagnetism – Rob Tan Aug 05 '20 at 07:37
  • The reason why the book does not answer those question is quite simple: there is no answer to those questions (yet) which currently allow verification by experiment. If anyone finds them or makes a considerable contribution towards it, it might be eligible for a nobel price. the hopes lie in finding a theory of quantum gravitation. – planetmaker Aug 05 '20 at 08:04
  • @planetmaker "This book does not tell why such a speed limit produces magnetic fields can some one explain that also?" I dont think it is a very hard question i am asking explanation of magnetic field wrt relativity and electric field – Thulashitharan D Aug 05 '20 at 08:19
  • @Thulashitharan that is an entirely different question to me. And can be answered by going through the Maxwell equations in a relativistic context which shows that there are a few invariants. https://en.wikipedia.org/wiki/Maxwell%27s_equations#Relativistic_formulations – planetmaker Aug 05 '20 at 08:36
  • If c is infinite then the rest energy would be infinite, so mass must be zero hence everything would move at infinite speed. Just another example of how you can arrive at absurd conclusions by fiddling with c. – my2cts Aug 05 '20 at 10:27
  • @my2cts .......some thing feels wrong......if c is infinite $E=mc^2$ wont be valid right.That eqn is defined based on assumption that c is constant am i right? – Thulashitharan D Aug 05 '20 at 11:53
  • @my2cts: “Souriau massless Galilean particle” is pretty much what you are describing (without the “everything” part). And it is not absurd, the limiting procedure could be made quite rigorous. – A.V.S. Aug 05 '20 at 19:31
  • If "all charges moved very slowly" there would be no current, so no electromagnets but there would still be electron spin and ferromagnetism. It is risky to fiddle around with fundaments. – my2cts Aug 05 '20 at 19:46
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    Possible duplicates: https://physics.stackexchange.com/q/128650/2451 Related: https://physics.stackexchange.com/q/553313/2451 – Qmechanic Aug 06 '20 at 15:46
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    This video may explain what you are looking for, how a magnetic field is produced through relativistic effects: https://www.youtube.com/watch?v=1TKSfAkWWN0&t=150s – Nickpick Aug 08 '20 at 08:59
  • @Nickpick thank you very much.That video and minute physics's follow up video resolved all my doubts. – Thulashitharan D Aug 08 '20 at 10:42

1 Answers1

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The physical laws should be stated in a Lorentz invariant way via the tensor formalism. If so, the electromagnetism is described by an electromagnetic four-potential $A^\mu$, a Lorentz covariant four-vector, from which the electromagnetic field can be derived as the electromagnetic tensor $F^{\mu \nu} = \partial^\mu A^\nu - \partial^\nu A^\mu$. The components of the electromagnetic tensor are the electric and magnetic fields which transform into each other in a Lorentz covariant way.

If in a reference frame you have only an electric field, in another reference frame you may experience a magnetic field as well.

To say "... if the speed of light were infinite ...", physically is like to say that the relative speed between different reference frames is infinitesimal, i.e. no relative motion. That is why in the above example you would not experience a magnetic field.

Similar considerations apply to other tensors describing other forces.

Michele Grosso
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