B Further Understanding Simultaneity Conventions

[Ibix]

In the earlier thread linked in the OP, he notes that not all physicists restrict themselves to conventions that forbid timelike (or lightlike) conventions.

You can, of course, use coordinate systems that do not have spacelike coordinate planes. Lightcone coordinates have been mentioned by at least two of us. But you would not call any of their coordinate planes "planes of simultaneity". (Not deliberately anyway - people have been known to make mistakes.)

As I said above, a simultaneity condition implies a coordinate system, or at least part of one. But a coordinate system does not necessarily imply a simultaneity condition.

 

[vanhees71]

Light-cone coordinates happen to be identical to the asymptotic coordinates of a hyperbola, with the corresponding squeeze mappings (=Lorentz transformations) being essentially known for thousands of years (Apollonius of Perga, ca. 200 BC).

Yes, and this makes the "hyperbolic" motion such a difficult issue concerning the question "does a hyperbolically moving charged particle radiate" ;-)).