Interesting. A wave front might imply a surface - a boundary - unless the wave is a pulse through a medium. A photon is a pulse: a wave.

If the past is a dimension, then perhaps it too can change, to fit the constraints of the present.

But is the wave a true wave through a medium, or is it a boundary? A wave - a pulse - through a medium has a wave speed that is different from the speed of the pulse. The pulse is the linear combination of all of the composite waves, half of which travel faster than the pulse.

And is there a way to detect this fifth dimension, in which time itself changes?