Space and Time Diagram

This diagram represents the external metric structure for any collection of objects, such as a ticking clock.

On the left side is the familiar space-time diagram of special relativity, showing light cones for the past and future. On the right side is the corresponding real space diagram, showing regions for external wave function expansion, which defines the forward sense of time. These are before the wave function collapse (at time 0) and afterwards.

The Cartesian axes shown correspond to the rest frame (of the collapse): the axes in green correspond to a moving frame. Space and time axes (intervals) are always locally orthogonal (ds·dτ = 0), so the same Lorentz transformation must be applied in both metric spaces (see The twin paradox).

The diagram above also describes internal activity, within confined matter (but here the axes represent proper length and proper time intervals and the inaccessible regions are absent). Here, heat energy expands in internal real spaces, describing the thermodynamic arrow of time. The same time sense is selected in both cases.

Robert Herrod
Örkelljunga, Sweden, April 2022