An Illustration Of A Path Integral Viewed Through Systemic Functional Linguistics

Penrose (2004: 668):

The most accessible illustration of a path integral is the case of a single point particle moving in some field of force (so the configuration space is now space itself). Here, we consider all the various histories, starting at some spacetime point a and finishing at some other spacetime point b as in Fig. 26.3a. These histories are taken to be continuous spacetime paths winding their way from a to b. We do not require that the path be a ‘legal’ one, according to the rules of special relativity (i.e. that it be constrained to lie within the light cones, as required by classical relativity), nor do we even require that the path proceed entirely into the future. The ‘history’ can wiggle up and down in time if it wants to (Fig. 26.3b)!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, 'all the various histories' constitute the potential of the quantum system. And from this perspective, there is no travelling in time. Time is dimension of the unfolding of processes, such as travelling. A process, and so a particle mediating the process, extends from one location in time to another. Travelling from 1pm to 2pm is extending from 1pm to 2pm, so duration, not motion.