## 8. Further Improvements

Our presentation of Maxwell's equations can be enhanced by rescaling the units of the electric field.

Everything gets even simpler, more beautyful, of higher symmetry, ...

- We define
**E**=**E**_{new}:=**E**_{old}/ c . So**E**and**B**are dual, no longer**E**and c·**B**.

**E**and**B**now have the same units 'Tesla'. - We divide both matrices F and M by c and ( with the new definition of
**E**) we have

No factor c needed any longer. - c disappears in the law of the electromagnetic force, too: ( german 'statt' means 'instead of' )

- Maxwell's equations get slightly simplified:

- The determinants of F and M get rid of the factor c
^{2}: Newly we have det(F) = det(M) = – (**E**·**B**)^{2} - The poduct of our matrices reduces to F·M =
**(E**·**B)**· Id - The other invariant is simplified to
**E**^{2}–**B**^{2}, and we have det (F + M) = det (F – M) = – (**E**^{2}–**B**^{2})^{2} - The equations describing the transformation of the components of
**E**and**B**under a Lorentz boost get completely symmetric now:

Earlier we had v instead of beta on the left side and v/c^{2}instead of beta on the right side! The 'duality' of the**E**and**B**field is completely established now ! ( beta = v/c ) - Of course, all this simplifications and enhancements of symmetry follow, if you change the units of space and time in a way the speed of light reduces to 1 (without any units). Long ago C.F. Gauss has made an even more radical suggestion: Change the units of the electric and the magnetic field in a way that both constants e
_{0}and µ_{0 }reduce to 1 ! Hence c will be equal to 1, too, and in our notation of Maxwell's equations µ_{0}will disappear (point 4 above).

The redefinition of**E**following point 1 above is just the*most minimal*operation to achieve the intended goal.