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From: Christoph Schiller <christoph_schiller.domain.name.hidden>

Date: Thu, 12 Oct 2000 03:57:36 -0700

('binary' encoding is not supported, stored as-is) 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

Date: Thu, 12 Oct 2000 03:57:36 -0700

('binary' encoding is not supported, stored as-is) 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 - 03:58:30 PDT

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