The very basic thing is the non-euclidean geometry.
One approach, not much used, is to define the time component as imaginary so that its square is automatically of opposite sign. The usual method using g is a bit more machinous but keeps things more "real"
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Apart from the distinction of indices as being co or contra, Lorentz covariance is basically the same as Euclidean covariance. If the two sides of the equation are of the same type, it holds in all coordinates. If instead you propose an equation in which mass depends on some function of the x component of some vector, people are gonna ask "Hey, but in whose coordinates?". There's not more to it but it's so "obvious" that professors don't always spell it out very well!!!
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Inutil insegnŕ al mus, si piart timp, in plui si infastiděs la bestie.
Hypography Forum PITA...... er, Administrator.
