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## Main Question or Discussion Point

It is customary, when discussing a particle's motion through spacetime, to talk about its path [itex] x^{\mu}(\lambda) [/itex], where [itex] x^{\mu} [/itex] are the the spacetime coordinates of the particle in some frame, and [itex] \lambda [/itex] is some parameter. I have a doubt regarding this parameter. Everywhere I've looked, people seem to say "this parameter can, for example, be the particle's proper time [itex] \tau [/itex]". And then they proceed to, for some reason,

Thanks in advance.

**only**use this very specific example (proper time) as the parameter for the particle's path (or any parameter of the form [itex] \tau'=a\tau+b [/itex]). So my question is: are there any other physically distinct parameters that can be used? (By physically distinct I mean something that isn't of the form [itex] a\tau+b [/itex]; that doesn't rely on the proper time.) If so, why is it that the proper time is almost always used?Thanks in advance.