Tensors and Relativity: Chapter 1

The null cone

next up previous index
Next: Consequences of the Einstein Up: Minkowski spacetime Previous: Minkowski spacetime

 

figure440
Figure 1.9: The lightcone.

Consider a null ray [ for example a light ray propagating in the x direction: then tex2html_wrap_inline1414 , so the null ray represents a particle moving at the speed of light. If we consider 3D Minkowski spacetime then the null rays lie on the surface of a cone [ see Figure 1.9 ]:

 

figure446


Figure 1.10: The views of space and time that I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself and time by itself are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. Hermann Minkowski

 

figure450


Figure 1.11: ict space

Before we look at some of the wonderful consequences of the Einstein postulates, let us return briefly to the Lorentz transformations. If we define tex2html_wrap_inline1418 we can write them in the following way:

eqnarray831

Formally this corresponds to a rotation through an angle tex2html_wrap_inline1420 in (ict,x) space [ see Figure 1.11 ].