GEM Blog 33: Sixth Snarky Puzzle Answers

This is a dramatic reading of "Sixth Snarky Puzzle Answers", a blog by the Stand-Up Physicist available at Science20.com. There was a minor controversy about one of the problems. There are two known Lorentz invariant quantities made up of the EM fields E and B: B^2 - E^2 and E.B. The hypercomplex gravity proposal has similar fields and a similar sorts of expressions, e^2 - b^2. In the puzzle, I asserted that was invariant. Well, it is not.

I set up a math experiment to test the hypothesis. If something is invariant under a Lorentz transformation, then its value will be the same under a 3D rotation or a boost. I created a Mathematica notebook to do the detailed work of rotations and boosts. There were plenty of controls on the tools themselves since the simple combinations are known to be invariant under a Lorentz boost. The work confirmed that both B^2 - E^2 and E.B are Lorentz invariants, but e^2 - b^2 is not.

Is breaking Lorentz symmetry a deadly result for the hypercomplex gravity proposal? General relativity also breaks Lorentz symmetry. This is a good thing.

Category:

Science & Technology

Tags:

• Science20
• Lorentz
• boost
• 3D
• rotation
• Snarky
• Puzzle
• answers
• GEM
• hypercomplex
• quaternions