Lorentz Electromagnetic Field Invariants

The electromagnetic field transforms under a Lorentz boost. The quantities B² - E² and E · B are Lorentz invariants, meaning they take the same value in all inertial frames.

Experiment

You can use the interactive module to explore these transformations and discover the cancellation frames. Follow these steps:

1. Set Electric y to 1 and Magnetic z to 2.
2. Set Boost beta to 0.5.
3. Observe that the Transformed electric y becomes exactly 0, showing that a frame moving at β = E/B cancels the electric field.
4. Change Electric y to 2 and Magnetic z to 1. The field is now electric-dominated.
5. Change Boost beta to 0.5. Now, the Transformed magnetic z becomes 0, because β = B/E cancels the magnetic field.
6. Set both to 1 to observe a null field where no subluminal frame can cancel either field.

Link to the interactive module: Lorentz Electromagnetic Field Invariants