If the definition of simultaneity is given from a moving system, the spherical surface will result when Einstein's definition with є = 1/2 is used, s… - Hans Reichenbach

Light signals alone provide the metrical structure of the four-dimensional space-time continuum. The construction may be called light axioms.

...the famous assertion by Einstein that the length of a rod depends on its velocity and on the chosen definition of simultaneity. ...is based on the fact that we do not measure the length of the rod, but its projection on a system at rest. How the length of the projection depends on the choice of simultaneity can be illustrated by reference to a photograph taken through a focal-plane shutter. Such a shutter... consists of a wide band with a horizontal slit, which slides down vertically. Different bands are photographed successively on the film. Moving objects are therefore strangely distorted; the wheels of a rapidly moving car for instance, appear to be slanted. The shape of the objects in the picture will evidently depend on the speed of the shutter. Similarly, the length of the moving segment depends on the definition of simultaneity. One definition of simultaneity differs from another because events that are simultaneous for one definition occur successively for another. What may be a simultaneity projection of a moving segment for one definition is a "focal-plane shutter photograph" for another.

If E₁ is the cause of E₂, then a small variation (a mark) in E₁ is associated with a small variation in E₂, whereas small variations in E₂ are not associated with variations in E₁. If we wish to express even more clearly that this concept does not contain the concept of temporal order, we can express it in the following form, where events that show a slight variation are designated E*: E₁E₂, E₁*E₂*, E₁E₂* and never the combination E₁*E₂.