I think your argument is invalid. It only proves that the universe cannot
be a set of space-time points that are arbitrarily close
together. Something like Penrose's spin network is consistent with there
being a shortest distance.
I looked at your web site. You make an error in deriving inequality
(28) from (26) and (27). From (26) you can obtain
T < m c^2 dt^2/h
and from (27)
m < c^3 dt/G
But (28) does not follow because the inequality for m is the wrong way.
Brent Meeker
On Thu, 12 Oct 2000, Christoph Schiller wrote:
>
> In this discussion list there were several threads
> on what could be the proper description of all of nature.
> Typical approaches are that the universe
> is to be described by mathematical concepts such as some
> special Hilbert space, some special type of category,
> or other very elaborate mathematical structures.
>
> There is a little problem however, which I would like to pose
> as discussion topic.
> All these structures are specialized sets, i.e. sets plus
> special properties and specialized relations between
> their elements.
>
> However, I seem to have a simple argument that the universe
> is not even a set. In short, it goes like this.
> To be a set, nature has te made of elements. Elements
> are distinguishable entities.
>
> (We are used to think that points in space or time, or events
> in space-time, as well as elementary particles are
> these elements)
>
> However, in the Planck domain, i.e. at scales
> around 10^-35 m or 10^-44 s it is easy to show that
> two different space-time points cannot be distinguished
> from each other clearly, nor two particles, nor even
> one from the other.
>
> It takes only a few lines, using the Compton wavelength and the
> Schwarzschild radius expression, to deduce this connection,
> which is based on the existence of the Planck length and the Planck time as shortest intervals appearing in nature.
>
> The universe seems to be a set only *approximately*, at energies
> or scales which are very low compared to the Planck energy or
> scales.
>
> And that would mean that all approaches trying to describe
> the universe as some complex mathematical structure are doomed.
> the universe cannot be described with any structure which contains
> a set, or which is built on a set.
>
> It is not clear what the correct structure should be; but
> the structure should be very simple, and quite a bit simpler than
> a set. If you have any proposals for such a structure, I'd
> be interested to hear about them.
>
>
> Christoph Schiller
> christoph_schiller.domain.name.hidden
>
>
>
> PS.I wrote up the argument in more detail in the file
>
> http://www.dse.nl/motionmountain/C11-LGSM.pdf
> and the preceding
> http://www.dse.nl/motionmountain/C10-QMGR.pdf
>
>
>
>
>
> ---
>
> Have a look at my free physics textbook, written to be
> surprising and challenging on every page:
>
> http://www.dse.nl/motionmountain/contents.html
>
> ---
>
> ------------------------------------------------------------
> --== Sent via Deja.com http://www.deja.com/ ==--
> Before you buy.
>
>
>
Received on Thu Oct 12 2000 - 11:13:08 PDT