We propose a precise meaning to the concepts of “experiment,” “measurement,” and “event” in the event-enhanced formalism of quantum theory. A minimal piecewise deterministic process is given that can be used for a computer simulation of real time series of experiments on single quantum objects. As an example a generalized cloud chamber is described, including the multiparticle case. Relation to the GRW spontaneous localization model is discussed.

This minicourse on quantum mechanics is intended for students who have already been rather well exposed to the subject at an elementary level. It is assumed that they have surmounted the first conceptual hurdles and also have struggled with the Schrödinger equation in one dimension.

(1996). Exploring the quantum jump from successive consciousness to planetary consciousness— an oriental perspective. World Futures: Vol. 47, No. 2-3, pp. 239-242.

Quantum theory determines the evolution of quantum states between quantum jumps. Quantum theory also allows us to calculate rates of quantum jumps and, on a probabilistic level, the outcomes of those quantum jumps. Both quantum jumps and the continuous evolution of quantum states are important in the time evolution of quantum systems, and the scattering matrix ties those seemingly disparate concepts together. Indeed, quantum jumps are (...) so essential in quantum dynamics that we should refocus discussion of a quantum ontology on the power and principal limitations of our knowledge about quantum jumps as encoded in the scattering matrix. On the one hand, one might argue that the lack of a dynamical resolution of quantum jumps indicates an inherent incompleteness of the theory. However, we would rather submit that quantum theory is complete and that the observations indicate a principal limitation to the description of the universe as a smoothly evolving dynamical system. The modern understanding of quantum jumps therefore calls for updates to the Copenhagen interpretation instead of modifications of quantum theory. (shrink)

Until quite recently, recombinant DNA technology was not able to deal with DNA molecules larger than 20–40 kb. This is a serious limitation for the study of mammalian, and in particular human genomes whose total length is approx. 3 × 106 kb, since the best resolution of genetic and chromosomal analysis is usually the rough equivalent of 1000–5000 kb. Three recently developed methods promise to bridge this gap: pulsed field gel electrophoresis, which can analyze megabase‐sized DNA fragments; cloning in yeast, (...) which can clone and propagate DNA fragments of several hundred kb; and jumping libraries, which allow ‘jumping’ over large distances along the chromosome. This review presents the current status of these very promising technologies. (shrink)

This conference brought together experts in different fields related to the foundations of quantum mechanics, ranging from mathematical physics to experimental physics, as well as the philosophy of science. The major topics discussed are: collapse models, Bohemian mechanics and their relativistic extensions, other alternative formulation of quantum mechanics, properties of entanglement, statistical physics and probability theory, new experimental results, as well as philosophical and epistemological issues.

With many Hamiltonians one can naturally associate a |Ψ|2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field theory, it is typically a jump process on the configuration space of a variable number of particles. We define these processes for regularized quantum field theories, thereby generalizing previous work of John S. Bell [3] and of ourselves [11]. We introduce a formula expressing (...) the jump rates in terms of the interaction Hamiltonian, and establish a condition for finiteness of the rates. (shrink)

Prologue: Stormclouds : London, April 1900 -- Quantum of action: The most strenuous work of my life : Berlin, December 1900 ; Annus Mirabilis : Bern, March 1905 ; A little bit of reality : Manchester, April 1913 ; la Comédie Française : Paris, September 1923 ; A strangely beautiful interior : Helgoland, June 1925 ; The self-rotating electron : Leiden, November 1925 ; A late erotic outburst : Swiss Alps, Christmas 1925 -- Quantum interpretation: Ghost field : (...) Oxford, August 1926 ; All this damned quantum jumping : Copenhagen, October 1926 ; The uncertainty principle : Copenhagen, February 1927 ; The 'Kopenhagener geist' : Copenhagen, June 1927 ; There is no quantum world : Lake Como, September 1927 -- Quantum debate: The debate commences : Brussels, October 1927 ; An absolute wonder : Cambridge, Christmas 1927 ; The photon box : Brussels, October 1930 ; A bolt from the blue : Princeton, May 1935 ; The paradox of Schrödinger's cat : Oxford, August 1935 -- Interlude: The first war of physics : Christmas 1938-August 1945 -- Quantum fields: Shelter Island : Long Island, June 1947 ; Pictorial semi-vision thing : New York, January 1949 ; A beautiful idea : Princeton, February 1954 ; Some strangeness in the proportion : Rochester, August 1960 ; Three quarks for Muster Mark! : New York, March 1963 ; The 'God particle' : Cambridge, Massachusetts, Autumn 1967 -- Quantum particles: Deep inelastic scattering : Stanford, August 1968 ; Of charm and weak neutral currents : Harvard, February 1970 ; The magic of colour : Princeton/Harvard, April 1973 ; The November revolution : Long Island/Stanford, November 1974 ; Intermediate vector bosons : Geneva, January/June 1983 ; The standard model : Geneva, September 2003 -- Quantum reality: Hidden variable : Princeton, Spring 1951 ; Bertlmann's socks : Boston, September 1964 ; The Aspect experiments : Paris, September 1982 ; The quantum eraser : Baltimore, January 1999 ; Lab cats : Stony Brook/Delft, July 2000 ; The persistent illusion : Vienna, December 2006 -- Quantum cosmology: The wavefunction of the universe : Princeton, July 1966 ; Hawking radiation : Oxford, February 1974 ; The first superstring revolution : Aspen, August 1984 ; Quanta of space and time : Santa Barbara, February 1986 ; Crisis? What crisis? : Durham, Summer 1994 -- A quantum of solace? : Geneva, March 2010. (shrink)

What is quantum mechanics about? The most natural way to interpret quantum mechanics realistically as a theory about the world might seem to be what is called wave function ontology: the view according to which the wave function mathematically represents in a complete way fundamentally all there is in the world. Erwin Schroedinger was one of the first proponents of such a view, but he dismissed it after he realized it led to macroscopic superpositions (if the wave function (...) evolves in time according to the equations that has his name). The Many-Worlds interpretation1 accepts the existence of such macroscopic superpositions but takes it that they can never be observed. Superposed objects and superposed observers split together in different worlds of the type of the one we appear to live in. For these who, like Schroedinger, think that macroscopic superpositions are a problem, the common wisdom is that there are two alternative views: "Either the wave function, as given by the Schroedinger equation, is not everything, or is not right" [Bell 1987]. The deBroglie-Bohm theory, now commonly known as Bohmian Mechanics, takes the first option: the description provided by a Schroedinger-evolving wave function is supplemented by the information provided by the configuration of the particles. The second possibility consists in assuming that, while the wave function provides the complete description of the system, its temporal evolution is not given by the Schroedinger equation. Rather, the usual Schroedinger evolution is interrupted by random and sudden "collapses". The most promising theory of this kind is the GRW theory, named after the scientists that developed it: Gian Carlo Ghirardi, Alberto Rimini and Tullio Weber.. It seems tempting to think that in GRW we can take the wave function ontologically seriously and avoid the problem of macroscopic superpositions just allowing for quantum jumps. In this paper we will argue that such "bare" wave function ontology is not possible, neither for GRW nor for any other quantum theory: quantum mechanics cannot be about the wave function simpliciter. That is, we need more structure than the one provided by the wave function. As a response, quantum theories about the wave function can be supplemented with structure, without taking it as an additional ontology. We argue in reply that such "dressed-up" versions of wave function ontology are not sensible, since they compromise the acceptability of the theory as a satisfactory fundamental physical theory. Therefore we maintain that: 1- Strictly speaking, it is not possible to interpret quantum theories as theories about the wave function; 2- Even if the wave function is supplemented by additional non-ontological structures, there are reasons not to take the resulting theory seriously. Moreover, we will argue that any of the traditional responses to the measurement problem of quantum mechanics (Bohmian mechanics, GRW and Many-Worlds), contrarily to what commonly believed, share a common structure. That is, we maintain that: 3- All quantum theories should be regarded as theories in which physical objects are constituted by a primitive ontology. The primitive ontology is mathematically represented in the theory by a mathematical entity in three-dimensional space, or space-time. (shrink)

The results of a hypothetical experiment requiring a sequence of quantum measurements are obtained retrospectively, after the experiment has been completed, from a single reading of an “apparatus register.” The experiment is carried out reversibly and Schrödinger's equation is satisfied until the terminal reading of the register. The technique is illustrated using a feasible method of measuring photon spin as the quantum “object” observable and using the photon energy as the “apparatus register.” The technique is used to discuss (...) the “watchdog” effect, the effect of repeated measurements inhibiting quantum jumps. (shrink)

Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of lightcnot being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constanthrequires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced by an (...) infinite manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics:To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values ofh, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action. (shrink)

The revolution brought about by quantum mechanics in the early 20th century was nothing short of remarkable. It shattered the foundational principles of classical physics, giving rise to a plethora of controversial and intriguing conceptual questions. Questions that still perplex and confound the scientific community today. Is the quantum mechanical description of physical reality complete? Are the objects of nature truly inseparable? And most importantly, do objects not have a specific position before measurement, and are there non-causal (...) class='Hi'>quantum jumps? These vital problems continue to garner more attention as time passes, particularly with the fading of positivism. If you're a student seeking to explore the fascinating philosophical foundations of quantum mechanics, this book might be just what you need. Written in Persian, brings you closer to the heart of quantum controversies and the fascinating world of quantum mechanics. (shrink)

In the last few decades, the relevance of quantum mechanics to the free-will debate has been discussed at length, especially in relation to the prospects of libertarianism. Basing his interpretation on Anscombe’s seminal work, Putnam argued in 1979 that, given that quantum mechanical indeterminacy is holistic at the macrolevel—i.e., it is not traceable to atomistic events such as quantum jumps of single atoms—it can provide libertarians with the kind of freedom they seek. As shown in this (...) article, however, Putnam ultimately reached the conclusion—together with the other author of this article—that his argument was wrong due to problems with the way it appealed to the Uncertainty Principle.**. (shrink)

Book to honor the work of GianCarlo Ghirardi.

We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle–wave characteristics of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources. The final world model treated here contains only gravonons and a scalar matter field. The gravonons (...) are localized in the environment of the massive particles which generate them. The solution of the Schrödinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: There is a chooser mechanism for the selection of the localization site. The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical. The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. The times at which telegraph like jumps occur depend on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical. The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of CQM is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schrödinger’s equation without the need of introducing a probabilistic interpretation. (shrink)

It is argued that a realistic interpretation of quantum mechanics is possible and useful. Current interpretations, from “Copenhagen” to “many worlds” are critically revisited. The difficulties for intuitive models of quantum physics are pointed out and possible solutions proposed. In particular the existence of discrete states, the quantum jumps, the alleged lack of objective properties, measurement theory, the probabilistic character of quantum physics, the wave–particle duality and the Bell inequalities are analyzed. The sketch of a (...) realistic picture of the quantum world is presented. It rests upon the assumption that quantum mechanics is a stochastic theory whose randomness derives from the existence of vacuum fields. They correspond to the vacuum fluctuations of quantum field theory, but taken as real rather than virtual. (shrink)

In [3] John S. Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |Ψ|2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; such processes we call Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the (...) efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to “second quantization.” As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field. (shrink)

The article analyzes the effectiveness of quantum theories of mental experience in relation to two ontological problems - the problem of the existence of consciousness in the material world and the problem of the interaction of consciousness and body. A critical analysis of the quantum theories of consciousness by Penrose-Hameroff, M. Tegmark, G. Stapp, M. Fischer and M.B. Mensky shows that they fail to fully explain how complex physical systems generate mental experience without violating the principle of causal (...) closure of the physical world and the principle of epistemological completeness of physics. Quantum mechanics provides specific processes that are the physical basis of the psyche, but do not explain the phenomenal aspect of subjective reality. Nevertheless, the Heisenberg uncertainty principle gives an understanding of how the interaction of consciousness and body within the scientific picture of the world can be carried out without violating the law of energy conservation. It is shown that the quantum theories of consciousness currently being developed have a predominantly panprotopsychic character, which faces a problem due to the fact that the protomental property of physical systems must be expressed quantitatively and correspond to the value included in the physical equations. As a result, it is concluded that in order to develop quantum theories of consciousness more effectively, it is necessary to give an emergent character, not jumping from the quantum level to the psychic, but explaining the mechanism of the emergence of systemic properties during the sequential transition between different ontological regions of existence, including physical, chemical, biological, neurophysiological and psychic. (shrink)

The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be (...) seen as informational in a generalized sense. This implies a fundamental connection between the physical and material, on the one hand, and the mathematical and ideal, on the other hand. Quantum measure unifies them by a common and joint informational unit. Furthermore the approach clears up philosophically how quantum mechanics and general relativity can be understood correspondingly as the holistic and temporal aspect of one and the same, the state of a quantum system, e.g. that of the universe as a whole. The key link between them is the notion of the Bekenstein bound as well as that of quantum temperature. General relativity can be interpreted as a special particular case of quantum gravity. All principles underlain by Einstein (1918) reduce the latter to the former. Consequently their generalization and therefore violation addresses directly a theory of quantum gravity. Quantum measure reinterprets newly the “Bing Bang” theories about the beginning of the universe. It measures jointly any quantum leap and smooth motion complementary to each other and thus, the jump-like initiation of anything and the corresponding continuous process of its appearance. Quantum measure unifies the “Big Bang” and the whole visible expansion of the universe as two complementary “halves” of one and the same, the set of all states of the universe as a whole. It is a scientific viewpoint to the “creation from nothing”. (shrink)

An expression of the Lindbladian form is proposed that ensures an unambiguous time-continuous reduction of the initial system-pointer wave-packet to one in which the readings and the observable’s values are aligned, formalized as the transition from an outer product to an inner product of the system’s and apparatus’ density matrices. The jump operators are in the basis of the observables, with uniquely determined parameters derived from the measurement set-up (thereby differing from S. Weinberg’s Lindbladian resolution of wave-packet formalism) and conforming (...) to Born’s probability rules. The novelty lies in formalising the adaptability of the surroundings (including the measuring device) to the mode of observation. Accordingly, the transition is of finite duration (in contrast to its instantaneousness in the von Neumann’s formulation). This duration is estimated for a simple half-spin-like model. (shrink)

The concept of quantum transition is critically examined from the perspective of the modern quantum theory of measurement. Historically rooted in the famous quantum jump of the Old Quantum Theory, the transition idea survives today in experimental jargon due to (1) the notion of uncontrollable disturbance of a system by measurement operations and (2) the wave-packet reduction hypothesis in several forms. Explicit counterexamples to both (1) and (2) are presented in terms of quantum measurement theory. (...) It is concluded that the idea of transition, or quantum jump, can no longer be rationally comprehended within the framework of contemporary physical theory. (shrink)

The traditional formalism of quantum mechanics is mainly used to describe ensembles of identical systems (with a density-operator formalism) or single isolated systems, but is not capable of describing single open quantum objects with many degrees of freedom showing pure-state stochastic dynamical behaviour. In particular, stochastic 'line-migration' as in single-molecule spectroscopy of defect molecules in a molecular matrix is not adequately described. Starting with the Bohr scenario of stochastic quantum jumps (between strict energy eigenstates), we try (...) to incorporate more general pure-state stochastic dynamical behaviour into the quantum mechanical formalism.Probability distributions of (approximately) pure states, arising through the stochastic pure-state dynamics for long times, give rise to appropriate decompositions of thermal density operators. These decompositions of density operators into pure states mediate between quantum mechanics for ensembles of molecules and quantum theory for single molecules (or single dressed quantum objects). We suggest that such decompositions should be consistent with infinite limits (e.g. the Born-Oppenheimer limit for infinite nuclear masses) in the sense that quantum fluctuations (around classical behaviour in the infinite limit) die out asymptotically. (shrink)

Einstein wrote his famous sentence "God does not play dice with the universe" in a letter to Max Born in 1920. All experiments have confirmed that quantum mechanics is neither wrong nor “incomplete”. One can says that God does play dice with the universe. Let quantum mechanics be granted as the rules generalizing all results of playing some imaginary God’s dice. If that is the case, one can ask how God’s dice should look like. God’s dice turns out (...) to be a qubit and thus having the shape of a unit ball. Any item in the universe as well the universe itself is both infinitely many rolls and a single roll of that dice for it has infinitely many “sides”. Thus both the smooth motion of classical physics and the discrete motion introduced in addition by quantum mechanics can be described uniformly correspondingly as an infinite series converges to some limit and as a quantum jump directly into that limit. The second, imaginary dimension of God’s dice corresponds to energy, i.e. to the velocity of information change between two probabilities in both series and jump. (shrink)

It is argued that the conventional formulation of quantum mechanics is inadequate: the usual interpretation of the mathematical formalism in terms of the results of measurements cannot be applied to situations in which discontinuous transitions (''quantum jumps'') are observed as they happen, since nothing that can be called a measurement happens at the moment of observation. Attempts to force such observations into the standard mould lead to absurd results: ''a watched pot never boils''. Experiments show both that (...) this result is correct when the experiment does indeed consist of a series of measurements, and that it is not when the experiment consists of a period of observation: quantum jumps do happen. The possibilities for improving the formulation by incorporating transitions in the basic postulates are reviewed, and a satisfactory postulate is obtained by modifying a suggestion of Bell's. This requires a distinction between the external description of the whole of a physical system and internal descriptions which are themselves physical events in the system. It is shown that this gives correct results for simple unstable systems and for the quantum-jump experiments. (shrink)

Durch eine Untersuchung der Stoßvorgänge wird die Auffassung entwickelt, daß die Quantenmechanik in der Schrödingerschen Form nicht nur die stationären Zustände, sondern auch die Quantensprünge zu beschreiben gestattet.

Eugene Wigner and others have speculated that the “collapse of the state vector” during an observation might be a physically real process so that some modification of current quantum theory would be required to describe the interaction with a conscious observer appropriately.Experimental reports on the “psychokinetic effect” as a mental influence on the outcome of quantum jumps suggest that perhaps this effect might be vital for an understanding of the observer's role in quantum mechanics.Combining these two (...) speculations we introduce a reduction principle that provides for the gradual reduction of a macroscopically ambiguous state and allows simultaneously for the occurrence of some psychokinetic effect in the process of observation.The resulting model leads to many of the paradoxical, but logically consistent, features of the psychokinetic effect that have been reported, and makes further testable predictions.The model does not touch on the more profound questions of consciousness. But the model implies that the result of a conscious observation, the collapse of the state vector, becomes accessible to the experimenter, with the psychokinetic effect as probe: Whether Schrödinger's cat has not or has collapsed the state vector determines whether or not the later human observer can still exert a psychokinetic influence on the result. (shrink)

The sequential patterns of the sixty-four hexagrams in the Yijing, variously known as I Ching (the Book of Changes) are structured to embrace the universe of possibilities, scenarios and probabilities. Each hexagram equates to each moment in space-time. With the arrow of time, a string of hexagrams represent a string of moments. A probability curve can be formed from the string of hexagrams. Physicists call this mathematical entity a wave function which is constantly changing and proliferating. A wave function is (...) mathematical representation of all possibilities that can happen to an observed entity when it interacts with an observer. The form of the wave function can be calculated by the Schrodinger wave equation for any part of the range of moments. The string of hexagrams deal with probabilities. Physicists deal mainly with two wave forms and functions – dynamic wave that follows the Schrodinger wave equation and the second phenomenon is the “collapse of the wave function” which is abrupt and discontinuous. Which part of the wave collapses is a matter of probability and chance. The wave transition from the first to the second is call the quantum jump. This exhibited phenomenon is very similar to how the hexagram in the Yijing. When unobserved, the sequential formation of the hexagrams, moment by moment, form a probability wave but when it is observed, it abruptly collapses. It is the abrupt collapse of all the development aspects of the wave function except the one that actualizes and that particular hexagram is therefore the mathematical representation of the observed entity. What spurs all the changes is the energy that flows through the system and all the interacting waves are interconnected and interdependent and they form the energy fields. Emphasis is on the stringed hexagrams, each possesses a sophisticated mathematical structure, suggesting at the same time that it would hold great significance as an integral part of the whole of the wave or energy field. The subject of this paper is on the quantum- informational theoretical framework of Yijing. (shrink)

Erwin Schrödinger and Werner Heisenberg were the originators of two approaches, known respectively as “wave mechanics” and “matrix mechanics”, to what is now called “quantum mechanics” or “quantum theory”. The two approaches appear to be extremely different, both in their technical forms, and in their philosophical underpinnings. Heisenberg arrived at his theory by effectively renouncing the idea of trying to represent a physical system, such as a hydrogen Bohr's atom model for example, as a structure in space—time, but (...) instead, following the lead of Einstein's 1905 theory of relativity, representing only empirically observable properties, such as the transition amplitudes between the stationary states of the atom. These amplitudes can be arranged in square arrays of numbers. In Heisenberg's scheme these arrays, and other like them, are combined according to certain rules that were later recognized by Max Born to be the rules of matrix multiplication. The whole scheme is abstract and mathematical, and avoids using any space—time picture of what is going on at the atomic level. Schrödinger, on the other hand, represented the electron in an atom by a cloudlike wave surrounding the nucleus. This is a space—time structure that, superficially at least, is more in line with the classical physical theories of the eighteenth and nineteenth centuries. -/- Niels Bohr invited Schrödinger to come to Copenhagen to present his ideas, and to discuss this subject with himself, Heisenberg, and others. Schrödinger arrived in Copenhagen on October 1st, 1926, and was immediately intensively engaged by Bohr and the others in a “debate” that lasted for days. Eventually, Schrödinger become ill, and was confined in Bohr's home to a bed, upon which Bohr sat, continuing the discussion. Schrödinger finally exclaimed “If all the quantum jumping is here to stay, then I am sorry that I ever became involved in quantum mechanics”. Bohr replied, “But we are glad that you did!”. (shrink)

This article discusses the historical similarities and differences between Schroedinger's and de Broglie's ideas on wave mechanics and gives a biographical account of their scientific relationship. Their arguments over questions such as quantum jumps, the viability of particles within wave mechanics theory, and the inclusion of space, time, and relativity in quantum mechanics are analyzed. The final section of the paper considers the overall role of Schroedinger's ideas in modern quantum mechanics.

Science has made a mighty advance since it originated in ancient Greece more than 2500 years ago. Yet we still live in Plato's cave today; we think everything around us moves continuously, but continuous motion is merely a shadow of real motion. This book will lead you to walk out the cave along a logical and comprehensible road. After passing Zeno's arrow, Newton's inertia, Einstein's light, and Schrodinger's cat, you will reach the real world, where every thing in the universe, (...) whether it is an atom or a ball or even a star, ceaselessly jumps in a random and discontinuous way. In a famous metaphor, God does play dice with the universe. Discovering motion is not continuous but discontinuous and random is like finding the Earth is not at rest but moving. The new discovery may finally solve Zeno's paradoxes and the quantum puzzle, and it will lead to a profound shift in our world view. (shrink)

Quantum Mechanics, and apparently its successors, claim that there are minimum quantities by which objects can differ, at least in some situations: electrons can have various “energy levels” in an atom, but to move from one to another they must jump rather than move via continuous variation: and an electron in a hydrogen atom going from -13.6 eV of energy to -3.4 eV does not pass through states of -10eV or -5.1eV, let along -11.1111115637 eV or -4.89712384 eV.

The problem of how mathematics and physics are related at a foundational level is of interest. The approach taken here is to work towards a coherent theory of physics and mathematics together by examining the theory experiment connection. The role of an implied theory hierarchy and use of computers in comparing theory and experiment is described. The main idea of the paper is to tighten the theory experiment connection by bringing physical theories, as mathematical structures over C, the complex numbers, (...) closer to what is actually done in experimental measurements and computations. The method replaces C by C n which is the set of pairs, R n,I n, of n figure rational numbers in some basis. The properties of these numbers are based on those of numerical measurement outcomes for continuous variables. A model of space and time based on R n is discussed. The model is scale invariant with regions of constant step size interrupted by exponential jumps. A method of taking the limit n→∞ to obtain locally flat continuum-based space and time is outlined. Also R n based space is invariant under scale transformations. These correspond to expansion and contraction of space relative to a flat background. The location of the origin, which is a space and time singularity, does not change under these transformations. Some properties of quantum mechanics, based on C n and on R n space are briefly investigated. (shrink)

Benveniste’s experiments were at the origin of a scientific controversy that has never been satisfactorily resolved. Hypotheses based on modifications of water structure that were proposed to explain these experiments were generally considered as quite improbable. In the present paper, we show that Benveniste’s experiments violated the law of total probability, one of the pillars of classical probability theory. Although this could suggest that quantum logic was at work, the decoherence process is however at first sight an obstacle to (...) describe this macroscopic experimental situation. Based on the principles of a personalist view of probability, a modeling could nevertheless be built that fitted the outcomes reported in Benveniste’s experiments. Indeed, in QBism, there is no split between microscopic and macroscopic, but between the world where an agent lives and his internal experience of that world. The outcome of an experiment is thus displaced from the object to its perception by an agent. By taking into account both the personalist view of probability and measurement fluctuations, all characteristics of Benveniste’s experiments could be described in a simple modeling: change of the biological system from resting state to “activated” state, concordance of “expected” and observed outcomes and apparent “jumping” of “biological activities” from sample to sample. No hypothesis on change of water structure was necessary. In conclusion, a modeling of Benveniste’s experiments based on a personalist view of probability offers for the first time a logical framework for these experiments that have remained controversial and paradoxical till date. (shrink)

"Why did Archimedes jump from his bath and run naked through the streets shouting 'Eureka!'? What is a quantum and where does it leap? Do you know your id from your ego? Does God play dice? his books answers all those questions and more, taking the revolutionary and perplexing ideas of Western thought and extracting their essence. From Greek philosophy to contemporary economics, physics and architecture, A Little Knowledge covers some of the most often heard but least understood theories (...) and explains them simply and entertainingly, including: Existentialism The Oedipus Complex Original Sin 'I think, therefore I am' Fuzzy Logic The Big Bang 'Religion is the Opium of the People'. (shrink)

The paper takes up Bell's “Everett theory” and develops it further. The resulting theory is about the system of all particles in the universe, each located in ordinary, 3-dimensional space. This many-particle system as a whole performs random jumps through 3N-dimensional configuration space – hence “Tychistic Bohmian Mechanics”. The distribution of its spontaneous localisations in configuration space is given by the Born Rule probability measure for the universal wavefunction. Contra Bell, the theory is argued to satisfy the minimal desiderata (...) for a Bohmian theory within the Primitive Ontology framework. TBM's formalism is that of ordinary Bohmian Mechanics, without the postulate of continuous particle trajectories and their deterministic dynamics. This “rump formalism” receives, however, a different interpretation. We defend TBM as an empirically adequate and coherent quantum theory. Objections voiced by Bell and Maudlin are rebutted. The “for all practical purposes”-classical, Everettian worlds exist sequentially in TBM. In a temporally coarse-grained sense, they quasi-persist. By contrast, the individual particles themselves cease to persist. (shrink)

The “memory of water” was a major international controversy that remains unresolved. Taken seriously or not, this hypothesis leads to logical contradictions in both cases. Indeed, if this hypothesis is held as wrong, then we have to explain how a physiological signal emerged from the background and we have to elucidate a bulk of coherent results. If this hypothesis is held as true, we must explain why these experiments were difficult to reproduce by other teams and why some blind experiments (...) were so disturbing for the expected outcomes. In this article, a third way is proposed by modeling these experiments in a quantum-like probabilistic model. It is interesting to note that this model does not need the hypothesis of the “memory of water” and, nevertheless, all the features of Benveniste’s experiments are taken into account (emergence of a signal from the background, difficulties faced by other teams in terms of reproducibility, disturbances during blind experiments, and apparent “jumps of activity” between samples). In conclusion, it is proposed that the cognitive states of the experimenter exhibited quantum-like properties during Benveniste’s experiments. (shrink)