Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Laws of physics in four-vector form. A question.

  1. Dec 14, 2004 #1
    Please explain me in mathematical way, why the laws of physics have to be written in four-vector form to remain unchanged in every inertial frame.
  2. jcsd
  3. Dec 14, 2004 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    The Lorentz interval is invariant. Using the 4-vector form makes the invariance of the Lorentz interval part of the formalism of the description of the laws of physics. It's possible to use other formalisms that don't have Lorentz invariance "built in", so in that sense you don't "have to" write the laws of physics in 4-vector form. It's just very convenient. An alternate description that got the same result would just "hide" the Lorentz invariance, rather than making it manifest.
  4. Dec 14, 2004 #3


    User Avatar
    Science Advisor

    As written, your question is a little too restrictive, I think. There are laws pertaining to electromagnetism, for instance, that can be written in terms of a certain antisymmetric tensor, which is not the same as a four-vector. (It so happens that the tensor in question can be written in terms of derivatives of a four-vector potential, but that's an issue for another day.) Maybe your question should be re-phrased as "Why do the laws have to be written in covariant tensor form?" But then, as pervect has pointed out, they don't absolutely have to be written that way. In fact, for decades electromagnetism used the fields E, D, B, and H, which in fact are three-vectors and three-pseudovectors, and thus are not covariant.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook