X-Message-Number: 11354
Date: Wed, 3 Mar 1999 14:08:31 EST
Subject: Re: The basis for quantum and other theories

In Message #11329 John de Rivaz wrotes about:
" The basis for quantum and other theories ":

 I wonder whether all the elaborate structures of mathematics built around 
 Pythagoras' theorem could have a simpler basis - like the introduction of 
 zero had on arithmetic after the Romans - that would explain the universe 
 without some of the wierd results theoreticians are throwing up at present. 
 I am not knocking it - I love the wierd results such that time travel may be 
 possible and so on, but is that *desire* for all this to be true any better 
 than the *desire* for there to be life-after-death that supports irrational 
 religions, based on a belief system founded on anecdotal evidence?

Beyond zero you "have" the empty set. For example if you have only a PC
you have zero Mac. If you have no computer and no room for any you have
zero computer and an empty set for both, PC and Mac.

More precisely about Pythagoras' theorem, Lorentz has produced many metrics or
way to define distances beyond the classical : square of the distance equal
the sum of the square of the coordinates. You may define distance as the sum
of the absolute value of each coordinate (seen in infinite dimensional spaces)
or you may have: distance = absolute value of the largest coordinate or
smallest one.

Another way to look at a different physics: in dynamics, things evolve so that
a quantity called action is minimised. What is overlooked very often is that
the minimum may be only local, so there may be many local minima. Even more
action needs only to be stationary (not changing neraby) that include all
local minima, maxima, flat zones and saddle points.

That may be dry at first look but think about a system driven "naturally" to
decay, you must now ask: decay at what action stationnary point? What if we
force it to another flat part of the action curve?

That is a way maths can help to put new ideas on "the market". If you want to
know more about that, you may read the book: The variational principles of
mechanics by C. Lanczos (Dover).

Yvan Bozzonetti.

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