In 1986, a stunning experimental discovery rocked the world of physics, that of High Temperature Superconductivity 1 . It was discovered in a material, La−Ba−Cu−0 (hereafter LBCO), for which no learned solid state physicist, either on the theoretical side or on the experimental one, would ever have believed it to occur. The superconductivity was observed at temperatures which had been thought until then to be impossibly high, as compared to that of all studied superconducting metals since the discovery of superconductivity in 1911 2 .
The search for higher temperature superconductivity (the highest one until then was 21 0 K) had motivated some researchers in the previous years, most had given up. Superconductivity was considered widely among condensed matter physicists as a "dead" topic, a topic where nothing significantly new would ever be found any more. Researchers had moved to other fields. Until then, it had been common knowledge among physicists that magnetic impurities were detrimental to superconductivity, as proved by scores of experiments (see for example ref. 3 ). A small concentration of magnetic impurities in a superconductor was known, and understood, to lower drastically the temperature below which superconductivity was present. In the new superconducting material, however, magnetic atoms were not only present, but in fact densely so throughout the material (see for example ref. 4 ). In fact LBCO was very close to being an antiferromagnet, i.e. a material where magnetic 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 ferromagnets where all spins have the same direction at low temperatures). Not only are magnetic ions dense in the new superconducting material, but superconductivity persists up to temperatures significantly larger than observed until then in non magnetic materials. In fact, very rapidly, superconductors of a class similar to LBCO reached superconducting temperatures an order of magnitude larger than any previously known material.
It was obvious to the vast majority of physicists that they were dealing with a qualitatively new phenomenon, immediately dubbed "High Temperature Superconductivity"(hereafter HTS). It quickly made head titles in the news of the world, predictions of a new technological era were made, or even an industrial revolution was hypothesized : in particular, if superconductivity could be made to persist up to ordinary temperatures, the old industrial problem of electricity storage promised to be solved, since superconducting rings can store electrical currents with vanishingly small resistive losses for very long times. Spectacular experiments showed levitating objects, or even people, above superconducting chunks of the new material, etc..
Technological expectations in various industries were huge. Financial ones as well.
Suddenly, condensed matter physicists were in the world news! As a result, hundreds of experimentalists turned to investigate the new materials, searching for even higher superconducting temperatures, and hundreds of solid state theorists around the world left more or less aside the projects they were previously interested in, to try and contribute theoretical advances in the understanding of HTS. An intense world competition among individuals, groups, laboratories, universities and research institutes developed.
At the time, I was at a turn of my career. I had led a small group of theorists during ten years from 1976 to 1986 with some success, about electronic properties of nearly one dimensional conductors. Those can be pictured as one dimensional atomic filaments weakly coupled by some chemical bonding, so that they exhibit very specific anisotropic properties. With my collaborators and PhD students we had gained some recognition for the discovery and understanding of a new phenomenon, dubbed Field Induced Spin Density Waves 6 . The explanation we had given of their observed Quantized Hall Effect had attracted attention. Our theoretical tools were those of Quantum Field Theory, in a theoretical framework called "perturbation theory" to deal with interactions between electrons in solids. The latter is the con-venient approach when there are sufficient hints that the phenomenon one wants to study cannot be understood if one neglects altogether the interactions between the charge carriers (conduction electrons) within the material. Taking into account interactions between electrons -contrary to what is needed to understand most physical properties of conductors such as Na, Cu, Ag, etc. -in the FISDW phenomenon is mandatory. However the interaction energy scale (written U ) in that system is small compared to the kinetic energy scale of electrons, in other words the width (written W ) of the electronic bands. This leads to what is called "perturbation theory": the theory relies on known results when U is zero, and introduces non zero U as a small perturbation to the zero U case. The theory of the "conventional" (low temperature) superconductivity is also based on perturbation theory 5 , so was the vast majority of theoretical papers on the interacting electron gas in Condensed Matter physics until the discovery of HTS. This basic starting point in the former case is summarized by the inequality below:
In fact, after writing my PhD in 1967 on magnetism in metals within this perturbation approach, which was the relevant one for magnetic transition metals, I became uneasy with the complications of perturbation expansions in powers of U of higher and higher order, demanding more and more complicated diagrammatic methods. I decided to explore the physics of systems governed by the opposite paradigm, the "strongly interacting limit", described by the following inequality:
The line of research based on equation (2) requires commpletely different theoretical tools, largely undeveloped ones at the time, and appeared at the time to be relevant in a much more reduced number of experimental situations: solid bcc 3 He, magnetic insulators such as Copper or Iron oxides (i.e. Cu0 or F e 2 0 3 ) and a few others. The challenge was interesting, I learnt some different physics, published a few papers, but after 1973, the number of interesting experiments stayed quite reduced, the interesting physics of 3 He required lower and lower temperatures, increasingly difficult to reach experimentally: I decided to revert to the study of experimental systems which were explored in my laboratory, and for which the approach of equation (1) was the relevant one. This led until 1986 to the FISDW work mentioned above. When HTS erupted, I was ready to dive into its mysteries, and perturbation theory seemed a sensible starting point. The new material was an anisotropic one, formed of parallel 2D arrays of CuO planes, weakly coupled to one another along the direction parallel to the plane, as depicted on figure (I).
A new theory of the interacting electron gas in two dimensions (2D) had just been published 7 within perturbation theory about a model which was an idealisation Superconductor: contrary to the vast majority of (lower temperature) BCS superconductors, which have a much simpler chemical structure and a much simpler (usually cubic) crystallographic one (in one guise or another)), this crystal is formed by parallel sheets of Cu-O (Copper oxide) planes. The "red" atoms here are oxygen atoms, the "blue" ones are Cu (Copper)atoms; two Cu-O planes are separated by "brown" atoms (such as Ytrium or Lanthanum while "green" atoms are divalent metals such as Ca or Ba. A large family of HT Superconductors exhibits the common feature of weakly coupled Cu-O planes which have a basic square elementary cell. The occurrence of linear arrays of Oxygen chains between copper planes is specific to the particular chemical (YBaCuO) shown above.
I am indebted to Julien Bobroff for providing me with the file for this figure. of the LBCO structure represented in figure (I). My first try at the theory of HTS was to work on this idealized model by taking into account a necessary improvement. The results were encouraging: they confirmed that the improved model exhibited a tendency to enhanced superconductivity. That work was sent for publication, and was published 8 in 1987. Then exploded the revolutionary Resonating Valence Bond (hereafter RVB) theory of Philip Anderson and collaborators 9 .
For the purpose of this paper, it is not essential to go into the details of the RVB proposal. Some however, are given in the Appendix, section (VII).
When I read the paper (reference 9 ), I was immediately deeply impressed by its audacity, and the novelty of the scheme he proposed to explain HTS. I had been a long time admirer of Phil Anderson's many brilliant and original contributions to physics, in various fields. The work on HTS in reference 9 was based on the hypothesis that the basic theoretical framework relevant to HTS was that of the inequality (2) . Instead of starting from the properties of a weakly interacting conducting electron gas, the starting point was that of the strongly interacting electron system of a quantum magnetic insulator. I was immediately seduced 10 by the RVB approach: there were various reasons for this : the audacity and the novelty of his proposal, the rationality of it, given Phil Anderson's previous work on RVB (see reference 4 for details), his scientific prestige; those three factors combined in my view with the novelty of the HTS phenomenon, the novelty of its experimental features, which were utterly contrary to all scientific rationale until then.
I decided to give up my previous approach based on condition (1) and decided to work on Phil Anderson's RVB approach, based on condition (2). Among condensed matter physicists, a fierce battle developed between champions of the weak interaction approach (expression (1)) and those of the strong one (expression (2), as described and analysed in ref. 4 .
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 11 group. Hidetoshi Fukuyama had spent some years at Bell Labs, at the time of its world fame, in collaboration with Phil Anderson. He had published many brilliant papers with the latter, together, among others, with Maurice Rice, another physicist I admired. Both had immediately adopted Phil Anderson's views and were active in developing the RVB strong interaction scheme.
I arrived in Tokyo and attended at first the International Conference on Superconductivity which was held that year in Japan.
A crucial 12 prediction of the RVB proposal was the existence at low temperature in superconducting HTS materials of a specific heat C v linear in temperature, i. e.
where γ in equation (3) is a constant for a given material. In all ordinary superconductors so far, theory and experiments agreed that γ was zero, in contrast to the normal (i.e. conducting but not superconducting) metal case where it is non zero, proportional to a quantity characteristic of the metal (the density of states at the Fermi level). A non zero sizeable γ in the new superconductors was a stunning prediction. Accordingly I paid special attention during the Superconductivity Conference to all experimental reports on the specific heat of LBCO. I found that there were large variations in the results; sometimes a non zero γ term was observed, with various magnitudes, sometimes there were none. The amount of Ba (Baryum) impurities to obtain superconductivity in LBCO was not accurately reported nor controlled. The Conference, where disagreements among theorists about the framework relevant to HTS were blatant, did not allow any conclusion to be drawn. I started my work in the ISSP laboratory in two directions; one was about consequences of the strong correlations (expression (2)) on the motion of doped holes in a magnetic insulator. The other was to visit two laboratories where I talked to experimentalists to encourage them in clarifying the experimental situation about the γ term. They had to study it while controling accurately the Ba concentration in their samples, and measuring the γ term both as a function of Ba concentration and of the superconducting temperature.
I talked to one group in Hokkaido, in the north of Japan, and to another one in XXX, in the south.
Three months after my arrival in Tokyo, I visited both groups, one after the other, to examine with them what were their results. What was shown to me in Hokkaido did not allow clear conclusions; accuracy in the Ba concentration was insufficient. It was agreed they had to improve that. In XXX, the situation was worse: no significant results were available.
However, to my surprise and delight, three weeks after my visit to Hokkaido, I received a fax from that group (internet was almost non existant...), exhibiting a significant rise of γ coinciding with the rise of the superconducting temperature! I had an immediate rise in adrenalin, I reported the results excitedly to Hidetoshi Fukuyama and my colleagues in ISSP. The news spread with the speed of lightning in Japanese labs. Phil Anderson's RVB theory was experimentally confirmed, along with its spectacular new hypothesis on the behaviour of strongly correlated electronic matter! I told the Hokkaido group they had to consider writing a report for publication.
A surprising news reached me two days later: I was told informally by ISSP colleagues that the head of the XXX group was reporting new experimental results, in a small physics meeting in Tokyo, of which I had not been aware. He claimed his group had obtained experimental confirmation of the significant γ term in LBCO! This was astonishing. Three weeks before, the XXX group I had visited had no result. They had communicated no new results since then. How could I understand?
My understanding of japanese ways of relating was obviously quite poor. I had noticed that some ISSP scientists whom I crossed in the hallways or in the staircase would behave as if I was transparent. I had understood that, not knowing my position in the hierarchy of science, they did not know how low they had to bow when they met me. The way out was for them to see through me.
With the claim by the XXX group leader that his group had results similar to those of the Hokkaido group, I could not but imagine that he was going to short the Hokkaido group about a historical result which had to become a landmark in the history of physics. On the other hand, his claim proved without doubt that the Hokkaido experimental results were undisputable.
When two different experimental groups, working independently in different labs in different parts of the world find the same results on the same object in the same conditions, the probability that the results are correct is very high.
There was no sign from the XXX group leader that he would share a publication with the Hokkaido group.
It was only fair, in such circumstances, to ensure that the Hokkaido group publish their results as quickly as possible, so as not to loose their obvious priority: this is a kind of ethical aspect widely shared in research. I thought it normal to add my name to those of the experimentalists authors of the paper. The paper was sent for publication in Physical Review Letters, which was the most widely read worldwide for new developments in physics.
Shortly thereafter, I traveled to a Conference in Aspen (Colorado, USA) where I reported about my work 13 and the experimental results of the Hokkaido group. Phil Anderson was a few yards away from me when I delivered my speech. I was proud to bring him such an important piece of experimental evidence in favour of his RVB approach.
The paper on the low temperature specific heat in the superconducting phase of LBCO was published (reference 14 ) only two weeks after it was submitted fro publication. This must have been one one of the most rapidly published papers in the history of Physical Review Letters. Usually, papers are sent to referees, who may ponder for months about the validity of the results, send various criticisms to the authors, ask for some change, for citing more or different authors, etc.. No such thing happened in this case. I suspect that Phil Anderson may have helped in convincing the editors of the journal.
The XXX group announced a communication to be delivered at a Conference in Interlaken (Switzeland) two months later, where they confirmed the linear specific heat in LBCO.
Barely two months after the paper with the Hokkaido group appeared, with my signature, it was spring time in Japan, the whole Institute was going to celebrate "Hanami", to watch the magnificent cherry trees blossoming, close to ISSP, ...in a graveyard near by.
On the very eve of that important social event, a report arrived about new experiments in a compound BSCO of the same class as LBCO with a much higher superconducting temperature, and much more reliable crystal composition than that of LBCO.
There was no sign of the C v linear term in temperature in the superconducting phase. It was clear that for one reason or other, the results displayed in 14 where not related to superconductivity 15 My participation in the joyful Hanami event is one of the worst memories of my stay in Japan. Not only had I publicly put my name on a paper reporting incorrect results, not only had I induced a japanese group to publish incorrect conclusions on a dubious experimental result; by specifying in the head of the paper that I was a member of the ISSP, I had put a stain on its international reputation. I had lost face. In japanese terms I had dishonoured my samuraï, I had to commit seppuku.
I did not commit seppuku, but I almost felt physically the weight of the shame on my shoulder. This shame and this stain remained with me during the remaining months of my stay in Japan.
At first sight, why spend any time writing about this episode? It looks simply like an experimental and theoretical blunder, why not let it rest in the graveyard of the host of incorrect papers?
However, I believe it deserves some more discussion. The development of this story, its context, its causes, its results, have some philosophical, sociological and epistemological interest.
To begin with, what was wrong with the experimental results? When one looks at the graph for γ(c Ba ), where c Ba is the Ba concentration in the LBCO samples, 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 compatible with the data, indicating a phenomenon triggered by Ba impurities and not superconductivity. The experiment did measure a significant low temperature γ term coinciding with the superconducting phase, and which was negligible in the non superconducting one, but the graph of the measurement was too inaccurate to suggest that the RVB prediction was confirmed. A well known fact is that the validity of any measure depends on the upper and lower limits of its accuracy.
So how come I did not worry about such indications, and ask the Hokkaido group to evaluate the error bars prior to publication? I worried at first about this, but dismissed my worries when the XXX group leader claimed he had the same crooked curve, with zero γ(c Ba ) until the critical Ba concentration for superconductivity to appear was reached.
This leads to a second question: why did the XXX group leader, who was a well known scientist, physics Professor in the XXX University, announce he had the same results as the Hokkaido group? I am convinced he had no such results, let alone results identical to those of Hokkaido.
Japan has 88 national universities, 7 of which are "imperial universities", founded before world war two. Tokyo University, Kyoto University, and Hokkaido University, and others, are parts of this University elite. When I happened to mention to japanese people that I was lecturer in Tokyo University, I was immediately considered with a lot of respect. XXX is a national University, founded in 1949, not an "imperial" one. Has this played a role in the attempt by the group leader in XXX to claim equal success with Hokkaido in the experimental investigation of the RVB theory? No one will ever know, but such human passions ("sad passions" discussed by Spinoza) in the science activity are frequent. The excitement about the HTS phenomenon was shared by most searchers in that field, with its promise for world scientific recognition in case of success. There are many occurrences, in the last decades of physics research, of deliberately fake reports in some of the best science reviews such as Nature, Science, Physical Review Letters, etc.. They are sometimes connected to an attempt to get approval of grants from specific peer committees for research funds, sometimes inspired by a search for recognition. There are numerous cases of scientific thefts, when a searcher publishes under his name a result obtained by others. The social pressure among scientists to succeed, to be invited for talks in conferences, for stable positions, for promotions, is producing those failures of scientific ethics. In the case of HTS in 1986, with the world spotlights on, and the excitement among physicists, all the elements for such ethical failures were enhanced 16 .
It was highly recommended for theorists in my laboratory in France to visit experimental facilities where experiments were conducted which were connected to theoretical problems of interest. Examining the apparatus, discussing with experimentalists how they were conducting experiments and what were the relevant theoretical questions: this was thought to be part of the theorist's job. I believe now that, among my japanese colleagues in ISSP, my visits to experimental groups to discuss relevant experiments about HTS and RVB were not viewed positively, although this was not openly expressed, because of politeness ethics. Similarly, I realized after a time that asking questions and emitting critical scientific comments while attending a science talk was not a polite thing to do...Had I been impolite with my XXX colleagues?
The episode I am discussing here is certainly due to a combination of various factors.
When I prompted two different groups to work on the confirmation, or the falsification, of the RVB prediction, I unleashed a competition which could have been fruitful if both competing groups, while working with their own ways and methods, had cooperated and exchanged informations about their mutual progress. An obvious lesson is that the competition, together with scientific cooperation between the two groups would have spared them, and me, the disgrace of a faulty publication, as well as misconceptions in the physics community during a few months...
Although the following is not all intimately connected with the episode of the incorrect specific heat paper 14 , it is useful to set the stage with general comments on the scientific activity and conceptions surrounding it.
Before commenting on connections of the story of 14 with various contemporary debates in epistemology, I briefly describe my own understanding on the process of knowledge of inanimate matter. The development of physics is a historical and social process. Since, roughly, the end of the nineteenth century, it combines the subjective activity of individuals, theorists and/or experimentalists, with that of groups of individuals, laboratories, networks of groups or laboratories, conferences where new results are publicized and where critical confrontations between conflicting views occur, scientific journals, national funding policies, etc.. Scientific results play an increasing role in industrial processes, a phenomenon which is also a practical proof of the effectiveness of science to account undeniably for a large number of real processes of nature.
A collective (social) physicist is formed as a result. This social activity deals with knowledge of objective properties of matter. The latter can be studied experimentally with repeated experiments by different independent actors in different places under identical conditions. The possibility of repeated experiments under identical conditions by very different actors is one of the specific features of physics (or biology) research, as compared to many issues in social sciences, for example. It allows to reduce the subjective part of the knowledge process. It allows to correct errors, as I learnt at my own cost 14 , and to elaborate grains of truth on inanimate matter, truths about the laws of nature, some of which may be absolute, undisputable, some which are relative to a given level of collective scientific knowledge, of technological progress, of measurements accuracy, etc.. The historical, social, practical knowledge process allows to "re-produce" 18 actual objective processes of nature, as is clear from its successful predictions and its infinitely many practical applications in social life.
Thanks to technological advances, and to continuous renewed social needs, the process of knowledge never stops asking new questions, abandoning refuted theories, and improving on previous re-productions of real processes with better and better accuracy.
Although I share with Popper 19 the observation that there is a cumulative progress of science, I do not agree with him that all knowledge is provisional. According to him, a theory is only valid as long as it is falsifiable.
Among many examples, the history of superconductivity is a good counter example. The BCS theory on the superconductivity of superconducting simple metals 21 has undisputable results. Whether RVB theory will end up being recognized as a fundamental addition to BCS theory for the understanding of HTS remains to be seen, as will be discussed later.
What I have described in the Introduction, namely the discovery of HTS, is a good example of what Bachelard 20 called a social production of science. LBCO and all the High Temperature Superconductors of the same class, i.e. based on coupled copper oxide layers, are chemically engineered compounds. They were made possible by advances in oxyde chemistry, both experimental and theoretical, by hosts of scientists of different fields. In that sense, HTS, as most advances of contemporary physics, is a social production. However, contrary to Bachelard's ambiguities about the subjectivity associated with social productions, HTS is also definitely an objective property of matter, in given conditions of temperature, pressure, magnetic field, independent of human thought as evidenced by its practical uses ( magnetic fields detection, levitating trains on superconducting material, permanent currents producing magnetic fields, for example), as well as the infinitely many repeated experiments in hundreds of different laboratories in the world.
The theorist 22 interested in solving the mechanisms of HTS does not, as Althusser wrote 23 when he battled succesfully with empiricism, work on the real object. The image of the LBCO crystal, which is shown on figure (I), is not the real object; it is a man-created image. The searchers work on an object of knowledge already elaborated by various social processes as discussed in the introduction. However they also work on a phenomenon which is independent of any thought process, i.e. superconductivity, an objective state of matter, however engineered by human practice: the "theoretical practice" is not disconnected from the real object, it is intimately connected, through a complex sensible, historical, technological, ideological process, to the phenomenon displayed by the real object, as discussed by Sève 18 . I would have been happy to confirm the γT term in the specific heat of HTS, but nature denied it, irrespective of my intentions and desires.
I do not feel it necessary to discuss various philosophical trends (see for example reference 24 on skepticism) which question how one can be sure (have a "true belief") that superconductivity exists and has such and such properties. I share Hacking's 25 argument on that matter: hundred years after Marx 26 , he rediscovered the criterion of practice as a criterion of reality.
I have used in the Introduction the notion of scientific revolution when discussing about HTS and RVB. Scientific Revolutions have been discussed in particular by Bachelard 20 and Kuhn 27 . Based on the history of physics ( Newtonian physics, relativity, quantum mechanics, and others), the latter author distinguished normal phases of scientific activity, which end when the paradigms of this activity are replaced, after a period of crisis, by new paradigms. An example he discussed is the replacement of geocentrism by heliocentrism; the emergence of quantum mechanics could be quoted as another example, although it did not invalidate many results of classical mechanics in their own domain of validity for most macro-scopic objects.
HTS has a number of aspects of a scientific revolution: the unexpected material where it was discovered, the stunning increase of superconductivity critical temperature in the new material, the revolutionary theoretical proposal such as RVB. Seventy five years after its discovery 2 in 1911, the belief that no superconductivity temperature larger than about 23K would ever be observed was shared by the vast majority of searchers in the field. Until 1986, superconductivity was thought to have no future as a research programme. It was not a period of "normal science" in Kuhn's sense: it was almost inactive. From 1986 on, the need for a new theory, fundamentally different from the "old" BCS superconductors 5 , was obvious, as I described in ref. 4 . The RVB paradigm 9 , at the basis of the episode described in this paper, might be one such new paradigm.
There is however a major difference with Kuhn's description of Scientific Revolutions. HTS did not falsify the BCS paradigm for the well known "old" superconductors. It opened a new field of condensed matter physics, about a new category of superconducting compounds. As discussed in a later section, it may evolve into blending the modern theories with the BCS one, i.e. into blending paradigms based on expression (1) and (2).
The category of Scientific Revolution is thus richer than that discussed by Kuhn: there are scientific revolutions which are based on new paradigms without falsifying previous ones.
Other comments deal with the reasons that led me to abandon the scheme based on (1) and adopt as research program the scheme based entirely on (2).
There were scientific, esthetical, institutional, psychological reasons, and also unconscious ones which I understood only years later, all more or less intermingled.
I believed that the novelty, audacity of the RVB proposal by Phil Anderson and collaborators 9 corresponded to the amount of novelty and surprises associated with the stunning discovery of HTS in compounds where all previous superconductivity culture would have denied its possibility. I believed this offered a possibility for a new field of condensed matter science to develop, a field I had abandoned ten years before for lack of experimental support. I believed that this new field -strong interactions in Condensed Matter physics -would develop within the non relativistic quantum theory which was the relevant theoretical framework to explain HTS. Thus my scientific reasons were both based on a number of beliefs: true beliefs about quantum mechanics, crystal structure of LBCO, existence of superconductivity, etc., and a subjective belief on the validity of RVB.
I felt the RVB proposal was so new, so seemingly well adapted to the structure and chemical composition of LBCO that there was an intellectual beauty about it. In 1973, Anderson 28 had developed the concept of RVB for a novel ground state of an insulating linear array of quantum 1/2 spins 29 ; this idea was in turn a generalization, for an infinite array of spins, of Linus Pauling's theory for the benzene molecule. At the time, the idea was original and interesting, it was a new concept in the field of magnetic insulators, but it had no obvious experimental counterpart. What Anderson did in 1986 for the theory of HTS was to extend this theory to a planar array of quantum 1/2 spins, and to postulate that the injection of "holes" (equivalent to suppression of electrons in the CuO plane) would result in a charged bosonic superfluid, i.e. a superconductor 30 . The progression of theoretical ideas from the benzene molecule to the doped CuO plane of spin 1/2 particles had for me a beauty in itself.
I was a CNRS searcher in 1986. My very social existence was based on investigating new condensed matter phenomena, explaining them, and publishing papers in good quality physics journals, so that the new published results would influence other research programs. I thought that as such, I had to participate in the attempt to understand, explain and develop the theory of HTS, both as a scientific challenge, and as an industrial one; HTS had potential applications for the fundamental problem of electricity storage, which would be an industrial revolution. If I made a significant contribution to some research topic, I would gain recognition among peers, perhaps a promotion, perhaps fame, etc..
Working in this new field, with its scientific and industrial challenges, was exciting; I had learnt to value the scientific stimulation connected to working on a topic of world wide scientific interest: research in such a field gave an impression of more intense intellectual life, together with the risk to fail in bringing forward significant novel results.
I shared a very general desire among researchers for social recognition through scientific achievements.
I believe now I had also unconscious reasons: I had met Phil Anderson several times in scientific meetings, during my career. He was seventeen years my elder, a scientific leader when I started research, and he had treated me in a friendly manner, showing appreciation for my PhD work... and my skills as a chess player. On the other hand, 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 Anderson had been my science adviser. In other words, his was a benevolent father image. By immediately adopting his RVB proposal, I became symbolically part of his family. This included a number of his collaborators, whose work I admired. One of them was Hidetoshi Fukuyama, head of the theory group in ISSP.
Ever since Plato and Aristotle, philosophers have discussed about the reasons to act: in the present case, I tried to describe the various reasons which led me to work within a scheme based on relation (2) rather than (1) . There are rich debates among them about the differences between "normative reasons" and "motivating", or "explanatory" ones. A normative reason is a reason to act. A motivating reason is the reason for which one does something. In my case, both types were clearly entangled. A study and complete bibliography about this topic is found in reference 31 .
The various personal reasons to choose one paradigm rather than another I have discussed above seem good examples of what Feyerabend discussed in his book Against Method 32 and also 33 . He criticizes the notion of scientific activity as based on a universal rational method. He stresses subjective reasons to adopt a theory. Although I seem to offer a good personal example in support of his claims, my own reasons were not devoid of belief in a fairly general method of science: I took into account new experimental results, which, in view of existing wisdom about superconductivity, seemed to require new concepts, and to confront them with experiments. Phil Anderson's RVB theory was a scientifically attractive proposal. I decided to study it theoretically, and simultaneously to test it experimentally, with the help of skilled experimental physicists. Furthermore, a large number of Condensed Matter physicists engaged in the same research program on RVB. Many had probably reasons analogous to my scientific ones, perhaps a sizeable number shared my esthetic reasons, perhaps others also tended, as I did, to pay attention to RVB because of Phil Anderson's fame as a physicist. Very few had psychological or unconscious reasons analogous to mine. For the vast majority, what mattered was to develop an understanding of HTS and of its phenomena. Individual reasons had in the end little or no weight in the social process of science.
I have described elsewhere (ref. 4 ) how various other theoretical ideas, different from RVB, were proposed since 1986 by various scientific leaders to explain HTS. I emphasized that each such new proposal was rooted in each author's scientific past, together with a general undisputable background knowledge of Condensed Matter physics. This reminds in some sense of Feyerabend's remark on the weight of existing research programs to prevent new ones from developing. It also seems to sup-port Feyerabend's relativism: various groups of scientists believed in various theories, some of which were incommensurable: at first sight expressions (1) and (2) are mutually exclusive. This in turn looks like an example for which the Duhem-Quine thesis 34,35 on the underdetermination of theory by experiments is temporarily valid. However, this state of scientific anarchy is but a transitory aspect of science progress, the process of research is constrained by the objective properties of inanimate matter. The latter allow to correct scientific programs with sufficient "protective belt" (see Lakatos 36 ), discriminate between theories after a certain time. For instance Duhem's energeticism 34 eventually had to be abandoned in favour of Boltzman's atomic theories. In HTS, there still prevails a state somewhat analogous to Feyerabend's anarchist theory of science or to some of his relativism. However, in spite of the many persisting disagreements among researchers on HTS, all agree on a number of basic physical laws governing superconductivity, which are undisputable properties of matter.
The absence of a γ term in HTS is now an undisputable irreversible truth. This is now established by various careful measurements by different searchers. Duhem 34 claimed that the role of theory is to account for appearances, and that no certainty can be obtained on the ontology of phenomena. If instruments are involved in an experiment, they can lead to experimental errors, they may have defects, and lead to artefacts. At first sight, the Hokkaido paper 14 would be a good proof of that thesis. But it is valid at a very restricted level, at most, for a certain time, for a few individuals or groups of individuals, and has no lasting universal validity, as discussed in ref. 38 . As shown by the XXX part of this story, other sources of errors, due to human passions involved in scientific research may play a role during a certain time. But scientific activity is a social one, as stressed above. Based on various well established technologies such as calorimetry, chemical synthesis of copper oxyde compounds, etc., contributions from various research groups in the world rapidly corrected the faulty paper and established the truth about the existence of a γ term in the superconducting phase of HTS.
Bacon 37 has introduced the notion of crucial experiment, which allows to discriminate between a truthful theory and an erroneous one. Duhem 34 has argued that there is no such thing. I have argued elsewhere 38 that Duhem's stand is falsified by his own admittance that "the theory of vibrating strings is certain". The notion of crucial experiment is vindicated in many cases by scien-tific practice and is intimately connected with the notion of truth, as I discussed in a previous paper 39 . The absence of a γ term in the specific heat of LBCO was a crucial result, but only in a limited way, as discussed below.
Following Popper 40 , the RVB proposal on HTS is a bona fide scientific theory, since it can be falsified. Phil Anderson's RVB original proposal predicted a specific heat linear in temperature in the superconductive phase. It is now well established that there is no such phenomenon in HTS.
According to Popper, this would ensure the falsification of RVB theory. It should be abandoned. However, this did not happen. The theory was slightly modified to take into account the zero γ result: instead of proposing a spherical symmetry ("s-wave" symmetry) for the superconducting order parameter in HTS, a so-called "dwave" symmetry was introduced 41 . This was not simply an ad-hoc change: it was more coherent with the basic hypothesis of inequality (2) . Indeed, a superconducting order parameter with d-wave symmetry implies that the interaction energy U between electrons is minimized in comparison with the s-wave case. The absence of a γ term in he specific heat of HTS is crucial to eliminate the possibility of s-wave symmetry for the HTS order parameter, not for the validity of RVB. This is in line with Lakatos' 36 and Feyerabend's 32 criticisms of Popper's Demarcation Criterion. Lakatos argues that a scientific research program consists of a "hard core" and a protective belt. Outside the hard core, there are a variety of auxiliary hypothesis to protect the hard core; changes and adjustments may occur in the protective belt, leaving the hard core untouched. This is what happened to the RVB research program when it was proved that the γ term is absent in HTS, at the cost of changing the s-wave original proposal to the d-wave one.
Following Feyerabend, conformism is likely among scientists to favour old theories rather than revolutionary ones. The history of HTS offers both examples and counter examples, so that Lakatos seems to be correct in pointing out the role of conflicts between theories in the progress of science.
Popper, Lakatos, and Feyerabend all neglect the role of practice to prove at least in an approximate way various truths about nature. "Old" superconductivity and HTS require different theories, but both evidence an undisputable fact of nature, i.e. superconductivity.
In contrast with relativistic Feyerabend's positions 33 , no serious physicist is free nowadays to argue that a non zero γ exists in HTS compounds of the LBCO class, because the incorrect paper(ref. 14 ) has convincingly been shown incorrect.
The conclusion of this paragraph is that RVB continued to be an active research program, even though one initial prediction was proved wrong. To this day, first half of year 2020, 34 years after the HTS discovery, the battle among theorists about the mechanism of HTS is still raging (see for more details ref. ( 4 ).
Contradictions?
I mentioned in the Introduction that my first published paper on the mechanism of HTS 8 was based on the weak coupling hypothesis (inequality (1)). This was written before I left for my one year stay in Japan. I reported about this paper only once in an international conference (in Genova in 1986). Thereafter I became so convinced that the RVB picture based on inequality (2) was the correct framework that I never even gave another talk about my weak coupling work in Japan. I felt it was an irrelevant approach, it would not interest my colleagues.
Both approaches seemed incompatible. If one thought the weak coupling (1) approach was the right one, no attention would be payed to works based on the strong coupling approach (2), and vice versa. Groups working on the (1) hypothesis would not talk to groups working on (2) and vice versa. The development of this battle is described in many more details in reference 4 . Inequalities (1) and (2) are a particular example of a general couple of contrary conditions which are basic in the description of physical processes: (1) is a special case of the domination of kinetic energy over potential energy, contrary to (2) . A paradigmatic example is the classical harmonic oscillator. Depending on which term dominates the total energy, the phase oscillates periodically around zero, or increases periodically by 2π. In both cases, both energies transform in time one into another. Internal energy and entropy are another couple of contraries in the free energy: the internal energy drives order, the entropy drives disorder.
There are well known examples of metals where inequality (1) applies without discussion in the description of their metallic properties Au, Ag, Cu,, transition elements of the first series in the periodic table, etc., for example. There are well known examples of magnetic insulators where inequality (2) applies without discussion:CuO, F e 2 O 3 , and all so called Mott insulators, or Quantum Hall systems 39 . Is it conceivable that materials exist -such as HTS materials -the theory of which has to resort simultaneously to both inequalities?
Sixteen years after my weak coupling paper on HTS 8 was published, the developments of experimental work on HTS caused theory to evolve towards a combination of (strong coupling) RVB theory (expression (2)) and weak coupling theory (expression (1)); the results of my 1986 paper were rediscovered. Citations of that paper started to appear in HTS research theory papers by groups who worked in developing the RVB approach.
In other words, research on HTS evolved after almost two decades towards a simultaneous account of both (contradictory) inequalities (1) and (2) 42 .
There are various examples, in the history of physics, of successful theories which have superseded what had appeared during many years as contradictory, i.e. in-compatible ones. Quantum physics for example supersedes the theoretcal contradictions between the continuous (wave like) and the discrete (corpuscular) theories of light or microscopic particles. The theory of ferromagnetism developed during years along two seemingly incompatible lines: that based on localized electrons on atomic sites in a crystal, and that based on band theory i.e. on electronic wave functions extending over the whole crystal volume. It is now based on a picture with both extended wave functions and localized magnetic moments (see the discussion in ref. 43 ). Another example is the long lasting historical battle between energeticists à la Duhem and exponents of the atomic theory of matter.
Even though my first HTS theoretical paper had results showing that the "weak coupling" theory based on (1) did exhibit interesting features (for example a sharp rise in the superconductivity critical temperature upon doping), in favour of framework (1), I neglected this result altogether after I became convinced of the relevance of 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 RVB theory appeared, I became blind to the interesting results of my own work! I had been probably too ignorant of Hegel's, Marx' and Engels' philosophical work on dialectics 26, 44, 45 . Had I been more learned in philosophy, I might had been capable of thinking that theories based on such dichotomies as the opposition between (1) and (2) often account, each, for only a partial aspect of the processes at work in the real object. Theory is often, if not always, constrained to evolve in time to take into account contradictory aspects of things, as forced upon knowledge by the growth of experimental information. Theory evolves in time to embody contradictions in the re-production of real processes. As far as HTS is concerned, data from a variety of experimental techniques seem to reveal that weak coupling and strong coupling theories are both simultaneously relevant. This is probably a sign that in the HTS material the actual situation is:
In some sense, this paper is a description of two scientific errors: one is the publication of an incorrect experimental paper 14 . The other is the failure to believe in the interest of my own work 8 in the search for a theoretical understanding of the HTS phenomenon.
Had I not been dogmatic in my belief in (2) , I would have publicised among HTS researchers the interesting results obtained ( 7,8 ), on the basis of expression (1), early in the HTS research development. This would have helped in promoting more quickly a better theory of HTS.
When a theory embodies contradictions in the representation of reality, can one argue that it is incoherent, only due the subjectivity of a human construct? This would deny that experiments yield results which are, at least in parts, independent of the preconceptions of experimentalists. The idea that contradictions are an on-tological aspects of things in nature has been developed in particular by Engels 44 , based on Hegel's dialectics 45 . This is considered by many philosophers of science as nonsensical 32, 33, 36, 40 . What can be stated safely at least is that theories are almost always driven to deal with conflicting theoretical terms. Physics continuously explains motions, evolutions, transitions, spontaneous breaking of symmetries, etc., on the ground of opposition between conflicting terms in the theory, as discussed above. The notion that conflicting terms in theory reproduce real ontological contraries is a logical one 26, 44, 45 . My own opinion on that matter agrees with Sève's views 18 who argues about the "dialecticity" of nature. He means by that term that the processes of nature constrain the theory to account for them in terms of dialectical development of contradictions.
I have described how I was led to put my name on an experimental paper the results and conclusions of which were found a few months later to be erroneous. I have described some of the questions which make this episode an example of the various factors which influence the development of knowledge at an individual, sociological and philosophical level.
In all superconducting materials known until 1986, the specific heat was well known to vanish exponentially with T . This was easily explained within the electron pairing mechanism in singlets described in 1958 in ref. 5 . The latter mechanism creates a forbidden energy gap ∆ ≃ k b T c at the Fermi surface, which freezes electronic excitations for temperatures T < T C , where T c is the temperature below which superconductivity appears.
In the initial RVB proposal, a fermionic Fermi surface of pure spin excitations coexisted with superconductivity down to T = 0, so that electronic spin excitations where just as possible as electronic charge excitations in a normal metal. As a result, the low temperature specific heat had to vary with T as in a normal metal, i.e. C v ∝ T .
The RVB proposal started with the known fact that the undoped CuO atomic layers carries one localized electron on each crystal site and is an insulator, almost a textbook example of a magnetic insulator. This localization of electrons on crystal sites is the result of the strong repulsion U , compared to the bandwidth W : expression (2) then is the correct starting point. Conventional wisdom 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 atom with down spins.
When two atoms labelled i and j in a crystal carry each an unpaired localized electron, the quantum state for the two electrons may have different forms, depending on the overlap between the atomic wave functions. Roughly speaking, the two spins 1/2 may couple to form a total spin S = 1, or they may (approximately) couple in alternate directions:spin projection S z,i = +1/2 on one atom, and S z,j = −1/2 on the other. If there is an ordered crystalline array of magnetic atoms, the two possibilities lead either to ferromagnetism (with all spins along the same direction) or to antiferromagnetism with an alternate order of spins along two opposite directions.
But there is a third possibility: both spins 1/2 at sites i and j may combine in a superposition of amplitudes to form a state S = 0 The superposition is that of state | + − > with | − + >, i.e. the state with spin 0 which is a singlet: 1/ √ 2(| + − > −| − + >) sharing the two atoms i and j. A singlet is a boson, formed with two spin 1/2 particles, which are fermions.
The Resonating Valence Bond proposal, first introduced in 1973 by Phil Anderson about a 1D model of localized spins 28 (the "railroad threstle"), is that the ground state of an ordered 2D crystal, such as CuO 2D atomic layer, with one unpaired electron spin per atom is the superposition of tensor products of all possible singlet states coupling electrons in the crystal in singlets associating electrons on atoms two by two. (In fact the ground state of a 2D crystal with localized electrons on crystal sites was studied in the late eighties by Monte Carlo computations which did not support the RVB ground state proposal; they found an antiferromagnetic ground state).
Superconductivity, according to the RVB scheme, was the result of doping the magnetic insulator with holes (i.e. of suppressing electrons by chemical doping) in a RVB ground state.
A doped hole in the RVB ground state breaks a singlet, thus liberates an unpaired spin 1/2, and an atomic site with zero localized spin: a spinless hole. Then each new particle, the spinless hole on one hand, and the neutral spin 1/2 can migrate in the crystal because of the atomic wave functions overlap.
A stunning result of this analysis is that, within the RVB scheme, in a strongly correlated 2D crystal, doping of holes results in a separation of charge and spin. In a weakly interacting electronic liquid (such as a normal metal like Cu, each electron carries simultaneously charge and spin 1/2.
At finite doping, the conclusion is that there exist a population of charged bosons called holons, and a population of neutral fermions with spin 1/2, called spinons. A liquid of bosons condenses in a a superfluid state (such as 4 He). Charged holons may condense in a charged superfluid state: a superconductor. A liquid of free spinons obeys Fermi statistics, and has a Fermi surface of spin excitations, similar to that of electrons in a normal metal.
With his revolutionary RVB proposal, Phil Anderson in 1986 seemed to take into account the main original properties of LBCO, and to provide an explanation for the superconductivity in a doped magnetic insulator.
The other starting point of the theory, i. e. expression (1) , which was at the basis of my first paper on HTS, leads to a different analysis of the ground state of the undoped crystal: with one electron per atom in extended wave functions, the crystal has a half filled band of delocalized electronic states (the filled band has twice as many states because of the degeneracy due to the electron spin). However, in the undoped 2D crystal, the Fermi surface is a square. In that case (a special case of so-called "nesting Fermi Surface"), weak interactions cause an instability of the normal metallic state and give rise to a Spin Density Wave (SDW) which has alternate spin density direction on each atom. This SDW causes an energy gap at the Fermi Surface, and thus the ground state is a (weak) antiferromagnetic insulator. Schulz 7 showed that in that case, there is a competition between the insulating SDW ground state and superconductivity. I showed with my students 8 in 1986 that a more realistic Fermi surface allows superconductivity to dominate.
Given the similarity between the results of the two scenarii, it is eventually not surprising that a correct theory combines concepts of both.