[Phys-L] Re: frame independence

[John Denker <jsd@AV8N.COM>]

A clarification is in order.

  -- In general, the dot product between two vectors is a scalar.
  -- In D=3, any such dot product is invariant under rotations.
   Homework:  prove this.
  -- In D=1+3 spacetime, any such dot product is invariant under
   rotations *and* boosts.  Homework:  prove this.

As Moses F. correctly pointed out, in D=3 a dot product such as
V dot Xhat is not invariant under boosts.  OTOH if we re-interpret
V and Xhat as four-vectors, then V dot Xhat *is* frame-independent.

The last sentence of my previous note was just plain wrong.  The
example I gave works fine in spacetime, but not in Euclidean space.
Sorry.
   http://lists.nau.edu/cgi-bin/wa?A2=ind0511&L=phys-l&P=27859
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