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2) Angular momentum = velocity cross position
This is better, because the rotation invariance is now
manifest. The law is written without mentioning anybody's
coordinate system.
However, the physics has a left/right symmetry that is
not manifest. You can't draw the cross product without
invoking a Right-Hand rule. But I emphasize that the
physics is still left/right symmetric!!!! The law is
just written in a misleading form.
3) Angular momentum = velocity wedge position
Of course the wedge product is manifestly rotationally
invariant, so we're OK in that department, too.
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To summarize:
++ writing a cross product or wedge product is better
than writing out the components, because the product
is manifestly rotationally invariant, whereas the
components are not.
-- the cross product doesn't exist in D=2
-- the cross product conceals the left/right invariance
of the real physics in D=3
-- the cross product is almost never what you want
in D=1+3 spacetime.
++ the wedge product works just fine in D=2, D=3, and
D=1+3. It looks the same and means the same in all cases.
++ The wedge product allows a left/right symmetric law
to be written in a way that looks left/right symmetric.
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