Editing Special relativity (section)

==== 4D spacetime ====

If we extend this to three spatial dimensions, the null geodesics are the 4-dimensional cone:
<math display="block"> ds^2 = 0 = dx_1^2 + dx_2^2 + dx_3^2 - c^2 dt^2 </math>
so
<math display="block"> dx_1^2 + dx_2^2 + dx_3^2 = c^2 dt^2. </math>

[[File:Concentric Spheres.svg|thumb|Figure 10–3. Concentric spheres, illustrating in 3-space the null geodesics of a 4-dimensional cone in spacetime.]]
As illustrated in Fig.&nbsp;10-3, the null geodesics can be visualized as a set of continuous concentric spheres with radii&nbsp;=&nbsp;''c&nbsp;dt''.

This null dual-cone represents the "line of sight" of a point in space. That is, when we look at the [[star]]s and say "The light from that star that I am receiving is ''X'' years old", we are looking down this line of sight: a null geodesic. We are looking at an event a distance <math display="inline">d = \sqrt{x_1^2 + x_2^2 + x_3^2} </math> away and a time ''d''/''c'' in the past. For this reason the null dual cone is also known as the "light cone". (The point in the lower left of the Fig.&nbsp;10-2 represents the star, the origin represents the observer, and the line represents the null geodesic "line of sight".)

The cone in the −''t'' region is the information that the point is "receiving", while the cone in the +''t'' section is the information that the point is "sending".

The geometry of Minkowski space can be depicted using [[Minkowski diagram]]s, which are useful also in understanding many of the [[thought experiment]]s in special relativity.