Re: Generalising physical theories

From: Jamie Vicary (jamievicary_at_gmail.com)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 22:03:54 +0000

Uncle Al wrote:
> Jamie Vicary wrote:
>
>>>OK in principle but not reducible to practice. It is like saying we
>>>could create literature by strumming random letters across a page.
>>>Call it a dot matrix printer 65-character line with 55 lines/page.
>>>We'll drop the q's and add a space,
>>>
>>>[(65)(55)]^(26) = 2.43x10^92 different pages
>>>
>>>Even a single line impossibly hurts,
>>>
>>>(65)^(26) = 1.37x10^47 different lines.
>>
>>Sure! That's an awful lot of possibilities. A huge great number of
>>theories could be generated. But I'm certainly not suggesting some kind
>>of manual search through every possible theory! I'm talking about some
>>mathematical way --- some kind of extension of category theory, perhaps
>>--- that you could use to isolate those possible theories which are
>>mutually inequivalent, and which admit interpretations confirming our
>>two well-established theories, GR and QFT.
>>
>>Some of these theories will be complicated, but some would be simpler,
>>letting the mathematical structure of GR and QFT emerge from the same
>>type of fundamental interaction between abstract objects. It's the
>>nature of those fundamental interactions that we're interested in, after
>>all.
>
> The small, countable infinity is the number of integers. The number
> of numbers (points on a line) is an infinitely bigger infinity and not
> countable at all. The number of functions through a point is
> infiniitely bigger than the number of points on a line. The number of
> theories will be inconveniently large to consider content in any way.
>
> Any viable interesting theory beyond GR and QM will
>
> 1) Be predictive.
> 2) Explicitly accept c=c, G=G, and h=h all simultaneously. Its
> real world-applicable subsections will selectively have c=infinity,
> G=0, and h=0 as limiting cases.
>
> That very nicely limits the number of "good" new theories to zero.
> Initiate with simplicity. Postulate c=c (speed limit of information
> propgation), G=G (gravitation scaling), h=h (limits to measurement
> certainty) and go on from there.

That is a very, very big statement, to say that that limits the number
of "good" new theories to zero. Certainly, it limits the number of
viable theories to a vanishingly small subset of the total. To say that
it truly limits the number to *zero*, though, is saying no unified
description of nature can exist. I hope many people would agree with me
when I say your pessimism is not generally accepted.

Of course we need a theory which involves, somehow, our three important
constants of nature; maybe, if we're unlucky, it needs other things like
coupling constants as well. Saying "Postulate c=c, G=G and h=h and go on
from there" is all very well --- but the question is, going on from
there is rather difficult, and has essentially been the driving force
behind a large section of physics for half a century! What I am
proposing is a methodology that would give direction to how to "go on
from there".

     Jamie

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