Re: starship-design: The speed of now

[Steve VanDevender <stevev@efn.org>]

Zenon Kulpa writes:
 > > From: wharton@physics.ucla.edu (Ken Wharton)
 > > 
 > [...]
 > > That value is D = [t ^ 2  -  x ^ 2].  The distance between any two 
 > > events, measured in terms of D (where t is the time-separation in 
 > > seconds and x is the distance separation in light-seconds) will be 
 > > identical in all frames.  
 > > 
 > As far as I remember it should be D = x^2 - t^2
 > (or rather:  D = x^2 + (it)^2, where i = Sqrt(-1)).
 > Or am I wrong?

This is partly a matter of convention.  You can choose either metric
((t^2 - x^2) or (x^2 - t^2)) as long as you're consistent.  _Spacetime
Physics_ by Taylor and Wheeler uses (t^2 - x^2), which I happen to like
because it's more computationally convenient for some purposes.
_Gravitation_ by Misner, Thorne and Wheeler uses (x^2 - t^2) (well, the
4-d version (x^2 + y^2 + z^2 - t^2)), and also includes a large
conversion chart showing the sign choices used by various authors, which
also indicates there apparently hasn't been much widespread agreement on
sign conventions.

The (x^2 + (i*t)^2) form has fallen into disfavor.  There's a sidebar in
_Gravitation_ where the authors explain why they don't like it.  It's
another attempt to make things computationally convenient but is
somewhat conceptually misleading.