Re: A question of discrete space-time.

robert bristow-johnson wrote:
> in article 1117224187.712096.271970@xxxxxxxxxxxxxxxxxxxxxxxxxxxx, Mike
> Helland at mobydikc@xxxxxxxxx wrote on 05/27/2005 16:48:
>
> > Ed Hanna wrote:
> >
> >> Does this make sense, or am I being overly simplistic?
> >
> > I think you're being overly simplistic. For example, your checkerboard
> > looks like:
> >
> >> 1 2 3 4 5 6 7 8 Position
> >> 1 |_o_|___|___|___|___|___|___|___|
> >> 2 |___|_x_|___|___|___|___|___|___|
> >> 3 |___|___|_x_|___|___|___|___|___|
> >> 4 |___|___|___|_x_|___|___|___|___|
> >> 5 |___|___|___|___|_x_|___|___|___|
> >> 6 |___|___|___|___|___|_x_|___|___|
> >> 7 |___|___|___|___|___|___|_x_|___|
> >> 8 |___|___|___|___|___|___|___|_x_|
> >> Time
> >
> >
> > And you say the discreteness of space-time is what implies the speed limit.
> >
> > Whereas I could just as easily do:
> >
> > 1 2 3 4 5 6 7 8 Position
> > 1 |_o_|___|___|___|___|___|___|___|
> > 2 |___|___|_x_|___|___|___|___|___|
> > 3 |___|___|___|___|_x_|___|___|___|
> > 4 |___|___|___|___|___|___|_x_|___|
> > 5 |___|___|___|___|___|___|___|___|
> > 6 |___|___|___|___|___|___|___|___|
> > 7 |___|___|___|___|___|___|___|___|
> > 8 |___|___|___|___|___|___|___|___|
> > Time
> >
> > Demonstrating that the speed limit can be broken in discrete space-time.
>
> not meaning to support this hypothesis (could be crackpot for all i know),
> but if the position cell width were 1 Planck Length and the time cell width
> were 1 Planck Time, would that not imply a speed limit of c and support the
> top diagram over the bottom?
>
> --
>
> r b-j rbj@xxxxxxxxxxxxxxxxxxxx
>
> "Imagination is more important than knowledge."

Dear Robert,

Thank you for your input. The problem with trying to choose between
the top diagram (with no gaps allowed) and the bottom diagram (with
gaps allowed) is that there is no easy way to tell if the rule of "no
gaps allowed" is in some sense a "true" reflection of nature, or if
this rule is being arbitrarily added to a discrete space-time
hypothesis just to counter the otherwise quite valid viewpoint
expressed by the lower diagram.

I.e., are rules being added primarily to "save the theory", or to
develop a logical and self-consistent theory?

In the end, the question cannot be settled without some concrete
testable predictions, which we haven't found yet.

In the meantime, either space-time really is a continuum, in which case
a hypothesis of discrete space-time is purely crackpot speculation,

*or*

space-time really is discrete is some sense, in which case, the fact
that FTL motion is not readily observed might mean that gaps (as shown
in the bottom diagram) are not allowed, or at least not normally
observed.

Too soon to say for sure.

Regards,
Ed Hanna

.