Astrofiend
Nov2-09, 07:39 AM
I've been studying relativity and standard model physics, and I don't understand how it is determined what 'things' go together to form a 4-vector. For example, there is the familiar energy momentum 4-vector, the charge-current density four vector, the phi-A (scalar/vector potential) 4-vector from electromagnetism, the frequency-wavevector four vector from special relativity, and so on and so forth.
Apart from the fact that these quantities evidently DO transform as four-vectors, is there some first principle argument that shows what quantities will go together to transform as a four-vector, like say in quantum mechanics where non-commuting operators indicate the existence of an uncertainty relation between quantities? Like how would you know that charge density and current density would form components of a 4vector and transform like one?
Apart from the fact that these quantities evidently DO transform as four-vectors, is there some first principle argument that shows what quantities will go together to transform as a four-vector, like say in quantum mechanics where non-commuting operators indicate the existence of an uncertainty relation between quantities? Like how would you know that charge density and current density would form components of a 4vector and transform like one?