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I just finished my first upper-division E&M course and have a question. Why do the electric field and the magnetic field have different units if they are essentially rotations of each other? Moreover if the same particle, the photon is the force carrying particle in QED how can they have different units. Thank you!

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  • $\begingroup$ In cgs units and units with $c=1$ they do have the same units $\endgroup$ – Kyle Kanos Sep 13 '18 at 22:39
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    $\begingroup$ In CGS or even using the SI, $E=cB$...Thus, no difference...The issue is the system of units... $\endgroup$ – riemannium Sep 13 '18 at 22:40
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    $\begingroup$ As an analogy, time and space have different units as well even though Lorentz boosts are (hyperbolic) rotations of space-time. $\endgroup$ – enumaris Sep 13 '18 at 22:41
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That is only an issue of the system of units you are using. In natural units $c=1$ and $E$ and $B$ have the same units, as $E=cB$, so dimensionally $E=B$ "naturally".

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  • $\begingroup$ where does $E = cB$ come from? $\endgroup$ – Larry Harson Sep 13 '18 at 23:05
  • $\begingroup$ but you don't even need natural units to have identical units for electric and magnetic fields. you need them in the Gaussian units convention. $\endgroup$ – robert bristow-johnson Sep 13 '18 at 23:08

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