nLab special relativity

Idea

In physics the theory of special relativity describes dynamics in physical spacetime in absence of a field of gravity.

Specifically, it models

• spacetime as a flat time-oriented pseudo-Riemannian manifold:

  Minkowski space;

• trajectories of point particles as timelike curves in Minkowski space.

• the electromagnetic field as a closed 2-form on Minkowski space.

• the Lorentz force exerted by the electromagnetic field on a charged particle as the contraction of that 2-form with the tangent vector of the trajectory of the particle.

If instead of restricting to Minkowski space, spacetime is allowed to be an arbitrary pseudo-Riemannian manifold one speaks of the resulting framework as the theory of general relativity.

Mathematically, special relativity is essentially the theory of Minkowski space as a pseudo-Riemannian manifold, hence equipped with the constant metric tensor which at each point is the bilinear form with signature $(-,+, \cdots, +)$ or else $(+,-,\cdots, -)$ (depending on convention). The null-vectors in this metric characterize the speed of light. The linear isometries of this metric are the Lorentz transformations and the fact that with the Minkowski metric these also preserve, hence, null rays is the mathematical model for the famous phenomenological observation that “the speed of light is the same in all reference systems”.

Related concepts

• speed of light

  Michelson-Morley experiment

• theory (physics)

• electromagnetism

• general relativity, gravity

• relativistic particle

• relativistic field theory

References

See also:

• Wikipedia, Special relativity

On the early history of the idea:

• Galina Weinstein: Max Born, Albert Einstein and Hermann Minkowski’s Space-Time Formalism of Special Relativity [arXiv:1210.6929]