Re: Creation (long)

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Tom Wayburn wrote:

> That makes two of us.   Well, I guess I can forage for a few scraps of
> preverbal cogitation.   In space-time we have replaced distance and
> period of time with the *interval* between two events.   Now, the reason
> we think traveling faster than the speed of light IS SILLY is that the
> interval between two events that lie on the light cone is zero.  I have
> been led to believe that if we traveled a just the speed of light, we would
> arrive at the same instant that we departed.  We can't expect to do better
> than that.   I thought that the interval between two events being zero made
> the departure and arrival at two coordinates separated in a space-like
> way coincident.   Now, I'm not so sure.

Two events with different coordinates on the light cone connected by a null
path are separated by *both* space *and* by time.  Actually the separation in
space equals the separation in time (in units where c = 1).  The actual
amount of this separation in both space and time depends on the particular
Lorentz frame in which these events are observed.  In all such allowed frames
this separation is not zero.  From the point of view of the photon connecting
these two events, however, both of them are coincident because the world of
the photon is two dimensional where all events along its path are coincident
in its own singular instant of proper time and its singular contracted space.

>                                         But, if interval were a metric,
> from the viewpoint of a photon every set of coordinates would seem like
> every other.  In a sense the Universe would have shrunk to a point.

Actually it would have shrunk to a 2-d spacelike surface.  Remember that 
spatial displacements perpendicular to a Lorentz boost are unaffected by
that boost -- even if that boost has the singular limit v --> c.

David Bowman
dbowman@gtc.georgetown.ky.us