Re: A question of discrete space-time.

Mike Helland wrote:
> 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.
>
> You may say "Yes, but that's because you moved more than one space per
> time, that's illegal".
>
> In which case, you might be exactly correct that I've broken the rules
> of the system you've created, but I think that demonstrates that
> discrete space-time does not necessarily imply a speed limit, but
> instead your rule that you can only move so far so fast *is* an explict
> statement of a speed limit.

Dear Mike,

Thank you for your well-reasoned reply. I agree with what you've
written as it stands, but I would like you to consider another factor
that I left out when I wrote "I've tried to keep the setup simple, and
I've left some stuff out" in the original posting.

(Let me also explain that I am not trying to create a system of rules
to block people's objections, so much as I am trying to discover what
the universe might be like if it really were a discrete space-time, and
see how far this basic hypothesis can take us.)

I'm uncomfortable with any unit particle diagram that has gaps in its
world-line for two reasons. The first is that if a unit particle could
have gaps in position (i.e., jump around like a knight on a chess
board), it might just as easily have gaps in time, like this:

_1_ _2_ _3_ _4_ _5_ _6_ _7_ _8_ Position
1 |_o_|___|___|___|___|___|___|___|
2 |___|___|_x_|___|___|___|___|___|
3 |___|___|___|___|_x_|___|___|___|
4 |___|___|___|___|___|___|___|___|
5 |___|___|___|___|___|_x_|___|___|
6 |___|___|___|___|___|___|___|___|
7 |___|___|___|___|___|___|_x_|___|
8 |___|___|___|___|___|___|___|___|
Time

Which makes me wonder where the unit particle is at time-4 and time-6.

The second reason is that if there were another nearby unit particle
with its own gaps, they might do something like this:

_1_ _2_ _3_ _4_ _5_ _6_ _7_ _8_ Position
1 |_o_|___|_o_|___|___|___|___|___|
2 |_x_|___|_x_|___|___|___|___|___|
3 |___|___|___|___|_x_|___|___|___|
4 |___|_x_|___|___|___|___|___|___|
5 |___|___|___|_x_|___|_x_|___|___|
6 |___|___|___|___|___|___|___|___|
7 |___|___|___|___|_x_|___|_x_|___|
8 |___|___|___|___|___|___|___|___|
Time

In this case there would be no logical world line connecting a unit
particle from moment to moment, creating an awful mess.

For these two reasons, I'm guessing that the universe does not allow
gaps, but this is just a postulate #2, that motion in a discrete
space-time lattice is a contiguous world line with no duplications or
gaps.

As you wrote, this postulate is an explict statement of a speed limit,
but it was not intentionally introduced to make the theory fit the
facts, so much as to avoid the ugly complications that arise with the
two examples I gave, and because this requirement just makes sense to
me.

And by the phrase "with no duplications", I mean the following where
there are two unit particles at time-3:

_1_ _2_ _3_ _4_ _5_ _6_ _7_ _8_ Position
1 |_o_|___|___|___|___|___|___|___|
2 |___|_x_|___|___|___|___|___|___|
3 |___|___|_x_|_x_|___|___|___|___|
4 |___|___|___|___|_x_|___|___|___|
5 |___|___|___|___|___|_x_|___|___|
6 |___|___|___|___|___|___|_x_|___|
7 |___|___|___|___|___|___|___|_x_|
8 |___|___|___|___|___|___|___|___|
Time

Thank you for the further information on Zene and the Zeno Stadium
Puzzle/paradox. I am not familiar with these, so I'd like to do some
research & mull it over.

Regards,
Ed Hanna

.

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