Einstein's famous mass-energy equivalence is also a Pythagorean relationpic.twitter.com/JtXG4VipBD
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if you must know .. special relativity is all about "invariants" .. in Minkowski spacetime the invariants are constructed by contractions with the metric tensor ημν in any two frames pμ*p^μ must be equal (since it's invariant).. this in turn means the green equality must holdpic.twitter.com/kXVUzMSRsL
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In Minkovski space, you have three spatial dimensions, and one time dimension. Instead of having (x,y,z), we have (x,y,z,ct). Analogously, the momentum vector p (spatial) becomes a momentum-and-energy/c vector in this formalism: (p1, p2, p3, E/c). 1/2
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"If you must know..." ...that's why I love this twitter account.Thanks. Twitter will use this to make your timeline better. UndoUndo
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I was used to using the g metric tensor for lowering and raising indexes/changing co- and contra-variant vectors .
@InertialObservr isn’t the \eta tensor used to emphasize the internal metric of a string? Although the invariant is still there of courseThanks. Twitter will use this to make your timeline better. UndoUndo
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The corner stone of the relativistic quantum field theory also if you switch to operators (and use gamma-matrices/Clifford algebras to get rid of the squares) !
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