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**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.