Just wondering about the definitions and usage of these three terms.
To my understanding so far, "covariant" and "form-invariant" are used when referring to physical laws, and these words are synonyms?
"Invariant" on the other hand refers to physical quantities?
Would you ever use "invariant" when talking about a law? I ask as I'm slightly confused over a sentence in my undergrad modern physics textbook:
"In general, Newton's laws must be replaced by Einstein's relativistic laws...which hold for all speeds and are invariant, as are all physical laws, under the Lorentz transformations." [emphasis added]
~ Serway, Moses & Moyer. Modern Physics, 3rd ed.
Did they just use the wrong word?