Principia's Promise and the Final Theory

                ________________________________________

 

                           Timothy Paul Smith

 

                          Department of Physics

                       University of New Hampshire

                           tim.smith@unh.edu

             (first printed - Vol. 2, No. 7 - March 1996)



	In the Stradtpark in Graz, Austria,  is a flower bed  and 

monument put up by the local Rotary club to commemorate Johannes Kepler, 

 who spent a few years in that city.  The flower bed is arranged in an 

oval,  with twelve lines of stone radiating from a near-central point.  

Each bed is planted in alternating red and white flowers.  The monument's 

inscription is left to only codify and clarify what was presented so 

pictorially in the flora. 1) The orbits of the planets are ellipses with 

the sun at a focus. 2) The planets sweep out equal areas in equal time. 

3) The square of the period is proportional to the cube of the radius.  

Yet the cause is missing.

	When I first came upon this monument in May of 1994 I had been 

reading Francis Bacon's book "Novum Oragum" ( in preparation for the 

July 1994 issue of this journal).  "Novum Oragum" is sometimes 

considered the original prescription of the Scientific Method.  A 

methodical raising up from simple observations to simple axioms,  and 

from these axioms to more global laws.  On that sunny May day,  standing 

in the gardens of Graz,  I realized that Bacon knew all about Kepler, 

(the planetary laws were published between 1609 and 1618,)  and he was 

paving the way to the more global theory of Isaac Newton.

	And then there was Principia.  No matter how much preparation 

was laid down by the planetary laws,  or the method by which one might 

combine and build up theories,  Principia stands as a turning point in 

the annals of human intellect.  In 1687 Newton unified secular and 

canonical mechanics,  celestial and terrestrial motion, the marriage of 

Heaven and Earth.

	Once we have witnessed this first great unification,  the  flood 

gates are open, and the intellectual potential staggering.  It is this 

possibility which Steven Weinberg identifies as the most important 

contribution of Newton.  I expect that Weinberg views this possibility 

as the driving motivation behind his own work,  as expressed in his 

popular writings, (such as "Dream of a Final Theory") and in the 

direction of his theoretical opus.

	I wouldn't venture to guess what a final theory will be like.  

Rather I am curious as to why we as humans think we have a chance at 

unraveling this ultimate enigma of the universe.  Let me attempt to 

gather a few thoughts on the subject.  There are two points which I will 

attempt to address which justify the seriousness of our pursuit of a 

Final Theory.  I will first argue for the necessary existence of a Final 

Theory.  Then I will discuss why we might have the audacity to think 

that we could unravel it.

	I like this term , "Final Theory", which Weinberg used in his 

book,  and in fact in some type of impact-per-word notion I think the 

title "Dream of a Final Theory" is one of the best parts of that book - 

I wish I had thought of it.

	The primary result of a final and ecliptic theory is that there 

must be order of some type in the world.  One of the mistakes which we 

have made in the past,  time and time again, is that we think we know 

what are the elements which will be important in the overall order of 

the universe.  Medieval scholastics saw order in geometry and in the 

universe of Ptolemy,  and waylaid us on our search for a final theory 

with the notion of crystalline planetary spheres.  Centuries later we 

thought that if we could reduce things to elements of an event's time and 

location we had decoupled a degree of complexity,  and so simplified the 

problem,  but Einstein showed us that in fact these two are coupled.  

Still there is some type of order in our world.  We perform the same 

experiment here-and-now or there-and-then,  and we find the same 

results.  On the occasions when we do not have the same results we 

conclude that we did not do the same experiment,  we did not identify 

the important parameters of the experiment.  We try to rebuild our 

ideas,  and our experiment, until the important parameters are  

identified.  And this system seems to work well in our universe.  Very 

well in fact.  But the success of a system such as science is not enough 

to conclude that there must be a final theory.

 

	Now, if things come from nothing, all things could

	Produce all kinds of things; nothing would need

	Seed of its own.  Men would burst out of the sea,

 

				- De Rerum Natura - The Way Things Are

 

Lucretius is a great deal more dramatic then most of us venture,  but 

his point is well taken.  As Thomas Hobbs would state,

 

	And in the same manner it may be shewn, that whatsoever

	effect are hereafter to be produced, shall have a necessary

	cause; so that all the effects that have been, or shall be

	produced,  have their necessity in things antecedent.

 

				-Elements of Philosophy. Concerning Body

	

If there were effects without cause the acumulative of these effects 

over the history of the universe could be staggering.

	I doubt that I can offer a tautology which would prove 

conclusively that there must be a final theory,  a cause to all effects, 

but I would venture to say the evidence is very strong.

	The second point to justify the pursuit of a final theory is 

the notion that the theory will be comprehensible.  First we recognize 

that the pursuit of a comprehensive final theory has come a long way,  

and is very successful.  One tends to see physics in terms of its present 

boundaries.  "The standard model is yet incomplete because of ... 

(insert Higgs or what ever) and string theory can not supplant it 

because of ... (calculation problem or what ever)", proclaim the 

nay-sayers.  But that belittles the three centuries since Newton (or 

three and a half centuries since Bacon - who told us it would take about 

one lifetime).  In some sense we really do know the `important things', 

like why the sky is blue and what causes rainbows,  why atoms bind to 

make all of chemistry,  why planets orbit, galaxies recede and what fuels 

stars.  We really have made an astonishing amount of progress.

	More to the point of why we might comprehend the final theory is 

the whole reductionist thesis; that the world can and should be 

understood in terms of its parts.  The weather is undoubtedly a complex 

and turbulent system,  yet all the jet-streams and tornadoes really are a 

consequence of atoms acting on their neighbors,  essentially Newton's 

laws of motion (with a little bit quantum mechanics / chemistry thrown 

in).



	In the end I fear I can not offer up the proofs of Euclid as to 

the existence and comprehensibility of a Final Theory.  What do we have? 

For existence; the world appears to be orderly,  and "every effect has 

a cause", a type of conservation of cause (what is the symmetry which 

Noether's theorem tells us must be there?).  For comprehensibility we 

have the success of science to date,  and the reductionist thesis.  I 

must apologize to those who have spent a great deal more time on this 

than I have.  I fear I have only touched the most superficial aspect of 

this problem.  However I think the type of evidence which one might 

uncover will be like what was presented here;  an appeal to reason 

(causality and reductionism) and experience.  And that is the best 

that science,  that inexact branch of mathematics,  can ever hope to 

accomplish.