arXiv subjects

Steven Kenneth Kauffmann

Publications and source records attributed to Steven Kenneth Kauffmann.

17 recordsLinked to original sources

arXiv2014

Universal Gravitation as Lorentz-covariant Dynamics

This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either, but a straightforward theoretical change does remedy that; however a proper fit to planetary perihelion precession data is not thus obtained. The author's stated philosophical objections to the Einstein equation can be dealt with in a markedly different way -- a new paper entitled "Unique Einstein Gravity from Feynman's Lorentz Condition" has been submitted. Einstein's equivalence principle implies that the acceleration of a particle in a "specified" gravitational field is independent of its mass. While this is certainly true to great accuracy for bodies we observe in the Earth's gravitational field, a hypothetical body of mass comparable to the Earth's would perceptibly cause the Earth to fall toward it, which would feed back into the strength as a function of time of the Earth's gravitational field affecting that body. In short, Einstein's equivalence principle isn't exact, but is an approximation that ignores recoil of the "specified" gravitational field, which sheds light on why general relativity has no clearly delineated native embodiment of conserved four-momentum. Einstein's 1905 relativity of course doesn't have the inexactitudes he unwittingly built into GR, so it is natural to explore a Lorentz-covariant gravitational theory patterned directly on electromagnetism, wherein a system's zero-divergence overall stress-energy, including all gravitational feedback contributions, is the source of its gravitational tensor potential. Remarkably, that alone completely determines Lorentz-covariant gravity's interaction with any conservative system of locally interacting classical fields; no additional "principles" of any kind are required. The highly intricate equation for the gravitational interaction contribution to such a system's Lagrangian density is only amenable to solution by successively refined approximation, however.

physics.gen-ph↗

arXiv2014

A Self-Gravitational Upper Bound on Localized Energy, Including that of Virtual Particles and Quantum Fields, which Yields a Passable "Dark Energy" Density Estimate

The self-gravitational correction to a localized spherically-symmetric static energy distribution is obtained from energetically self-consistent upgraded Newtonian gravitational theory. The result is a gravitational redshift factor that is everywhere finite and positive, which both rules out gravitational horizons and implies that the self-gravitationally corrected static energy contained in a sphere of radius r is bounded by r times the fourth power of c divided by G. Even in the absence of spherical symmetry this energy bound still applies to within a factor of two, and it cuts off the mass deviation of any quantum virtual particle at about a Planck mass. Because quantum uncertainty makes the minimum possible energy of a quantum field infinite, such a field's self-gravitationally corrected energy attains the value of that field's containing radius r times the fourth power of c divided by G. Roughly estimating any quantum field's containing radius r as c times the age of the universe yields a "dark energy" density of 1.7 joules per cubic kilometer. But if r is put to the Planck length appropriate to the birth of the universe, that energy density becomes the enormous Planck unit value, which could conceivably drive primordial "inflation". The density of "dark energy" decreases as the universe expands, but more slowly than the density of ordinary matter decreases. Such evolution suggests that "dark energy" has inhomogeneities, which may be "dark matter".

physics.gen-ph↗

arXiv2013

Klein-Gordon Transformation sans Extraneous Insertions: the Isomorphic Classical Complement to a Quantum System

The historical Klein-Gordon transformation of complex-valued first-order in time Schroedinger equations iterates these in a naively straightforward way which changes them into complex-valued second-order in time equations that have a plethora of extraneous solutions -- the transformation is an operator-calculus analogue of the squaring of both sides of an algebraic equation. The real and imaginary parts of a Schroedinger equation, however, are well known to be precisely the dynamical equation pair of the real-valued classical Hamiltonian functional which is numerically equal to the expectation value of that Schroedinger equation's Hermitian Hamiltonian operator. The purely real-valued second-order in time Euler-Lagrange equation of the corresponding classical Lagrangian functional is also isomorphic to that Schroedinger equation, and for symmetric Hamiltonians has exactly the same formal appearance as the corresponding naive complex-valued Klein-Gordon equation, but none of the latter's extraneous solutions. These quantum Schroedinger-equation isomorphisms to classical Euler-Lagrange equations are the technical manifestation of a key theoretical aspect of the principle of complementarity, one which is elegantly illustrated by the isomorphic free-photon wave-function complement to the vector potential of source-free classical electrodynamics.

physics.gen-ph↗

arXiv2013

Obtaining the Probability Vector Current Density in Canonical Quantum Mechanics by Linear Superposition

The quantum mechanics status of the probability vector current density has long seemed to be marginal. On one hand no systematic prescription for its construction is provided, and the special examples of it that are obtained for particular types of Hamiltonian operator could conceivably be attributed to happenstance. On the other hand this concept's key physical interpretation as local average particle flux, which flows from the equation of continuity that it is supposed to satisfy in conjunction with the probability scalar density, has been claimed to breach the uncertainty principle. Given the dispiriting impact of that claim, we straightaway point out that the subtle directional nature of the uncertainty principle makes it consistent with the measurement of local average particle flux. We next focus on the fact that the unique closed-form linear-superposition quantization of any classical Hamiltonian function yields in tandem the corresponding unique linear-superposition closed-form divergence of the probability vector current density. Because the probability vector current density is linked to the quantum physics only through the occurrence of its divergence in the equation of continuity, it is theoretically most appropriate to construct this vector field exclusively from its divergence -- analysis of the best-known "textbook" special example of a probability vector current density shows that it is thus constructed. That special example in fact leads to the physically interesting "Ehrenfest subclass" of probability vector current densities, which are closely related to their classical peers.

physics.gen-ph↗

arXiv2012

Nonperturbational "Continued-Fraction" Spin-offs of Quantum Theory's Standard Perturbation Methods

The inherently homogeneous stationary-state and time-dependent Schroedinger equations are often recast into inhomogeneous form in order to resolve their solution nonuniqueness. The inhomogeneous term can impose an initial condition or, for scattering, the preferred permitted asymptotic behavior. For bound states it provides sufficient focus to exclude all but one of the homogeneous version's solutions. Because of their unique solutions, such inhomogeneous versions of Schroedinger equations have long been the indispensable basis for a solution scheme of successive perturbational corrections which are anchored by their inhomogeneous term. Here it is noted that every such perturbational solution scheme for an inhomogeneous linear vector equation spins off a nonperturbational continued-fraction scheme. Unlike its representation-independent antecedent, the spin-off scheme only works in representations where all components of the equation's inhomogeneous term are nonzero. But that requirement seems to confer theoretical physics robustness heretofore unknown: for quantum fields the order of the perturbation places a bound on unperturbed particle number, the spin-off scheme contrariwise has only basis elements of unbounded unperturbed particle number. It furthermore is difficult to visualize such a continued-fraction spin-off scheme generating infinities, since its successive iterations always go into denominators.

physics.gen-ph↗

arXiv2012

The Significance to Quantum Computing of the Classical Harmonic Nature of Energy Eigenstates

Since a pure quantum system is incapable of faithfully simulating the solutions of the Schroedinger equation that actually pertains to itself, it is proposed that quantum computing technology (as opposed to cryptographic technology) not be based on pure quantum systems such as qubits but instead on physical systems which by their nature faithfully simulate the solutions of Schroedinger equations. Every Schroedinger equation is within a unitary transformation of being a set of mutually independent classical simple harmonic oscillator equations. Thus classical simple harmonic oscillators, or "chobits", are the mathematically fundamental building blocks for all Schroedinger equations. In addition, classical harmonic oscillators are, as a practical matter, far easier to deal with than any pure quantum system -- e.g., their phases and absolute amplitudes are readily physically accessible, they have little predilection for environmental decoherence, and they abound as cavity electromagnetic standing-wave modes. We study in mathematical detail the use of chobits to compute discrete quantum Fourier transforms, including gates, chobit counts, and chobit operation counts. The results suggest that thirty chobits and under a thousand chobit phase operations could generate discrete quantum Fourier transforms of a billion terms. Chobits can be technologically realized as semiconductor dynatron-type electronic oscillator circuits, which ought to be amenable to very considerable miniaturization.

physics.gen-ph↗

arXiv2011

The Schroedinger-equation presentation of any oscillatory classical linear system that is homogeneous and conservative

The time-dependent Schroedinger equation with time-independent Hamiltonian matrix is a homogeneous linear oscillatory system in canonical form. We investigate whether any classical system that itself is linear, homogeneous, oscillatory and conservative is guaranteed to linearly map into a Schroedinger equation. Such oscillatory classical systems can be analyzed into their normal modes, which are mutually independent, uncoupled simple harmonic oscillators, and the equation of motion of such a system linearly maps into a Schroedinger equation whose Hamiltonian matrix is diagonal, with h times the individual simple harmonic oscillator frequencies as its diagonal entries. Therefore if the coupling-strength matrix of such an oscillatory system is presented in symmetric, positive-definite form, the Hamiltonian matrix of the Schroedinger equation it maps into is h times the square root of that coupling-strength matrix. We obtain a general expression for mapping this type of oscillatory classical equation of motion into a Schroedinger equation, and apply it to the real-valued classical Klein-Gordon equation and the source-free Maxwell equations, which results in relativistic Hamiltonian operators that are strictly compatible with the correspondence principle. Once such an oscillatory classical system has been mapped into a Schroedinger equation, it is automatically in canonical form, making second quantization of that Schroedinger equation a technically simple as well as a physically very interpretable way to quantize the original classical system.

physics.gen-ph↗

arXiv2011

Unambiguous quantization from the maximum classical correspondence that is self-consistent: the slightly stronger canonical commutation rule Dirac missed

Dirac's identification of the quantum analog of the Poisson bracket with the commutator is reviewed, as is the threat of self-inconsistent overdetermination of the quantization of classical dynamical variables which drove him to restrict the assumption of correspondence between quantum and classical Poisson brackets to embrace only the Cartesian components of the phase space vector. Dirac's canonical commutation rule fails to determine the order of noncommuting factors within quantized classical dynamical variables, but does imply the quantum/classical correspondence of Poisson brackets between any linear function of phase space and the sum of an arbitrary function of only configuration space with one of only momentum space. Since every linear function of phase space is itself such a sum, it is worth checking whether the assumption of quantum/classical correspondence of Poisson brackets for all such sums is still self-consistent. Not only is that so, but this slightly stronger canonical commutation rule also unambiguously determines the order of noncommuting factors within quantized dynamical variables in accord with the 1925 Born-Jordan quantization surmise, thus replicating the results of the Hamiltonian path integral, a fact first realized by E. H. Kerner. Born-Jordan quantization validates the generalized Ehrenfest theorem, but has no inverse, which disallows the disturbing features of the poorly physically motivated invertible Weyl quantization, i.e., its unique deterministic classical "shadow world" which can manifest negative densities in phase space.

quant-ph↗

arXiv2010

Equivalence of classical Klein-Gordon field theory to correspondence-principle first quantization of the spinless relativistic free particle

It has recently been shown that the classical electric and magnetic fields which satisfy the source-free Maxwell equations can be linearly mapped into the real and imaginary parts of a transverse-vector wave function which in consequence satisfies the time-dependent Schroedinger equation whose Hamiltonian operator is physically appropriate to the free photon. The free-particle Klein-Gordon equation for scalar fields modestly extends the classical wave equation via a mass term. It is physically untenable for complex-valued wave functions, but has a sound nonnegative conserved-energy functional when it is restricted to real-valued classical fields. Canonical Hamiltonization and a further canonical transformation maps the real-valued classical Klein-Gordon field and its canonical conjugate into the real and imaginary parts of a scalar wave function (within a constant factor) which in consequence satisfies the time-dependent Schroedinger equation whose Hamiltonian operator has the natural correspondence-principle relativistic square-root form for a free particle, with a mass that matches the Klein-Gordon field theory's mass term. Quantization of the real-valued classical Klein-Gordon field is thus second quantization of this natural correspondence-principle first-quantized relativistic Schroedinger equation. Source-free electromagnetism is treated in a parallel manner, but with the classical scalar Klein-Gordon field replaced by a transverse vector potential that satisfies the classical wave equation. This reproduces the previous first-quantized results that were based on Maxwell's source-free electric and magnetic field equations.

physics.gen-ph↗

arXiv2010

Source-free electromagnetism's canonical fields reveal the free-photon Schroedinger equation

Classical equations of motion that are first-order in time and conserve energy can only be quantized after their variables have been transformed to canonical ones, i.e., variables in which the energy is the system's Hamiltonian. The source-free version of Maxwell's equations is purely dynamical, first-order in time and has a well-defined nonnegative conserved field energy, but is decidedly noncanonical, an issue that has attracted little attention. The opposite parities of the electric and magnetic fields and consequent curl operations that typify Maxwell's equations are especially at odds with their being canonical fields. Transformation of the magnetic field into the transverse part of the vector potential helps but is not sufficient; further simple nonnegative symmetric integral transforms, which commute with all differential operators, are needed for both fields; such transforms also supplant the curls in the equations of motion. The canonical replacements of the source-free electromagnetic fields remain transverse-vector fields, but are more diffuse than their predecessors. Combined as the real and imaginary parts of a complex field, the canonical fields prove to be the transverse-vector wave function of a time-dependent Schroedinger equation whose Hamiltonian operator is the quantization of the free photon's square-root relativistic energy. Thus proper quantization of the source-free Maxwell equations is identical to second quantization of free photons that have normal square-root energy. There is no physical reason why first and second quantization of any relativistic free particle ought not to proceed in precise parallel, utilizing the square-root Hamiltonian operator. This natural procedure leaves no role for the completely artificial Klein-Gordon and Dirac equations, as accords with their grossly unphysical properties.

physics.gen-ph↗

arXiv2010

Orthodox quantization of Einstein's gravity: might its unrenormalizability be technically fathomable and physically innocuous?

Many physical constants related to quantized gravity, e.g., the Planck length, mass, curvature, stress-energy, etc., are nonanalytic in G at G=0, and thus have expansions in powers of G whose terms are progressively more divergent with increasing order. Since the gravity field's classical action is inversely proportional to G, the path integral for gravity-field quantum transition amplitudes shows that these depend on G only through the product hG, and are nonanalytic in G at G=0 for the same reason that all quantum transition amplitudes are nonanalytic in h at h=0, namely their standard oscillatory essential singularity at the classical "limit". Thus perturbation expansions in powers of G of gravity-field transition amplitudes are also progressively more divergent with increasing order, and hence unrenormalizable. While their perturbative treatment is impossible, the exceedingly small value of hG makes the semiclassical treatment of these amplitudes extraordinarily accurate, indeed to such an extent that purely classical treatment of the gravity field ought to always be entirely adequate. It should therefore be fruitful to couple classical gravity to other fields which actually need to be quantized: those fields' ubiquitous, annoying ultraviolet divergences would thereupon undergo drastic self-gravitational red shift, and thus be cut off.

physics.gen-ph↗

arXiv2010

Do experiment and the correspondence principle oblige revision of relativistic quantum theory?

Recent preliminary data gathered by the Fermilab MINOS Collaboration suggest with 95% confidence that the mass of the muon neutrino differs from that of its antineutrino partner, which contradicts the entrenched relativistic quantum theory notion that a free antiparticle is a negative-energy free particle compelled to travel backwards in time. Also a discrepancy of about five standard deviations in the value of the proton charge radius recently obtained from muonic hydrogen versus that previously obtained from electronic hydrogen casts doubt on the calculation of the dominant relativistic QED contributions to the effects that are actually measured (e.g., the Lamb shift): these QED contributions dominate proton charge radius contributions less in muonic hydrogen than in electronic hydrogen. The negative-energy "free particles" of entrenched relativistic quantum theory are well-known features of the Klein-Gordon and Dirac equations, which are shown to have many other unphysical features as well. The correspondence principle for relativistic particles is incompatible with these two equations, produces no unphysical features and implies only positive energies for free particles, which eliminates the very basis of the entrenched notion of antiparticles, as well as of the CPT theorem. This principle thus requires antiparticles to arise from charge conjugation (or more generally CP) invariance, whose known breaking is naturally expected to produce mass splitting between particle and antiparticle, in consonance with the preliminary MINOS data. It also requires revamping of relativistic QED, which is in accord with the doubt cast on it by the proton charge radius results, and implies that QED is nonlocal, i.e. has no Hamiltonian density.

physics.gen-ph↗

arXiv2010

Getting path integrals physically and technically right

Feynman's Lagrangian path integral was an outgrowth of Dirac's vague surmise that Lagrangians have a role in quantum mechanics. Lagrangians implicitly incorporate Hamilton's first equation of motion, so their use contravenes the uncertainty principle, but they are relevant to semiclassical approximations and relatedly to the ubiquitous case that the Hamiltonian is quadratic in the canonical momenta, which accounts for the Lagrangian path integral's "success". Feynman also invented the Hamiltonian phase-space path integral, which is fully compatible with the uncertainty principle. We recast this as an ordinary functional integral by changing direct integration over subpaths constrained to all have the same two endpoints into an equivalent integration over those subpaths' unconstrained second derivatives. Function expansion with generalized Legendre polynomials of time then enables the functional integral to be unambiguously evaluated through first order in the elapsed time, yielding the Schroedinger equation with a unique quantization of the classical Hamiltonian. Widespread disbelief in that uniqueness stemmed from the mistaken notion that no subpath can have its two endpoints arbitrarily far separated when its nonzero elapsed time is made arbitrarily short. We also obtain the quantum amplitude for any specified configuration or momentum path, which turns out to be an ordinary functional integral over, respectively, all momentum or all configuration paths. The first of these results is directly compared with Feynman's mistaken Lagrangian-action hypothesis for such a configuration path amplitude, with special heed to the case that the Hamiltonian is quadratic in the canonical momenta.

physics.gen-ph↗

arXiv2010

The basis of quantum mechanics' compatibility with relativity--whose impairment gives rise to the Klein-Gordon and Dirac equations

Solitary-particle quantum mechanics' inherent compatibility with special relativity is implicit in Schroedinger's postulated wave-function rule for the operator quantization of the particle's canonical three-momentum, taken together with his famed time-dependent wave-function equation that analogously treats the operator quantization of its Hamiltonian. The resulting formally four-vector equation system assures proper relativistic covariance for any solitary-particle Hamiltonian operator which, together with its canonical three-momentum operator, is a Lorentz-covariant four-vector operator. This, of course, is always the case for the quantization of the Hamiltonian of a properly relativistic classical theory, so the strong correspondence principle definitely remains valid in the relativistic domain. Klein-Gordon theory impairs this four-vector equation by iterating and contracting it, thereby injecting extraneous negative-energy solutions that are not orthogonal to their positive-energy counterparts of the same momentum, thus destroying the basis of the quantum probability interpretation. Klein-Gordon theory, which thus depends on the square of the Hamiltonian operator, is as well thereby cut adrift from Heisenberg's equations of motion. Dirac theory confuses the space-time symmetry of the four-vector equation system with such symmetry for its time component alone, which it fatuously imposes, thereby breaching the strong correspondence principle for the free particle and imposing the starkly unphysical momentum-independence of velocity. Physically sensible alternatives, with external electromagnetic fields, to the Klein-Gordon and Dirac equations are derived, and the simple, elegant symmetry-based approach to antiparticles is pointed out.

physics.gen-ph↗

arXiv2010

Covariant isolation from an Abelian gauge field of its nondynamical potential, which, when fed back, can transform into a "confining Yukawa"

For Abelian gauge theory a properly relativistic gauge is developed by supplementing the Lorentz condition with causal determination of the time component of the four-vector potential by retarded Coulomb transformation of the charge density. This causal Lorentz gauge agrees with the Coulomb gauge for static charge densities, but allows the four-vector potential to have a longitudinal component that is determined by the time derivative of the four-vector potential's time component. Just as in Coulomb gauge, the two transverse components of the four-vector potential are its sole dynamical part. The four-vector potential in this gauge covariantly separates into a dynamical transverse four-vector potential and a nondynamical timelike/longitudinal four-vector potential, where each of these two satisfies the Lorentz condition. In fact, analogous partition of the conserved four-current shows each to satisfy a Lorentz-condition Maxwell equation system with its own conserved four-current. Because of this complete separation, either of these four-vector potentials can be tinkered with without affecting its counterpart. Since it satisfies the Lorentz condition, the nondynamical four-vector potential times a constant with dimension of inverse length squared is itself a conserved four-current, and so can be fed back into its own source current, which transforms its time component into an extended Yukawa, with both exponentially decaying and exponentially growing components. The latter might be the mechanism of quark-gluon confinement: in non-Abelian color gauge theory the Yukawa mixture ratio ought to be tied to color, with palpable consequences for "colorful" hot quark-gluon plasmas.

physics.gen-ph↗

arXiv2010

Equivalence of Maxwell's source-free equations to the time-dependent Schroedinger equation for a solitary particle with two polarizations and Hamiltonian |cp|

It was pointed out in a previous paper that although neither the Klein-Gordon equation nor the Dirac Hamiltonian produces sound solitary free-particle relativistic quantum mechanics, the natural square-root relativistic Hamiltonian for a nonzero-mass free particle does achieve this. Failures of the Klein-Gordon and Dirac theories are reviewed: the solitary Dirac free particle has, inter alia, an invariant speed well in excess of c and staggering spontaneous Compton acceleration, but no pathologies whatsoever arise from the square-root relativistic Hamiltonian. Dirac's key misapprehension of the underlying four-vector character of the time-dependent, configuration-representation Schroedinger equation for a solitary particle is laid bare, as is the invalidity of the standard "proof" that the nonrelativistic limit of the Dirac equation is the Pauli equation. Lorentz boosts from the particle rest frame point uniquely to the square-root Hamiltonian, but these don't exist for a massless particle. Instead, Maxwell's equations are dissected in spatial Fourier transform to separate nondynamical longitudinal from dynamical transverse field degrees of freedom. Upon their decoupling in the absence of sources, the transverse field components are seen to obey two identical time-dependent Schroedinger equations (owing to two linear polarizations), which have the massless free-particle diagonalized square-root Hamiltonian. Those fields are readily modified to conform to the attributes of solitary-photon wave functions. The wave functions' relations to the potentials in radiation gauge are also worked out. The exercise is then repeated without the considerable benefit of the spatial Fourier transform.

physics.gen-ph↗

arXiv2009

Sound relativistic quantum mechanics for a strictly solitary nonzero-mass particle, and its quantum-field reverberations

It is generally acknowledged that neither the Klein-Gordon equation nor the Dirac Hamiltonian can produce sound solitary-particle relativistic quantum mechanics due to the ill effects of their negative-energy solutions; instead their field-quantized wavefunctions are reinterpreted as dealing with particle and antiparticle simultaneously--despite the clear physical distinguishability of antiparticle from particle and the empirically known slight breaking of the underlying CP invariance. The natural square-root Hamiltonian of the free relativistic solitary particle is iterated to obtain the Klein-Gordon equation and linearized to obtain the Dirac Hamiltonian, steps that have calculational but not physical motivation, and which generate the above-mentioned problematic negative-energy solutions as extraneous artifacts. Since the natural square root Hamiltonian for the free relativistic solitary particle contrariwise produces physically unexceptionable quantum mechanics, this article focuses on extending that Hamiltonian to describe a solitary particle (of either spin 0 or spin one-half) in relativistic interaction with an external electromagnetic field. That is achieved by use of Lorentz-covariant solitary-particle four momentum techniques together with the assumption that well-known nonrelativistic dynamics applies in the particle's rest frame. Lorentz-invariant solitary particle actions, whose formal Hamiltonization is an equivalent alternative approach, are as well explicitly displayed. It is proposed that two separate solitary-particle wavefunctions, one for a particle and the other for its antiparticle, be independently quantized in lieu of "reinterpreting" negative energy solutions--which indeed don't even afflict proper solitary particles.

physics.gen-ph↗