Re: A question of discrete space-time.

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.

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.

The idea of discrete space-time and speed limits has also been
discussed by Zene in a way that you might find insightful.

Consider 2 dimensional space now, with 3 rows of bodies, aligned in
staggers:

__A1__A2__A3
B1__B2__B3
______C1__C2__C3

Now imagine that fastest a body could move in an instant is one space.

So in a single instant, the bodies align themselves:

__A1__A2__A3
__B1__B2__B3
__C1__C2__C3

The issue here is that if you observed this from a stationary position,
such as anywhere in row A, you would notice the bodies of rows B and C
moving one space in an instant.

All fine, right?

But if you were are row B, you would have seen row C move two spaces in
a single instance (due to relative motion). This breaks the rules of
the system.

This is called "Zeno's Stadium Puzzle" or paradox, whatever.

So the conclusion of this puzzle is:

1. space-time is not discrete
or
2. space-time is not a dimensional medium

Since 1 is alot easier to understand than 2, conclusion 1 is what most
people automatically assume must be true.

I'm personally a fan of conclusion 2.

.