Invariant quantities in the EM field

  • Thread starter Mentz114
  • Start date
Mentz114
Gold Member
5,424
290

Main Question or Discussion Point

I understand that the quantities

[tex]E^2 - B^2[/tex]

[tex]\vec{E} \cdot \vec{B}[/tex]

(the dot is vector inner product).
where E and B are the electric and magnetic components of an EM wave,
are invariant under Lorentz/Poincare transformations.
Can someone explain the physical significance of this ? Is either quantity related to the velocity of light ( or the invariance of the velocity of light ) ?

The second expression must be zero at all times surely ?
 
Last edited:

Answers and Replies

dextercioby
Science Advisor
Homework Helper
Insights Author
12,965
536
I understand that the quantities

[tex]E^2 - B^2[/tex]

[tex]\vec{E} \cdot \vec{B}[/tex]

(the dot is vector inner product).
where E and B are the electric and magnetic components of an EM wave,
are invariant under Lorentz/Poincare transformations.
Can someone explain the physical significance of this ? Is either quantity related to the velocity of light ( or the invariance of the velocity of light ) ?

The second expression must be zero at all times surely ?
Not necessarily wave. An EM wave is just a particular case of a radiated EM field. That's why the scalar product is not always 0, because the radiated EM field is not always a wave.

There's not too much physical significance of the invariants, just that the first one is good for a lagrangian density since it leads to field equations second order in time.

Daniel.
 
Mentz114
Gold Member
5,424
290
Thanks, Daniel.

I didn't know there are solutions to Maxwells equations other than the EM wave.

It's hard getting my head around the idea that the E and B fields 'mix' like space and time, when boosted.
 

Related Threads for: Invariant quantities in the EM field

  • Last Post
2
Replies
30
Views
2K
Replies
8
Views
6K
Replies
6
Views
774
Replies
9
Views
3K
Replies
0
Views
400
Replies
3
Views
588
Top