SPECIAL RELATIVITY

When Einstein proposed his ideas about the nature of light in 1905 the world of physic changed fundamentally. He proposed that the speed of light is always a fix constant independent of the observer and that the measurements of time and distance are the relative properties. The transformation of physical properties from one coordinate system to another needs to incorporate the relative speed between the two systems w.r.t. the light speed. The mathematical methods were developed by Lorentz. Thus, the Lorentz transformation has to be used when transferring data from one observer to another observer. There exist nothing like an absolute time or space reference system like the classical physics assumed. Later these ideas are summarized in Einstein's Theory of Special Relativity. The fundamental principle that

casual effects propagate maximally with the speed of light

has a lot of implications on the mathematical description of our physical world.

The position of an object is not described by 3 coordinates (x,y,z) but by 4 coordinates (x,y,z,ct) with c is the velocity of light and t is the time. Thus time and space are not separated but are connected by the speed of light.

Minkowski Metric

In flat (Euclidean) space, bodies move in a background of space and time. Newton called it absolute space and absolute time. Einstein changed this view radically in 1915 when he completed his general theory of relativity which resulted in a unified 4-dimensional space-time. All distances along a world line are called separations, and they are measured by the metric:

This metric defines flat Minkowski space-time, and is much like Newtons absolute space plus a time dimension (note the sign of the time is negative).

The World Line

The separation defines the allowed kind of world line which can be timelike, spacelike or lightlike. The following space-time diagram sums it up:

All material bodies, or heavy particles, follow a world line which is timelike or inside the cone. Those events which are absolute separated is outside the lightcone, and they have no causal contact. Photons and other ultra-relativistic particles moves at the speed of light, and their world lines lie at the sides of the lightcone. The lightcone is only a 2D analogy of the 3D propagation of light. If light (eg. from a star) propagates in all directions, it defines a sphere with increasing radius as time passes.

Exotic Matter

The normal matter follows timelike paths. Light quants follow lightlike paths. Normal matter can never reach the speed of light. Whereas, light always runs with the same speed, independent of the observer coordinate systems, i.e. the observer's speed. Nevertheless, all the equations hold when switching signs. Thus, some propose Tachyones which follow spacelike paths. Such matter will have always a speed above the speed of light and can never be slowed down to rest.

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