According to the BSM- Supergravitation Unified Theory (BSM-SG), the energy is indispensable feature of matter, while the matter possesses hierarchical levels of organization from a simple to complex forms, with appearance of fields at some levels. Therefore, the energy also follows these levels. At the fundamental level, where the primary energy source exists, the matter is in its primordial form, where two super-dense fundamental particles (FP) exist in a classical pure empty space (not a physical vacuum). They are (...) associated with the Planck scale parameters of frequency and distance and interact by Supergravitational forces. These forces are inverse proportional to the cube of distance at pure empty space and they are based on frequency interactions. Since the two FPs have different intrinsic frequencies, the SG forces appear different for interactions between the like and unlike FPs and may change the sign. This primordial form of matter exists in the super-heavy black holes located in the center of each well formed galaxy. The next upper level of matter organization includes the underlying structure of the physical vacuum, called a Cosmic Lattice, and the structure of elementary particles. They have common substructure elements obtained by specific crystallization process preceding the formation of the observable galaxies. The Cosmic Lattice, forming a space known as a physical vacuum, is responsible for the existence and propagation of the physical fields: electrical, magnetic, Newtonian gravity and inertia. The energy of physical vacuum is in two forms: Static (enormous) and Dynamic (weak). The Static energy is directly related to the Newtonian mass by the Einstein equation E = mc^2 and it is a primary source of the nuclear energy. The Dynamic energy is responsible for the existence of the electric and magnetic fields, the constant speed of light and the quantum mechanical properties of the physical vacuum. The next upper energy level is the dynamical energy of excited atoms and molecules. At this level a hidden energy wells exit, such as the internal energy of the electron and the internal energy of atoms with more than one electron. The next upper energy level is at some organic molecules and particularly in the biomolecules that contain ring atomic structures. In such a structure, some quantum states are not emitted immediately, but rotating in the ring. While in organic molecules the energy stored in such a ring is released by a chemical process, in the long chain molecule of proteins in the living organism the stored energy can be released simultaneously by triggering. A huge number of atomic rings are contained in the DNA strands. The release of the energy stored in DNA, for example, is an avalanche process that causes an emission of entangled photons possessing a strong penetrating capability. A sequence of entangled photons emitted by DNA should carry the genetic information encoded by the cordons. This mechanism, predicted in BSM-SG theory, is very important for intercommunication between the cells of the living organism. The next upper level of energy organization may exist in the brain. The brain is an organ of a most abundant number of atomic rings, while its tissue environment might permit complex energy interactions. The human brain contains billions of atomic rings. The next hypothetical upper level of energy organization is an information field, physically existed outside, but connected with the living brain. It corresponds to a specific field known as aura, while the possibility of its existence is still not accepted by the main stream science. The problem is that this field could not be detected by the currently existing technical means used for EM communications. The BSM-SG predicts that this field might differ from the EM field we use for communication, but it is a subject of a further theoretical development that must be supported by experiments using specifically designed technical means. According to the BSM-SG theory, the energy conversion from the primary energy source to the complex levels of matter and field organization is a permanent syntropic process based on complex resonance interactions. (shrink)

Physical vacuum is a special superfluid medium populated by enormous amount of virtual particle-antiparticle pairs. Its motion is described by the modified Navier–Stokes equation: the pressure gradient divided by the mass density is replaced by the gradient from the quantum potential; time-averaged the viscosity vanishes, but its variance is not zero. Vortex structures arising in this medium show infinitely long lifetime owing to zero average viscosity. The nonzero variance is conditioned by exchanging the vortex energy with zero-point vacuum fluctuations. (...) The vortex has a non-zero core where the orbital speed vanishes. The speed reaches a maximal value on the core wall and further it decreases monotonically. The vortex trembles around some average value and possesses by infinite life time. The vortex ball resulting from topological transformation of the vortex ring is considered as a model of a particle with spin. Anomalous magnetic moment of electron is computed. (shrink)

A model of a three-dimensional quantum vacuum based on Planck energy density as a universal property of a granular space is suggested. The possibility to provide an unifying explanation of dark matter and dark energy as phenomena linked with the fluctuations of the three-dimensional quantum vacuum is explored. The changes and fluctuations of the quantum vacuum energy density generate a curvature of space–time similar to the curvature produced by a “dark energy” density. The formation of large (...) scale structures in the universe associated to the flattening of the orbital speeds of the spiral galaxies can be explained in terms of primary fluctuations of the quantum vacuum energy density without attracting the idea of dark matter. (shrink)

Two different derivations of the observed vacuum energy density are presented. One is based on a class of proper and novel generalizations of the de Sitter solutions in terms of a family of radial functions R that provides an explicit formula for the cosmological constant along with a natural explanation of the ultraviolet/infrared entanglement required to solve this problem. A nonvanishing value of the vacuum energy density of the order of ${10^{- 123} M_{\rm Planck}^4}$ is derived in agreement with (...) the experimental observations. A correct lower estimate of the mass of the observable universe related to the Dirac–Eddington–Weyl’s large number N = 1080 is also obtained. The presence of the radial function R is instrumental to understand why the cosmological constant is not zero and why it is so tiny. Finally, we rigorously prove why the proper use of Weyl’s Geometry within the context of Friedman–Lemaitre–Robertson–Walker cosmological models can account for both the origins and the value of the observed vacuum energy density. The source of dark energy is just the dilaton-like Jordan–Brans–Dicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. The full theory involving the dynamics of Weyl’s gauge field Aμ is very rich and may explain also the anomalous Pioneer acceleration and the temporal variations of the fundamental constants resulting from the expansion of the Universe. This is consistent with Dirac’s old idea of the plausible variation of the physical constants but with the advantage that it is not necessary to invoke extra dimensions. (shrink)

The Lorentz transformation is derived without assuming that the velocity of light is a constant. This suggests that the constantc which appears in the transformation has a deeper significance than heretofore commonly assumed. It is hypothesized that there exists, in all of physical reality, velocities of only one magnitude. The magnitude isc, the speed of light in vacuum. This hypothesis forces us to view a fundamental particle as an extended object and matter in general as a field ρ(t, r, (...) θ), which we give the generic name “stuff.” An important feature of the ρ field is that at each spacetime point(t, r) stuff travels in all directions θ with speedc. In order to elucidate the nature of ρ(t, r, θ), the equations determining ρ for a one-dimensional world are derived and solved. Fundamental particles are shown to exist and their structure is obtained. (shrink)

We discuss a new theory of the universe in which the vacuum energy is of classical origin and dominates the energy content of the universe. As usual, the Einstein equations determine the metric of the universe. However, the scale factor is controlled by total energy conservation in contrast to the practice in the Robertson–Walker formulation. This theory naturally leads to an explanation for the Big Bang and is not plagued by the horizon and cosmological constant problem. It naturally accommodates the (...) notion of dark energy and proposes a possible explanation for dark matter. It leads to a dual description of the universe, which is reminiscent of the dual theory proposed by Milne in 1937. On the one hand one can describe the universe in terms of the original Einstein coordinates in which the universe is expanding, on the other hand one can describe it in terms of co-moving coordinates which feature in measurements. In the latter representation the universe looks stationary and the age of the universe appears constant. The paper describes the evolution of this universe. It starts out in a classical state with perfect symmetry and zero entropy. Due to the vacuum metric the effective energy density is infinite at the beginning, but diminishes rapidly. Once it reaches the Planck energy density of elementary particles, the formation of particles can commence. Because of the quantum nature of creation and annihilation processes spatial and temporal inhomogeneities appear in the matter distributions, resulting in residual proton (neutron) and electron densities. Hence, quantum uncertainty plays an essential role in the creation of a diversified complex universe with increasing entropy. It thus seems that quantum fluctuations play a role in cosmology similar to that of random mutations in biology. Other analogies to biological principles, such as recapitulation, are also discussed. (shrink)

We argue that the Standard Model in the Higgs phase does not suffer from a “hierarchy problem” and that similarly the “cosmological constant problem” resolves itself if we understand the SM as a low energy effective theory emerging from a cutoff-medium at the Planck scale. We actually take serious Veltman’s “The Infrared–Ultraviolet Connection” addressing the issue of quadratic divergences and the related huge radiative correction predicted by the SM in the relationship between the bare and the renormalized theory, usually (...) called “the hierarchy problem” and claimed that this has to be cured. We discuss these issues under the condition of a stable Higgs vacuum, which allows extending the SM up to the Planck cutoff. The bare Higgs boson mass then changes sign below the Planck scale, such that the SM in the early universe is in the symmetric phase. The cutoff enhanced Higgs mass term as well as the quartically enhanced cosmological constant term provide a large positive dark energy that triggers the inflation of the early universe. Reheating follows via the decays of the four unstable heavy Higgs particles, predominantly into top–antitop pairs, which at this stage are massless. Preheating is suppressed in SM inflation since in the symmetric phase bosonic decay channels are absent at tree level. The coefficients of the shift between bare and renormalized Higgs mass as well as of the shift between bare and renormalized vacuum energy density exhibit close-by zeros at about \ and \, respectively. The zero of the Higgs mass counter term triggers the electroweak phase transition, from the low energy Higgs phase and to the symmetric phase above the transition point. Since inflation tunes the total energy density to take the critical value of a flat universe and all contributing components are positive, it is obvious that the cosmological constant today is naturally a substantial fraction of the total critical density. Thus taking cutoff enhanced corrections seriously the Higgs system provides besides the masses of particles in the Higgs phase also dark energy, inflation and reheating in the early universe. The main unsolved problem in our context remains the origin of dark matter. Higgs inflation is possible and likely even unavoidable provided new physics does not disturb the known relevant SM properties substantially. The scenario highly favors to understand the SM and its main properties as a natural structure emerging at long distance. This in particular concerns the SM symmetry patterns and their consequences. (shrink)

The claim that certain fundamental constants of nature are fine tuned for life and that this provides strong evidence for supernatural design is perhaps the best scientific argument for the existence of God since Paley’s watch. Even atheist physicists find these so called “anthropic coincidences” difficult to explain and need to invoke the Weak Anthropic Principle and multiple universes to do so. Certainly if there are many universes, fine tuning is simple. Our form of life was fined tuned (...) to our universe by evolution. While multiple universes are expected from modern cosmological theories, theists and some scientists object that invoking the unobservable is not science. Of course, God is unobservable too, so the best theists can claim is a standoff. This is the first in a series of columns based on a book in the works that attempts to show that the apparent fine tuning of fundamental constants can be understood from basic physics without invoking multiple universes. In some cases the explanation is provable. In other cases, it is not provable but plausible. Fine tuning by design is a God of the Gaps argument. The proponent has the burden if proving that no possible natural explanation can be found. Thus a plausible natural explanation is sufficient to defeat the argument. A list of thirty four parameters that seem to be fine tuned has been assembled by Rich Deem on the God and Science website. Several of Deem’s constants, such as the speed of light in a vacuum, c, Newton’s constant of gravity, G, and Planck’s constant, h, are just arbitrary numbers that are determined simply by the unit system you are using. They can be set equal to any number you want, except zero, with no impact on the physics. So no fine tuning can possibly be involved, just as the number p is not fine tuned. I will focus first on the five parameters that have the most significance because, if interpreted correctly, they seem to pretty much rule out almost any conceivable kind of life without fine tuning: · Ratio of electrons to protons · Ratio of electromagnetic force to gravity Expansion rate of the universe · Mass density of the universe · Cosmological constant I will admit that the features a universe would have for slightly different values of these parameters, all other parameters remaining the same, would render unlikely any form of life even remotely like ours, that is, one that is based on a lengthy process, chemical or otherwise, by which complex matter evolved from simpler matter. Let me discuss each in turn, with the last, the most difficult, reserved for a future column.. (shrink)

There exist two methods for finding the magnetic moment of the electron. The first method employed in quantum electrodynamics consists in calculating the energy of the electron placed in a constant magnetic field, the extra energy due to the field being proportional to the magnetic moment. It is also possible to use the second method proceeding from the fact that the asymptotic form of the vector potential at infinity is proportional to the magnetic moment. If the (...) electron were point-like, both the methods would yield identical results. In the present paper is studied the magnetic field created by the electron in hydrogen-like ions, which enables one to find the electron magnetic moment by the second method. The electron magnetic moment in this case proves to be different in different states of the electron in the Coulomb field of the ions and, moreover, is distinct from the magnetic moment calculated by the first method. The results of the paper show that the electron is not small and is deformable under action of external fields. (shrink)

The reason for physics’ failure to find a final theory of the universe is examined. Problems identified are: the lack of unequivocal definitions for its fundamental elements (time, length, mass, electric charge, energy, work, matter-waves); the danger of relying too much on mathematics for solutions; especially as philosophical arguments conclude the universe cannot have a mathematical basis. It does not even need the concept of number to exist. Numbers and mathematics are human inventions arising from the human predilection for measurement. (...) Following Aristotle, a single fundamental cause is proposed to explore the efficacy of using pure non-mathematical philosophy to explain the universe, contrary to current quantum physical views. The cause is taken as Time, which is then defined, surprisingly leading automatically to a definition of a three-dimensional space answering the question into what can a universe be placed (space before space seems non-sensical). This enables the philosophical arguments to derive a universal rule giving clear-cut descriptions (definitions) of force (both gravitational and electromagnetic), motion, energy, and particles. The formation of atomic nuclei and atomic properties together with an unexpected role for neutrinos follow. In particular, a Popper-test can be prepared by introducing the concept of measurement to allow the philosophy arguments to be tested in another discipline - mathematics. The solution agrees with human physical observations to a remarkable degree of accuracy, automatically explaining and predicting values for Planck’s and the fine-structure constants. Although mathematical, it is included as confirming the efficacy of philosophy in attaining a final theory. (shrink)

Novel forms of matter, such as states made of gluons (glueballs), multiquark mesons or baryons and hybrid mesons are predicted by low energy QCD, for which several candidates have recently been identified. Searching for such exotic states of matter and studying their production and decay properties in detail has become a flourishing field at the experimental facilities now available or being built - e.g. BESIII in Beijing, BELLE II at SuperKEKB, GlueX at Jefferson Lab, PANDA at FAIR, J-PARC and in (...) the upgraded LHC experiments, in particular LHCb. A modern primer in the field is required so as to both revive and update the teaching of a new generation of researchers in the field of QCD. These lectures on hadron spectroscopy are intended for Master and PhD students and have been originally developed for a course delivered at the Stefan Meyer Institute of the Austrian Academy of Sciences. They are phenomenologically oriented and intended as complementary material for basic courses in particle and nuclear physics. The book describes the spectra of light and heavy mesons and baryons, and introduces the fundamental properties based on symmetries. Further, it derives multiplet structures, mixing angle, decay coupling constants, magnetic moments of baryons, and predictions for multiquark states and compares these with suitable experimental data. Basic methods of calculating decay angular distributions and determining masses and widths of resonances are also presented. The appendices provide students and newcomers to the field with the necessary background information, and include a set of problems and solutions. (shrink)

The fine structure constant α ≡ e2/ c ≈ 1/137 is one of the fundamental parameters of the standard model of particle physics. There is a long history of attempts to derive the measured value of α from an underlying theory, or exhibit it in the form of a compact mathematical expression [2–4, 6, 8, 14–16]. The most significant advance in this endeavour was made by Dirac, who showed that if magnetic monopoles exist, with magnetic charge (...) μ, then.. (shrink)

A Clifford-algebraic interpretation is proposed of the charge, mass, spin relationship found recently by Cooperstock and Faraoini, which was based on the Kerr–Newman metric solutions of the Einstein–Maxwell equations. The components of the polymomentum associated with a Clifford polyparticle in four dimensions provide for such a charge, mass, spin relationship without the problems encountered in Kaluza–Klein compactifications which furnish an unphysically large value for the electron charge. A physical reasoning behind such charge, mass, spin relationship is provided, followed by (...) a discussion on the geometrical derivation of the fine structure constant by Wyler, Smith, Gonzalez-Martin and Smilga. To finalize, the renormalization of electric charge is discussed and some remarks are made pertaining the modifications of the charge–scale relationship, when the spin of the polyparticle changes with scale, that may cast some light into the alleged Astrophysical variations of the fine structure constant. (shrink)

We address anticipated fermion–antifermion and dimension-4 gauge-field vacuum-condensate contributions to the magnetic portion of the fermion–photon vertex function in the presence of a vacuum with nonperturbative content, such as that of QCD. We discuss how inclusion of such condensate contributions may lead to a vanishing anomalous magnetic moment, in which case vacuum condensates may account for the apparent consistency between constituent quark masses characterizing baryon magnetic moments and those characterizing baryon spectroscopy.

According to the BSM Supergravitation Unified Theory, the physical vacuum contains energy that is not of electromagnetic origin. The Heterodyne Resonance Mechanism (HRM) predicted by the theory permits access to this hidden energy by a process involving the anomalous magnetic moment and the quantum mechanical spin flipping of the electron. Plasma experiments and analysis of lightning observations indicate that the HRM effect could be involved in the natural lightning phenomena. Although the energy density of this hidden (...) source is much smaller than nuclear energy, the opportunity to access this energy will lead to some new practical applications. The derived physical model of the HRM effect provides the opportunity for development of new technologies. This book could be an useful handbook for researchers and experimenters. (shrink)

Matter is pictured as a primitive fluid substratum having the fundamental property of fluctuating at a constant frequency. From this are derived the discrete properties of space and time, and it follows that, at the microlevel, talk of pure space and pure time involves us in ambiguities. A new interpretation of Planck's constant emerges according to which it is a quantum of matter-time combination. Thus, a quantum of matter-space combination should exist. On pursuing further the hydrodynamic model, such a (...) constant is in fact discovered as the drag-quantum of the quantum fluid. A fourth-degree differential equation is considered which, with the help of this new constant, generates spectra of frequency, mass, and fine structure constants. The theory seems to answer some important fundamental questions. (shrink)

Precision testing of the quantum electrodynamics (QED) and the standard model provides some of the most secure knowledge in the history of physics. These tests can also be used to constrain and search for new physics going beyond the standard model. We examine the evidential structure of relationships between theoretical predictions from QED, precision measurements of these phenomena, and the indirect determination of the fine structure constant. We argue that "pure QED" is no longer sufficient to predict (...) the electron's anomalous magnetic moment, and that standard model effects are needed. The details relevant to low-energy QED are robust against future theory change. (shrink)

The electron is considered as a massless point-particle which moves in a spacetime with (3+3) dimensions subjected to a field that attracts it towards the (3+1) standard spacetime. This field is assumed to be described by the radial time component of the e.m. 6-potential and to be due to the vacuum polarization arising when the charge of the electron is removed from the (3+1) spacetime. The pertinent Klein-Gordon equitation in 6 dimensions is solved and the right values for the electron (...) magnetic moment and spin are derived. The rest mass of the electron, as it appears in the standard (3+1) spacetime, is obtained as an integration constant from the motion in the two extra time dimensions. The very simple form assumed as a first approximation for the attractive potential does not give quantized rest masses. (shrink)

A mirror world consisting of matter which interacts with ordinary matter via gravity and weakly via other forces has been considered, inter alia, as a model for dark matter. A discrete symmetry under the interchange of fields means that both sectors experience the same forces. Separately it has been shown that it is possible to unify gravitation and electromagnetism by using a degenerate metric in five dimensions; in this theory there are two possible representations of charge, and there is (...) a reflection symmetry between them which, along with a gauge-like invariance, achieves the unification. Here it is shown that mirror matter arises naturally out of the degenerate theory, and as a result a new means for measuring the Brans–Dicke constant is obtained. (shrink)

We derive the first analytical formula for the density of "Dark Matter" (DM) at all length scales, thus also for the rotation curves of stars in galaxies, for the baryonic Tully–Fisher relation and for planetary systems, from Einstein's equations (EE) and classical approximations, in agreement with observations. DM is defined in Part I as the energy of the coherent gravitational field of the universe, represented by the additional equivalent ordinary matter (OM), needed at all length scales, to explain classically, (...) with inclusion of the OM, the _observed coherent_ gravitational field. Our derivation uses both EE and the Newtonian approximation of EE in Part I, to describe semi-classically in Part II the advection of DM, created at the level of the universe, into galaxies and clusters thereof. This advection happens proportional with their own classically generated gravitational field g, due to self-interaction of the gravitational field. It is based on the universal formula ρ D = λgg′ 2 for the density ρ D of DM advected into medium and lower scale structures of the observable universe, where λ is a universal constant fixed by the Tully–Fisher relations. Here g′ is the gravitational field of the universe; g′ is in main part its own source, as implied in Part I from EE. We start from a simple electromagnetic analogy that helps to make the paper generally accessible. This paper allows for the first time the exact calculation of DM in galactic halos and at all levels in the universe, based on EE and Newtonian approximations, in agreement with observations. (shrink)

In this work, a neo-classical relativistic mechanics theory is presented where the spin of an electron is an inherent part of its world space-time path as a point particle. The fourth-order equation of motion corresponds to the same covariant Lagrangian function in proper time as in special relativity except for an additional spin energy term. The theory provides a hidden-variable model of the electron where the dynamic variables give a complete description of its motion, giving a classical mechanics explanation of (...) the electron’s spin, its dipole moments, and Schrödinger’s zitterbewegung, These features are also described mathematically by quantum mechanics theory, of course, but without any physical picture of an underlying reality. The total motion of the electron can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called here the spin center. The global motion is sub-luminal and described by Newton’s Second Law in proper time, the time for a clock fixed at the spin center, while the total motion occurs at the speed of light c, consistent with the eigenvalues of Dirac’s velocity operators having magnitude c. The local spin motion is an inherent perpetual motion, which for a free electron is periodic at the ultra-high zitterbewegung frequency and its path is circular in a spin-center reference frame. In an electro-magnetic field, this spin motion generates magnetic and electric dipole energies through the Lorentz force on the electron’s point charge. The electric dipole energy corresponds to the spin-orbit coupling term involving the electric field that appears in the corrected Pauli non-relativistic Hamiltonian, which has long been used to explain the doublet structure of the spectral lines of the excited hydrogen atom. Pauli’s spin-orbit term is usually derived, however, from his magnetic dipole energy term, including also the effect of Thomas precession, which halves this energy. The magnetic dipole energy from Pauli’s and Dirac’s theory is twice that in the neo-classical theory, a discrepancy that has not been resolved. By defining a spin tensor as the angular momentum of the electron’s total motion about its spin center, the fundamental equations of motion can be re-written in an identical form to those of the Barut–Zanghi electron theory. This allows the equations of motion to be expressed in an equivalent form involving operators applied to a state function of proper time satisfying a neo-classical Dirac–Schrödinger spinor equation. This state function produces the dynamic variables from the same operators as in Dirac’s theory for the electron but without any probability implications. It leads to a neo-classical wave function that satisfies Dirac’s relativistic wave equation for the free electron by applying the Lorentz transformation to express proper time in the state function in terms of an observer’s space-time coordinates, showing that there is a close connection between the neo-classical theory and quantum mechanics theory for the electron’s dynamics. (shrink)

We investigate the novel problem of what happens in special relativity and in relativistic field theories whenthree-dimensional space is quantized. First we examine the equation for elastic waves on a linear chain, the simplest example of a quantized medium, and propose, on its analogy, a nonlinearp-k relationp=ħk(sinhkl)/kl for light and material waves. Here,kl is a new variable which represents the space-quantization effect on the plane wave of wave numberk=|k|. (Note thatkl=0 givesp=ħk.) This relation makes the light velocity in vacuum (...) dependent onkl. We postulate, however, that the phase and group velocities of each individual light wave are still invariant, and try to generalize special relativity to the case ofkl ≠ 0. This can be simply done if the invariance ofkl is assumed. Our results suggest that “localization” might be a relative concept. One interesting consequence of our proposal is that relativistic field theories become automatically finite. This comes out without violating unitarity or causality. A precise measurement of velocities of high-energy photons or massive particles is desirable for checking our proposal. (shrink)

Unitary field theories and “SUPER-GUT” theories work with an universal continuum, the structured spacetime of R. Descartes, B. Spinoza, B. Riemann, and A. Einstein, or a (Machian (1–3) ) structured vacuum according the quantum theory of unitary fields (Dirac, (4,5) and Heisenberg (6–8) ). The atomistic aspect of the substantial world is represented by the fundamental constants which are invariant against “all transformations” and which “depend on nothings” (Planck (9–11) ). A satisfactory unitary theory has to involve (...) these constants like the mathematical numbers. Today, Planck's conception of the three elementary constants ħ, c, and G may be the key to general relativistic quantum field theory like unitary theory. However, the elementary constants are a question of measurement-theory, also.According to Popper's theory (12–16) of induction, such unitary theories are “universal explaining theories.” The fundamental constants involve the complementarity between the universal statements in unitary theory and the “basic statements” in the language of classical observables. (shrink)

The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate operators (ISaTCO) (...) derived directly from c without any assumptions. This paper does not change any of the accurate QED calculations of hydrogen’s energy levels, given the simplistic model of the proton used in these calculations [1]. The Proton Radius Puzzle [2, 3] may indicate that new physics is necessary beyond the Standard Model (SM), and this paper describes the bizarre, and very different, situation when the electron and muon are located “inside” the spatially extended proton with their Centers of Charge (CoCs) orbiting the proton at the speed of light in S energy states. The electron/muon center of charge (CoC) is a structureless point that vibrates rapidly in its inseparable, non-random vacuum whose geometry and time structure are defined by the electron/muon ISaTCO discrete geometry. The electron/muon self mass becomes finite in a natural way due to the ISaTCOs cutting off high virtual photon energies in the photon propagator. The Dirac-Maxwell-Wilson (DMW) Equations are derived from the ISaTCO for the EM fields of an electron/muon, and the electron/muon “look” like point particles in far field scattering experiments in the same way the electric field from a sphere with evenly distributed charge “e” “looks” like a point with the same charge in the far field (Gauss Law). The electron’s/muon’s three fluctuating CoC internal spatial coordinate operators have eight possible eigenvalues [4, 5, 6] that fall on a spherical shell centered on the electron’s CoM with radius in the rest frame. The electron/muon internal time operator is discrete, describes the rapid virtual electron/positron pair production and annihilation. The ISaTCO together create a current that produce spin and magnetic moment operators, and the electron and muon no longer have “intrinsic” properties since the ISaTCO kinematics define spin and magnetic moment properties. (shrink)

The aim of science is the explanation of complicated systems by reducing it to simple subsystems. According to a millennia-old imagination this will be attained by dividing matter into smaller and smaller pieces of it. The popular superstition that smallness implies simplicity seems to be ineradicable. However, since the beginning of quantum theory it would be possible to realize that the circumstances in nature are exactly the other way round. The idea “smaller becomes simpler” is useful only down to the (...) atoms of chemistry. Planck’s formula shows that smaller extensions are related to larger energies. That more and more energy should result in simpler and simpler structures, this does not only sound absurd, it is absurd. A reduction to really simple structures leads one to smallest energies and, thus, to utmost extended quantum systems. The simplest quantum structure, referred to as quantum bit, has a two-dimensional state space, and it establishes a cosmological structure. Taking many of such quantum bits allows also for the construction of localized particles. The non-localized fraction of quantum bits can appear as “dark matter”. (shrink)

It is suggested that the apparently disparate cosmological phenomena attributed to so-called ‘dark matter’ and ‘dark energy’ arise from the same fundamental physical process: the emergence, from the quantum level, of spacetime itself. This creation of spacetime results in metric expansion around mass points in addition to the usual curvature due to stress-energy sources of the gravitational field. A recent modification of Einstein’s theory of general relativity by Chadwick, Hodgkinson, and McDonald incorporating spacetime expansion around mass points, (...) which accounts well for the observed galactic rotation curves, is adduced in support of the proposal. Recent observational evidence corroborates a prediction of the model that the apparent amount of ‘dark matter’ increases with the age of the universe. In addition, the proposal leads to the same result for the small but nonvanishing cosmological constant, related to ‘dark energy,’ as that of the causet model of Sorkin et al. (shrink)

By making use of the method of moments we study some aspects of the statistical behavior of the nonrelativistic harmonic oscillator according to stochastic electrodynamics. We show that the random rotations induced on the particle by the zero-point field account for the magnitude of the spin of the electron, the result differing from the correct one(3/4)h 2 by a factor of2. Assuming that the measurement of a spin projection may be effectively taken into account by considering the action of only (...) the subensemble of the field with the corresponding circular polarization, the calculated value of the spin projection comes out to be the correct one within a factor of order unity. The radiative corrections give rise to both the Lamb shift and the anomalous magnetic moment of the electron, the latter being evaluated to within a factor of2. The magnetic and gyromagnetic properties of the electron come out to be in agreement with quantum mechanics. Interference effects are shown to occur when evaluating the average value of the square of the angular momentum. (shrink)

We develop a geometro-dynamical approach to the cosmological constant problem (CCP) by invoking a geometry induced by the energy-momentum tensor of vacuum, matter and radiation. The construction, which utilizes the dual role of the metric tensor that it structures both the spacetime manifold and energy-momentum tensor of the vacuum, gives rise to a framework in which the vacuum energy induced by matter and radiation, instead of gravitating, facilitates the generation of the gravitational constant. The non-vacuum sources comprising matter and radiation (...) gravitate normally. At the level of classical gravitation, the mechanism deadens the CCP yet quantum gravitational effects, if strong, can keep it existent. (shrink)

Fundamental Theory has been called an "unfinished symphony" and "a challenge to the musicians among natural philosophers of the future". This book, written in 1944 but left unfinished because Eddington died too soon, proved to be his final effort at a vision for harmonization of quantum physics and relativity. The work is less connected and internally integrated than 'Protons and Electrons' while representing a later point in the author's thought arc. The really interested student should read both books together.The (...) class='Hi'>physical and mathematical reasoning are very deep, but it is possible to enjoy much of the flavor of the book even without following everything. The tidbits given below illustrate Eddington's beautiful and mellifluous English style. This edition contains a clickable table of contents and some interesting illustrations.WARNING: Due to the complexity of the mathematical typesetting, the only way to reproduce this book has been as a series of scanned page images. We believe this work is scientifically and culturally important, and despite a few imperfections and the inevitably small print, have brought it back into print as part of our continuing commitment to the preservation of Eddington's work. On a portable electronic reader the pages come out pretty small, but they are legible. On a desktop computer running the Amazon app, they are perfectly fine. We appreciate your understanding, and hope you enjoy this valuable book.TIDBITS:The number of protons and electrons in the universe would, in itself, be merely a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; that number is N. The present investigation seeks to determine N directly from the principles of measurement. We have to show, not that there are N particles in the universe, but that anyone who accepts certain elementary principles of measurement must, if he is consistent, think there are. We have to express in mathematical symbolism what we think we are doing when we measure things; for if we had no conception of what we were doing, the results of the measurements would not persuade us to believe anything in particular. All our results are derived from the condition that the conceptual interpretation which we place on the results of measurement must be consistent with our conceptual interpretation of the process of measurement.If we play about with a pin and a meter standard, we do not become aware of any number in particular unless the standard has been graduated, or unless we use a process of displacement which we interpret as adding pin-extensions. The fact is that, although measurement is primarily a process involving four entities, the conceptual interpretation of measurement postulates in addition the existence (in the structure contemplated) as something referred to as Z. The existence of Z is the condition that makes graduation an exact concept. In the actual universe there exists a basis which is uniform to a very high approximation, and this serves for almost all purposes; but to the much higher approximation required in the calculation of N the ideal exact basis of uniformity does not exist. The finitude of N is, in fact, the cause of the failure of the approximation.It must be remembered that we are now working to what would ordinarily be considered a fantastically high approximation. For ordinary purposes a measurable has 16 eigenvalues; but under the super-magnification here employed (which is not content to overlook 1 part in 10E39) there is a fine structure which splits each of them into 16 components. (shrink)

During the past decade, M.W. Evans and his coworkers have been developing so-called “Evans” or “ECE theory” that intends to serve as an unified field theory. One of its predictions is an existence of a radiation magnetic field called a “B(3)-field” which should accompany a circularly polarized electromagnetic radiation. This field should affect free electrons in two ways: (1) the electrons should behave in the B(3)-field in the same way as in a classical magnetic field (i.e., Larmor (...) precession) and moreover, (2) the electrons should undergo quantum interaction with the B(3)-field with the formation of a spin connection resonance. This paper presents an experimental test of the B(3)-field existence by observing the changes in trajectories of free electrons in special detector, when strong (up to 200 W/m2) continuous circularly polarized microwave radiation of a frequency of 2.45 GHz is applied. We have not detected any sign of B(3)-field in presented experiment. It follows that if the B(3)-field really exists, it should be at least 4 orders of magnitude smaller than the Evans’ theory predicts. (shrink)

Fundamental Theory has been called an "unfinished symphony" and "a challenge to the musicians among natural philosophers of the future". This book, written in 1944 but left unfinished because Eddington died too soon, proved to be his final effort at a vision for harmonization of quantum physics and relativity. The work is less connected and internally integrated than 'Protons and Electrons' while representing a later point in the author's thought arc. The really interested student should read both books together.The (...) class='Hi'>physical and mathematical reasoning are very deep, but it is possible to enjoy much of the flavor of the book even without following everything. The tidbits given below illustrate Eddington's beautiful and mellifluous English style. This edition contains a clickable table of contents and some interesting illustrations.WARNING: Due to the complexity of the mathematical typesetting, the only way to reproduce this book has been as a series of scanned page images. We believe this work is scientifically and culturally important, and despite a few imperfections and the inevitably small print, have brought it back into print as part of our continuing commitment to the preservation of Eddington's work. On a portable electronic reader the pages come out pretty small, but they are legible. On a desktop computer running the Amazon app, they are perfectly fine. We appreciate your understanding, and hope you enjoy this valuable book.TIDBITS:The number of protons and electrons in the universe would, in itself, be merely a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; that number is N. The present investigation seeks to determine N directly from the principles of measurement. We have to show, not that there are N particles in the universe, but that anyone who accepts certain elementary principles of measurement must, if he is consistent, think there are. We have to express in mathematical symbolism what we think we are doing when we measure things; for if we had no conception of what we were doing, the results of the measurements would not persuade us to believe anything in particular. All our results are derived from the condition that the conceptual interpretation which we place on the results of measurement must be consistent with our conceptual interpretation of the process of measurement.If we play about with a pin and a meter standard, we do not become aware of any number in particular unless the standard has been graduated, or unless we use a process of displacement which we interpret as adding pin-extensions. The fact is that, although measurement is primarily a process involving four entities, the conceptual interpretation of measurement postulates in addition the existence (in the structure contemplated) as something referred to as Z. The existence of Z is the condition that makes graduation an exact concept. In the actual universe there exists a basis which is uniform to a very high approximation, and this serves for almost all purposes; but to the much higher approximation required in the calculation of N the ideal exact basis of uniformity does not exist. The finitude of N is, in fact, the cause of the failure of the approximation.It must be remembered that we are now working to what would ordinarily be considered a fantastically high approximation. For ordinary purposes a measurable has 16 eigenvalues; but under the super-magnification here employed (which is not content to overlook 1 part in 10E39) there is a fine structure which splits each of them into 16 components. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Dark Matters: Pessimism and the Problem of Suffering by Mara van der LugtStefano BrogiMara van der Lugt. Dark Matters: Pessimism and the Problem of Suffering. Princeton, NJ: Princeton University Press, 2021. Pp. xi + 450. Hardback, $37.00.Mara van der Lugt's book (awarded Honorable Mention for the JHP Book Prize in 2022) has the merit of bringing attention to some crucial yet often overlooked topics by providing (...) a contribution that cannot fail to elicit broad interest. Her book does not simply discuss the theodicy and anti-theodicy of the modern age; against this background, she also brings out the often-ignored tradition of philosophical pessimism. What interests van der Lugt, however, is not "future-oriented" pessimism, which is opposed to "progressivist" theories of history, but an ontological or "value-oriented" pessimism that stresses "the terrible side of [End Page 163] life" in order to answer a series of crucial questions in a way very different from Leibniz's or Pope's approaches: Are there more evils than goods in our lives? Is life worth living for all of us, for any of us? Why do some people choose death despite their blessings? Why do some people choose life despite their sufferings? Do animals suffer as we do? Are we responsible for our own happiness? Is it better never to have been? According to van der Lugt, "The various ways in which these questions have been answered throughout the centuries have created the competing philosophical traditions known as optimism and pessimism. This book traces the intersection of the debate on the problem of evil with the debate on pessimism from the late seventeenth century onwards, seeking throughout to evaluate pessimism on its own terms" (20).A reassessment of this kind of pessimism serves an explicitly theoretical and moral purpose: van der Lugt herself states that her book is not exclusively a contribution to the history of philosophy, but "partly ethical or evaluative" (18). Indeed, pessimism and optimism "go hand in hand": they stem from a moral need and aim to respond to the evil present in the world by opening up glimmers of "hope, compassion, and consolation" (12, emphasis in original). Pessimism, in particular, is not intended to be "a philosophy of despair"; rather, it draws its strength from an "ethical commitment." Stemming from the latter is a tradition that "may be reinterpreted as a moral source" (22) and which "has not only its own epistemological and methodological concerns and presuppositions but, crucially, its own sets of virtues and moral aims" (13).The theoretical/moral purpose of Dark Matters is evident through its unfolding, even though eight of its nine chapters are roughly devoted to providing an accurate historical-philosophical reconstruction. Here, in brief, are the titles of the chapters that make up the over four hundred pages of this volume, which provide a good idea of the main authors discussed: (1) "The Complaint: Bayle and Malebranche on Physical Evil"; (2) "The Optics of Optimism: Leibniz and King Respond to Bayle"; (3) "Of Hope and Consolation: Voltaire and the Deists"; (4) "When Stoicism Meets Pessimism: La Mettrie and Maupertuis"; (5) "The Dispositional Problem of Evil: David Hume"; (6) "The Art of Suffering: Jean-Jacques Rousseau"; (7) "The Failure of Theodicy: Immanuel Kant"; (8) "The Flute-Playing Pessimist: Arthur Schopenhauer"; and (9) "Dark Matters: Pessimism as a Moral Source." To some extent, the rich itinerary provided by van der Lugt may be compared to those studies that have long undermined the idea of a monolithic and compact Enlightenment, characterized by unlimited faith in reason and its potential for liberation, and—more specifically—by a fundamental optimism with regard to human nature and the possibility of reformulating social and political structures in such a way as to enable each person to pursue happiness. However, the historical reconstruction provided here is based on an attempt to bring out the recurrent theoretical core of a philosophical perspective that first emerges with Pierre Bayle and runs through the modern and contemporary age, resurfacing in an evident way in the present-day antinatalism of David Benatar (often cited in the footnotes).According to van der Lugt, it is with Bayle (and not... (shrink)

The models of the electric charge and magnetic moment are presented based on the nonlinear response of a vacuum on the applied electric and magnetic fields. The model of the electric charge contains one parameter—the radius of charge—and predicts one value of the electric charge for all elementary particles independently on the value of this radius. Different values of this parameter for the electron are discussed.

Paradigm-shifts, termed scientific revolutions, occur periodically in the course of sciences development. The twentieth century witnessed o number of revolutions, first by Albert Einstein and then by Niels Bohr in physics, and subsequently in biology, cosmology and, trough the pioneering work of Pierre Teilhard de Chardin, in the transdisciplinary area that includes human mind and consciousness. But scientific development did not come to a standstill: while the spirit of Einstein and Teilhard is as present as ever their specific theories (...) are object to the dynamic of theory development troughs periods of "normal" and "revolutionary" science. Today another revolution lo about to occur, bringing science to the threshold of a more comprehensive and integrated account of the observed phenomenon. The currently emerging transdisciplinary unified theory is consistent whit the goals and vision of both Albert Einstein and Teilhard de Chardin. It penetrates deeper into the domains of reality than the 2Otis century's mainstream physical, biological and psychological theories did - below the level of the quanta that populate space-time, to the quantum vacuum, better termed cosmic plenum, that generates the quanta and interconnects them throughout space and time. In the twentieth century Einstein 's general relativity gave us the relativistically interlinked universe, where all things are connected by signals propagating across the geometric structure of space-time, and Teilhard de Chardin laid the foundations of a unified theory where life and mind emerge consistently out of the physical world. In the twenty-first century transdisciplinary unified theory will extend these conceptions and give us the coherent universe, where all things are intrinsically connected by a fundamental information and virtual-energy field at a fundamental level of physical reality. (shrink)

Paradigm-shifts, termed scientific revolutions, occur periodically in the course of science's development The twentieth century witnessed a number of revolutions, first by Albert Einstein and then by Niels Bohr in physics, and subsequently in biology, cosmology and, through the pioneering work of Pierre Teilhard de Chardin, in the transdisciplinary area that includes human mind and consciousness. But scientific development did not come to a standstill: while the spirit of Einstein and Teilhard is as present as ever, their specific theories (...) are subject to the dynamics of theory development through periods of "normal" and "revolutionary" science. Today another revolution is about to occur, bringing science to the threshold of a more comprehensive and integrated account of the observed phenomena. The currently emerging transdisciplinary unified theory is consistent with the goals and vision of both Albert Einstein and Teilhard de Chardin. It penetrates deeper into the domains of reality than the 20th century's mainstream physical, biological and psychological theories did -below the level of the quanta that populate space-time, to the quantum vacuum, better termed cosmic plenum, that generates the quanta and interconnects them throughout space and time. In the twentieth century Einstein's general relativity gave us the relativistically interlinked universe, where all things are connected by signals propagating across the geometric structure of space-time, and Teilhard de Chardin laid the foundations of a unified theory where life and mind emerge consistently out of the physical world. In the twenty-first century transdisciplinary unified theory will extend these conceptions and give us the coherent universe, where all things are intrinsically connected by a fundamental information and virtual-energy field at a fundamental level of physical reality. /// A mudança de paradigmas, a que frequentemente damos o nome de revoluções científicas, ocorrem periodicamente no decurso da evolução científica. O século XX testemunhou uma importante série de revoluções científicas, primeiro por Albert Einstein e depois por Niels Bohr no âmbito da física, e subsequentemente em biologia, cosmo-logia e, graças ao trabalho pioneiro de Pierre Teilhard de Chardin, na área transdisci-plinar que inclui os fenómenos da mente humana e da consciência. Mas o desenvolvimento científico não estagnou: enquanto que o espírito de Albert Einstein e de Teilhard de Chardin continua certamente presente, a verdade é que as suas teorias têm-se necessariamente submetido à dinâmica própria do desenvolvimento das teorias, o que acontece ao longo de períodos de ciência ditos "normais" quer "revolucionários". Segundo o autor do artigo, a humanidade está hoje a ponto de assistir a uma nova revolução, a qual colocará a ciência no limiar de produzir uma narrativa mais compreensiva e integrada dos fenómenos observados. Nesse sentido, a teoria transdisciplinar unificada é perfeitamente consistente com os objectivos e a visão tanto de Albert Einstein como de Teilhard de Chardin. Com efeito, esta teoria penetra mais fundo nos domínios da realidade do que as teorias mais comuns que o século XX produziu seja no domínio da física, da biologia ou da psicologia — passando do domínio dos quanta que povoam o espaço-tempo, para o quantum vacuum, mais precisamente designado plenum cósmico que gera os quanta e os interconecta através do espaço-tempo. No século XX, a teoria da relatividade generalizada de Einstein deu-nos um universo relativisticamente interconectado, no qual todas as coisas estão conectadas por sinais que se propagam através da estrutura geométrica do espaço-tempo. Por seu lado, Teilhard de Chardin lançou os fundamentos de uma teoria unificada em que os fenómenos da vida e da consciência emergem consistentemente do mundo físico. Agora, no século XXI, diz o autor do artigo, a teoria transdisciplinar unificada destina-se a alargar o âmbito destas concepções geniais de modo a dar-nos um universo coerente em que todas as coisas estão intrinsecamente conectadas por uma informação fundamental e um campo energético virtual ao nível mais profundo da realidade física. (shrink)

The magnetic dipole moment of the Kerr–Newman metric, defined by mass \, electrical charge \ and angular momentum \, is \, corresponding, for all values of \, to a gyromagnetic ratio \, which is also the value of the intrinsic gyromagnetic ratio of the electron, as first noted by Carter. Here, we argue that this result can be understood in terms of the particle-wave complementarity principle. For \ can only be defined at asymptotic spatial infinity, where the metric appears (...) to describe a spinning point particle, and therefore setting \, \, we necessarily have a model of the electron. From the Dirac equation we can construct a covariantly conserved four-current \ that is the source of the electromagnetic field generated by the charge \. The result \ then follows from the minimal gauge principle \ which is implicit in the formulation of the spinorial wave equation, and which can also be justified from the line action for a spin-1/2 point particle interacting with an external electromagnetic field, due to Berezin and Marinov. By contrast, analysis of the gyrogravito-magnetic effect, investigated classically by Wald and quantum mechanically by Adler et al., yields the result \ in all non-relativistic cases, which can be explained from the principle of equivalence. The results are in accord with the correspondence principle. (shrink)

In 1924, Bohr, Kramers and Slater tried to introduce into microphysics conservation principles that hold only on the average. This attempt was abandoned in the light of the Compton-Simon experiment. Since that time, except for a moment of doubt in 1936, it has been thought that the classical conservation laws hold in quantum theory for each individual interaction, in a way that yields the classical exchange-and-balance of momentum familiar from the laws of elastic collisions. It has been thought, that (...) is, that in each individual “collision” what one part of the total system loses in linear momentum another part gains, so as to maintain the same total amount afterwards as before. To those familiar with discussions of the interpretation of quantum theory, however, it will be apparent that the very concepts needed to express this idea of an elastic collision are generally not admitted in the theory. For one needs the idea that both before and after collision the total system has a well-defined value for the conserved quantity and, moreover, that the various component parts of the system have well-defined values for those quantities out of which the conserved one is composed. But in the case of spin, for example, it is customary to say that although total spin may be conserved in certain interactions one cannot attribute values to the separate components of spin because the associated operators do not commute. Moreover, one does not generally refer to the values of quantities except in eigenstates. Hence, in general, one would not refer to the value of the conserved quantity before and after interaction, except for interactions initiated in eigenstates. (shrink)

In the range of his intellectual interests and the profundity of his mathematical thought Hermann Weyl towered above his contemporaries, many of whom viewed him with awe. This volume, the most ambitious study to date of Weyl's singular contributions to mathematics, physics, and philosophy, looks at the man and his work from a variety of perspectives, though its gaze remains fairly steadily fixed on Weyl the geometer and space‐time theorist. Structurally, the book falls into two parts, described in the general (...) introduction by the editor: Part 1 contains four essays on particular aspects of Weyl's work, highlighting ideas he developed in various editions of his classic Raum‐Zeit‐Materie. Part 2 presents a lengthy study by Robert Coleman and Herbert Korté covering nearly the whole gamut of Weyl's mathematical research, an impressive feat. Both in the introduction as well as in footnotes to the articles Erhard Scholz's editorial voice chimes in discreetly, helping tie all five studies together.Coleman and Korté begin chronologically with Weyl's early work in analysis and the modern theory of Riemann surfaces before turning to differential geometry, unified field theory, and the space problem, a topic they use as a springboard for a discussion of their own recent work on the foundations of space‐time. They then take up Weyl's shift to group representation theory and its applications to quantum mechanics, ending with his much earlier research on the structure of the continuum. All of these topics are well handled, but the authors' own agendas coupled with their penchant for overlooking chronology in order to package Weyl's work into neat little bundles leave one feeling rather stranded and far removed from the sources of Weyl's inspiration. Moreover, the narrative style makes this part of the volume read like a technical appendix, albeit a most informative one. Readers who tackle Scholz's far more contextualized essay will be amply rewarded by comparing his views with the opinions set forth by Coleman and Korté in Part 2.Scholz gives a masterful account of Weyl's intellectual journeys from 1917 to 1925 in a study that serves as a fulcrum for the entire volume. Drawing on a number of recently published studies, including his own, on the interplay between mathematics and physics inspired by Einstein's theory of general relativity, Scholz describes how Weyl responded to this challenge by developing a truly infinitesimal space‐time geometry that generalized classical Riemannian geometry. Although unconvinced by Einstein's critique of his unified field theory, Weyl shifted his focus from this realm to the classical space problem, analyzed earlier with more primitive techniques by Hermann Helmholtz and Sophus Lie. In this connection, it should be mentioned that Thomas Hawkins has given a probing analysis of Weyl's related work on the representation of Lie groups in his tour‐de‐force work, Emergence of the Theory of Lie Groups . Scholz argues that Weyl's struggle to tame his modernized version of the space problem stemmed from a deep‐seated belief in his geometrical ideas, which in turn were nourished by philosophical musings. By demonstrating the closely related conceptual links that motivated Weyl's research in infinitesimal geometry, space‐time physics, and the foundations of mathematics, Scholz nicely illuminates the underlying fabric of epistemological concerns that occupied Weyl's attention during this fertile period.The three remaining essays in Part 1 focus on other aspects of Weyl's work in mathematical physics and cosmology. Skuli Sigurdsson's “Journeys in Spacetime” offers a broad interpretation of Weyl's career, one that emphasizes Weyl's sensitivity to cultural tensions as reflected in his philosophical roots, which combined phenomenology with facets of German idealism. Shaken by the annihilation of cultural values in Nazi Germany, Weyl became deeply aware of the gulf that separated his earlier life in Göttingen and Zurich from the one he took up at Princeton's Institute for Advanced Study in 1933. He tried to adapt, but felt out of place in an Anglo‐American scientific culture openly hostile toward metaphysics and speculative philosophy. Sigurdsson stresses these tensions, contrasting the introspective, creative individual against the backdrop of the collective in the age of the machine, but without spelling out which collective were most important for him. Wolfgang Pauli thought he knew and, like Einstein before him, he had no compunction about bluntly telling Weyl he was a mathematician, not a physicist.Pauli's opinions notwithstanding, Weyl did far more than just dabble around the mathematical edges of the new physics. If Coleman and Korté perhaps press their case for his visionary accomplishments too far, Norbert Straumann's essay “Ursprünge der Eichtheorien” suggests why Weyl's reputation among physicists has risen steadily ever since the advent of Yang‐Mills theory in the 1950s. In the course of describing Weyl's adaptation of his gauge transformation formalism to Dirac's electron theory, Straumann sheds considerable light on Pauli's role as self‐appointed watchman guarding the disciplinary boundary that separated theoretical physics from physical mathematics . He further suggests that disciplinary jealousy was a major reason why Pauli dismissed Weyl's two‐component formalism for spinors out of hand.In the realm of cosmology, on the other hand, Weyl's work has long since passed into the dustbins of history, as Hubert Goenner remarks in recounting a fascinating chapter in the infancy of space‐time physics. While doing so, Goenner shows how initially Weyl almost slavishly adopted what Einstein called Mach's principle, which asserts that the metric structure of space‐time is solely determined by the distribution of matter in the universe. This notion was quickly challenged by Willem De Sitter, who showed that Einstein's matter‐free field equations admitted a global solution with non‐zero constant curvature. Both Einstein and Weyl tried to argue that invisible masses must be present just over the “spatial horizon” of De Sitter's world in order to account for its curvature. Goenner meticulously analyzes the physical and mathematical issues at stake in this debate, stressing how Weyl gradually moved away from a strong physical interpretation to one in which mathematics models rather than physics models simply reveal natural phenomena. He argues further that Weyl's cosmological principle arose as the final expression of his search for a deeper physical meaning.Given the quality of these essays, it is regrettable that this book contains so little about Weyl's professional career, a weakness the editor could have redressed at least partially in his general introduction. This omission is all the more unfortunate given the dearth of readily accessible information about Weyl's life available elsewhere. For however mundane his outward existence may have been, the reader cannot be expected to appreciate the interplay between the world Weyl knew and his creative responses to it without fairly detailed knowledge of his biography. Shorn from these contexts, it becomes difficult to form a flesh‐and‐blood image of Weyl beyond the cliché‐ridden stereotype that sees him as a “heroic thinker in the grand German tradition.” While none of the authors falls into this trap, the collective impression they leave suggests a most enigmatic figure. Either Weyl the man tends to get lost in the shadows of his collected scientific output or he appears as a mystic loner, an outcast who abhorred the machine age in which he lived. Closer attention to the people in his life would no doubt produce a very different picture of the man and his interests. This major lacuna notwithstanding, the present volume will surely remain an indispensable resource for any future investigations of Weyl's staggering intellectual achievements. (shrink)

The discrete light-cone quantization (DLCQ) of a supersymmetric gauge theory in 1+1 dimensions is discussed, with particular attention given to the inclusion of the gauge zero mode. Interestingly, the notorious “zero-mode” problem is now tractable because of special supersymmetric cancellations. In particular, we show that anomalous zero-mode contributions to the currents are absent, in contrast to what is observed in the nonsupersymmetric case. An analysis of the vacuum structure is provided by deriving the effective quantum mechanical Hamiltonian of (...) the gauge zero mode. It is shown that the inclusion of the zero modes of the adjoint scalars and fermions is crucial for probing the phase properties of the vacua. We find that the ground-state energy is zero and thus consistent with unbroken supersymmetry and conclude that the light-cone Fock vacuum is unchanged with or without the presence of matter fields. (shrink)

In recent years, very little that is new has happened in that branch of particle physics which investigates the structure of particles. In an earlier period, certain doubts had existed about the applicability of quantum electrodynamics at distances of the order of 10-14 cm. Experiments that are universally known, in which pairs of electrons and mu-mesons arose, contradicted the theory somewhat. Later, however, it became clear that all this was a consequence of certain methodological inaccuracies.

The origin of the wave properties of matter is discussed from the point of view of stochastic electrodynamics. A nonrelativistic model of a charged particle with an effective structure embedded in the random zeropoint radiation field reveals that the field induces a high-frequency vibration on the particle; internal consistency of the theory fixes the frequency of this jittering at mc2/ħ. The particle is therefore assumed to interact intensely with stationary zeropoint waves of this frequency as seen from its proper (...) frame of reference; such waves, identified here as de Broglie's phase waves, give rise to a modulated wave in the laboratory frame, with de Broglie's wavelength and phase velocity equal to the particle velocity. The time-independent equation that describes this modulated wave is shown to be the stationary Schrödinger equation (or the Klein-Gordon equation in the relativistic version). In a heuristic analysis appled to simple periodic cases, the quantization rules are recovered from the assumption that for a particle in a stationary state there must correspond a stationary modulation.Along an independent and complementary line of reasoning, an equation for the probability amplitude in configuration space for a particle under a general potential V(x) is constructed, and it is shown that under conditions derived from stochastic electrodynamics it reduces to Schrödinger's equation. This equation reflects therefore the dual nature of the quantum particles, by describing simultaneously the corresponding modulated waveand the ensemble of particles. (shrink)

In the existing expositions of the Károlyházy model, quantum mechanical uncertainties are mimicked by classical spreads. It is shown how to express those uncertainties through entities of the future unified theory of general relativity and quantum theory.

“Artworks are not being but a process of becoming” —Theodor W. Adorno, Aesthetic Theory In the everyday use of the concept, saying that something is grotesque rarely implies anything other than saying that something is a bit outside of the normal structure of language or meaning – that something is a peculiarity. But in its historical use the concept has often had more far reaching connotations. In different phases of history the grotesque has manifested its forms as a means (...) of subversive resistance against society’s prevailing notions of form and power. What aids this impact and distinguishes two of its basic stylistic features is the grotesque’s dissolution of form and its hyperbole. Such grotesqueries, however, soon solidify into new forms, new structures of meaning, hierarchy and practice, and in this sense the history of the grotesque is, on one hand, a continual opposition and transgression of the prevailing notions of art as well as of God and humanity, while on the other hand it offers continual resistance to its own solidifying process. As such the grotesque will not and cannot be contained in form without it losing the very thing that makes it grotesque. Even though it is somewhat easy to point out certain stylistic features of the grotesque, the sum of those features tell us very little about what is at play within it. Definitions concerned with the grotesque’s content rather than its form faces similar difficulties. Throughout history, expressions relating to the grotesque have been used in defense of a whole host of different social and cultural discourse including, for instance, Catholicism (See Erhard Schön’s Der Teufel mit der Sackpfeife , 1536), Protestantism (See Lucas Cranach’s Der Papstesel , 1523), a material folk culture (see Mikhail Bakhtin’s Rabelais and his World , 1984) and an idealistic romantic structure of meaning (see Wolfgang Kayser’s The Grotesque in Art and Literature , 1957). Thus though the grotesque cannot be reduced to the expression of certain forms or meanings, in order to examine what the grotesque is about one has to try to see how it’s relationship to flow and process and how, by maintaining this relationship, it attempts to avoid solidifying into form and meaning. The process of the grotesque alluded to here revolves around a play between periphery and center, the marginalized and the dominant. Most often this is expressed as a direct negation of the center of power. In the medieval grotesque tradition of the carnival, for example, it is expressed by its emphasis on the nether regions of the body as the center of creation of meaning. Spirit does not come from above, but from the belly, buttocks and genitals, and there is, expressed in this manner, a mockery of the predominant Christian notion of truth and meaning. Such inversions of the sites of meaning most often explicitly express an increased interest in materiality instead of ideal content which comes to the fore through the play between periphery and center. Even in early grotesque Renaissance art (for example in the works of Raphael) the depiction of the mythological or ideal reveals an exploration of the possibilities of the material. The works of art thus explore their own boundaries rather than act as vessels of the divine and in this way the grotesque explores the limits of form and materiality. This in turn brings to the fore a metaphysical dimension in the workings of the grotesque: It is an immanent exploration of its own boundaries. Materiality and metaphysics are joined together, because it is through the awareness of itself as a structuring (dis)order that it places itself in opposition to the prevailing notions of form and power. This way the grotesque expresses an awareness of the division of sign and reality and a search for this reality. It implicitly expresses the awareness that meaning is not something God-given and static, but fluctuating and man-made. In modern explorations of the history of the grotesque it is commonly seen as a form of realism that manifests a shift from the ideal towards the material, freeing art from representing some hidden higher order and instead making the work of art the very site of creation and meaning. Going even further, the grotesque actively opposes the notions of the ideal by marking a shift from an ahistorical view of the world towards the historical. However, this also makes clear why the grotesque has a tendency to solidify into new static forms of meaning, for by establishing itself as a subversive counterforce there is an idea of transgression and emancipation. That is why the grotesque often historicizes and relativizes only to repeat the mistakes of that which it negates: putting itself in the king’s chair. The exploration of the material seems to create new forms and notions of the ideal. The representation of an otherness outside the prevailing notions of meaning and truth becomes a positive manifestation of this otherness as truth itself. Thus the historical “truths” of the grotesque are superseded by history itself. When the expressions of the grotesque solidify into static form and meaning, they become mere objects like anything else in the world. Instead of being this elusive thing of process and flow, it becomes tangible to the existing hierarchy of power as well as history itself. In this way the grotesque can be expunged, included or simply revealed as yet another false notion of truth, which is precisely what has happened with the grotesque throughout the course of history. If from the beginning the expression of the grotesque has not already been in the service of some structure of meaning and truth, it has quickly been included or has quickly included itself in such a structure. But by doing so it rejects its own basis: the tension between periphery and center is replaced by the attempt to create a new center, a new structure of meaning and truth. The doubleness, ambiguity and flow of the grotesque are then rejected by the grotesque itself. THE NON-FORM OF FORM In the critical thinking of Theodor W. Adorno (1903-69) the problem of art, caught between a reductive and prevalent notion of truth and meaning and a peripheral and alienated otherness, is reexamined and reformulated. For Adorno, the instrumental rationality of Enlightenment itself reverts into a new form of mythology which is every bit as static and exclusive as the hierarchies of religion it supersedes. All is excluded that is non-identical to the instrumental mastery of the objects of the world, "For the Enlightenment, anything which cannot be resolved into numbers, and ultimately into one, is illusion; modern positivism consigns it to poetry." 1 As such the non-identical has been banished from the realm of thought and action, and banished specifically to the realm of art. But the realm of art is not able to provide a decent home for it because even modern art is not something entirely autonomous. While it is excluded from the notions of truth and meaning provided by instrumental rationality, it still originates from society. Just like instrumental rationality art is about mastery, structuring and exclusion. Therefore, the problem for art is that it cannot directly provide a space for the non-identical because its mode of operation is similar to that of instrumental rationality. Even worse, art has very few possibilities to free itself from this. If it becomes l’art pour l’art it is at the same time reduced to the very thing instrumental rationality claims it to be: a subjective judgment of taste.expressionism also stands as an example of this. Conversely, art cannot work within the framework of the identity-thinking of society, because any notion of freedom or emancipation would reproduce the exclusive practices of instrumental rationality. For example: Explicit socialist literature may establish itself in opposition to instrumental rationality while at the same time reproducing it. Its language may seem different, but in reality it merely provides a different set of reductive schematics for human life and experience. The problem for the art of the grotesque was, as I mentioned earlier, that far too often it was merely a symbolic manifestation of a notion of otherness—not otherness itself. Because of this the subversive character of the grotesque ends up shaping and containing otherness instead of providing a space for it. According to Adorno the only way to avoid this is to radicalize the grotesque. In order to avoid solidifying into form the work of art has to be an object which cannot be contained in thought or form—a non-form of form. The work of art has to work in a way that it strives for autonomy but without entirely leaving a discernible reality. In other words, it has to pull in two directions at once. Thus the work of art is a paradox. It is autonomous in the sense that it closes itself off from everything outside of the work of art, trying to shy away from the contaminating influence of the identity thinking of instrumental rationality. At the same time though the work of art is heteronomous in the sense that it originates from a specific historical context and is bound to be what society is not. Autonomy and heteronomy are inseparably intertwined. Unable to display otherness itself, but still trying to be a refuge for it, there is only one option for art: It has to turn against itself and destroy its own logic of form, thereby demonstrating how any representation of otherness is impossible. Art becomes a lamentation of the victims of the identity thinking of instrumental rationality and shows the traces of the otherness that is unable to appear. Adorno’s pessimistic theory of art and history stages art as a negative dialectical process where the work of art closes itself off and rejects everything outside, while the individual elements in the work of art destroys its very own logic of form from within: Artworks synthetize ununifiable, nonidentical elements that grind away at each other; they truly seek the identity of the identical and nonidentical processually because even their unity is only an element and not the magical formula of the whole […]. The resistance to them of otherness, on which they are nevertheless dependent compels them to articulate their own formal language, to leave not the smallest unformed particle as remnant. This reciprocity constitutes art’s dynamic; it is an irresolvable antithesis that is never brought to rest in the state of being. 2 Relative to a traditional understanding of the grotesque, Adorno radicalizes the tension between center and periphery, autonomy and heteronomy. In the traditional understanding of the grotesque, as we find it for example in the writings of Mikhail Bakhtin, the grotesque establishes the display of otherness as a new center of meaning and truth. However Adorno rejects such notions and argues instead for a modernism of the grotesque in which both center and periphery are included in a negative dialectical process and continually synthesizing and destabilizing each other’s positions. A modernism of the grotesque works on the inside of the sign or the artwork, continually outlining and questioning the boundaries between materiality and form. This moves the focus away from the relation between the sign or work of art as a conceptual manifestation on one side and the object it refers to on the other side. Instead it implicitly points to the amorphous mass from which the signs and thereby meaning have been carved, the remnants that have been left behind. Modernism of the grotesque does not imply that it is emancipatory or that it reconciles man with nature, and does not represent a new position or a new ideology. It merely remembers and insists on the double nature of man and art: to write or paint yourself or an artwork whole by inscribing meaning in life or by applying form on a canvas is at the same time both creation and destruction. The very signs we use to center meaning in our lives carry its own alienation in them. Meaning surfaces only when process and flow comes to a halt—solidifying, but at the same time excluding parts that do not fit into that particular structure of meaning. NOTHING DONE AND NOTHING UNDONE It has always been difficult for art historians to find a suitable category for the works of the Danish artist Leif Lage (b. 1933). In his paintings the sensitive figuration seems so fragile that it is on the verge of turning into abstraction. Or conversely: the figurative emerges cautiously and hesitantly out of abstraction. As an art critic once wrote, he can almost paint things away. 3 Working in some undefinable space between abstraction and figuration, the Lage’s works shy away from the realm of words, and as a result few critics have been able to write anything meaningful about his works. In fact even fewer have been able to write more than one or two pages. The Danish author and art critic Leif Hjernøe is one of those few, but even he starts off by saying how impossible it is to write about Lage, confessing that his works exist both as process and in a field of in-between which words cannot reach. He writes: Always you find yourself in a place where nothing is done and nothing left undone, and where the elements of the work of art rest in a continuous motion. Always there is the open wound, where infection rather than surgical intervention is considered as an opportunity. And the conflict between matter and antimatter makes all diagnoses uncertain and allows conditions of uncertainty to spread in a place of raw presence. 4 The art works against the diagnosis and the certainty. Words are being eaten up by what is outside the realm of words: tension, process and doubleness. An approach to an understanding of the work of Lage could be to follow his connection to Samuel Beckett (1906-89). One can note, therefore, that Lage has illustrated several of the Danish translations of Beckett’s works. Though one is an author and the other a painter both seek a place where figuration, where the word, erodes. For both this entails an attempt to question and examine and so move in behind the façade of the surface in an exploration of that something or nothing that may be behind representation. At the same time even in the vanishing point of figuration or words, the meaningless words or the disjointed lines still stand as signs of human activity—signs of movement in emptiness. With very few exceptions Lage’s artworks revolve around one motif: Man—most often “en face.” But unlike traditional portraitures Lage’s people are found within. The artworks do not sense the reality of appearances, but rather the existential dimensions within man. As a seismograph they are sensitive to the utmost subjectivity in order to display an objective, sensuous depiction of the very problem of subjectivity. Instead of a static façade of a man, Lage’s “en face” shows the process-character of man. The people in Lage’s paintings are always in process—in the midst of becoming or dissolving. I will take a closer look in the following at the ways in which Lage establishes this sense of being in constant process, of being in-between modes or categories. THE DOUBLENESS OF THE STROKE Lage’s etchings attract attention in particular for the tension conveyed there between the material and the form. The material physically opposes the violence of the needle. But instead of embracing the violence of the needle and the victory over matter—instead of making the artistic creation and figuration express a heroic mastery of the background it is made out of—Lage uses the stroke to express the very tension between stroke and material, figuration and background. In the drypoint etching Untitled from 1983, which illustrated the Danish translation of Beckett’s Ill Seen, Ill Said , the needle tears up the material in long rough lines: Together, the primarily horizontal and vertical lines form a face. Thus the force needed to etch a line in the metal-plate draws attention to itself: It is there in the absence of curves and nuances. Man emerges on the metal-plate after great exertion and in a very simplistic form. This way Lage enhances the nature of the material, as the material’s resistance is not something to overcome. On the contrary the figuration is smitten by its very resistance and as such expresses the violence of its own becoming. Even more pronounced is the fact that the lines do not just show the violence of creation—it actively erases figuration in the same process that creates it. For example the mouth consists of 8-10 horizontal strokes, of which some seem to be connected to each other as if the mouth has been quickly scratched out. The mouth speaks of the inability to speak. In the same way, the eyes are black holes due to a large amount of criss-cross cuts, which together form a dark middle. Those lines, at the same time, form the eyes of the figuration and scratch out the eyes of the figuration. The extroverted aspects of the face—connected to speech and sight—are portrayed as introverted as well. Just as the etchings down into the metal-plate makes something appear. Leif Lage, Untitled , 1983 (etching) The figuration of the etching is connected to creation. It expresses that something is wrought into existence out of nothing by sheer artistic force. However, this force is at the same time presented as a violence of creation, which makes it impossible for form to truly emerge. Herein lies one of the basic principles of Lage’s art, namely that art cannot be that nothing or something behind the realm of words or signs. Without form, art would lose its ability to express anything at all. Form is a necessity if art is to avoid becoming as devoid of expression as the reality is that we cannot reach behind the appearance of things. On the other hand, art cannot raise itself above its own material in joyous celebration of the beauty of form. This would use the material in the manner of an instrument and thus would suppress the otherness it attempts to rescue. When art becomes mere form, any traces of otherness will have dissolved. Then art would be a question of technique, in no way different from the instrumental rationality of society. Therefore art works in a particular space between form and non-form. As Hjernøe says of the works of Lage, it is in the center of the event, in the in-between where things neither are nor are not, "And everything takes place just before it changes character. As the blood just before it coagulates, as the milk just before it separates, as fried egg just before it turns white […]." 5 The precise emphasis on the in-between of Lage’s art points in particular to the work of art as both outside of and in time. The work of art is a singular point in time, but at the same time it is continually in process. In the borderland between form and non-form, between creation and destruction, it shimmers like a fata morgana . The work is done but at the same time undone. It is only there as a cry in response to the inability to come into being. Akin to the etching is the drawing, but while both, of course, use the stroke or line as their main instrument, the paper does not resist the line in the same sense as the metal-plate of the etching. As a result in Lage’s drawings the stroke frolics in a space with almost no tension at all. There is nothing there to keep the pencil stroke at bay, but at the same time this means that there is nothing there to keep it together. One of the more expressive examples of this is found in an untitled drawing from Tegninger og Text ( Drawings and Text ) from 1999. The drawing consists of one unbroken pencil stroke. It is as if the stroke is confused—it darts around on the paper making doodles on the way or gathers itself in more straight lines in the center of the paper. It is in this manner that the semblance of a body is established. A couple of small circles serve as eyes and are the reason that the rest can be read as both face and body instead of pure abstraction. In fact the unbroken stroke serves as both abstraction and figuration as on the one hand it is the stroke that seemingly outlines the shape of a figure, while on the other hand the unbroken stroke dissolves any truly recognizable figuration by continuously, without end or aim, overflowing the boundaries of the figure. Seen again here is a doubleness to the stroke and the act of creation. In the etching it was all about the tension between the resistance of the material which created the doubleness. Here it is the opposite. It is the lack of tension. The stroke is free to do anything, but has no aim: without some kind of resistance, there is nothing to hold figuration together. It threatens to dissolve into nothingness. Conversely, the drawing can also be seen as a process of becoming. Like a form of automatic writing, the pencil darts around until it finds a point of densification. But even in such an interpretation of the drawing, the figuration appears artificial—it points to itself as the result of the artistic act of creation. The stroke is primarily stroke and only secondarily figuration. With its wild movement it calls attention to itself as stroke. Thus the figuration never becomes something in its own right. It points to the basic principle of creation: Someone has drawn me, I am the result of artistic endeavors, and therefore I am not for myself but always overflowing the boundaries that contain me. It is the stroke that in the very same movement creates figuration and dissolves it. Leif Lage, Untitled , 1999 (drawing) THE LIGHTNESS OF COLOR, THE DENSITY OF PAPER Often the watercolor is used as a precursor for larger paintings, because it has an immediacy in which one can quickly paint the main lines of a composition. However, Lage’s watercolors are not temporary points in a process leading to another final painting. They are not sketches, later to be filled with details in another material. For him watercolor is an end in itself. This also implies that he doesn’t try to work against the paper’s absorption of the water color and its tendency to absorb detail. On the contrary, he examines the possibilities inherent in this blurring of the line and absorption of color. As in the previous examples, there are of course recognizable shapes in Lage’s water colors. But these shapes are rarely separable from color, line or even paper. In other words: the figurative and the abstract more or less become one. One of the reasons for this is that Lage often works on wetted paper which means that the paper hungrily absorbs color into its fabric instead of it being on top of the paper. The paper becomes line because it is the absorption of the color which, together with the brush stroke itself, separates the colors from each other. The line is also color and the color is also line, because there is no separation between the different colors other than the colors themselves. At times this results in almost complete abstraction. In such cases Lage add lines with a pencil as if he wants to hold some sort of figuration together. At other times it is the other way around: the strokes of the pencil are a being dissolved by the water color blurring out the figuration. Untitled 1 from 1999 displays various tones of green. The contour of the colors appears unusually rough. Most of all it is reminiscent of a shoreline which has found its form through the work of thousands of years between water and land. Pockets of resistance surface as islands not yet drowned in color—as paper or color not yet consumed by the dominant color. The shape of the colors does not seem created by the hand of the artist, but rather by the inner workings of the watercolor: color against color over time has resulted in this very image, as if it is all a part of a natural process of change and decay. Despite the fact that there are no strong differences in color there seems to be a struggle taking place in the watercolor. For example, inexplicable holes in the dark color, which cover most of the right side of the watercolor, appear as if the underlying color is eating away the dark color, or that the dark color is in the process of covering up the underlying color. The small pockets of resistance demonstrate a process and development that, almost as a happy accident, evokes a couple of small eyes and a large mouth. Behind the colors a few slanted lines can be discerned, but the hand of the artist has long ago disappeared behind the life of the colors. Thus the watercolor seems to be held at precisely the point in time where figuration randomly appears. The small eyes and wide mouth seemingly express the realization of the figuration’s temporality. It is just a moment in time, soon to be consumed again in the life of the colors. The nature, the background it stems from and is part of, moves on undeterred, continuing its everlasting process of creation and decay. In this sense, the watercolor provides an experience of how neither artist nor man is able to transcend the materiality they consist of. The colors of man, the materials man consists of are “becoming” and “progress” but also “decay” and “disappearance”. The artist’s pencil strokes have been eaten up long ago, and the figuration is living on borrowed time. Human or artistic activity is about creating form, transcending mere matter by shaping and applying meaning to it. But Untitled 1 shows the doubleness of such creation: the transience and fragility of human life. Should the figuration come into being, should it rise and transcend the material, which binds it to its temporal existence, it would become nothing because its very existence is conditioned by the life and work of the colors. In the same sense man cannot escape his own temporality. He too, for better or worse, must accept a life in the volatility of sensation. Leif Lage, Untitled 1 , 1999 (watercolor) In most of Lage’s watercolors there seem to be a stronger artistic control than in Untitled 1 . Most often both the arrangement of colors and the technique in which they are painted express the hand of the artist. An example of this is Untitled 2 from 1999. While figuration in Untitled 1 seemed to appear as a happy accident, the figuration is much more “created” in Untitled 2 . Here the most important parts of the figuration, the eyes, the mouth and part of the skull, are colored black and painted on top of the background’s play of colors. The background primarily consists of blue and yellow tones. Only parts of the paper are covered in color, however, which yet again stresses the act of painting: There is a surface which is being filled by color by an artist. The blue tones are concentrated in the figuration, while the yellow tones surround it. All this means that the figuration stands out more clearly in this watercolor. This is also underlined by the fact that the blue and dark tones cover part of the yellow tones as spots here and there. Thus it is not a background which is in the process of consuming figuration, but rather the emerging figuration which blots out the background. Such an understanding is even suggested by how the mouth and eyes are placed in the larger blue color field. The eyes and mouth are in the center of the watercolor, while the blue color field is placed from center out towards the left side. This gives the impression of a face turned slightly to the right and slightly upwards, which again makes the mouth appear to emerge from the paper. It also helps that the mouth cuts the center axis of the watercolor. In other words, the arrangement of the blue and black colors create some depth and perspective which gives the illusion of a figuration, seen partially in profile, emerging from the background. Seen in profile, the eyes and mouth seem extroverted—they almost seem as if they are put on top of the face. But at the same time they are painted as black holes, sucking in the gaze of the onlooker. The watercolor is even more challenging if one follows what may be the faint outline of the skull, which, on the right side of the watercolor, no longer works together with the blue color, but rather alone postulates the outline of the skull. If not the blue color field, but this line, is the outline of the skull, then all of a sudden the face is not in profile but “en face”—staring directly towards the onlooker. Outline and color seemingly work against each other and establish two different expressions. Without the slightly upward tilted expression of the profile, the eyes and mouth do not seem to emerge from the paper. On the contrary, seen “en face,” the eyes and mouth are really gaping pits of darkness. In this sense Untitled 2 is at the same time surface and depth of perspective. The line gives form but at the same time it dissolves the form created by the colors, and vice versa. Leif Lage, Untitled 2 , 1999 (watercolor) As the last example of Lage’s artistic method, I have chosen another untitled work (as indeed nearly all of Lage’s artworks are)—this time from 2000. This is perhaps one of the most figurative watercolors Lage has created, though that doesn’t tell us too much. The painting depicts a human face in blue and green tones on a yellow toned background. The colors create a clear demarcation between the figure and the background, which compensate for the watercolor’s lack of outline. Beneath the face darker tones imply the beginning of the torso, and nuances of color even hint at something which could be a collar. The hair is in even darker tones and its structure is emphasized using pencil strokes on top of the water color. One eye is marked by a brown spot with a darker spot in the middle, while the other eye is added by pencil. The mouth is a round, red dot. In Untitled from 2000 the work between abstraction and figuration is much less pronounced than in the previous examples cited here. Nonetheless the watercolor has a delicacy to it which almost makes the figuration disappear, even as it appears. This has something to do with the fact that all the individual brush strokes have dissolved. The only outlines are those created by the clash of colors. Even the red mouth seems to be more paint than mouth—unable to be formed truly as anything other than a speck of color with some small semblance to a mouth. In contrast to the other watercolors, there is no movement, no progress or decay, just a vibrating standstill. The figure is not emerging or disappearing but embedded in and as surface, and as such it makes the figure seem stuck in its condition rather than freed by the act of giving form: mouth open as a wound. Pencil strokes add detail and life to the hair as an attempt to help the figure emerge. But all this does is create two levels in the watercolor: The pencil strokes are put on top of the figuration rather than being part of it. Thus they end up highlighting the endless distance between the movement and form-giving of the pencil strokes and the static and stuck figure behind these strokes. Leif Lage, Untitled , 2000 (watercolor) MAN AND THE VIEW OF THE ONLOOKER Lage’s works seem at the same time to be an examination of tensions between form and material in art and a display of an image of man full of the same tensions. This is because the people who are emerging in Lage’s images are not just in his works, They are his works. This means that man is not something emerging from a background but is part of this background and vice versa. The art of Lage inscribes man in its surroundings and background. Man is not the ruler of nature. Man does not rise above matter; there is no truly transcendent position for man to occupy in the art of Lage. Instead man is a part of the very matter, it, at the same time, tries to distance itself from in order to distinguish itself from its surroundings. Man emerges in an attempt not to be line, stroke, color. In an attempt to free itself of matter. Should it succeed in this, however, it would turn into nothing. On the other hand, if man fully accepted itself as mere matter it would disappear in it—in instincts, urges and lack of reflection. The appearance of man is thus subject to a state of being in-between. Only in the tension between material and its negation can the outlines of man be traced. However this also means that in the art of Lage man is never something in itself but always in process—on the way to its freedom and its loss. However, Lage’s art is not just about showing the tensions inherent in man but also about showing such tension on the verge of breaking point. In the moment before everything is done, or when nothing yet has been done, the delicate tension between form and material has been stretched to its utmost in such a way that man’s character of process emerges and is contained on the paper or canvas. Therefore, Lage’s art contain traces of human life. Not only is it an autonomous unity of tensions where man is stretched out between its singularity and the surroundings it is a part of. It is also this pulsation between figuration and material which brings about the traces of human endeavor and activity. Even when man almost seems to have disappeared into the material, strokes and lines are still there as a reminder of human activity and potential creative power—as a reminder that hope is still possible and that man is still there. The view of the onlooker seeks out forms and meaning. It seeks outlines and edges. But first and foremost it is the eyes in Lage’s works of art that allow the onlooker to decode the figuration at play. This creates a distinctive relationship between the onlooker and the artwork. The onlooker tries to wrest the enigma from the artwork, tries to reduce it to solid, meaningful form. But the very same moment that hints at such a possibility sees the view of the onlooker confronted with a gaze of its own. The eyes of the figure in the work of art are most often dark pits, as if they were an illustration of the violence committed against the eyes of the onlookers and their search for meaning. Or as if they were a dark reflection of the onlooker’s failed attempts to delineate the traces of life in the artwork to a solid meaningful form. Therefore, the gaze of the figuration speaks not only of its own powerlessness but also of the powerlessness of the onlooker. When the view or sight has trouble finding solid meaningful forms, it has something to do with the fact that the precondition for sight, light, no longer stems from something transcendent. In Lage’s art there is nothing outside the works of art, nothing outside of human life, and as such nothing to shed light on the works of art or human life and reveal solid meaningful forms. All light comes from within. In a western context, light as a medium for sight is central to the understanding of meaning. People speak of the clarity of thought, while knowledge is tied together with enlightenment, and so forth. But the light no longer originates from a divine point of view. It originates from man, who has created himself in the image of God. The problem with this is that light always covers up its own base. Light illuminates something but at the same time it hides itself. 6 While it was previously God who was unknowable, now it is man. It is also problematic that sight and the medium of sight stem from the same place. Following this thought one can posit two final problems. Firstly, the immediacy and presence established by light by making forms and objects accessible to sight is fake. Light is not some independent entity which present things in a neutral manner for the onlooker. It is inextricably tied together with the gaze’s desire after meaning. In other words: Light perverts the appearance of things because it doesn’t originate from some objective entity which allows them to appear as they are. Instead light is based upon and originates from the subject and its conquering gaze, seeking out meaning and form constantly. Secondly, the joining of sight and light makes introspection within human life impossible. Everything can be illuminated by its use value for the subject but only as long as it is separated from the subject, as long as it is an object. But the subject itself cannot be illuminated. Lage’s art tears down such a dividing line between subject and matter, but it does so without reestablishing a divine position from where the light emanates. Therefore, the light in Lage’s art may not illuminate very well. It may not have the certainty presented by modern science or the religions of yesterday. But it does show what such light tries to hide, namely, the subject as it is in its material reality—inscribed in time and death, which are the basic conditions of materiality, but at the same time also full of life in its joy and will to create. For the onlooker the meeting of the gaze in Lage’s works of art is thus also a destruction of the view of the onlooker. The ability to see is challenged in a radical way. Those outlines will not solidify into static form, as if the light was too dim to see. Just as in Lage’s figurations, the view of the onlooker turns to black: turns towards the onlooker in recognition and becoming—or disappearance. NOTES Max Horkheimer and Theodor W. Adorno. Dialectic of Enlightenment . (Palo Alto: Stanford University Press, 2002): 4-5. Theodor W. Adorno. Aesthetic Theory . (London & New York, 2002): 176. Carsten Bach-Nielsen. “Mere glæde end gru.” Kristeligt Dagblad . September 24, 2002. Leif Hjernøe. “Den yderliggående inderlighed.” LEIF LAGE—Retrospektiv udstilling 1983 . (Copenhagen: Brøndum, 1983): 18. Ibid. Maurice Blanchot. The Infinite Conversation . (Minneapolis: University of Minnesota Press, 1993): 162-163. (shrink)

Quantum electrodynamics is the theory of electrons and other elementary charged particles, interacting through the exchange of light quanta. Albert Einstein introduced the light quantum in 1905, but for about three decades physicists applied quantum ideas mainly in theories of the structure and behavior of matter, not to electromagnetic radiation itself, which was always treated semi-classically. This began to change after 1923 with the discovery of the Compton effect and its kinematic description by Arthur Compton and (...) Peter Debye, based on the light quantum. In this paper we review the study of high-energy radiation that led to Compton's discovery. We discuss the analysis of the intensity distribution of Compton-scattered radiation that together with the ''new'' quantum theory beginning in 1925, resulted in the development, especially by Pascual Jordan and Paul Dirac, of a quantum theory of electromagnetic radiation in interaction with matter. (shrink)

Unifying the Universe: The Physics of Heaven and Earth presents a non-technical approach to physics for the lay-science enthusiast. This popular textbook, which evolved from a conceptual course at Cornell University, is intended for non-science undergraduate students taking their first physics module. This second edition maintains its unique approach in crossing boundaries between physics and humanities, with connections to art, poetry, history, and philosophy. It explores how the process of scientific thought is inextricably linked with cultural, creative, and aesthetic aspects (...) of human endeavor, opening the readers up to new ways of looking at the world. The text has been fully updated throughout to address current and exciting new topics in the field, such as exo-planets, the accelerating Universe, dark matter, dark energy, gravitational waves, super-symmetry, string theory, big bang cosmology, and the Higgs boson. There is also an entirely new chapter on the Quantum World, which connects the fascinating topics of quantum entanglement and quantum computing. Key Features: Provides a solid, yet accessible, background to basic physics without complex mathematics Uses a human interest approach to show how science is significant for more than its technological consequences Discusses the arts and philosophies of historical periods that are pertinent to the subject. (shrink)

The Special Theory of Relativity and the Theory of the Electron have had an interesting history together. Originally the electron was studied in a non-relativistic context and this opened up the interesting possibility that lead to the conclusion that the mass of the electron could be thought of entirely in electromagnetic terms without introducing inertial considerations. However the application of Special Relativity lead to several problems, both for an extended electron and the point electron. These inconsistencies have, contrary to popular (...) belief not been resolved satisfactorily to date, even within the context of Quantum Theory. Thus they are not merely of historical interest. Nevertheless these and subsequent studies bring out the interesting result that Special Relativity (and the theory of the electron) breaks down within the Compton scale or when the Compton scale is not neglected. This again runs contrary to an uncritical notion that Special Relativity is valid for point particles. Furthermore, it is pointed out that experiments have been recently suggested to test these ideas. These considerations lead to a characterization of the Planck constant in classical terms. (shrink)

The electron is conceived here as a complex structure composed of a subparticle that is bound to a nearly circular motion. Although in quantum mechanics the spin is not representable, in classical stochastic physics this corresponds to the angular momentum of the subparticle. In fact, assuming Schrödinger-type hydrodynamic equations of motion for the subparticle, the spin-1/2 representation in configuration space and the corresponding Pauli matrices for the electron are obtained. The Hamiltonian of Pauli's theory as the nonrelativistic limit of (...) Dirac's equation is also derived. (shrink)

How is mind related to matter? This ancient question in philosophy is rapidly becoming a core problem in science, perhaps the most important of all because it probes the essential nature of man himself. The origin of the problem is a conflict between the mechanical conception of human beings that arises from the precepts of classical physical theory and the very different idea that arises from our intuition: the former reduces each of us to an automaton, while the latter (...) allows our thoughts to guide our actions. The dominant contemporary approaches to the problem attempt to resolve this conflict by clinging to the classical concepts, and trying to explain away our misleading intuition. But a detailed argument given here shows why, in a scientific approach to this problem, it is necessary to use the more basic principles of quantum physics, which bring the observer into the dynamics, rather than to accept classical precepts that are profoundly incorrect precisely at the crucial point of the role of human consciousness in the dynamics of human brains. Adherence to the quantum principles yields a dynamical theory of the mind/brain/body system that is in close accord with our intuitive idea of what we are. In particular, the need for a self-observing quantum system to pose certain questions creates a causal opening that allows mind/brain dynamics to have three distinguishable but interlocked causal processes, one micro-local, one stochastic, and the third experiential. Passing to the classical limit in which the critical difference between zero and the finite actual value of Planck's constant is ignored not only eliminates the chemical processes that are absolutely crucial to the functioning of actual brains, it simultaneously blinds the resulting theoretical construct to the physical fine structure wherein the effect of mind on matter lies: the use of this limit in this context is totally unjustified from a physics perspective. (shrink)

I provide an account of precision testing in particle physics that makes a virtue of theory-ladenness in experiments. Combining recent work on the philosophy of experimentation with a broader view of the scientific process allows one to understand that the most precise and secure knowledge produced in a mature science cannot be achieved in a theory-independent fashion. I discuss precision tests of the muon’s magnetic moment and effective field theory as a means to repurpose precision tests for exploratory purposes.