Science is always presupposing some basic concepts that are held to be useful. These absolute presuppositions (Collingwood) are rarely debated and form the framework for what has been termed “paradigm” by Kuhn. Our currently accepted scientific model is predicated on a set of presuppositions that have difficulty accommodating holistic structures and relationships and are not geared towards incorporating non-local correlations. Since the theoretical models we hold also determine what we perceive and take as scientifically viable, it is important to look for an alternative model that can deal with holistic relationships. One approach is to generalise algebraic quantum theory, which is an inherently holistic framework, into a generic model. Relaxing some restrictions and definitions from quantum theory proper yields an axiomatic framework that can be applied to any type of system. Most importantly, it keeps the core of the quantum theoretical formalism. It is capable of handling complementary observables, i.e. descriptors which are non-commuting, incompatible and yet collectively required to fully describe certain situations. It also predicts a generalised form of non-local correlations that in quantum theory are known as entanglement. This generalised version is not quantum entanglement but an analogue form of holistic, non-local connectedness of elements within systems, predicted to occur whenever elements within systems are described by observables which are complementary to the description of the whole system. While a considerable body of circumstantial evidence supports the plausibility of the model, we are not yet in a position to use it for clear cut predictions that could be experimentally falsified. The series of papers offered in this special issue are the beginning of what we hope will become a rich scientific debate.
Science is always presupposing some basic concepts that are held to be useful. These absolute presuppositions (Collingwood) are rarely debated and form the framework for what has been termed “paradigm” by Kuhn. Our currently accepted scientific model is predicated on a set of presuppositions that have difficulty accommodating holistic structures and relationships and are not geared towards incorporating non-local correlations. Since the theoretical models we hold also determine what we perceive and take as scientifically viable, it is important to look for an alternative model that can deal with holistic relationships. One approach is to generalise algebraic quantum theory, which is an inherently holistic framework, into a generic model. Relaxing some restrictions and definitions from quantum theory proper yields an axiomatic framework that can be applied to any type of system. Most importantly, it keeps the core of the quantum theoretical formalism. It is capable of handling complementary observables, i.e. descriptors which are non-commuting, incompatible and yet collectively required to fully describe certain situations. It also predicts a generalised form of non-local correlations that in quantum theory are known as entanglement. This generalised version is not quantum entanglement but an analogue form of holistic, non-local connectedness of elements within systems, predicted to occur whenever elements within systems are described by observables which are complementary to the description of the whole system. While a considerable body of circumstantial evidence supports the plausibility of the model, we are not yet in a position to use it for clear cut predictions that could be experimentally falsified. The series of papers offered in this special issue are the beginning of what we hope will become a rich scientific debate.
BACKGROUND AND PROBLEM: A main problem for the acceptance of many methods belonging to the broad spectrum of complementary and alternative medicine (CAM) is that there is no conceivable theoretical bridge between the mainstream biomedical model and CAM theories and practice. Although empirical evidence is one important side of the coin of credibility, theoretical feasibility is the other. History of science teaches that no amount of empirical evidence will convince sceptics and followers of more conventional paradigms as long as there is no good theoretical model to make empirical findings plausible. METHODS AND SOLUTION: I therefore propose to broaden the spectrum of theoretical concepts beyond the reigning local-causalist model toward a non-local model that encompasses effects as encountered in CAM. Such a model can be derived from a generalized and weaker version of quantum theory recently developed and published by my colleagues and I as weak quantum theory (WQT). This theoretical model predicts nonlocal correlations analogous to Einstein-Podolsky-Rosen (EPR)-like correlations in quantum mechanics proper. The discerning moment, though, is that these nonlocal correlations within WQT are not EPR correlations postulated to extend into the classical world, but a broader, generalized version of entanglement not dependent on the strict quantum nature of the system under question. WQT predicts entanglement between elements of a system if two variables or observables are complementary: one describing a global and one the local aspects of the system. Entanglement then ensues between those local elements of a system that are complementary to the global description or observable of that system. DISCUSSION AND CONCLUSIONS: This paper explores this rather abstract and general notion and expands it into more concrete examples. It is at the moment a purely explanatory structure, which, however, lends itself to exact empirical testing due to rather precise predictions, which will be developed. Because this structure of generalized entanglement is ubiquitous and also operative in conventional medicine, and because it is derived from one of the strongest theories that science has developed so far, it would constitute a theoretical bridge between the different medical and scientific traditions.
Introduction The historical development of scientific progress teaches us that every theory that was established and broadly accepted at a certain time was later inevitably replaced by a deeper and more fundamental theory of which the old one remains a special case. One celebrated example is Newtonian (classical) mechanics, which was superseded by quantum mechanics at the beginning of the last century. It is natural to ask whether in a similar manner there could be logically consistent theories that are more generic than quantum theory itself. It could then turn out that quantum mechanics is an effective description of such a theory, only valid within our current restricted domain of experience. At present, quantum theory has been tested against very specific alternative theories that, both mathematically and in their concepts, are distinctly different. Instances of such alternative theories are non-contextual hidden-variable theories [1], local hidden-variable theories [2], crypto-nonlocal hidden-variable theories [3, 4], or some nonlinear variants of the Schrödinger equation [5–8]. Currently, many groups are working on improving experimental conditions to be able to test alternative theories based on various collapse models [9–14]. The common trait of all these proposals is to suppress one or the other counterintuitive feature of quantum mechanics and thus keep some of the basic notions of a classical worldview intact. Specifically, hidden-variable models would allow us to preassign definite values to outcomes of all measurements; collapse models are mechanisms for restraining superpositions between macroscopically distinct states, and nonlinear extensions of the Schrödinger equation may admit more localized solutions for wave-packet dynamics, thereby resembling localized classical particles.
Leibniz' notion of "pre-established harmony" is one of the central notions of his philosophy. It is the conceptual hinge which allows all monads to be interrelated and coordinated yet not influenced by each other through causal interactions, allowing Leibniz to construct a model of the world where moral justice can be philosophically incorporated. This concept has been viewed with some misgivings during the history of philosophy, finally being dismantled during the post-modern turn. We suggest its revival, based on the concept of a weak or generalised quantum theory, an axiomatic, systems theoretical approach, modelled along the same lines as the algebraic quantum theory. In contrast to quantum theory this drops a lot of definitions and restrictions, and is also applicable to different types of systems. Interestingly, its formalism preserves one central element of the quantum mechanical formalism: the handling of non-commuting or complementary observables. In consequence, the model predicts a generalised form of entanglement, i.e. non-local correlations across distance and time, that are not mediated through signals, but through the make up of the system as such. This seems to be a "mechanism" or coordination which could operate independent of and complementary to standard causal interactions, akin to the way Leibniz conceived pre-established harmony. We argue that such a generalised version of entanglement (GET) is in fact a systematic novel interpretation of pre-established harmony. If this line or argument is prolonged into the realm of morality and ethics, we have in fact a full fledged revival of Leibniz pre-established harmony.
In the Preface of this book, we have mentioned several approaches [ 1 , 2 , 3 , 4 ] to the problem of connecting quantum theory and general relativity theory. In our opinion, before a final thinking around this problem, it is vital to make some efforts to find a new and less formal foundation of quantum theory. This has now been done by the first author in a process starting with the book [ 5 ] and further developed in a series of articles. A summary of the theory is now given in [ 6 ]. Central to the theory is a simple model of the mind of an observer, a model which may be generalized to the mind of any person. It first relies on what is called theoretical variables , which may be physical variables, but in the process of planning, doing, or interpreting experiments, the variables are also assumed to exist in the mind of a relevant actor. From a mathematical point of view, our only requirement for the theoretical variables is the following: If λ is a theoretical variable and θ = f ( λ ) for some fixed function f , then θ is also a theoretical variable.
Quantum theory is the soul of contemporary physics. It was discovered in an adventurous way, under the urge to solve the puzzles posed by atomic spectra and blackbody radiation. But after its invention, it immediately became clear that it was not just a theory of specific physical systems: it was rather a new language of universal applicability. Already in 1928, the theory had received solid mathematical foundations by Hilbert, von Neumann, and Nordheim, and this work was brought to completion in the monumental work of von Neumann, in the form that we still study nowadays. The theory is extraordinarily successful, and its predictions have been confirmed to an astonishing level of precision in a large spectrum of experiments. However, almost 90 years after von Neumann's book, quantum theory remains mysterious. Its mathematical formulation – based on Hilbert spaces and self-adjoint operators – is far from having an intuitive interpretation. The association of physical systems to Hilbert spaces whose unit vectors represent pure states, the representation of transformations by unitary operators and of observables by self-adjoint operators – all such postulates look artificial and ad hoc . A slightly more operational approach is provided by the C * -algebraic formulation of quantum theory – still, this formulation relies on the assumption that observables form an algebra , where the physical meanings of the multiplication and the sum are far from clear. In short, the postulates of quantum theory impose mathematical structures without providing any simple reason for this choice: the mathematics of Hilbert spaces is adopted as a magic blackbox that “works well” at producing experimental predictions. However, in a satisfactory axiomatization of a physical theory the mathematical structures should emerge as a consequence of postulates that have a direct physical interpretation. By this we mean postulates referring, e.g., to primitive notions like physical system, measurement, or process, rather than notions like, e.g., Hilbert space, C * -algebra, unit vector, or selfadjoint operator. The crucial question thus remains unanswered: why quantum theory? Which are the principles at the basis of the theory? A case that is often invoked in contrast is that of Special Relativity theory, which directly follows from the simple understandable principle of relativity.
Homeopathy is scientifically banned, both for lack of consistent empirical findings, but more so for lack of a sound theoretical model to explain its purported effects. This paper makes an attempt to introduce an explanatory idea based on a generalized version of quantum mechanics (QM), the weak quantum theory (WQT). WQT uses the algebraic formalism of QM proper, but drops some restrictions and definitions typical for QM. This results in a general axiomatic framework similar to QM, but more generalized and applicable to all possible systems. Most notably, WQT predicts entanglement, which in QM is known as Einstein-Podolsky-Rosen (EPR) correlatedness within quantum systems. According to WQT, this entanglement is not only tied to quantum systems, but is to be expected whenever a global and a local variable describing a system are complementary. This idea is used here to reconstruct homeopathy as an exemplification of generalized entanglement as predicted by WQT. It transpires that homeopathy uses two instances of generalized entanglement: one between the remedy and the original substance (potentiation principle) and one between the individual symptoms of a patient and the general symptoms of a remedy picture (similarity principle). By bringing these two elements together, double entanglement ensues, which is reminiscent of cryptographic and teleportation applications of entanglement in QM proper. Homeopathy could be a macroscopic analogue to quantum teleportation. This model is exemplified and some predictions are derived, which make it possible to test the model.