Light cones for reasoning about space and time

Post Einstein children deserve access to a post Newtonian model of space and time, allowing access to the best that physics can offer in a way of thinking about the most fundamental elements of our environment.

Here I sketch out an approach to a two-week long teaching sequence to illuminate some of the central insights of Special and General Relativity based on reasoning with light cones. Light cones are developed as a representation based on the two postulates of Special Relativity and then used to illustrate the slower ticking of clocks in a gravitational field based on physical evidence rather than on the metric(judged too complex derive from Einstein's field equations). The aim is to illuminate and reify rather than to prove – much like current approaches to teaching Newtonian mechanics.

For Einstein there are a multiplicity of local witnesses only. There is no global witness to who we can appeal for a privileged point of view. The model of space and time instructs one witness(a watcher) in the procedures to be followed to reconstruct an accurate picture of what another witness will view. These transformations are more complex than the Galilean, but the principle is the same: to achieve reliable intra-subjective knowledge you need to be able to figure out what others will notice and record from what you notice and record. Establishing this epistemological understanding, based on operationalised measures, is best expressed using a local, rather than global geometry. Choose a point of view: Alice, Bob or Charlie. Any of these three could be a witness, local to the phenomenon, or a watcher, not local to the phenomenon. Both watchers and witnesses experience the same physics, but for the watcher to figure out what the witness notices and records from what they notice and record turns out to redefine common sense.

That’s the reason for the focus on the light cone, which shows the structure of space and time and therefore the causal structures of the universe: which happenings can affect or be affected by other happenings.