I have struggled to follow the explanation of this Unit as there seems to be an inconsistency that I cannot understand! Throughout the introductory sections of Unit 30 it was established that if the invariant interval between two events on a space-time diagram given by the condition: −(c∆t)2 + (∆x)2 is 0 then they can’t, they are causally disconnected if =0 then they are at a causal boundary However throughout the exercises (30.5) and the problem (30.6) it was stated that the invariant interval was given by: ∆t2 − ∆x2 and that if the resultant value: is 0 the events can be causally connected if =0 the events are at a causal boundary Nevertheless I did follow the initial version for the invariant interval to a correct conclusion.

Sadly my text (above) became scrambled when I copied it across! However, I am now more enlightened - the original definition of the invariant interval (when c = 1) does readily transpose into (△t)² - (△x)² but, of course, the outcome must also be transposed. So a negative value (less than 0) that relates to a potential causal connection in the original definition becomes a positive value (greater than 0) for a potential causal connection in the transposed version :-)

Timelike, spacelike, lightlike separations. The sad life of a photon actually being invariant. Study group diagram- https://3.bp.blogspot.com/-VQ7YE-yOZEU/W4fGXHkrdSI/AAAAAAAAAOY/9COvSw90lm8j1oQ9wXZRP3u5n29o0gSPgCLcBGAs/s1600/Causally%2BConnected%2Bspacetime%2Bdiagram.PNG