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The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

The special theory of relativity is an extension of 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. ).

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

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

An alternative formulation of Special Relativity is that of Minkoswski, which unifies space and time into a single (affine) vector space, called . 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

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 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 .

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 .

When the curvature of spacetime becomes dynamical, the resulting theory goes under the name of . 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 . The resulting theory, called , is the most accurate one known to mankind.

External resources

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