🚀 go-pugleaf

In article <1989Jan24.121432.3544@cs.rochester.edu>, dietz@cs.rochester.edu (Paul Dietz) writes:
> In article <8901241509.AA20873@NMSU.Edu> space-request+@ANDREW.CMU.EDU writes:
> >Those who find this FTL talk interesting will want to see this month's
> >Discover magazine, which has the cover story "Beyond Einstein".  It
> >contains some fascinating reference to tachyon theory, etc.  Nothing
> >for the hard-core physicist, but easy reading, at least.
> 
> It would be amusing indeed if someone discovered tachyons and used
> them in a reaction drive.
> 
(Prior apologies for any notable discrepancies in what I am about to
say--it has been 9 years since I took relativity, and I am trying to
quote from memory)

Now that the disclaimer is out of the way, let me briefly describe the
work of Minkowski on relativity.  If we consider a 2-dimensional space-time,
with coordinates x and t, then the region of the coordinate system we can
get to is a cone, described by t<0 and |x| < t, assuming that the equations
for relativity are valid (and there is certainly no reason TO DATE to doubt
those equations).  However, if we multiply the mass of an object by i, and
carefully manipulate the equations, we find that the slowest that an object
can go is c, and that the permitted region of the space-time plane is now
bounded by t > 0 and |x| > t.  Moreover, the new, 'imaginary' plane can be
viewed as a permutation of the original 'real' plane.  Using this permutation,
it can be shown that the 'imaginary' permitted region corresponds exactly to
the 'real' region with x > 0 and |t| < x.  I.e. changing the mass to an 
imaginary quantity can permit FTL travel in the 'real' space-time.  Nothing
earth-shaking about this.  We just created a tachyon.

Now for the fun part.  If we assume that space-time, mass, velocity, etc.
are complex quantities, then normal space that we perceive is merely the
real part of space-time.  Further, if we assume this 8-D structure is folded
on itself such that Re(x) corresponds to the Im(y) axis, etc, then it is 
mathematically possible to show that Minkowski's transformation holds, and
all the equations of special relativity are satisfied with the set of
complex masses, velocities, momenta, and coordinates.

What, you may be asking yourself, does this have to do with sci.space?
Well, not a lot really.  It just happens to be one of my favorite things
to throw out whenever FTL discussions come up.  Besides, someone might
someday discover what 'i' really is, and find out that this postulation is
correct.  (Of course, by then I'll probably be dead, so it won't do me any
good.)


Norman Kluksdahl              Arizona State University
            ..ncar!noao!asuvax!enuxha!kluksdah

standard disclaimer implied