Physicists From Belgium

"Poincaré analyses how the reality of three dimensional Euclidean (or non-Euclidean) space, has been constructed from our daily experiences as a human being with the objects that are most important for us (rigid bodies), and closely around. This does not mean that this three dimensional space is an ‘invention’ of humanity. It exists, but the way we have ordered, and later on formalized it, by means of specific mathematical models, does make part of it. In other words, what we call the three dimensional reality of space partly exists in its own and partly exists by the structures that we have constructed, relying on our specific human experience with it."

"In classical Newtonian physics there was a clear understanding of 'what reality is'. Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in 'the present'. Often it is stated that three dimensional space and one dimensional time have been substituted by four dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that what is 'present', cannot be retained. Is reality then the four dimensional manifold of relativity theory? And if so, what is then the meaning of 'change in time'?"

"The classical concept of 'physical entity', be it particle, wave, field or system, has become a problematic concept since the advent of relativity theory and quantum mechanics. The recent developments in modern quantum mechanics, with the performance of delicate and precise experiments involving single quantum entities, manifesting explicit non-local behavior for these entities, brings essential new information about the nature of the concept of entity."

"What is reality? What is space? And what is time? These are the three questions that we want to investigate taking into account the knowledge that we have gained by modern physics. Our intuitive prescientific conception of the world in relation with these three concepts is not very precise but could be summarised as follows. - Reality is everything that exists now in the present. The past has been real but is not anymore and the future is what shall become real but is not yet. - Space is the theatre where reality is in. It englobes all of reality. Till the birth of relativity theory all physical theories where compatible with this intuitive scheme. But when relativity theory entered the scene, these intuitive conceptions of space and time, and what is less recognised even till today, also the conception of reality, has got into problems."

"The world around us can be construed as a huge "house" that we share with other humans, as well as with animals and plants. It is in this world that we exist, fulfilling our tasks, enjoying things, developing social relations, creating a family. In short, we live in this world. We thus have a deep human need to know and to trust it, to be emotionally involved in it. Many of us, however, experience an increasing feeling of alienation. Even though, with the expansion of society, virtually the entire surface of the planet has become a part of our house, often we do not feel "at home" in that house. With the rapid and spontaneous changes of the past decades, so many new wings and rooms have been constructed or rearranged that we have lost familiarity with our house. We often have the impression that what remains of the world is a collection of isolated fragments, without any structure and coherence. Our personal "everyday" world seems unable to harmonise itself with the global world of society, history and cosmos. It is our conviction that the time has come to make a conscious effort towards the construction of global world views, in order to overcome this situation of fragmentation. There are many reasons why we believe in the benefit of such an enterprise, and in the following pages we shall attempt to make some of them clear."

"World views, as related to the sciences, ethics, arts, politics and religions, are integral parts of all cultures. They have a strongly motivating and inspiring function. A socially shared view of the whole gives a culture a sense of direction, confidence and self-esteem. Moreover, interactions between cultures change constantly."

"A world view is a coherent collection of concepts and theorems that must allow us to construct a global image of the world, and in this way to understand as many elements of our experience as possible. Societies, as well as individuals, have always contemplated deep questions relating to their being and becoming, and to the being and becoming of the world. The configuration of answers to these questions forms their world view. Research on world views, although we are convinced of its practical value and necessity, will always be primarily an expression of a theoretical interest. It reflects the unlimited openness of the human mind to reality as a whole. Even if this research would not appear to be of any immediate value or necessity – quod non – we still should promote and encourage it energetically, because it also expresses the most unselfish striving of humanity “the desire to know,” a property of “Homo sapiens sapiens.”"

"A world view is a system of co-ordinates or a frame of reference in which everything presented to us by our diverse experiences can be placed. It is a symbolic system of representation that allows us to integrate everything we know about the world and ourselves into a global picture, one that illuminates reality as it is presented to us within a certain culture."

"We are quickly approaching the end of the millennium and the 'magical' year 2000. Many futurologists in the sixties thought science and technolo­gy would offer man unprecedented possibilities for solving his problems. The fall of the Iron Curtain and the implosion of the Eastern Block also created, just a, few years ago, grand expectations. The dream did not come true, however. Rather than ending up in a technological paradise and a peace-loving world, we woke up in a torn world with virtually unsolvable environmental problems and agonising social conditions."

"Although world views grow organic ly and historically, they can also be developed. The construction of world views is comparable to the work of cartographers in antiquity and in the Middle Ages. They mapped out the world on the basis of information from sailors, mer­ chants and explorers."

"We continually speak of world views in the plural because a unique and monolithic world view - considering the immense complexity of reality - will remain an unattainable ideal."

"In the construction of world views one can distinguish seven important tasks that correspond with the various components of a world view and that must provide an answer to a number of fundamental questions. First we must design a model of the world. What is the world like in which we live? How is the world structured and how does it function? What are the most suitable metaphors for speaking of the whole? Are mechanistic or organic models to be given preference? An explanation of reality must then follow. Why are the world and mankind as they are? Is a completely different world possible? What general explanatory principles apply?"

"The broader scope of our investigations is the search for the way in which concepts and their combinations carry and influence meaning and what this implies for human thought. More specifically, we examine the use of the mathematical formalism of quantum mechanics as a modeling instrument and propose a general mathematical modeling scheme for the combinations of concepts."

"We have come to suspect that `the way concepts combine and how they carry and communicate meaning' is governed by the presence of quantum structure in cognition."

"In our study of applying quantum to cognition we have identified five main aspects that play a fundamental role and that are specific to quantum structures as compared to classical structures. They are (i) contextual in influence (ii) emergence due to superposition, (iii) interference, (iv) entanglement and (v) quantum field theoretic aspects."

"Prigogine was also concerned with the broader philosophical issues raised by his work. In the 19th century the discovery of the second law of thermodynamics, with its prediction of a relentless movement of the universe toward a state of maximum entropy, generated a pessimistic attitude about nature and science. Prigogine felt that his discovery of self-organizing systems constituted a more optimistic interpretation of the consequences of thermodynamics. In addition, his work led to a new view of the role of time in the physical sciences."

"The statistical probability that organic structures and the most precisely harmonized reactions that typify living organisms would be generated by accident, is zero."

"The evolution of a physicochemical system leads to an equilibrium state of maximum disorder."

"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy.”"

"The ideas of nonequilibrium order and of the search for stability extend Darwin’s concept back to the prebiotic stage by redefining the “fittest”."

"The functional order maintained within living systems seems to defy the Second Law; nonequilibrium thermodynamics describes how such systems come to terms with entropy."

"The probability that at ordinary temperatures a macroscopic number of molecules is assembled to give rise to the highly ordered structures and to the coordinated functions characterizing living organisms is vanishingly small. The idea of spontaneous genesis of life in its present form is therefore highly improbable, even on the scale of the billions of years during which prebiotic evolution occurred."

"My colleague Paul Glansdorff and I have investigated the problem as to if the results of near-equilibrium can be extrapolated to those of far - from-equilibrium situations and have arrived at a surprising conclusion: Contrary to what happens at equilibrium, or near equilibrium, systems far from equilibrium do not conform to any minimum principle that is valid for functions of free energy or entropy production."

"Given my interest in the concept of time, it was only natural that my attention was focused on the second principle, as I felt from the start that it would introduce a new, unexpected element into the description of physical world evolution. No doubt it was the same impression illustrious physicists such as Boltzmann and Planck would have felt before me. A huge part of my scientific career would then be devoted to the elucidation of macroscopic as well as microscopic aspects of the second principle, in order to extend its validity to new situations, and to the other fundamental approaches of theoretical physics, such as classical and quantum dynamics."

"The problem of time in physics and chemistry is closely related to the formulation of the second law of thermodynamics. Therefore another possible title of this lecture could have been: “the macroscopic and microscopic aspects of the second law of thermodynamics”"

"It is a remarkable fact that the second law of thermodynamics has played in the history of science a fundamental role far beyond its original scope. Suffice it to mention Boltzmann’s work on kinetic theory, Planck’s discovery of quantum theory or Einstein’s theory of spontaneous emission, which were all based on the second law of thermodynamics"

"The denial of becoming by physics estranged science from philosophy... [and] became a dogmatic assertion directed against all those (chemists, biologists, physicians) for whom a qualitative diversity existed in nature... Today we believe that the epoch of certainties and absolute oppositions is over. Physicists belong to their culture, to which, in their turn, they make an essential contribution."

"Equilibrium thermodynamics was an achievement of the nineteenth century, nonequilibrium thermodynamics was developed in the twentieth century, and Onsager's relations mark a crucial point in the shift of interest away from equilibrium to non-equilibrium."

"Entropy is the price of structure"

"Whatever we call reality, it is revealed to us only through the active construction in which we participate."

"The threat lies in the realization that in our universe the security of stable, permanent rules are gone forever. We are living in a dangerous and uncertain world that inspires no blind confidence. Our hope arises from the knowledge that even small fluctuations may grow and change the overall structure. As a result, individual activity is not doomed to insignificance"

"We are at a very exciting moment in history, perhaps a turning point, said Ilya Prigogine, who won the 1977 Nobel prize for a theory that describes transformations, not only in the physical sciences but also in society—the role of stress and "perturbations" that can thrust us into a new, higher order. Science, he said, is proving the reality of a deep cultural vision. The poets and philosophers were right in their intimations of an open, creative universe. Transformation, innovation, evolution—these are the natural responses to crisis."

"Prigogine's great contribution lies in his successful development of a satisfactory theory of non-linear thermodynamics in states which are far removed from equilibrium. In doing so he has discovered phenomena and structures of completely new and completely unexpected types, with the result that this generalized, nonlinear and irreversible thermodynamics has already been given surprising applications in a wide variety of fields. Prigogine has been particularly captivated by the problem of explaining how ordered structures - biological systems, for example - can develop from disorder. Even if Onsager's relations are utilized, the classical principles of equilibrium in thermodynamics still show that linear systems close to equilibrium always develop into states of disorder which are stable to perturbations and cannot explain the occurrence of ordered structures."

"Coherent behavior is the characteristic feature of biological systems."

"We have seen that the formation and maintenance of self-organizing systems are compatible with the laws of physical chemistry.”"

"Dear \sqrt{\text{Trotsky×Bohr}} = \text{Rosenfeld}!"

"In the history of science literature Rosenfeld is largely a blank sheet, but he was at the centre of modern physics as one of the pioneers of quantum field theory and quantum electrodynamics in the late 1920s and the 1930s. Today he is best known for his publications with Niels Bohr in 1933 and 1950 on measurability in quantum electrodynamics and as the fierce spokesman of Bohr's interpretation of quantum mechanics after the Second World War."

"Each word is a singularity, or is connected with a singularity, in our way of understanding existence."

"No physical concept is sufficiently defined without the knowledge of its domain of validity."

"Wesentliche Fortschritte in der Formulierung der allgemeinen Quantengesetze der elektromagnetischen und materiellen Wellenfelder haben neuerdings Heisenberg und Pauli… erzielt, indem sie die von Dirac erfundene "Methode der nochmaligen Quanteln" systematisch entwickelten. Neben gewissen sachlichen Schwierigkeiten, die viel tiefer liegen, trat dabei eine eigentumliche Schwierigkeit formaler Natur auf: der zum skalaren Potential kanonisch konjugierte Impuls verschwindet identisch, so daß die Aufstellung der Hamiltonischen Funktion und der Vertauschungsrelationen nicht ohne weiteres gelingt. Zur Beseitigung dieser Schwierigkeit sind bisher drei Methoden vorgeschlagen worden, die zwar ihren Zweck erfullen, aber doch schwerlich als befriedigend betrachtet werden können. (Heisenberg and Paull have recently made significant progress in the formulation of the general quantum laws of electromagnetic and material wave fields by systematically developing the "method of repeated quantization" invented by Dirac. In addition to certain factual difficulties which lie much deeper, a peculiar difficulty of a formal nature arose: the momentum which is canonically conjugated to the scalar potential vanishes identically, so that the establishment of the Hamiltonian function and the commutation relations is not easy. To overcome this difficulty, three methods have been proposed which, although they fulfil their purpose, can hardly be regarded as satisfactory.)"

"Mathematical physics represents the purest image that the view of nature may generate in the human mind; this image presents all the character of the product of art; it begets some unity, it is true and has the quality of sublimity; this image is to physical nature what music is to the thousand noises of which the air is full..."