The special theory of relativity is an extension of classical-mechanics that describes the motion and dynamics of objects moving at significant fractions of the speed of light.

In Einstein's original 1905 formulation, The postulates of Special Relativity are that

• The Principle of Relativity is that the laws of physics are the same in every inertial reference frame (cf. reference-frames).

• The Speed of Light is the same in every reference frame (cf. speed-of-light).

In Special Relativity, the Galilean transformations are replaced with the Lorentz transformations, which form the Lorentz group (cf. lorentz-symmetry).

An alternative formulation of Special Relativity is that of Minkoswski, which unifies space and time into a single (affine) vector space, called spacetime. From the postulate that the spacetime interval between any two points is independent of the frame of reference, the Lorentz transformations can be derived.

Kinematics

The postulates of Special relativity, either in the form originally postulated by Einstein or in the geometric reformulation of Minkowski, have several consequences that usually challenge the intuition we have developed from our interaction with the non-relativistic world. Some prominent examples are

• The loss of an absolute concept of simultaneity.

• time-dilation and length-contraction.

Dynamics

The equations of motion for point particles, analogous to Newton's equation, are postulated to be $$ \dot p^\mu=F^\mu $$ where the dot denotes differentiation with respect to proper time.

From this equation, together with some kinematical considerations, one may derive, for example, the well-known mass-energy equivalence principle.

The force $F^\mu$ in the equations of motion is a force field which may depend, in principle, on the position, momentum and proper time of the test body. One of the most important examples of such a force field is the one given by the laws of electromagnetism.

General relativity

The geometrical picture of spacetime admits a straightforward generalisation to curved manifolds. One readily discovers that such a formalism allows us to naturally introduce gravitation into the picture in a way that is manifestly independent of the observer and that respects the equivalence-principle.

When the curvature of spacetime becomes dynamical, the resulting theory goes under the name of general-relativity. It is, as of today, the most accurate description of gravitational phenomena that we know of. When the gravitational field is absent, it reduces to special relativity.

Quantum mechanics

It is possible to combine the postulates of special relativity with those of quantum-mechanics. The resulting framework, called quantum-field-theory, is the most accurate one known to mankind. Examples of quantum field theories (and hence of applications of Special Relativity) include, but are not limited to, quantum-electrodynamics, quantum-chromodynamics, the standard-model of particle-physics, among many others.

External resources

• Galileo and Einstein is a free ebook used as a text for a history of science course. Chapters 23 through 30 discuss special relativity in a very pedagogical manner. Chapters 21 and 22 discuss the speed-of-light and the Michelson-Morley experiment, and help put special relativity into its historical context.
• A.P. French, Special Relativity is a short book treating just special relativity. It includes historical background.
• Kleppner and Kolenkow, An Introduction to Mechanics discusses relativity in chapters 11 through 14. It begins by deriving the Lorentz transformations from mechanical considerations. It also introduces relativistic momentum, four-vectors, and invariances in relativity.
• Marion and Thorton, Classical Dynamics of Particles and Systems also introduces relativity from mechanical considerations, in chapter 14. This text also discusses four-vectors, and introduces the lagrangian-formalism of special relativity.
• E. M. Purcell, Electricity and Magnetism is an introductory book in electromagnetism. Chapter 5 uses special relativity to derive the existence of magnetic-fields and the form of the Lorentz force. Appendix A gives a review of special relativity.
• J. D. Jackson, Classical Electrodynamics is a graduate-level book in electrodynamics. Chapter 11 gives a thorough discussion of special relativity, including methods from group-theory. Chapter 12 discusses dynamics and how the lagrangian-formalism and hamiltonian formalism interact with special relativity.