Additions:
//Methods.// Kets are defined as formal conditional clauses referring to measurements in a formal language and have a natural structure as a vector space. Addition is logical disjunction. The dual space consists of consequent clauses, such that the inner product is a set of statements in the subjunctive mood. The probability interpretation gives truth values for corresponding future tense statements when the initial state is prepared and the final state is to be measured.
Deletions:
//Methods.// Kets are defined as formal conditional clauses referring to measurements in a formal language and have a natural structure as a vector space. Addition is logical disjunction. The dual space consists of consequent clauses, such that the inner product is a set of statements in the subjunctive mood. The probability interpretations gives truth values for corresponding future tense statements when the initial state is prepared and the final state is to be measured.
Additions:
//Methods.// Kets are defined as formal conditional clauses referring to measurements in a formal language and have a natural structure as a vector space. Addition is logical disjunction. The dual space consists of consequent clauses, such that the inner product is a set of statements in the subjunctive mood. The probability interpretations gives truth values for corresponding future tense statements when the initial state is prepared and the final state is to be measured.
Deletions:
//Methods.// Kets are defined as formal conditional clauses referring to measurements in a formal language and have a natural structure as a vector space. Addition is logical disjunction. The dual space consists of consequent clauses, such that the inner product is a set of statements in the subjunctive mood. A probability is a truth value for such a statements when the initial state is prepared and the final state is to be measured.
Additions:
//Methods.// Cosmological parameters are calculated and compared to supernova redshift data. Treatments are given for gravitational bending of light, and for light from distant objects in uniform motion, and in galactic orbits. A test is applied to look for a signature of the spectral prediction in measurements of local stars. A separate test is applied for a population of halo stars.
//Results.// Good agreement is found between predictions and supernova redshifts for a closed Friedmann Cosmology with no cosmological constant and expanding at half the rate of the standard model. Previously unmodelled components of cosmological redshift account for the anomalous Pioneer blueshift and for the flattening of galaxy rotation curves. For orbiting bodies the unmodelled component simulates a MONDian law with a value for the critical MOND acceleration in agreement with observation. Distant lenses have a quarter of the mass required by standard general relativity. Missing mass can be accounted by a massive neutrino. Missing mass can be accounted by a massive neutrino. Neither dark energy nor CDM is required. Based on accurate kinematic data on local stars, we reject the null hypothesis, //there is no systematic error in spectrographic determinations of heliocentric radial velocity//, with up to 99.95% confidence.
//Context:// While CDM models and MOND give explanations for flat rotation curves of other galaxies, both present observational problems and the local gradient of the Milky Way’s rotation curve is not flat.
//Aims:// We consider whether flat rotation curves could be an artifact of an unmodelled component in spectral shift.
//Methods:// In the absence of astrometric determinations of radial velocity, we apply a statistical test on a population of 20 440 Hipparcos stars inside 300 pc with known radial velocities and with accurate parallaxes in the New Hipparcos Reduction.
//Results:// The test rejects the null hypothesis, //there is no systematic error in spectrographic determinations of heliocentric radial velocity//, with 99.95% confidence. In a separate test on metal-poor stars, we find tension between calculations of the orbital velocity of the Sun and three populations of halo stars inside and outside of a cone of 60° semi-angle from the direction of rotation. Tension cannot be removed with only systematic distance adjustments.
//Conclusions:// We conclude that the most probable explanation is an unmodelled element in spectrographic determinations of heliocentric radial velocity with a probable cosmological origin, and propose that this unmodelled component, rather than CDM or MOND, is responsible for the apparent flatness of galaxy rotation curves.
Deletions:
//Methods.// Cosmological parameters are calculated and compared to supernova redshift data. Treatments are given for gravitational bending of light, and for light from distant objects in uniform motion, and in galactic orbits. A test is applied to look for a signature of the spectral prediction in measurements of local stars.
//Results.// Good agreement is found between predictions and supernova redshifts for a closed Friedmann Cosmology with no cosmological constant and expanding at half the rate of the standard model. Previously unmodelled components of cosmological redshift account for the anomalous Pioneer blueshift and for the flattening of galaxy rotation curves. For orbiting bodies the unmodelled component simulates a MONDian law with a value for the critical MOND acceleration in agreement with observation. Distant lenses have a quarter of the mass required by standard general relativity. Missing mass can be accounted by a massive neutrino. Missing mass can be accounted by a massive neutrino. Neither dark energy nor CDM is required. Based on accurate kinematic data on local stars, we reject the null hypothesis, there is no systematic error in spectrographic determinations of heliocentric radial velocity, with up to 99.95% confidence.
While CDM models and MOND give explanations for flat rotation curves of other galaxies, it is observed that the local gradient of the Milky Way’s rotation curve is not flat. We consider whether flat rotation curves could be an artifact of an unmodelled component in spectral shift. In the absence of astrometric determinations of radial velocity, we apply a statistical test on a population of 20 608 Hipparcos stars inside 300 pc with known radial velocities and with accurate parallaxes in the New Hipparcos Reduction. The tests reject the null hypothesis, //there is no systematic error in spectrographic determinations of heliocentric radial velocity//, with 99.99999% confidence. In a separate test on metal-poor stars, we find tension between calculations of the orbital velocity of the Sun and three populations of halo stars inside and outside of a cone of 60° semi-angle from the direction of rotation. Tension cannot be removed with only systematic distance adjustments. We conclude that the most probable explanation is an unmodelled element in spectrographic determinations of heliocentric radial velocity with a probable cosmological origin, and propose that this unmodelled component, rather than CDM or MOND, is responsible for the apparent flatness of galaxy rotation curves.
Additions:
//Results.// Good agreement is found between predictions and supernova redshifts for a closed Friedmann Cosmology with no cosmological constant and expanding at half the rate of the standard model. Previously unmodelled components of cosmological redshift account for the anomalous Pioneer blueshift and for the flattening of galaxy rotation curves. For orbiting bodies the unmodelled component simulates a MONDian law with a value for the critical MOND acceleration in agreement with observation. Distant lenses have a quarter of the mass required by standard general relativity. Missing mass can be accounted by a massive neutrino. Missing mass can be accounted by a massive neutrino. Neither dark energy nor CDM is required. Based on accurate kinematic data on local stars, we reject the null hypothesis, there is no systematic error in spectrographic determinations of heliocentric radial velocity, with up to 99.95% confidence.
Deletions:
//Results.// Good agreement is found between predictions and supernova redshifts for a closed Friedmann Cosmology with no cosmological constant and expanding at half the rate of the standard model. Previously unmodelled components of cosmological redshift account for the anomalous Pioneer blueshift and for the flattening of galaxy rotation curves. For orbiting bodies the unmodelled component simulates a MONDian law with a value for the critical MOND acceleration in agreement with observation. Distant lenses have a quarter of the mass required by standard general relativity. Missing mass can be accounted by a massive neutrino. Missing mass can be accounted by a massive neutrino. Neither dark energy nor CDM is required. Based on accurate kinematic data on local stars, we reject the null hypothesis, there is no systematic error in spectrographic determinations of heliocentric radial velocity, with up to 99.99999% confidence.
Additions:
[[http://arxiv.org/abs/0904.3973 arXiv:0904.3973]]
Deletions:
[[http://arxiv.org/abs/0903.5193 arXiv:0904.3973]]
Additions:
//Context.// While causal perturbation theory and lattice regularisation allow rigorous treatment of the ultraviolet divergences in qed, they do not resolve the Landau pole, or address questions of physical interpretation. Relational Quantum Gravity I (RQG I) presented an interpretation of quantum mechanics as a theory of measurements of particles, and found a representation of finite dimensional Hilbert space using in smooth wave functions such that differential operators are defined and a form of covariance is obeyed.
Deletions:
//Context.// While causal perturbation theory and lattice regularisation allow rigorous treatment of the ultraviolet divergences in qed, they do not resolve the Landau pole, or address questions of physical interpretation. Relational Quantum Gravity I (RQG I) presented an interpretation of quantum mechanics as a theory of measurements of particles, and found a representation of finite dimensional Hilbert space using in smooth wave functions such that differential operators are defined and a form of covariance is obeyed. The Schrödinger equation is shown from the requirements of the probability interpretation.
Additions:
//Context.// There are substantial observational and theoretical problems both for &Lambda-CDM models and for MOND.
//Aims.// To show that observations currently attributed to &Lambda-CDM and/or MOND can reasonably be accounted for by the cosmological redshift predictions of relational quantum gravity.
//Methods.// Cosmological parameters are calculated and compared to supernova redshift data. Treatments are given for gravitational bending of light, and for light from distant objects in uniform motion, and in galactic orbits. A test is applied to look for a signature of the spectral prediction in measurements of local stars.
//Results.// Good agreement is found between predictions and supernova redshifts for a closed Friedmann Cosmology with no cosmological constant and expanding at half the rate of the standard model. Previously unmodelled components of cosmological redshift account for the anomalous Pioneer blueshift and for the flattening of galaxy rotation curves. For orbiting bodies the unmodelled component simulates a MONDian law with a value for the critical MOND acceleration in agreement with observation. Distant lenses have a quarter of the mass required by standard general relativity. Missing mass can be accounted by a massive neutrino. Missing mass can be accounted by a massive neutrino. Neither dark energy nor CDM is required. Based on accurate kinematic data on local stars, we reject the null hypothesis, there is no systematic error in spectrographic determinations of heliocentric radial velocity, with up to 99.99999% confidence.
Deletions:
//Context.// There are substantial observational and theoretical problems for both CDM and MOND.
//Aims.// To show that observations currently attributed to CDM and/or MOND can reasonably be accounted for by the cosmological redshift predictions of relational quantum gravity.
//Methods.// Cosmological parameters are calculated and compared to supernova redshift data. Treatments are given for gravitational bending of light, and for light from distant objects in uniform motion, and in galactic orbits.
//Results.// Good agreement is found between predictions and supernova redshifts for a closed Friedmann Cosmology with no cosmological constant and expanding at half the rate of the standard model. Previously unmodelled components of cosmological redshift account for the anomalous Pioneer blueshift and for the flattening of galaxy rotation curves. For orbiting bodies the unmodelled component simulates a MONDian law with a value for the critical MOND acceleration in agreement with observation. Distant lenses have a quarter of the mass required by standard general relativity. Missing mass can be accounted by a massive neutrino. CDM is not required.
Additions:
A representation of a finite dimensional Hilbert space using smooth wave functions is shown. A continuum of states, ""
"" for ""
"", is defined such that the inner product can be expressed either as a finite sum or as an integral. The orthogonality condition can be expressed using either a Kronecker or Dirac delta, where the Dirac delta is a smooth function. Operators do not generally have an integral form. The representation has potential applications in quantum theory, particularly with regard to the treatment of divergences in quantum electrodynamics.
Deletions:
A representation of a finite dimensional Hilbert space using smooth wave functions is shown. A continuum of states, """" for """", is defined such that the inner product can be expressed either as a finite sum or as an integral. The orthogonality condition can be expressed using either a Kronecker or Dirac delta, where the Dirac delta is a smooth function. Operators do not generally have an integral form. The representation has potential applications in quantum theory, particularly with regard to the treatment of divergences in quantum electrodynamics.
Additions:
A representation of a finite dimensional Hilbert space using smooth wave functions is shown. A continuum of states, """" for """", is defined such that the inner product can be expressed either as a finite sum or as an integral. The orthogonality condition can be expressed using either a Kronecker or Dirac delta, where the Dirac delta is a smooth function. Operators do not generally have an integral form. The representation has potential applications in quantum theory, particularly with regard to the treatment of divergences in quantum electrodynamics.
Deletions:
I exhibit a representation of a finite dimensional Hilbert space using smooth wave functions and such that integrals are interchangeable with sums in the inner product, and the Dirac delta is interchangeable with the Kronecker delta, up to normalisation. The position operator does not have an integral form, and the canonical commutation relation appears in the limit of infinite dimensions. The representation has potential applications in quantum theory, particularly with regard to the treatment of divergences in quantum electrodynamics.
Additions:
//Results.// The mathematical structure of quantum mechanics is formulated in terms of discrete measurement results at finite level of accuracy and does not depend on an assumption of a background spacetime continuum. Discrete position functions are uniquely embedded into smooth wave functions such that differential operators are defined. Using finite dimensional Hilbert space, a continuum of states, """" for """", is defined such that the inner product can be expressed either as a finite sum or as an integral. Operators do not in general have an integral form. The Schrödinger equation is shown from the requirements of the probability interpretation.
Deletions:
//Results.// The mathematical structure of quantum mechanics is formulated in terms of discrete measurement results at finite level of accuracy and does not depend on an assumption of a background spacetime continuum. Discrete position functions are uniquely embedded into smooth wave functions such that differential operators are defined. Using finite dimensional Hilbert space, a continuum of states, ""
"" for ""
"", is defined such that the inner product can be expressed either as a finite sum or as an integral. Operators do not in general have an integral form. The Schrödinger equation is shown from the requirements of the probability interpretation.
Additions:
//Results.// The mathematical structure of quantum mechanics is formulated in terms of discrete measurement results at finite level of accuracy and does not depend on an assumption of a background spacetime continuum. Discrete position functions are uniquely embedded into smooth wave functions such that differential operators are defined. Using finite dimensional Hilbert space, a continuum of states, """" for """", is defined such that the inner product can be expressed either as a finite sum or as an integral. Operators do not in general have an integral form. The Schrödinger equation is shown from the requirements of the probability interpretation.
Deletions:
//Results.// The mathematical structure of quantum mechanics is formulated in terms of discrete measurement results at finite level of accuracy and does not depend on an assumption of a background spacetime continuum. Discrete position functions are uniquely embedded into smooth wave functions such that differential operators are defined. Using finite dimensional Hilbert space, a continuum of states, ""
"" for ""
"", is defined such that the inner product can be expressed either as a finite sum or as an integral. Operators do not in general have an integral form. The Schrödinger equation is shown from the requirements of the probability interpretation.
Additions:
//Results.// The mathematical structure of quantum mechanics is formulated in terms of discrete measurement results at finite level of accuracy and does not depend on an assumption of a background spacetime continuum. Discrete position functions are uniquely embedded into smooth wave functions such that differential operators are defined. Using finite dimensional Hilbert space, a continuum of states, """" for """", is defined such that the inner product can be expressed either as a finite sum or as an integral. Operators do not in general have an integral form. The Schrödinger equation is shown from the requirements of the probability interpretation.
""PDF (700KB)""
Deletions:
//Results.// The mathematical structure of quantum mechanics is formulated in terms of discrete measurement results at finite level of accuracy and does not depend on an assumption of a background spacetime continuum. Discrete position functions are uniquely embedded into smooth wave functions such that differential operators are defined. The position operator does not have an integral form, and the canonical commutation relation appears in the limit of infinite dimensions. The Schrödinger equation is shown from the requirements of the probability interpretation.
""PDF (600KB)""
Additions:
While CDM models and MOND give explanations for flat rotation curves of other galaxies, it is observed that the local gradient of the Milky Way’s rotation curve is not flat. We consider whether flat rotation curves could be an artifact of an unmodelled component in spectral shift. In the absence of astrometric determinations of radial velocity, we apply a statistical test on a population of 20 608 Hipparcos stars inside 300 pc with known radial velocities and with accurate parallaxes in the New Hipparcos Reduction. The tests reject the null hypothesis, //there is no systematic error in spectrographic determinations of heliocentric radial velocity//, with 99.99999% confidence. In a separate test on metal-poor stars, we find tension between calculations of the orbital velocity of the Sun and three populations of halo stars inside and outside of a cone of 60° semi-angle from the direction of rotation. Tension cannot be removed with only systematic distance adjustments. We conclude that the most probable explanation is an unmodelled element in spectrographic determinations of heliocentric radial velocity with a probable cosmological origin, and propose that this unmodelled component, rather than CDM or MOND, is responsible for the apparent flatness of galaxy rotation curves.
Deletions:
While CDM models and MOND give explanations for flat rotation curves of other galaxies, it is observed that the local gradient of the Milky Way’s rotation curve is not flat. We consider whether flat rotation curves could be an artifact of an unmodelled component in spectral shift. In the absence of astrometric determinations of radial velocity, we apply a statistical test on a population of 20 574 Hipparcos stars inside 300 pc with known radial velocities and with accurate parallaxes in the New Hipparcos Reduction. The test rejects the null hypothesis, //there is no systematic error in spectrographic determinations of heliocentric radial velocity//, with 99.9993% confidence. In a separate test on metal-poor stars, we find tension between calculations of the orbital velocity of the Sun and three populations of halo stars inside and outside of a cone of 60° semi-angle from the direction of rotation. Tension cannot be removed with only systematic distance adjustments. We conclude that there is an unmodelled element in spectrographic determinations of heliocentric radial velocity with a probable cosmological origin, and propose that this unmodelled component, rather than CDM or MOND, is responsible for the apparent flatness of galaxy rotation curves.
Additions:
Deletions:
Additions:
===""""Relational Quantum Gravity V: Paradox===
""PDF (422KB)""
Quantum theory is famous for a number of conceptual paradoxes which have lead many physicists to think that interpretation in terms of visualizable mechanistic processes is not possible. Relational quantum gravity challenges this viewpoint, by developing a model from first principles in which Hilbert space is seen to make statements concerning measurements in a model in which the fundamental objects are particles, and in which all measurements are relative, in the sense that they involve comparison between matter and matter and such that the quantification of a relationship between matter and a background spacetime is meaningless at the fundamental level of the theory. A consistent mathematical model incorporating qed and general relativity was constructed from this interpretation. I review conceptual aspects of the model, and discuss the resolution of the important conceptual paradoxes of quantum mechanics.
Additions:
//Context.// While causal perturbation theory and lattice regularisation allow rigorous treatment of the ultraviolet divergences in qed, they do not resolve the Landau pole, or address questions of physical interpretation. Relational Quantum Gravity I (RQG I) presented an interpretation of quantum mechanics as a theory of measurements of particles, and found a representation of finite dimensional Hilbert space using in smooth wave functions such that differential operators are defined and a form of covariance is obeyed. The Schrödinger equation is shown from the requirements of the probability interpretation.
===""""Lindblad’s epicycles – valid method or bad science?===
[[http://arxiv.org/abs/0911.1594 arXiv:0911.1594 (astro-ph)]]
""Standard resolution pdf (0.5MB)""
""High Resolution pdf (1.8MB)""
The study of Galactic orbits in the last eighty years has been dominated by statistical assumptions made because of the lack of empirical evidence available in the early 20th century. Using evidence from Hipparcos and recent radial velocity surveys, Francis and Anderson recently showed that spiral structure is primarily a consequence of gravitational alignments of stellar orbits. I review the mechanism which creates spiral structure, consider the validity of widely held assumptions in galactic dynamics and the implications to notions such as the asymmetric drift and disc heating. I identify a number of fundamental mathematical and physical errors in Lindblad’s epicycle theory and in density wave theory. Students should be made aware that these ideas can no longer be considered as science, and authors of textbooks should consider whether they merit anything more than a historical note.
Deletions:
//Context.// While causal perturbation theory and lattice regularisation allow rigorous treatment of the ultraviolet divergences in qed, they do not resolve the Landau pole, or address questions of physical interpretation. Relational Quantum Gravity I (RQG I) presented an interpretation of quantum mechanics as a theory of measurements of particles, and found a representation of finite dimensional Hilbert space using in smooth wave functions such that differential operators are defined and a form of covariance is obeyed.
Additions:
//Context.// While causal perturbation theory and lattice regularisation allow rigorous treatment of the ultraviolet divergences in qed, they do not resolve the Landau pole, or address questions of physical interpretation. Relational Quantum Gravity I (RQG I) presented an interpretation of quantum mechanics as a theory of measurements of particles, and found a representation of finite dimensional Hilbert space using in smooth wave functions such that differential operators are defined and a form of covariance is obeyed.
Deletions:
//Context.// While causal perturbation theory and lattice regularisation allow rigorous treatment of the ultraviolet divergences in qed, they do not resolve the Landau pole, or address questions of physical interpretation. Relational Quantum Gravity I (RQG I) presented an interpretation of quantum mechanics as a theory of measurements of particles, and found a representation of finite dimensional Hilbert space using in smooth wave functions such that differential operators are defined and a form of covariance is obeyed. The Schrödinger equation is shown from the requirements of the probability interpretation.
Additions:
Proc Roy Soc A, [[http://dx.doi.org/10.1098/rspa.2009.0036 DOI: 10.1098/rspa.2009.0036]]
Deletions:
Accepted for publication by Proc Roy Soc A.
Additions:
Accepted for publication by Proc Roy Soc A.
