1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Em field 6 degrees of freedoms & 4-potential

  1. Dec 11, 2013 #1

    kye

    User Avatar

    What does it mean that the electromagnetic field strength includes six degrees of freedom (three for the electric field strength, three for the magnetic field strength), whereas the four-potential includes only three degrees of freedom (two for the photon, one for the Higgs boson)? What is the four-potential? Why isn't it adjusted to be able to encompass 6 degrees of freedom too?
     
  2. jcsd
  3. Dec 11, 2013 #2
    You don't really have 6 degrees of freedom... You can't just arbitrarily pick all the electric and magnetic field components and expect them to satisfy Maxwell's equations. As a simple example, suppose [itex]E_x(x,y,z,t) = cos(\omega t + k z) [/itex] and set everything else to zero for all space and time ([itex]E_y = E_z = B_x = B_y = B_z = 0[/itex]). Those particular electric and magnetic fields are not allowed by Maxwell's equations. Specifically, if you plug them into Faraday's law
    [tex]\vec{\nabla}\times\vec{E} = -\frac{\partial \vec{B}}{\partial t}[/tex]
    you'll find that the left hand side is non-zero while the right hand side is zero, which is obviously a contradiction. There's no charge density/current density combination I can pick which will give me those particular fields.

    So you don't really have 6 degrees of freedom because not all combinations of [itex](E_x, E_y, E_z, B_x, B_y, B_z)[/itex] are allowed. They need to satisfy Maxwell's equations.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Em field 6 degrees of freedoms & 4-potential
  1. Degree of freedom (Replies: 9)

  2. Degrees of freedom (Replies: 7)

  3. Degrees of Freedom (Replies: 3)

  4. Degrees of freedom (Replies: 2)

Loading...