Re: A question of discrete space-time.
- From: "Ed Hanna" <stq50@xxxxxxxxx>
- Date: Tue, 31 May 2005 06:35:19 +0000 (UTC)
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.
>
<snip>
>
> 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.
Dear Mike,
Thank you again for your reply. I have done some more thinking about
your question and my previous reply to it. Yours is the first posting
within this topic that speaks explicitly to the issue of rules, and
that has given me pause for thought in a more formal sense.
In the process of studying an issue like discrete space-time, certain
things seem (to me) to be logical steps/outcomes based on previous
steps/outcomes, which everyone should be able to agree on. We might
refer to these things that everyone agrees upon as "facts". Other
things are more like coming to a point where you have to make an
educated guess of some sort, where everyone may not be in agreement.
We should call these "postulates". (I'm probably just stating the
obvious here, and I hope no one is offended as a result.)
Since this thread started with a guess that space-time might be
discrete rather than a continuum, this should be more formally stated
as:
Postulate #1 - Space-Time is composed of contiguous quantum units that
cannot be divided.
This postulate #1, being only an educated guess (some might say an
ignorant guess), will be a parting of the ways with many readers.
To simplify things, I had left out of the original posting that it is
my (then unspoken) educated guess that nature does not allow gaps or
dups. This is based on the issue that you pointed out - if gaps were
to happen, then there would be no upper limit to speed, and this seems
contrary to nature. I also feel (as described in my first reply to
your posting) that gaps in a unit particle's world line allows too many
messy / ugly things to happen, and nature is inherently simple and
beautiful. Thirdly, I also strongly suspect that when we speak of a
"particle", it is more important to consider the world-line itself as
the entity of which we speak, rather than just the stand-alone particle
itself.
Sorry to belabor the point, but I'm trying to be extra formal here, and
give my reasoning. This second guess should be more formally stated
as:
Postulate #2 - Apparent motion is a contiguous world-line with no
duplications or gaps.
Once again, this postulate is only an educated guess, and will be a
parting of the ways for still more readers.
However - given these two postulates, there would be a maximum speed
within the universe that could never be exceeded (as you said, by
definition). I find this to be a very interesting prediction related
to relativity. It is also a testable prediction, but it is not novel
enough to distinguish between existing theory and a theory of discrete
space-time.
So in addition to the two possibilities you listed, I would like to
respectfully add a third:
3) Space-time may be discrete and it does not allow gaps.
Thank you for keeping me honest.
Regards,
Ed Hanna
.
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- A question of discrete space-time.
- From: Ed Hanna
- A question of discrete space-time.
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