Just wondering about the definitions and usage of these three terms. To my understanding so far,...

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?

Expert Solution

These words do have different meanings, this is a general guide to their differences. In different fields they may have slightly varying definitions. I would recommend looking them up to be certain.

Invariant means does not change at all. Everything is the same (whether physical law, quantity or anything). In terms of vectors, invariant is a scalar which does not transform.

Form-invariant means the form does not change, for example the inverse square law, will always be inverse square but the constants may differ.

Covariant, has a specific meaning when relating it to vectors, as it specifies the transformation rules. (This is as opposed to contravariant which is the other one). For more information see wikipedia, towards the end of the Mathematics of four vectors section.

To specifically answer your question on the phrase, Einsten's relativistic laws are invariant under Lorentz transformations, the laws don't change at all. The constants don't change, neither does the form.

genius_generous answered 6 months ago

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