A Case Study of a Scientific Blunder. History and Philosophical Teachings
aa r X i v : . [ phy s i c s . h i s t - ph ] J u l A Case Study of a Scientific Error: Context, History and Philosophical Teachings
P. Lederer
Centre National de la Recherche ScientifiqueDirecteur de Recherche honoraire au C.N.R.S.14 rue du Cardinal Lemoine, 75005-Parise-mail: [email protected]
I was led in 1988 to publish in Physical Review Letters, in cooperation with a team of experimentalphysicists, a crucial experimental result dealing with a revolutionary new theory. The conclusionsof my paper were proved incorrect a few months later. I discuss the various factors – scientific,instrumental, but also psychological, sociological ones – which led to this blunder. Although thisstory is a personal one, I believe it sheds some light on the process of scientific discovery, falsification,confirmation, and errors.
PACS numbers: 01.70.+w,*43.10.Mq,74.72.-h,74.20.-z74.25.-q
I. INTRODUCTION
In 1986, a stunning experimental discovery rockedthe world of physics, that of High TemperatureSuperconductivity . It was discovered in a material, La − Ba − Cu − LBCO ), for which no learnedsolid state physicist, either on the theoretical side or onthe experimental one, would ever have believed it to oc-cur. The superconductivity was observed at tempera-tures which had been thought until then to be impossiblyhigh, as compared to that of all studied superconductingmetals since the discovery of superconductivity in 1911 .The search for higher temperature superconductivity(the highest one until then was 21 K ) had motivatedsome researchers in the previous years, most had givenup. Superconductivity was considered widely among con-densed matter physicists as a "dead" topic, a topic wherenothing significantly new would ever be found any more.Researchers had moved to other fields.Until then, it had been common knowledge amongphysicists that magnetic impurities were detrimental tosuperconductivity, as proved by scores of experiments(see for example ref. ). A small concentration of mag-netic impurities in a superconductor was known, andunderstood, to lower drastically the temperature belowwhich superconductivity was present. In the new super-conducting material, however, magnetic atoms were notonly present, but in fact densely so throughout the ma-terial (see for example ref. ). In fact LBCO was veryclose to being an antiferromagnet, i.e. a material wheremagnetic ions are present in a regular crystaline array,with an alternate order in the lattice of + spins and − spins at low temperatures (in contrast with ferromagnetswhere all spins have the same direction at low temper-atures). Not only are magnetic ions dense in the newsuperconducting material, but superconductivity persistsup to temperatures significantly larger than observed un-til then in non magnetic materials. In fact, very rapidly,superconductors of a class similar to LBCO reached su-perconducting temperatures an order of magnitude largerthan any previously known material. It was obvious to the vast majority of physicists thatthey were dealing with a qualitatively new phenomenon,immediately dubbed "High Temperature Superconduc-tivity"(hereafter HTS). It quickly made head titles inthe news of the world, predictions of a new technolog-ical era were made, or even an industrial revolution washypothesized : in particular, if superconductivity couldbe made to persist up to ordinary temperatures, the oldindustrial problem of electricity storage promised to besolved, since superconducting rings can store electricalcurrents with vanishingly small resistive losses for verylong times. Spectacular experiments showed levitatingobjects, or even people, above superconducting chunksof the new material, etc..Technological expectations in various industries werehuge. Financial ones as well.Suddenly, condensed matter physicists were in theworld news!As a result, hundreds of experimentalists turned to in-vestigate the new materials, searching for even higher su-perconducting temperatures, and hundreds of solid statetheorists around the world left more or less aside theprojects they were previously interested in, to try andcontribute theoretical advances in the understanding ofHTS. An intense world competition among individuals,groups, laboratories, universities and research institutesdeveloped.At the time, I was at a turn of my career. I had leda small group of theorists during ten years from 1976 to1986 with some success, about electronic properties ofnearly one dimensional conductors. Those can be pic-tured as one dimensional atomic filaments weakly cou-pled by some chemical bonding, so that they exhibit veryspecific anisotropic properties. With my collaboratorsand PhD students we had gained some recognition forthe discovery and understanding of a new phenomenon,dubbed Field Induced Spin Density Waves . The expla-nation we had given of their observed Quantized Hall Ef-fect had attracted attention. Our theoretical tools werethose of Quantum Field Theory, in a theoretical frame-work called "perturbation theory" to deal with interac-tions between electrons in solids. The latter is the con-venient approach when there are sufficient hints that thephenomenon one wants to study cannot be understoodif one neglects altogether the interactions between thecharge carriers (conduction electrons) within the mate-rial. Taking into account interactions between electrons– contrary to what is needed to understand most phys-ical properties of conductors such as Na, Cu, Ag, etc.– in the FISDW phenomenon is mandatory. Howeverthe interaction energy scale (written U ) in that system issmall compared to the kinetic energy scale of electrons,in other words the width (written W ) of the electronicbands. This leads to what is called "perturbation the-ory": the theory relies on known results when U is zero,and introduces non zero U as a small perturbation to thezero U case. The theory of the "conventional" (low tem-perature) superconductivity is also based on perturbationtheory , so was the vast majority of theoretical papers onthe interacting electron gas in Condensed Matter physicsuntil the discovery of HTS. This basic starting point inthe former case is summarized by the inequality below: U << W (1)In fact, after writing my PhD in 1967 on magnetism inmetals within this perturbation approach, which was therelevant one for magnetic transition metals, I became un-easy with the complications of perturbation expansionsin powers of U of higher and higher order, demandingmore and more complicated diagrammatic methods. Idecided to explore the physics of systems governed bythe opposite paradigm, the "strongly interacting limit",described by the following inequality: U >> W (2)The line of research based on equation (2) requires comm-pletely different theoretical tools, largely undevelopedones at the time, and appeared at the time to be rel-evant in a much more reduced number of experimentalsituations: solid bcc He , magnetic insulators such asCopper or Iron oxides (i.e. Cu F e ) and a few oth-ers. The challenge was interesting, I learnt some differentphysics, published a few papers, but after 1973, the num-ber of interesting experiments stayed quite reduced, theinteresting physics of He required lower and lower tem-peratures, increasingly difficult to reach experimentally:I decided to revert to the study of experimental systemswhich were explored in my laboratory, and for which theapproach of equation (1) was the relevant one. This leduntil 1986 to the FISDW work mentioned above.When HTS erupted, I was ready to dive into its mys-teries, and perturbation theory seemed a sensible startingpoint. The new material was an anisotropic one, formedof parallel 2D arrays of CuO planes, weakly coupled toone another along the direction parallel to the plane, asdepicted on figure (I).A new theory of the interacting electron gas in twodimensions (2D) had just been published within pertur-bation theory about a model which was an idealisation FIG. 1:
This figure exhibits the atomic structure of a typical HTSuperconductor: contrary to the vast majority of (lower tempera-ture) BCS superconductors, which have a much simpler chemicalstructure and a much simpler (usually cubic) crystallographic one(in one guise or another)), this crystal is formed by parallel sheetsof Cu-O (Copper oxide) planes. The “red” atoms here are oxygenatoms, the “blue” ones are Cu (Copper)atoms; two Cu-O planes areseparated by “brown” atoms (such as Ytrium or Lanthanum while“green” atoms are divalent metals such as Ca or Ba. A large familyof HT Superconductors exhibits the common feature of weakly cou-pled Cu-O planes which have a basic square elementary cell. Theoccurrence of linear arrays of Oxygen chains between copper planesis specific to the particular chemical (YBaCuO) shown above.
I am indebted to Julien Bobroff for providing me with thefile for this figure. of the
LBCO structure represented in figure (I). My firsttry at the theory of HTS was to work on this idealizedmodel by taking into account a necessary improvement.The results were encouraging: they confirmed that theimproved model exhibited a tendency to enhanced su-perconductivity. That work was sent for publication, andwas published in 1987.Then exploded the revolutionary Resonating ValenceBond (hereafter RVB) theory of Philip Anderson andcollaborators .For the purpose of this paper, it is not essential to gointo the details of the RVB proposal. Some however, aregiven in the Appendix, section (VII).When I read the paper (reference ), I was immediatelydeeply impressed by its audacity, and the novelty of thescheme he proposed to explain HTS. I had been a longtime admirer of Phil Anderson’s many brilliant and orig-inal contributions to physics, in various fields. The workon HTS in reference was based on the hypothesis thatthe basic theoretical framework relevant to HTS was thatof the inequality (2). Instead of starting from the proper-ties of a weakly interacting conducting electron gas, thestarting point was that of the strongly interacting elec-tron system of a quantum magnetic insulator.I was immediately seduced by the RVB approach:there were various reasons for this : the audacity and thenovelty of his proposal, the rationality of it, given PhilAnderson’s previous work on RVB (see reference for de-tails), his scientific prestige; those three factors combinedin my view with the novelty of the HTS phenomenon, thenovelty of its experimental features, which were utterlycontrary to all scientific rationale until then.I decided to give up my previous approach based oncondition (1) and decided to work on Phil Anderson’sRVB approach, based on condition (2). Among con-densed matter physicists, a fierce battle developed be-tween champions of the weak interaction approach (ex-pression (1)) and those of the strong one (expression (2),as described and analysed in ref. .In August 1987, I flew with my family to Tokyo,where I was to spend one year as an invited lecturer,in Hidetoshi Fukuyama’s ISSP Tokyo group. HidetoshiFukuyama had spent some years at Bell Labs, at thetime of its world fame, in collaboration with Phil Ander-son. He had published many brilliant papers with the lat-ter, together, among others, with Maurice Rice, anotherphysicist I admired. Both had immediately adopted PhilAnderson’s views and were active in developing the RVBstrong interaction scheme. II. MY STAY IN TOKYO UNIVERSITY
I arrived in Tokyo and attended at first the Interna-tional Conference on Superconductivity which was heldthat year in Japan.A crucial prediction of the RVB proposal was theexistence at low temperature in superconducting HTSmaterials of a specific heat C v linear in temperature, i.e. C v = γT (3)where γ in equation (3) is a constant for a given mate-rial. In all ordinary superconductors so far, theory andexperiments agreed that γ was zero, in contrast to thenormal (i.e. conducting but not superconducting) metalcase where it is non zero, proportional to a quantity char-acteristic of the metal (the density of states at the Fermilevel). A non zero sizeable γ in the new superconductorswas a stunning prediction.Accordingly I paid special attention during the Super-conductivity Conference to all experimental reports onthe specific heat of LBCO . I found that there were largevariations in the results; sometimes a non zero γ termwas observed, with various magnitudes, sometimes therewere none. The amount of Ba (Baryum) impurities toobtain superconductivity in LBCO was not accuratelyreported nor controlled. The Conference, where disagree-ments among theorists about the framework relevant toHTS were blatant, did not allow any conclusion to bedrawn. I started my work in the ISSP laboratory in two di-rections; one was about consequences of the strong cor-relations (expression (2)) on the motion of doped holesin a magnetic insulator. The other was to visit two labo-ratories where I talked to experimentalists to encouragethem in clarifying the experimental situation about the γ term. They had to study it while controling accuratelythe Ba concentration in their samples, and measuring the γ term both as a function of Ba concentration and of thesuperconducting temperature.I talked to one group in Hokkaido, in the north ofJapan, and to another one in XXX, in the south.Three months after my arrival in Tokyo, I visited bothgroups, one after the other, to examine with them whatwere their results. What was shown to me in Hokkaidodid not allow clear conclusions; accuracy in the Ba con-centration was insufficient. It was agreed they had toimprove that. In XXX, the situation was worse: no sig-nificant results were available. III. THE PAPER IS PUBLISHED
However, to my surprise and delight, three weeks aftermy visit to Hokkaido, I received a fax from that group (in-ternet was almost non existant...), exhibiting a significantrise of γ coinciding with the rise of the superconductingtemperature! I had an immediate rise in adrenalin, I re-ported the results excitedly to Hidetoshi Fukuyama andmy colleagues in ISSP. The news spread with the speed oflightning in Japanese labs. Phil Anderson’s RVB theorywas experimentally confirmed, along with its spectacularnew hypothesis on the behaviour of strongly correlatedelectronic matter!I told the Hokkaido group they had to consider writinga report for publication.A surprising news reached me two days later: I wastold informally by ISSP colleagues that the head of theXXX group was reporting new experimental results, in asmall physics meeting in Tokyo, of which I had not beenaware. He claimed his group had obtained experimentalconfirmation of the significant γ term in LBCO!This was astonishing. Three weeks before, the XXXgroup I had visited had no result. They had communi-cated no new results since then. How could I understand?My understanding of japanese ways of relating was ob-viously quite poor. I had noticed that some ISSP scien-tists whom I crossed in the hallways or in the staircasewould behave as if I was transparent. I had understoodthat, not knowing my position in the hierarchy of science,they did not know how low they had to bow when theymet me. The way out was for them to see through me.With the claim by the XXX group leader that his grouphad results similar to those of the Hokkaido group, Icould not but imagine that he was going to short theHokkaido group about a historical result which had to be-come a landmark in the history of physics. On the otherhand, his claim proved without doubt that the Hokkaidoexperimental results were undisputable.When two different experimental groups, working inde-pendently in different labs in different parts of the worldfind the same results on the same object in the same con-ditions, the probability that the results are correct is veryhigh.There was no sign from the XXX group leader that hewould share a publication with the Hokkaido group.It was only fair, in such circumstances, to ensure thatthe Hokkaido group publish their results as quickly aspossible, so as not to loose their obvious priority: thisis a kind of ethical aspect widely shared in research. Ithought it normal to add my name to those of the ex-perimentalists authors of the paper. The paper was sentfor publication in Physical Review Letters, which wasthe most widely read worldwide for new developments inphysics.Shortly thereafter, I traveled to a Conference in Aspen(Colorado, USA) where I reported about my work andthe experimental results of the Hokkaido group. Phil An-derson was a few yards away from me when I deliveredmy speech. I was proud to bring him such an impor-tant piece of experimental evidence in favour of his RVBapproach.The paper on the low temperature specific heat inthe superconducting phase of LBCO was published(reference ) only two weeks after it was submitted fropublication. This must have been one one of the mostrapidly published papers in the history of Physical Re-view Letters. Usually, papers are sent to referees, whomay ponder for months about the validity of the re-sults, send various criticisms to the authors, ask for somechange, for citing more or different authors, etc.. No suchthing happened in this case. I suspect that Phil Andersonmay have helped in convincing the editors of the journal.The XXX group announced a communication to bedelivered at a Conference in Interlaken (Switzeland) twomonths later, where they confirmed the linear specificheat in LBCO .Barely two months after the paper with the Hokkaidogroup appeared, with my signature, it was spring timein Japan, the whole Institute was going to celebrate"Hanami", to watch the magnificent cherry trees blos-soming, close to ISSP, ...in a graveyard near by.On the very eve of that important social event, a reportarrived about new experiments in a compound
BSCO of the same class as
LBCO with a much higher super-conducting temperature, and much more reliable crystalcomposition than that of
LBCO .There was no sign of the C v linear term in tempera-ture in the superconducting phase. It was clear that forone reason or other, the results displayed in where notrelated to superconductivity My participation in the joyful Hanami event is one ofthe worst memories of my stay in Japan. Not only had Ipublicly put my name on a paper reporting incorrect re-sults, not only had I induced a japanese group to publishincorrect conclusions on a dubious experimental result; by specifying in the head of the paper that I was a mem-ber of the ISSP, I had put a stain on its internationalreputation. I had lost face. In japanese terms I had dis-honoured my samuraï, I had to commit seppuku.I did not commit seppuku, but I almost felt physicallythe weight of the shame on my shoulder. This shameand this stain remained with me during the remainingmonths of my stay in Japan.
IV. LESSONS AND COMMENTS
At first sight, why spend any time writing about thisepisode? It looks simply like an experimental and the-oretical blunder, why not let it rest in the graveyard ofthe host of incorrect papers?However, I believe it deserves some more discussion.The development of this story, its context, its causes, itsresults, have some philosophical, sociological and episte-mological interest.To begin with, what was wrong with the experimen-tal results? When one looks at the graph for γ ( c Ba ),where c Ba is the Ba concentration in the LBCO sam-ples, one finds no indication of experimental error bars.The probability is that if the error bars were indicated,a straight line in function of c Ba would be compatiblewith the data, indicating a phenomenon triggered by Ba impurities and not superconductivity. The experimentdid measure a significant low temperature γ term coin-ciding with the superconducting phase, and which wasnegligible in the non superconducting one, but the graphof the measurement was too inaccurate to suggest thatthe RVB prediction was confirmed. A well known fact isthat the validity of any measure depends on the upperand lower limits of its accuracy.So how come I did not worry about such indications,and ask the Hokkaido group to evaluate the error barsprior to publication? I worried at first about this, but dis-missed my worries when the XXX group leader claimedhe had the same crooked curve, with zero γ ( c Ba ) until thecritical Ba concentration for superconductivity to appearwas reached.This leads to a second question: why did the XXXgroup leader, who was a well known scientist, physicsProfessor in the XXX University, announce he had thesame results as the Hokkaido group? I am convinced hehad no such results, let alone results identical to those ofHokkaido.Japan has 88 national universities, 7 of which are "im-perial universities", founded before world war two. TokyoUniversity, Kyoto University, and Hokkaido University,and others, are parts of this University elite. When I hap-pened to mention to japanese people that I was lecturerin Tokyo University, I was immediately considered witha lot of respect. XXX is a national University, foundedin 1949, not an "imperial" one. Has this played a role inthe attempt by the group leader in XXX to claim equalsuccess with Hokkaido in the experimental investigationof the RVB theory? No one will ever know, but such hu-man passions ("sad passions" discussed by Spinoza) in thescience activity are frequent. The excitement about theHTS phenomenon was shared by most searchers in thatfield, with its promise for world scientific recognition incase of success. There are many occurrences, in the lastdecades of physics research, of deliberately fake reportsin some of the best science reviews such as Nature, Sci-ence, Physical Review Letters, etc.. They are sometimesconnected to an attempt to get approval of grants fromspecific peer committees for research funds, sometimesinspired by a search for recognition. There are numer-ous cases of scientific thefts, when a searcher publishesunder his name a result obtained by others. The socialpressure among scientists to succeed, to be invited fortalks in conferences, for stable positions, for promotions,is producing those failures of scientific ethics. In the caseof HTS in 1986, with the world spotlights on, and theexcitement among physicists, all the elements for suchethical failures were enhanced .It was highly recommended for theorists in my labora-tory in France to visit experimental facilities where ex-periments were conducted which were connected to the-oretical problems of interest. Examining the apparatus,discussing with experimentalists how they were conduct-ing experiments and what were the relevant theoreticalquestions: this was thought to be part of the theorist’sjob. I believe now that, among my japanese colleaguesin ISSP, my visits to experimental groups to discuss rel-evant experiments about HTS and RVB were not viewedpositively, although this was not openly expressed, be-cause of politeness ethics. Similarly, I realized after atime that asking questions and emitting critical scien-tific comments while attending a science talk was not apolite thing to do...Had I been impolite with my XXXcolleagues?The episode I am discussing here is certainly due to acombination of various factors.When I prompted two different groups to work on theconfirmation, or the falsification, of the RVB prediction,I unleashed a competition which could have been fruitfulif both competing groups, while working with their ownways and methods, had cooperated and exchanged infor-mations about their mutual progress. An obvious lessonis that the competition, together with scientific cooper-ation between the two groups would have spared them,and me, the disgrace of a faulty publication, as well asmisconceptions in the physics community during a fewmonths... V. EPISTEMOLOGY
Although the following is not all intimately connectedwith the episode of the incorrect specific heat paper , itis useful to set the stage with general comments on thescientific activity and conceptions surrounding it.Before commenting on connections of the story of with various contemporary debates in epistemology, Ibriefly describe my own understanding on the processof knowledge of inanimate matter.The development of physics is a historical and socialprocess. Since, roughly, the end of the nineteenth cen-tury, it combines the subjective activity of individuals,theorists and/or experimentalists, with that of groups ofindividuals, laboratories, networks of groups or labora-tories, conferences where new results are publicized andwhere critical confrontations between conflicting viewsoccur, scientific journals, national funding policies, etc..Scientific results play an increasing role in industrial pro-cesses, a phenomenon which is also a practical proof ofthe effectiveness of science to account undeniably for alarge number of real processes of nature.A collective (social) physicist is formed as a result.This social activity deals with knowledge of objectiveproperties of matter. The latter can be studied experi-mentally with repeated experiments by different indepen-dent actors in different places under identical conditions.The possibility of repeated experiments under identicalconditions by very different actors is one of the specificfeatures of physics (or biology) research, as compared tomany issues in social sciences, for example. It allows toreduce the subjective part of the knowledge process. Itallows to correct errors, as I learnt at my own cost , andto elaborate grains of truth on inanimate matter, truthsabout the laws of nature, some of which may be absolute,undisputable, some which are relative to a given level ofcollective scientific knowledge, of technological progress,of measurements accuracy, etc.. The historical, social,practical knowledge process allows to "re-produce" ac-tual objective processes of nature, as is clear from itssuccessful predictions and its infinitely many practicalapplications in social life.Thanks to technological advances, and to continuousrenewed social needs, the process of knowledge neverstops asking new questions, abandoning refuted theories,and improving on previous re-productions of real pro-cesses with better and better accuracy.Although I share with Popper the observation thatthere is a cumulative progress of science, I do not agreewith him that all knowledge is provisional. According tohim, a theory is only valid as long as it is falsifiable.Among many examples, the history of superconductiv-ity is a good counter example. The BCS theory on the su-perconductivity of superconducting simple metals hasundisputable results. Whether RVB theory will end upbeing recognized as a fundamental addition to BCS the-ory for the understanding of HTS remains to be seen, aswill be discussed later. A. General comments
What I have described in the Introduction, namely thediscovery of HTS, is a good example of what Bachelard called a social production of science. LBCO and all theHigh Temperature Superconductors of the same class,i.e. based on coupled copper oxide layers, are chemicallyengineered compounds. They were made possible by ad-vances in oxyde chemistry, both experimental and theo-retical, by hosts of scientists of different fields. In thatsense, HTS, as most advances of contemporary physics,is a social production. However, contrary to Bachelard’sambiguities about the subjectivity associated with socialproductions, HTS is also definitely an objective propertyof matter, in given conditions of temperature, pressure,magnetic field, independent of human thought as evi-denced by its practical uses ( magnetic fields detection,levitating trains on superconducting material, permanentcurrents producing magnetic fields, for example), as wellas the infinitely many repeated experiments in hundredsof different laboratories in the world.The theorist interested in solving the mechanisms ofHTS does not, as Althusser wrote when he battled suc-cesfully with empiricism, work on the real object. Theimage of the LBCO crystal, which is shown on figure(I), is not the real object; it is a man-created image. Thesearchers work on an object of knowledge already elabo-rated by various social processes as discussed in the intro-duction. However they also work on a phenomenon whichis independent of any thought process, i.e. superconduc-tivity, an objective state of matter, however engineeredby human practice: the "theoretical practice" is not dis-connected from the real object, it is intimately connected,through a complex sensible, historical, technological, ide-ological process, to the phenomenon displayed by the realobject, as discussed by Sève . I would have been happyto confirm the γ T term in the specific heat of HTS, butnature denied it, irrespective of my intentions and de-sires.I do not feel it necessary to discuss various philosoph-ical trends (see for example reference on skepticism)which question how one can be sure (have a "true be-lief") that superconductivity exists and has such and suchproperties. I share Hacking’s argument on that matter:hundred years after Marx , he rediscovered the criterionof practice as a criterion of reality. B. Scientific revolutions.
I have used in the Introduction the notion of scientificrevolution when discussing about HTS and RVB. Sci-entific Revolutions have been discussed in particular byBachelard and Kuhn . Based on the history of physics( Newtonian physics, relativity, quantum mechanics, andothers), the latter author distinguished normal phasesof scientific activity, which end when the paradigms ofthis activity are replaced, after a period of crisis, by newparadigms. An example he discussed is the replacementof geocentrism by heliocentrism; the emergence of quan-tum mechanics could be quoted as another example, al-though it did not invalidate many results of classical me-chanics in their own domain of validity for most macro- scopic objects.HTS has a number of aspects of a scientific revolu-tion: the unexpected material where it was discovered,the stunning increase of superconductivity critical tem-perature in the new material, the revolutionary theoret-ical proposal such as RVB. Seventy five years after itsdiscovery in 1911, the belief that no superconductivitytemperature larger than about 23 K would ever be ob-served was shared by the vast majority of searchers inthe field. Until 1986, superconductivity was thought tohave no future as a research programme. It was not a pe-riod of "normal science" in Kuhn’s sense: it was almostinactive. From 1986 on, the need for a new theory, funda-mentally different from the "old" BCS superconductors ,was obvious, as I described in ref. . The RVB paradigm ,at the basis of the episode described in this paper, mightbe one such new paradigm.There is however a major difference with Kuhn’s de-scription of Scientific Revolutions. HTS did not falsifythe BCS paradigm for the well known "old" superconduc-tors. It opened a new field of condensed matter physics,about a new category of superconducting compounds. Asdiscussed in a later section, it may evolve into blendingthe modern theories with the BCS one, i.e. into blendingparadigms based on expression (1) and (2).The category of Scientific Revolution is thus richerthan that discussed by Kuhn: there are scientific rev-olutions which are based on new paradigms without fal-sifying previous ones.Other comments deal with the reasons that led me toabandon the scheme based on (1) and adopt as researchprogram the scheme based entirely on (2).There were scientific, esthetical, institutional, psycho-logical reasons, and also unconscious ones which I under-stood only years later, all more or less intermingled. C. Scientific reasons
I believed that the novelty, audacity of the RVB pro-posal by Phil Anderson and collaborators correspondedto the amount of novelty and surprises associated withthe stunning discovery of HTS in compounds where allprevious superconductivity culture would have denied itspossibility. I believed this offered a possibility for a newfield of condensed matter science to develop, a field Ihad abandoned ten years before for lack of experimentalsupport. I believed that this new field – strong inter-actions in Condensed Matter physics – would developwithin the non relativistic quantum theory which wasthe relevant theoretical framework to explain HTS. Thusmy scientific reasons were both based on a number ofbeliefs: true beliefs about quantum mechanics, crystalstructure of LBCO , existence of superconductivity, etc.,and a subjective belief on the validity of RVB.
D. Esthetical reasons
I felt the RVB proposal was so new, so seemingly welladapted to the structure and chemical composition of
LBCO that there was an intellectual beauty about it. In1973, Anderson had developed the concept of RVB fora novel ground state of an insulating linear array of quan-tum 1/2 spins ; this idea was in turn a generalization,for an infinite array of spins, of Linus Pauling’s theoryfor the benzene molecule. At the time, the idea was orig-inal and interesting, it was a new concept in the field ofmagnetic insulators, but it had no obvious experimentalcounterpart. What Anderson did in 1986 for the theoryof HTS was to extend this theory to a planar array ofquantum 1/2 spins, and to postulate that the injectionof "holes" (equivalent to suppression of electrons in the CuO plane) would result in a charged bosonic superfluid,i.e. a superconductor . The progression of theoreticalideas from the benzene molecule to the doped CuO planeof spin 1/2 particles had for me a beauty in itself.
E. Institutional reasons
I was a CNRS searcher in 1986. My very social ex-istence was based on investigating new condensed mat-ter phenomena, explaining them, and publishing papersin good quality physics journals, so that the new pub-lished results would influence other research programs.I thought that as such, I had to participate in the at-tempt to understand, explain and develop the theory ofHTS, both as a scientific challenge, and as an industrialone; HTS had potential applications for the fundamen-tal problem of electricity storage, which would be an in-dustrial revolution. If I made a significant contributionto some research topic, I would gain recognition amongpeers, perhaps a promotion, perhaps fame, etc..
F. Psychological reasons
Working in this new field, with its scientific and indus-trial challenges, was exciting; I had learnt to value thescientific stimulation connected to working on a topic ofworld wide scientific interest: research in such a field gavean impression of more intense intellectual life, togetherwith the risk to fail in bringing forward significant novelresults.I shared a very general desire among researchers forsocial recognition through scientific achievements.I believe now I had also unconscious reasons: I had metPhil Anderson several times in scientific meetings, duringmy career. He was seventeen years my elder, a scientificleader when I started research, and he had treated mein a friendly manner, showing appreciation for my PhDwork... and my skills as a chess player. On the otherhand, I resented the lack of support, scientific or moral,or human warmth, from my scientific adviser. I felt my life as a searcher would have been richer if Phil Andersonhad been my science adviser. In other words, his was abenevolent father image. By immediately adopting hisRVB proposal, I became symbolically part of his family.This included a number of his collaborators, whose workI admired. One of them was Hidetoshi Fukuyama, headof the theory group in ISSP.Ever since Plato and Aristotle, philosophers have dis-cussed about the reasons to act: in the present case, Itried to describe the various reasons which led me towork within a scheme based on relation (2) rather than(1). There are rich debates among them about the dif-ferences between "normative reasons" and "motivating",or "explanatory" ones. A normative reason is a reasonto act. A motivating reason is the reason for which onedoes something. In my case, both types were clearly en-tangled. A study and complete bibliography about thistopic is found in reference . G. Anarchist epistemology?
The various personal reasons to choose one paradigmrather than another I have discussed above seem good ex-amples of what Feyerabend discussed in his book
AgainstMethod and also . He criticizes the notion of scientificactivity as based on a universal rational method. Hestresses subjective reasons to adopt a theory. AlthoughI seem to offer a good personal example in support ofhis claims, my own reasons were not devoid of belief ina fairly general method of science: I took into accountnew experimental results, which, in view of existing wis-dom about superconductivity, seemed to require new con-cepts, and to confront them with experiments.Phil Anderson’s RVB theory was a scientifically at-tractive proposal. I decided to study it theoretically, andsimultaneously to test it experimentally, with the helpof skilled experimental physicists. Furthermore, a largenumber of Condensed Matter physicists engaged in thesame research program on RVB. Many had probably rea-sons analogous to my scientific ones, perhaps a sizeablenumber shared my esthetic reasons, perhaps others alsotended, as I did, to pay attention to RVB because of PhilAnderson’s fame as a physicist. Very few had psycho-logical or unconscious reasons analogous to mine. Forthe vast majority, what mattered was to develop an un-derstanding of HTS and of its phenomena. Individualreasons had in the end little or no weight in the socialprocess of science.I have described elsewhere (ref. ) how various othertheoretical ideas, different from RVB, were proposedsince 1986 by various scientific leaders to explain HTS.I emphasized that each such new proposal was rootedin each author’s scientific past, together with a generalundisputable background knowledge of Condensed Mat-ter physics. This reminds in some sense of Feyerabend’sremark on the weight of existing research programs toprevent new ones from developing. It also seems to sup-port Feyerabend’s relativism: various groups of scientistsbelieved in various theories, some of which were incom-mensurable: at first sight expressions (1) and (2) are mu-tually exclusive. This in turn looks like an example forwhich the Duhem-Quine thesis on the underdeter-mination of theory by experiments is temporarily valid.However, this state of scientific anarchy is but a transi-tory aspect of science progress, the process of researchis constrained by the objective properties of inanimatematter. The latter allow to correct scientific programswith sufficient "protective belt" (see Lakatos ), discrim-inate between theories after a certain time. For instanceDuhem’s energeticism eventually had to be abandonedin favour of Boltzman’s atomic theories. In HTS, therestill prevails a state somewhat analogous to Feyerabend’sanarchist theory of science or to some of his relativism.However, in spite of the many persisting disagreementsamong researchers on HTS, all agree on a number of ba-sic physical laws governing superconductivity, which areundisputable properties of matter. H. Establishing truths
The absence of a γ term in HTS is now an undisputableirreversible truth. This is now established by variouscareful measurements by different searchers. Duhem claimed that the role of theory is to account for appear-ances, and that no certainty can be obtained on the on-tology of phenomena. If instruments are involved in anexperiment, they can lead to experimental errors, theymay have defects, and lead to artefacts. At first sight,the Hokkaido paper would be a good proof of that the-sis. But it is valid at a very restricted level, at most, fora certain time, for a few individuals or groups of individ-uals, and has no lasting universal validity, as discussedin ref. . As shown by the XXX part of this story, othersources of errors, due to human passions involved in sci-entific research may play a role during a certain time. Butscientific activity is a social one, as stressed above. Basedon various well established technologies such as calorime-try, chemical synthesis of copper oxyde compounds, etc.,contributions from various research groups in the worldrapidly corrected the faulty paper and established thetruth about the existence of a γ term in the supercon-ducting phase of HTS. I. Crucial experiment. Popper’s falsificationismfalsified
Bacon has introduced the notion of crucial experi-ment, which allows to discriminate between a truthfultheory and an erroneous one. Duhem has argued thatthere is no such thing. I have argued elsewhere thatDuhem’s stand is falsified by his own admittance that"the theory of vibrating strings is certain". The notion ofcrucial experiment is vindicated in many cases by scien- tific practice and is intimately connected with the notionof truth, as I discussed in a previous paper . The ab-sence of a γ term in the specific heat of LBCO was acrucial result, but only in a limited way, as discussedbelow.Following Popper , the RVB proposal on HTS is abona fide scientific theory, since it can be falsified. PhilAnderson’s RVB original proposal predicted a specificheat linear in temperature in the superconductive phase.It is now well established that there is no such phe-nomenon in HTS.According to Popper, this would ensure the falsifica-tion of RVB theory. It should be abandoned. However,this did not happen. The theory was slightly modifiedto take into account the zero γ result: instead of propos-ing a spherical symmetry ("s-wave" symmetry) for thesuperconducting order parameter in HTS, a so-called "d-wave" symmetry was introduced . This was not simplyan ad-hoc change: it was more coherent with the basichypothesis of inequality (2). Indeed, a superconductingorder parameter with d-wave symmetry implies that theinteraction energy U between electrons is minimized incomparison with the s-wave case. The absence of a γ term in he specific heat of HTS is crucial to eliminatethe possibility of s-wave symmetry for the HTS orderparameter, not for the validity of RVB.This is in line with Lakatos’ and Feyerabend’s crit-icisms of Popper’s Demarcation Criterion. Lakatos ar-gues that a scientific research program consists of a "hardcore" and a protective belt. Outside the hard core, thereare a variety of auxiliary hypothesis to protect the hardcore; changes and adjustments may occur in the pro-tective belt, leaving the hard core untouched. This iswhat happened to the RVB research program when itwas proved that the γ term is absent in HTS, at the costof changing the s-wave original proposal to the d-waveone.Following Feyerabend, conformism is likely among sci-entists to favour old theories rather than revolutionaryones. The history of HTS offers both examples andcounter examples, so that Lakatos seems to be correctin pointing out the role of conflicts between theories inthe progress of science.Popper, Lakatos, and Feyerabend all neglect the role ofpractice to prove at least in an approximate way varioustruths about nature. "Old" superconductivity and HTSrequire different theories, but both evidence an undis-putable fact of nature, i.e. superconductivity.In contrast with relativistic Feyerabend’s positions ,no serious physicist is free nowadays to argue that a nonzero γ exists in HTS compounds of the LBCO class,because the incorrect paper(ref. ) has convincingly beenshown incorrect.The conclusion of this paragraph is that RVB contin-ued to be an active research program, even though oneinitial prediction was proved wrong. To this day, firsthalf of year 2020, 34 years after the HTS discovery, thebattle among theorists about the mechanism of HTS isstill raging (see for more details ref. ( ). J. Contradictions?
I mentioned in the Introduction that my first publishedpaper on the mechanism of HTS was based on the weakcoupling hypothesis (inequality (1)). This was writtenbefore I left for my one year stay in Japan. I reportedabout this paper only once in an international conference(in Genova in 1986). Thereafter I became so convincedthat the RVB picture based on inequality (2) was thecorrect framework that I never even gave another talkabout my weak coupling work in Japan. I felt it was anirrelevant approach, it would not interest my colleagues.Both approaches seemed incompatible. If one thoughtthe weak coupling (1) approach was the right one, noattention would be payed to works based on the strongcoupling approach (2), and vice versa. Groups workingon the (1) hypothesis would not talk to groups workingon (2) and vice versa. The development of this battle isdescribed in many more details in reference . Inequalities(1) and (2) are a particular example of a general coupleof contrary conditions which are basic in the descriptionof physical processes: (1) is a special case of the domi-nation of kinetic energy over potential energy, contraryto (2). A paradigmatic example is the classical harmonicoscillator. Depending on which term dominates the totalenergy, the phase oscillates periodically around zero, orincreases periodically by 2 π . In both cases, both energiestransform in time one into another. Internal energy andentropy are another couple of contraries in the free en-ergy: the internal energy drives order, the entropy drivesdisorder.There are well known examples of metals where in-equality (1) applies without discussion in the descrip-tion of their metallic properties Au, Ag, Cu, , transitionelements of the first series in the periodic table, etc.,for example. There are well known examples of mag-netic insulators where inequality (2) applies withoutdiscussion:
CuO, F e O , and all so called Mott insulators,or Quantum Hall systems . Is it conceivable that mate-rials exist – such as HTS materials – the theory of whichhas to resort simultaneously to both inequalities?Sixteen years after my weak coupling paper on HTS was published, the developments of experimental work onHTS caused theory to evolve towards a combination of(strong coupling) RVB theory (expression (2)) and weakcoupling theory (expression (1)); the results of my 1986paper were rediscovered. Citations of that paper startedto appear in HTS research theory papers by groups whoworked in developing the RVB approach.In other words, research on HTS evolved after almosttwo decades towards a simultaneous account of both(contradictory) inequalities (1) and (2) .There are various examples, in the history of physics,of successful theories which have superseded what hadappeared during many years as contradictory, i.e. in- compatible ones. Quantum physics for example super-sedes the theoretcal contradictions between the contin-uous (wave like) and the discrete (corpuscular) theoriesof light or microscopic particles. The theory of ferro-magnetism developed during years along two seeminglyincompatible lines: that based on localized electrons onatomic sites in a crystal, and that based on band the-ory i.e. on electronic wave functions extending over thewhole crystal volume. It is now based on a picture withboth extended wave functions and localized magnetic mo-ments (see the discussion in ref. ). Another example isthe long lasting historical battle between energeticists àla Duhem and exponents of the atomic theory of matter.Even though my first HTS theoretical paper had re-sults showing that the "weak coupling" theory based on(1) did exhibit interesting features (for example a sharprise in the superconductivity critical temperature upondoping), in favour of framework (1), I neglected this re-sult altogether after I became convinced of the relevanceof the strong correlation scheme based on (2).This attitude of mine was a dichotomic one: either (1)had to be the valid starting point, or (2). After RVBtheory appeared, I became blind to the interesting re-sults of my own work! I had been probably too igno-rant of Hegel’s, Marx’ and Engels’ philosophical work ondialectics . Had I been more learned in philosophy,I might had been capable of thinking that theories basedon such dichotomies as the opposition between (1) and(2) often account, each, for only a partial aspect of theprocesses at work in the real object. Theory is often,if not always, constrained to evolve in time to take intoaccount contradictory aspects of things, as forced uponknowledge by the growth of experimental information.Theory evolves in time to embody contradictions in there-production of real processes. As far as HTS is con-cerned, data from a variety of experimental techniquesseem to reveal that weak coupling and strong couplingtheories are both simultaneously relevant. This is proba-bly a sign that in the HTS material the actual situationis: U ≃ W (4)In some sense, this paper is a description of two scien-tific errors: one is the publication of an incorrect experi-mental paper . The other is the failure to believe in theinterest of my own work in the search for a theoreticalunderstanding of the HTS phenomenon.Had I not been dogmatic in my belief in (2), I wouldhave publicised among HTS researchers the interestingresults obtained ( ), on the basis of expression (1),early in the HTS research development. This would havehelped in promoting more quickly a better theory of HTS.When a theory embodies contradictions in the repre-sentation of reality, can one argue that it is incoherent,only due the subjectivity of a human construct? Thiswould deny that experiments yield results which are, atleast in parts, independent of the preconceptions of ex-perimentalists. The idea that contradictions are an on-0tological aspects of things in nature has been developedin particular by Engels , based on Hegel’s dialectics .This is considered by many philosophers of science asnonsensical . What can be stated safely at leastis that theories are almost always driven to deal with con-flicting theoretical terms. Physics continuously explainsmotions, evolutions, transitions, spontaneous breaking ofsymmetries, etc., on the ground of opposition betweenconflicting terms in the theory, as discussed above. Thenotion that conflicting terms in theory reproduce real on-tological contraries is a logical one . My own opin-ion on that matter agrees with Sève’s views who arguesabout the "dialecticity" of nature. He means by thatterm that the processes of nature constrain the theory toaccount for them in terms of dialectical development ofcontradictions. VI. CONCLUSION
I have described how I was led to put my name on anexperimental paper the results and conclusions of whichwere found a few months later to be erroneous. I havedescribed some of the questions which make this episodean example of the various factors which influence thedevelopment of knowledge at an individual, sociologicaland philosophical level.
VII. APPENDIX
In all superconducting materials known until 1986, thespecific heat was well known to vanish exponentially with T . This was easily explained within the electron pairingmechanism in singlets described in 1958 in ref. . The lat-ter mechanism creates a forbidden energy gap ∆ ≃ k b T c at the Fermi surface, which freezes electronic excitationsfor temperatures T < T C , where T c is the temperaturebelow which superconductivity appears.In the initial RVB proposal, a fermionic Fermi surfaceof pure spin excitations coexisted with superconductivitydown to T = 0, so that electronic spin excitations wherejust as possible as electronic charge excitations in a nor-mal metal. As a result, the low temperature specific heathad to vary with T as in a normal metal, i.e. C v ∝ T .The RVB proposal started with the known fact that theundoped CuO atomic layers carries one localized electronon each crystal site and is an insulator, almost a text-book example of a magnetic insulator. This localizationof electrons on crystal sites is the result of the strong re-pulsion U , compared to the bandwidth W : expression(2) then is the correct starting point. Conventional wis-dom had it in the seventies that the ground state of CuO atomic layers would be a 2D insulating antiferromagnet,with electronic spins up alternating from atom to atomwith down spins.When two atoms labelled i and j in a crystal carryeach an unpaired localized electron, the quantum state for the two electrons may have different forms, depend-ing on the overlap between the atomic wave functions.Roughly speaking, the two spins 1/2 may couple to forma total spin S = 1, or they may (approximately) cou-ple in alternate directions:spin projection S z,i = +1 / S z,j = − / / i and j may combine in a superposition of amplitudesto form a state S = 0 The superposition is that of state | + − > with | − + > , i.e. the state with spin 0 which is asinglet: 1 / √ | + − > −| − + > ) sharing the two atoms i and j . A singlet is a boson, formed with two spin 1/2particles, which are fermions.The Resonating Valence Bond proposal, first intro-duced in 1973 by Phil Anderson about a 1D model of lo-calized spins (the "railroad threstle"), is that the groundstate of an ordered 2D crystal, such as CuO
2D atomiclayer, with one unpaired electron spin per atom is thesuperposition of tensor products of all possible singletstates coupling electrons in the crystal in singlets associ-ating electrons on atoms two by two. (In fact the groundstate of a 2D crystal with localized electrons on crystalsites was studied in the late eighties by Monte Carlo com-putations which did not support the RVB ground stateproposal; they found an antiferromagnetic ground state).Superconductivity, according to the RVB scheme, wasthe result of doping the magnetic insulator with holes(i.e. of suppressing electrons by chemical doping) in aRVB ground state.A doped hole in the RVB ground state breaks a singlet,thus liberates an unpaired spin 1/2, and an atomic sitewith zero localized spin: a spinless hole. Then each newparticle, the spinless hole on one hand, and the neutralspin 1/2 can migrate in the crystal because of the atomicwave functions overlap.A stunning result of this analysis is that, within theRVB scheme, in a strongly correlated 2D crystal, dop-ing of holes results in a separation of charge and spin.In a weakly interacting electronic liquid (such as a nor-mal metal like Cu , each electron carries simultaneouslycharge and spin 1/2.At finite doping, the conclusion is that there exist apopulation of charged bosons called holons, and a popu-lation of neutral fermions with spin 1/2, called spinons.A liquid of bosons condenses in a a superfluid state (suchas He ). Charged holons may condense in a charged su-perfluid state: a superconductor. A liquid of free spinonsobeys Fermi statistics, and has a Fermi surface of spin ex-citations, similar to that of electrons in a normal metal.With his revolutionary RVB proposal, Phil Andersonin 1986 seemed to take into account the main originalproperties of LBCO , and to provide an explanation forthe superconductivity in a doped magnetic insulator.The other starting point of the theory, i. e. expression1(1), which was at the basis of my first paper on HTS,leads to a different analysis of the ground state of theundoped crystal: with one electron per atom in extendedwave functions, the crystal has a half filled band of de-localized electronic states (the filled band has twice asmany states because of the degeneracy due to the elec-tron spin). However, in the undoped 2D crystal, theFermi surface is a square. In that case (a special caseof so-called "nesting Fermi Surface"), weak interactionscause an instability of the normal metallic state and giverise to a Spin Density Wave (SDW) which has alternate spin density direction on each atom. This SDW causesan energy gap at the Fermi Surface, and thus the groundstate is a (weak) antiferromagnetic insulator. Schulz showed that in that case, there is a competition betweenthe insulating SDW ground state and superconductivity.I showed with my students in 1986 that a more realisticFermi surface allows superconductivity to dominate.Given the similarity between the results of the two sce-narii, it is eventually not surprising that a correct theorycombines concepts of both. G.Bednorz and K. A. Mueller,
Z. Phys , B64 , 189, 1986. H. Kamerlingh Onnes,
Leiden Com. , ,1911. M. Tinkham,
Introduction to Superconductivity ,McGRAW-HILL International Editions, 1996. P. Lederer
The Battle of High Temperature Superconduc-tivity arXiv:1510:08808. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. , 1175, 1957. P. Lederer,
The Quantum Hall Effect of Field Induced SpinDensity Wave Phases , Jour. Physique, vol6 , 1899, 1996;see also G. Montambaux,M. Héritier, P. Lederer, Phys.Rev. Lett. , 2078, 1985; D. Poilblanc, G. Montambaux,M. Héritier, and P. Lederer, Phys. Rev. Lett., , 270,1987. H. Schulz, Europhys. Lett. , 997, 1987. P. Lederer, G. Montambaux, D. Poilblanc, J. Phys. France , 1613-1618 1987. P. W. Anderson, G. Baskaran, Z. Zou, and T. Hsu, Phys.Rev. Lett. , 2790, 1987. This seduction is commented upon in a later section of thispaper. ISSP = Institute for Sol State Physics. Crucial predictions and experiments are discussed in sec-tion (V). I had published in Journal of the Physical Society of Japanthe first paper showing the scale of HTS in the RVB frame-work could not be the band width W of holes, but theexchange energy J among spinons. This paper, perhapsbecause it was published in Japan and with 8 monthsdelay (!), is hardly ever quoted, even though I reportedabout it in Aspen. K. Kumagai, Y. Nakamichi, I. Watanabe, Y. Nakamura,H. Nakajima, N. Wada, and P. Lederer,
Linear temperatureterm of heat capacity in insulating and superconducting La-Ba-Cu-O systems , Phys. Rev. Lett.Âă60, 724, - Published22 February 1988. The linear specific term reported in
LBCO is due in factto a particular impurity disorder effect. This paper is written during the Covid-19 pandemy. Per-haps the race among epidemiologists and searchers in bi-ology to find a treatment will help understand the HTSsituation in 1986... P. Lederer,
Kinetic Energy of Holes in the Hubbard Model
Journal of the Physical Society of Japan , 1729-1742,1988. L. Sève,
Sciences et dialectiques de la nature , La Dispute, Paris, 1998;
Penser avec MArx aujourd’hui, Tome III “ LaPhilosophie?” ,La Dispute, 2014. K. Popper
Conjectures and Refutations: The Growth ofScientific Knowledge , London: Routledge, 1963. G. Bachelard,
Le nouvel esprit scientifique , Paris, PUF,1934. Such as Tin, Mercury, Zinc, Vanadium, etc.. A "problem solver" as Popper put it . L. Althusser, J. Rancière, P, Macherey,
Lire le Capital ,Maspéro, 1965. https://plato.stanford.edu/entries/skepticism-content-externalism/ I. Hacking,
Representing and Intervening. Introductorytopics in the philosophy of natural science , CambridgeUniversity Press, 1983. K. Marx
Zur Krtitik de politischen Ökonomie , 1859. T. Kuhn,
The Structure of Scientific Revolutions. , Uni-versity of Chicago Press, 1962. P. W. Anderson, Mater. Res. Bull. , 153, 1973. In fact a model somewhat analogous to a railroad, he called"railroad threstle". See sectionVII. Alvarez, Maria,
Reasons for Action: Justification, Mo-tivation, Explanation , The Stanford Encyclopedia ofPhilosophy (Winter 2017 Edition), Edward N. Zalta(ed.),
URL =
Against Method , London: Verso, 1975. P. Feyerabend,
Science in a Free Society , London: NewLeft Books, 1978. P. Duhem,
Sauver les apparences. Sur la notion de théoriephysique de Platon à Galilée , Vrin,
Bibliothèque des TextesPhilosophiques - Poche , 2004;
La théorie physique , 1906,réédition Vrin 1989. W. V. Quine,
A System of Logic , Cambridge, Mass, Har-vard, 1934. I. Lakatos, it The Methodology of Scientific Research Pro-grams, Philosophical Papers Volume1, Cambridge Univer-sity Press, 2001;
Proofs and Refutations , Cambridge: Cam-bridge University Press, 1976. Francis Bacon
Novum Organum P. Lederer,
Sur la thèse de Duhem sur la sous-détermination , Cahiers rationalistes, , 2011. P. Lederer,
The Quantum Hall Effects: a PhilosophicalApproach , Studies in the History and Philosophy of Mod-ern Physics, , 25-42, 2015. K. Popper,
Objective Knowledge, an Evolutionary Ap- proach , Clarendon Press, 1972. see ref. . This is apparent in particular in the work by the ETHZurich group led by Maurice Rice, another historical col-laborator of Phil Anderson’s. P. Lederer and D. L. Mills, Phys. Rev. , 590, 1968. F. Engels,
Dialectique de la Nature , Éditions Sociales,1952. G. W. F. Hegel
Wissenschaft der Logik , 1812 to 1816. Immanuel Kant