[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: starship-design: The speed of now
Zenon Kulpa writes:
> > From: email@example.com (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
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.