Reductionism Primas

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Hans PrimasChemistryQuantum Mechanicsand ReductionismPerspectives in Theoretical Chemistry

Spri nger-VerlagBerlin Heidelberg New York Tokyo 1 ~ 8 3


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uthorHans PrimasLaboratory for Physical ChemistrySwiss Federal Institute of Technology ETH)ETH-Zentrum, CH-8092 ZOrich

Second corrected edition 1983.First edition 1981) published in the series:Lecture Notes in Chemistry, Vol. 24Springer-Verlag Berlin Heidelberg New York Tokyo

ISBN-13: 978-3-642-69367-0 e-ISBN-13: 978-3-642-69365-6001: 10.1007/978-3-642-69365-6

This work is subject to copyright. All rights are reserved, whether the whole or part of thematerial is concerned, specifically those of Translation, reprinting, re-use of illustrations,broadcasting, reproduction by photocopying machine or similar means, and storage in databanks. Under 54 of the German Copyright Law where copies are made for other thanprivate use a fee is payable to Verwertungsgesellschaft Wort , Munich. by Springer-Verlag Berlin Heidelberg 1983Softcover reprint of the hardcover 2nd edition 1983The use of registered names, trademarks, etc. in this publication does not imply, even in theabsence of a specific statement, that such names are exempt from the relevant protectivelaws and regulations and therefore free for general use.2152/3140 543210


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CONTENTS

FOlLe lAJoltd by Paul FeyeJLa bendPlLe6a.c.e X

Chap {:eJr 1: Open P b l ~ 06 the PlLuent Va.y TheOlLe ttc.ai. Che rni6bty1.1 The Overproduction of Truth 11 2 Chemi ca1 Theori es 31.3 We can calculate everything 51.4 Some Puzzles of Molecular Quantum Mechanics 101. 5 New Poi nts of Vi ew Are Needed 16

Chap:teJr 2: On :the S:tItuc.:twte 06 Scienti6 Lc. ThwJUu2.1 A Good Theory should be Consistent, Confirmed and Intuitable 182.2 No Theory can be Proved to be Free from Inner Contradictions 232.3 Experiments can neither Prove a Theory True nor False 252.4 Preconceptions and Prior Conceptions 282.5 There is no Insight without Inner Pictures 322.6 Are Theories dangerous? 382.7 Summing Up 43

Cha p:teJr 3: P ioneeJr. Q u a ntum Mec.ha.Mc.t. a nd ..i;tt InteJr pJr e:ta tion3.1 Introductory Remarks and Preview 453.2 The Historical Development of the Hilbert-Space Model ofPi oneer Quantum Mechani cs 503.3# Outline of the Hilbert-Space Formalism of Pioneer Quantum

Mechanics 663.4 The Copenhagen Interpretation of Pioneer Quantum Mechanics 983.5 The von Neumann London Bauer Interpretation of PioneerQuantum Mechani cs : 1123.6 The Everett Interpretation of Pioneer Quantum Mechanics 1283.7 Einstein-Podolsky-Rosen Correlations 1363.8 Conclusion: The Status of Pioneer Quantum Mechanics 147


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Cha.ptV1. 4: Be.yond Pia ne V1 Quantum Me.c.ha.niC44.1 Introduction 1604.2 Algebraic Quantum Mechanics 1634 3 ~ Algebraic Statistical Mechanics 1794.4 The Development of Quantum Logics 1954. Non-Boolean Probabil ity Theory 2204.6 Interrelations and Synthesis 246

ChaptV1. 5: A FJtameJoJtk 60Jt The.oJteUc.ai Cherr0dJty5.1 Reevaluation for the Paradigms of Theoretical Chemistry 2505.2 The Logic of Properties 2545.3 Orthomodular Temporal Logic and its Ontic Interpretation 2605.4 W -Logic for Chemistry 2675.5 Theory Reduction 2795.6 Objects in a Quantum World 292

ChaptV1. 6: Re.ductiorU6m Howm and Compte.me.n;taJr.ily6.1 The Controversy Reductionism vs. Holism 3086.2 Complex Systems 3146.3 Patterns in Holistic Systems 3246.4 A New Look at Molecular Patterns 3356.5 One Way of Telling is not Enough 347

BibliogMphy and AuthoJt Inde.x 356Inde.x 44


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FOR E W 0 R DConsidering the great variety of facts, theories, forms

of l i fe that has existed at any time in the history of Western thought and that has become quite overwhelming today,scientists and philosophers have adopted the one or the otherof the following three points of v i ~ w :

1 P o ~ i t i v i ~ m : things are what they are - all we can dois to collect what exists and to order i t

2 R e a l i ~ m : things are not what they seem to be but thereis. an underlying reality. I t is the task of the scientist (phi-losopher) to discover this reality and to explain everythingon i ts basis.

Positivism and realism are well known in the 20th centu-ry - but they have great ancestors. Thus some early Greekthinkers assembled 'wonderful facts ' such as earthquakes,solar eclipses, the periodic rising of the Nile and tried toexplain them, using different explanations for different facts.The procedure is quite old; i t can s t i l l be found in Herodotusand in part of the Hippocratic corpus. Today we have the ten-dency to collect facts and increase the precision of measurements without any theoretical rationale. Facts, i t is assumedby those who follow the trend, have value in themselves nomatter how well they f i t into or clash with abstract conceptions and no matter what their ( theoretical, or ' social ' )significance.

Positivism was criticised already in antiquity. To knowa lot writes Heraclitus does not teach reason . Anaximanderdeveloped a comprehensive point of view that explained theorigin and structure of the world: the world is an orderedarrangement, i t is a cosmos and i t is uniform - the same lawsare valid throughout. Dreams, gods, Tartarus have no room inthis world, they become homeless and the question arises howbelief in them can be accounted for. The question becomesurgent in the case of Parmenides who showed, by an intricate


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and forceful argument that there can be neither motion nordifference. For now not only gods and dreams but the entireworld of commonsense turns out to be unreal.

I t is interesting to see how certain features of thisextreme view survive even today. Thus the theory of rela-t ivi ty gives what one might call a static account of motionand leaves essential properties to the consciousness of theobserver while there are many physicists who claim that important differences quantum theory vs. the laws and factsof classical mechanics, chemistry, biology are in fact nonexistent. I t is also well known how often philosophers andphysicists have tried to understand quantum theory in clas-sical terms. Modern realism differs from Parmenides in tryingto reduce appearance to the underlying reality instead ofthrowing t out. It agrees with him in assuming that real iswhat can be so reduced.

In antiquity the two traditions just described were soonjoined by a third which, for want of a better term, I shallcall

3 the ~ t ~ u e t u ~ a l a p p ~ o a e h According to this approachpositivism and realism neglect phenomena which, far frombeing passing fancies of nimble minds are relied upon andused by them even when they propose radical views such asthose of Parmenides. Positivism assumes that facts have nostructure - hence all we can do is to collect them and parcelthem off in convenient ways. Realism assumes that there isonly one kind of structure to be considered. ommonsense andthe work of scientists and philosophers are built in a dif-ferent way; they are spli t into domains each domain beingheld together by certain principles. If we want to maintainthe forms of l i fe on which our science and our existence asrational human beings depends then we must take these prin-ciples into account and use them as boundary conditions ofresearch.

The foremost ancient exponent of the structural view


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was Aristotle. Aristotle rejected positivism on the groundsthat we know not only facts but also principles. The principles may not cover all there is but there are sizeabledomains held together by the same set of principles. It isthe task of the philosopher-scientist to identify the domainsand to formulate the principles appropriate to them. Aris

t o t l ~ rejected realism by simply pointing to the results ofa research of this kind: z h e ~ e a ~ e different domains guidedby different principles none of which can be pushed aside or'reduced' to other principles. However there may exist ageneral theory of being which permits us to bring order intothe principles discovered.

Realism and especially the mechanical philosophy playedan important role in the rise and the development of modernscience. Helmholtz s t i l l maintained that an explanation wassatisfactory only i i t used mechanical models. Mach uhemand following them Einstein then looked for theories of adifferent kind (called theories of principle by Einstein)which covered large areas but without giving a detailed account of the systems concerned while Einstein and especiallyBohr introduced the idea that such theories may be contextdependent, different theories being valid in different do-mains. Combining these ideas with abstract mathematics suchas various algebras, lat t ice theory, logics then led to apowerful revival of the structural approach. Thus the searchfor a generalized quantum theory is exactly in Aristotle 'sspiri t : we do not take i t for granted that the quantum theories we have are the best way of dealing with everything,looking either for new interpretations or suitable approxima-tion methods to solve hairy cases; we rather try to identifydomains and theories suited for them and then look for waysof relating these theories to each other.

Professor Primas explains the structural approach anddemonstrates i ts power in the domain of chemistry. In doingso he reviews major standpoints and problems of modern science

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nd philosophy of s c i e n c e ~ he shows how some of the problemscan be solved by the structural approach. Freeing researchersfrom the agnosticism of the positivists and the dogmatism ofthe realists he liberates their imagination and prepares afruitful collaboration of science, philosophy and abstract(non numerical mathematics. In the past these subjects wereoften separated, or combined in a one sided manner. ProfessorPrimas rejoins them nd points the w y to a new philosophy ofnature that is not only useful nd e x a c ~ but also contains ametaphysics, i .e. a comprehensive picture of the world ndman s place in i t

Berkeley Paul Feyerabend


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PRE F ACEThe purpose of this book is to provide a deeper insight into the

modern theories of molecular matter. It incorporates the most importantdevelopments which have taken place during the last decades and reflectsthe modern trend to abstraction. At the present state of the art we haveacquired a fairly good knowledge of how to. compute small molecules us-ing the methods of quantum chemistry. Yet, in spite of many statementsto the contrary and many superficial discussions, the theoretical basisof chemistry and biology is not safely in our hands.

It is all but impossible to summarize the modern developments ofthe theory of matter in nontechnical language. But I hope that I can givesome feeling for the problems, the intellectual excitements and the wor-ries of some theoreticians. I know very well that such an enterprise isa dangerous adventure and that one says that a clever scientist shouldtake care of his reputation by barricading himself behind the safe wallof his speciality.

This volume is not meant to be a textbook. in many respects i t hascomplementary goals. For good and bad reasons, most textbooks ignore thehistorical and philosophical aspects and go ahead on the basis of crudesimplifications; many even lie like the devil and do not shrink from naiveindoctrination. Some sections of this book can be read as commentaries onour standard texts, they are intended to stir the waters with controversy.These parts certainly reflect the tastes the inclination and the pre-judices of the author.

Since all our textbooks are ultraconservative and strictly censornew developments, these notes are in part also a progress report, intendedto increase the chemist s information about what the theoreticians havebeen up to in the last decades. Modern theoretical developments like quan-tum logiCS and algebraic quantum mechanics are now sufficiently mature todemand the interest of more than a few speCialists. I tried to informrather than to instruct, to give the gist of arguments rather than routinedetails and I hope the reader will obtain an overall view of the subject.ne or the other reader may deplore the lack of detail or think that I make


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excessive demands on his previous knowledge. In that case, he is urgedto consult the references where he is likely to find more complete information. The references to the bibliography - which is extensive but farfrom complete - are by name of the authors and date. A few sections areon a technically more difficult level and are marked by the symboland some sections I wrote for my own benefit. y feelings will not behurt if the reader chooses to skip them. I shall be delighted if thereare at least a few sections in which he finds some inspiration.

The modern theory of matter reveals an amazing continuity of philosophical and scientific problems. There is no novel idea in contemporaryresearch which could not be ultimately be traced to the ancients. Ourdominant mode of explanation is still Pythagorean mathematization; likePlato we try to understand reality in terms of some underlying mathemat-ical structure. Most words in the scientist s and philosopher s vocabularyhave changed their meaning over the past few hundred years. Yet the question raised in Platon s dialogue Panmenide two thousand years ago arestill our questions, all that has changed is our approach. Our mathemat-ical tools are much sharper and our empirical knowledge has vastly increased while the style of modern research has become distinctly unbalancedand irresponsible.

One of the worst features of modern science is the high degree ofspecialization and the exclusion of all historical and philosophical aspects. It is bad that the contemporary research programs force so many researchers in one area to be totally ignorant of most other areas. The waysof thinking, experiencing and behaving, the mode of activity exhibited bycontemporary science strikingly reminds one of what Shapiro 1965) hascalled the paranoid style. It is characteristic of this style that bridgesbetween related problems are broken down so that things remain neatly andrigidly separated. Scientists who cultivate a paranoid research style areusually extremely acute and intense, show an exorbitant respect for compart-mentalizations and computers, and firmly demand complete autonomy for theirnarrowly fixed ideas. They like over-precise and rigid formulations butare not able to see the associated narrowing of interests. The separationof philosophy and science has led to the so-called realistic world view


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and to the blindness of many experts who are entirely unaware of the ab-stracting and isolating nature of modern science.

Basically, experiment and theory work together beautifully andcomplement each other perfectly. f the reader is not convinced of theparanoid tendencies of modern science, he should ponder on the wisdom ofseparating experiment and theory. This dissociation poses most severesociological and psychological problems and may easily have disastrousconsequences for the development of science. The most striking characteristic of modern theoretical science is the tendency to go to higher andhigher levels of abstraction. Much to the dismay of the experimentalists,the theoreticians move away from specific problems and turn to compara-tive studies of theoretical structures. In the words of Marshall Stone(1966), the abstract of today becomes the concrete of tomorrow. Now-adays, mathematics is the most important language of theoretical sciencebut few scientists can indulge in the luxury of keeping up with the increasing mathematical character of our most fundamental theories. Thisdeplorable separation of experiment and theory forces the experimentaliststo discuss so-called models of the phenomenon under investigation, using rather superficial and unreflected ideas about abstraction, idealization and approximation. Since the new developments in theoretical chem-istry require a broader mathematical training than is customary in ourpresent-day chemical education, most chemists do not realize that newwell-founded concepts and powerful mathematical techniques are availablefor the design and interpretation of experiments. Here, I do ot refer tothe useful bust vastly overrated methods of numerical quantum chemistry.Quantum chemistry is but a narrow subfield of theoretical chemistry andnumerical quantum chemistry is nothing but a powerful tool.

Much of the material covered in this volume has been presented inlectures that I gave at the Swiss Federal nstitute of Technology ETH)in ZUrich during the last ten years. lowe a special obligation to mystudents who criticized the lectures as well as the notes. Some of theconceptually difficult material was distributed privately several yearsago in form of lecture notes. In turn I received encouragement and con-structive critique from many people, yet I find i t impossible to list

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them all in a fair way. However, I would like to single out the influenceof the late Joseph Maria Jauch (1914-1974). I had the benefit of many moststimulating conversations and correspondences with Professor Jauch on interpretation problems of quantum mechanics which have been essential inshaping my views. In particular, Jauch convinced me in a long and toughdiscussion in May 1970 that the concept of classical observab1es (or essential observab1es , as he called them) was the missing link betweenphysics and chemistry.

Without the action of a friendly pressure group the various lecturenotes and manuscripts would never have been transformed into the presentshape. There existed a variety of preliminary versions, but again it isnot possible to enumerate all the people who read and criticized them. Iam greatly indebted to all of them. I would like to mention at least myformer and present coworkers Dr. Peter Brand, Dr. Peter Pfeifer, WolfgangGasche, Dr. Ulrich MUller-Herold, Werner Gans, Guido Raggio, EberhardMUller and Anton Amann. Their feedback was always stimulating and veryessential, their original contributions have been indispensable.

A special word of thanks is due to Miss H.Rohrer who not only didan impressive and beautiful job with the final version but also drew upand typed many drafts with skill and humor and has devoted enormous energyto improve presentation and style.

Finally, I wish to express my sincere thanks to Paul K Feyerabendwho managed to find time to read the final manuscript. He even took thepains of going meticulously through the script correcting a staggeringnumber of linguistic errors, making many stylistic improvements, and therewith teaching me that anything goes is not a rule that can be applied tothe English language. Any remaining errors are of course my responsibilityalone.

ZUrich Hans Primas

Reductionism Primas

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