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Mathematics for Physics

191 Principle of Relativity

The postulate that the laws of physics take the same form in every inertial frame, so there is no preferred absolute state of rest.

(\(c = \text{constant in all inertial frames}\)).

The first postulate of special relativity. The laws of physics take the same mathematical form in every inertial frame. A law of physics is a relation that holds for nature. This principle is used to show that no inertial frame is a preferred state of rest.

The equivalence of inertial observers. Two observers in uniform relative motion are equivalent. Uniform relative motion is motion at constant velocity of one observer with respect to the other. This principle is used to treat only relative velocity as a measurable quantity.

The extension of relativity to electromagnetism. The same requirement applies to electromagnetism and to light, not only to mechanics. An electromagnetic field is a physical influence throughout space that exerts electric and magnetic forces. This principle is used to keep Maxwell’s equations in the same form after a change of inertial frame.

Coordinate covariance. Equations that state the laws of nature must stay covariant under a change of coordinates. Covariance is the property that the form of an equation is unchanged by that change of coordinates. This principle is used to write laws that do not depend on which inertial grid an observer chooses.

Note: Also called Einstein’s principle of relativity.

191.1 References

  1. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — source for the heading explanation.
  2. Griffiths, D. J. Introduction to Electrodynamics. Cambridge University Press, 2024. — laws of physics have the same form in every inertial frame; Maxwell’s equations included.
  3. Shankar, R. Fundamentals of Physics I. Yale University Press, 2019. — equivalent observers in uniform relative motion.
  4. Emam, M. H. Covariant Physics. Oxford University Press, 2021. — covariance of the laws under coordinate transformations.