Damon So - Academia.edu (original) (raw)
Papers by Damon So
Fortress Press eBooks, 2010
The paper by Einstein, Podolsky and Rosen (1935) is rigorously critiqued but its major implicatio... more The paper by Einstein, Podolsky and Rosen (1935) is rigorously critiqued but its major implication is explicitly brought out – non-determinism implies non-locality. This implication and Bell’s theorem (with its associated experiments) are used to logically identify the possible sets of universes to which our universe can theoretically belong – the set of universes with non-deterministic non-locality and the set of universes with deterministic non-locality. The Pilot Wave Theory, a deterministic non-local theory and therefore a theoretically possible theory to describe our universe, is presented and legitimate questions and difficulties are raised about this theory. An alternative theory named Wave Surfing Theory, which is non-deterministic and non-local in nature, is presented. This theory is shown to be consistent with ten observed quantum phenomena: the de Broglie relation between momentum and wavelength, the Planck-Einstein relation between energy and frequency, non-locality, Born’s rule, spin angular momentum, wavy interference pattern of the two-slit experiment, replacement of the interference pattern by two localised density distributions at measurement, discrete nature of particles detected on detection screen, tunnelling and reduction of mass/inertia concomitant with production of energy in nuclear fusion and fission. An interpretation of probability density and the related definition of measurement are proposed. At a measurement event, it is proposed that there is an exchange of momentum between the measured particle and the measuring agent. The domain of the validity of the Schrödinger equation is also identified with respect to the interpretation of probability density and the definition of measurement. Most of the physical quantities in the Wave Surfing Theory are non-deterministic and all the physical quantities have definite values. The theory therefore avoids the problems of superposition and wave function collapse, and the paradox of the Schrödinger cat, and it avoids other conceptual problems with the ontology of particles. In this theory, a measurement event or a local change of the classical potential will instantaneously cause a wholesale transformation of the wave function and its probability density over the whole relevant spatial domain, rather than a wave function collapse. The theory therefore has the potential to explore the detailed dynamics of particle entanglement and non-locality. Using de Broglie’s relation between momentum and wavelength, the velocity components of a particle can be logically projected into their relativistic forms. Based on these relativistic velocity components, an inexpensive experiment is identified and suggested for verifying or falsifying the Wave Surfing Theory. This experiment will also help to verify or falsify the suggested definitions of the mass/inertia and energy of a particle. These two fundamental definitions suitably and fundamentally lead to the well-known expression for rest energy, , without invoking electromagnetism, but they require verification or falsification by the suggested experiment. If the experiment verifies the Wave Surfing Theory, then possible future studies include the full relativistic version of the theory with all its details, its relationships with Quantum Field Theory (particularly on annihilation and creation of particles) and the Standard Model, dark matter, particle entanglement and dark energy.
Transformation: An International Journal of Holistic Mission Studies, 2006
Transformation: An International Journal of Holistic Mission Studies, 2008
The paper examines the emphasis on knowing the inner life of Jesus by a prominent 19th century Li... more The paper examines the emphasis on knowing the inner life of Jesus by a prominent 19th century Liberal Protestant, and Albert Schweitzer's decisive blow to the Life of Jesus movement at the beginning of the 20th century. It gives critiques to both the former and the latter, and identifies the approach of the Liberal Protestants as ‘subjective’ in two senses. While the subjectivity of an interpreter can pose problems in the interpretation of Jesus, it is maintained that the possibility of knowing some aspects of the subjectivity of Jesus cannot be ruled out a priori. A method of correlation is suggested to give a more objective and connected interpretation of Jesus' outer words/actions and his mind.
Quarterly Journal of the Royal Meteorological Society, 2007
ABSTRACT The two-dimensional dynamics of multicell and unicell squall lines are examined using a ... more ABSTRACT The two-dimensional dynamics of multicell and unicell squall lines are examined using a numerical model. Both types feature a convective jump updraught with extensive, deep, rearward-extending anvils. the multicell case contains travelling convection cells and is unsteady but persistent, whereas the unicell case is quasi-steady.In the multicell case, an extensive density current is produced by the evaporation and drag of rain falling from a succession of convection cells which travel rearwards relative to the density current head. the circulation within the density current is complex and consists of three mutually interactive branches: a rotor, a cold downdraught, and a subsidence region.In the unicell case, a density current is not produced and the updraught is forced by a propagating wave of elevation, generated as an interaction between the updraught, water loading and evaporation in a very localized area.The squall line structure is compared with other models and it is shown that certain propagating two-dimensional tropical and mid-latitude squall lines are dynamically similar, their detailed structure being controlled by the inflow wind profile.The multicell case is compared with a quasi-two-dimensional West African squall line which occurred on 22 June 1981 during the Convection Profonde Tropicale (COPT 81) experiment performed in the northern part of the Ivory Coast. Good agreement is found between the model and the observations, and hence the dynamics of the observed squall line is quantified. the unicell case, in which a density current and conventional downdraughts are absent, has yet to be identified in atmospheric observations.
Journal of the Atmospheric Sciences, 1990
Based on a relativistic model for a quantum particle, the paper proposes a new definition of ener... more Based on a relativistic model for a quantum particle, the paper proposes a new definition of energy which takes into account the additional localised surfing motion of the particle on its phase surface which is perpendicular to its translational motion. The conventional relativistic formula for energy is found to be a limiting case for this new definition of energy when the characteristic parameter in the new energy formula is set to zero. For a particle at rest translationally, the two formulae yield the same energy, but in general for the same non-zero translational velocity they yield different energies, the difference being dependent on the value of the characteristic parameter. A certain kinetic energy range has been theoretically identified where the performances of the conventional formula and the new formula of energy can be best tested against experimental data. The new definition of energy prompts a definition of rest mass, m, which is the surfing momentum of the particle ...
The paper presents an interpretation of quantum mechanics in which a particle’s motion is inheren... more The paper presents an interpretation of quantum mechanics in which a particle’s motion is inherently non-deterministic while it has definite unambiguous momentum and position whose existence is independent of measurement. It is therefore distinct from the Copenhagen Interpretation while it is also distinct from the pilot wave theory in that this interpretation is inherently non-deterministic. This paper paves the way for rigorous investigation into the spins of particles in the succeeding paper.
The preceding paper [1] proposed an alternative interpretation of quantum mechanics which is dist... more The preceding paper [1] proposed an alternative interpretation of quantum mechanics which is distinct from the Copenhagen Interpretation and the pilot wave theory. This alternative interpretation and its associated non-deterministic velocity component are tested here with reference to particle spins. A mechanism for generating particle spins is rigorously identified for the case of a free particle and the case of the hydrogen electron. The mechanism can be generalised for electrons in other atoms and other particles. The incomplete nature of the Schrödinger equation with regard to its inability to incorporate particle spin is demonstrated. The adoption of Born’s rule by the physicist community for interpreting the probability density is seen as implicitly acknowledging the mechanism for generating particle spin but this mechanism was far from being made explicit by that rule. The crucial question of the need for sensitive non-deterministic information input to maintain particle spin...
Wave-Particle Duality, Spin, Mass and Energy1 Damon Wai Kwan So2 Oxford Centre for Mission Studie... more Wave-Particle Duality, Spin, Mass and Energy1 Damon Wai Kwan So2 Oxford Centre for Mission Studies, Woodstock Road, Oxford OX2 6HR. Abstract A previous paper [1] proposed an alternative interpretation of quantum mechanics which is distinct from the Copenhagen Interpretation and the pilot wave theory. This alternative interpretation and its associated nondeterministic surfing velocity on the S (phase) surface are applied here to model point-like entities (particles and photons) with non-deterministic trajectories in the one-slit experiment and the two-slit experiment. The diffraction integral for these point-like entities, as a solution to the Helmholtz equation, is in the same form as the diffraction integral found in optical studies so that the mathematical results in optical studies regarding diffraction and interference patterns can be readily applied to the point-like entities modelled here. The nonrelativistic model for slowly moving particles and the relativistic model for fas...
This book presents a dynamic picture of Jesus in his majestic Lordship and freedom, his humble se... more This book presents a dynamic picture of Jesus in his majestic Lordship and freedom, his humble servanthood and obedience, his compassion for needy humanity in his public ministry, his courageous entry into Jerusalem and his sacrificial love revealed in his death there, his resurrection from the dead and his universal reign. This dynamic picture is related closely to Jesus’ fundamental and underlying relationship with his Father through the Holy Spirit. The concrete expression of that Trinitarian relationship in Jesus’ life, ministry, death, and resurrection is presented in a unified manner, avoiding the pitfall of majoring on only one of these aspects. This holistic and dynamic picture of Jesus in intimate fellowship with his Father through the Spirit gives the readers a valuable glimpse into the mystery of the Trinity and invites them to reflect on what it means to follow Jesus as individuals and as communities in the context of the twenty-first century with its many challenges. Je...
The Benjamin (1968) analysis of a two-fluid density current is extended to include the effect of ... more The Benjamin (1968) analysis of a two-fluid density current is extended to include the effect of vorticity within the current. In the case of constant vorticity, the density-current depth is shown to lie between the limits of half and two-thirds of the channel depth. More general vorticity distributions are also considered, namely those that have : (i) a maximum in the upper and lower regions of the density current ; and (ii) a maximum in the middle of the density current. In the former, as in the case of constant vorticity , density-current structures exist, whereas in the latter, deep overturning circulations predominate which can cause a ' blocking ' of the upstream inflow. A generalized propagation formula which includes the effects of finite depth and rear inflow into the density current is established and the uniqueness issue is considered. The analysis is further extended to a three-fluid system, composed of physically distinct component flows, namely, a density current, an overturning updraught region in upper levels ahead of the density current and an updraught in which the fluid ascends without overturning to its outflow level. Two types of behaviour are identified. First, a symmetric mode in which the density current and the overturning updraught have the same depth and, second, an asymmetric mode with solutions restricted to a certain parameter range. A special case in which the fluids have the same density illustrates the basic dynamics of the problem and also the nature of the vertical transport of momentum.
The datasets by Bertozzi [9] and by Lund and Uggerhøj [10] show that an electron with kinetic ene... more The datasets by Bertozzi [9] and by Lund and Uggerhøj [10] show that an electron with kinetic energy (normalised with respect to its rest energy) near to or greater than 2 is underestimated by Einstein’s generalised formula for the energy of a moving object/particle. Also, the datasets show that the highest kinetic deficit in Einstein’s formula occurs at the data point with the highest kinetic energy or highest speed. This energy deficit or anomaly becomes evident when energy is plotted again speed. It is not so evident vice versa, as is often the case; hence the anomaly was not identified. A new definition of energy incorporating the surfing momentum of a particle on its phase (S) surface is proposed. This new definition predicts or explains the observed energy deficit in Einstein’s generalised formula and can further our understanding of the nature of rest mass, rest energy and massless particles. Using the criterion of least squares, it is shown that the new formula performs bett...
Transformation: An International Journal of Holistic Mission Studies
Drafts by Damon So
Based on a relativistic model for a quantum particle, the paper proposes a new definition of ener... more Based on a relativistic model for a quantum particle, the paper proposes a new definition of energy which takes into account the additional localised surfing motion of the particle on its phase surface which is perpendicular to its translational motion. The conventional relativistic formula for energy is found to be a limiting case for this new definition of energy when the characteristic parameter in the new energy formula is set to zero. For a particle at rest translationally, the two formulae yield the same energy, but in general for the same non-zero translational velocity they yield different energies, the difference being dependent on the value of the characteristic parameter. The new definition of energy prompts a definition of rest mass, m, which is the surfing momentum of the particle on its phase surface divided by c. The surfing energy of the particle is its surfing momentum multiplied by c. The surfing energy is therefore given by mc2 which has been conventionally understood as the rest energy. The theoretical analysis therefore shows from the new definition of energy how the link between surfing momentum and mass, and the link between surfing momentum and surfing energy (rest energy), lead to the well known relationship between rest mass and rest energy, without invoking electromagnetism. Surfing energy, though identical to rest energy, affords a more physically intuitive understanding than rest energy because it can be visualised. Surfing energy, validly understood as an internal kinetic energy of the particle, can be converted into other forms of energy which is accompanied by a reduction of the particle’s rest mass due to a simultaneous reduction in its surfing momentum. A certain kinetic energy range has been theoretically identified where the performance of the conventional equation linking energy and velocity (by Einstein) and the performance of the corresponding new equation can be best tested against experimental data. The dataset provided by Lund and Uggerhøj [13] has been used to demonstrate that, for the energy range given by the dataset, the proposed new relationship between kinetic energy and translational velocity is more consistent with the dataset than Einstein’s equation, if one allows for a systematic error in the ToF measurement. More experiments to be performed at the critical energy range will further clarify the comparison. Verification of the new theory will have significant implications for our understanding of dark matter and other questions in physics.
This paper tackles the problem of superposition and the associated paradox of the Schrödinger's c... more This paper tackles the problem of superposition and the associated paradox of the Schrödinger's cat by proposing a theoretical model in which an ontologically discrete free particle in non-deterministic motion with a real trajectory can fulfil the statistical expectation of Born's rule. The suggested expressions or constraints for a set of three orthogonal velocity components of the particle in this model are consistent with these observations: de Broglie's relation between wave length and momentum, particle spin and Born's rule. Two of these velocity components are deterministic but the third component is non-deterministic and is subjected to the overall statistical constraint of Born's rule. These three consistencies with observations give credibility to these velocity components and the theoretical model. Energy is defined by including the quantum potential term and it satisfies the observed Planck-Einstein relation, hence giving credibility to this definition. Superposition is understood as an illusionary phenomenon as a result of the process of averaging the presence of the particle over multiple instants. Just as Richard Feynman commented in his lecture on the two-slit experiment that the average family of America had two and a half children-and such a fictitious family is merely the result of an averaging process and is therefore not real, the spread-out presence of a particle in space at a single instant is merely the result of an averaging process where the multiple pictures of the particle at multiple positions over multiple instants are averaged over those multiple instants to yield an average picture of the particle per instant but the instant in 'per instant' is a fictitious instant which is not a real instant. As the family in '2.5 children per family' is not a real family, so the superposition of the particle per instant is not physically real (because the instant in per instant is fictitious). This understanding of superposition dissolves the paradox of the Schrödinger's cat. The proposed theoretical model of a free particle with three orthogonal velocity components also provides a possible and consistent mechanism for the generation of particle spin which therefore supports the model. An experiment to further verify or falsify the theoretical model will be proposed in a later paper. A crucial difference between the textbook treatment of a free particle and the theoretical model here is that the former artificially and unnecessarily only allows the Laplacian in the Schrödinger equation to operate in the translational direction (thus generating plane waves) while the treatment in this paper allows the Laplacian to operate fully and therefore properly in all three dimensions. The theoretical model, when verified by experiment, can lead to a new interpretation of quantum mechanics.
This paper tackles the problem of superposition and the associated paradox of the Schrödinger's c... more This paper tackles the problem of superposition and the associated paradox of the Schrödinger's cat by proposing a theoretical model in which an ontologically discrete free particle in non-deterministic motion with a real trajectory can fulfil the statistical expectation of Born's rule. The suggested expressions or constraints for a set of three orthogonal velocity components of the particle in this model are consistent with these observations: de Broglie's relation between wave length and momentum, particle spin and Born's rule. Two of these velocity components are deterministic but the third component is non-deterministic and is subjected to the overall statistical constraint of Born's rule. These three consistencies with observations give credibility to these velocity components and the theoretical model. Energy is defined by including the quantum potential term and it satisfies the observed Planck-Einstein relation, hence giving credibility to this definition. Superposition is understood as an illusionary phenomenon as a result of the process of averaging the presence of the particle over multiple instants. Just as Richard Feynman commented in his lecture on the two-slit experiment that the average family of America had two and a half children-and such a fictitious family is merely the result of an averaging process and is therefore not real, the spread-out presence of a particle in space at a single instant is merely the result of an averaging process where the multiple pictures of the particle at multiple positions over multiple instants are averaged over those multiple instants to yield an average picture of the particle per instant but the instant in 'per instant' is a fictitious instant which is not a real instant. As the family in '2.5 children per family' is not a real family, so the superposition of the particle per instant is not physically real (because the instant in per instant is fictitious). This understanding of superposition dissolves the paradox of the Schrödinger's cat. The proposed theoretical model of a free particle with three orthogonal velocity components also provides a possible and consistent mechanism for the generation of particle spin which therefore supports the model. An experiment to further verify or falsify the theoretical model will be proposed in a later paper. A crucial difference between the textbook treatment of a free particle and the theoretical model here is that the former artificially and unnecessarily only allows the Laplacian in the Schrödinger equation to operate in the translational direction (thus generating plane waves) while the treatment in this paper allows the Laplacian to operate fully and therefore properly in all three dimensions. The theoretical model, when verified by experiment, can lead to a new interpretation of quantum mechanics.
Fortress Press eBooks, 2010
The paper by Einstein, Podolsky and Rosen (1935) is rigorously critiqued but its major implicatio... more The paper by Einstein, Podolsky and Rosen (1935) is rigorously critiqued but its major implication is explicitly brought out – non-determinism implies non-locality. This implication and Bell’s theorem (with its associated experiments) are used to logically identify the possible sets of universes to which our universe can theoretically belong – the set of universes with non-deterministic non-locality and the set of universes with deterministic non-locality. The Pilot Wave Theory, a deterministic non-local theory and therefore a theoretically possible theory to describe our universe, is presented and legitimate questions and difficulties are raised about this theory. An alternative theory named Wave Surfing Theory, which is non-deterministic and non-local in nature, is presented. This theory is shown to be consistent with ten observed quantum phenomena: the de Broglie relation between momentum and wavelength, the Planck-Einstein relation between energy and frequency, non-locality, Born’s rule, spin angular momentum, wavy interference pattern of the two-slit experiment, replacement of the interference pattern by two localised density distributions at measurement, discrete nature of particles detected on detection screen, tunnelling and reduction of mass/inertia concomitant with production of energy in nuclear fusion and fission. An interpretation of probability density and the related definition of measurement are proposed. At a measurement event, it is proposed that there is an exchange of momentum between the measured particle and the measuring agent. The domain of the validity of the Schrödinger equation is also identified with respect to the interpretation of probability density and the definition of measurement. Most of the physical quantities in the Wave Surfing Theory are non-deterministic and all the physical quantities have definite values. The theory therefore avoids the problems of superposition and wave function collapse, and the paradox of the Schrödinger cat, and it avoids other conceptual problems with the ontology of particles. In this theory, a measurement event or a local change of the classical potential will instantaneously cause a wholesale transformation of the wave function and its probability density over the whole relevant spatial domain, rather than a wave function collapse. The theory therefore has the potential to explore the detailed dynamics of particle entanglement and non-locality. Using de Broglie’s relation between momentum and wavelength, the velocity components of a particle can be logically projected into their relativistic forms. Based on these relativistic velocity components, an inexpensive experiment is identified and suggested for verifying or falsifying the Wave Surfing Theory. This experiment will also help to verify or falsify the suggested definitions of the mass/inertia and energy of a particle. These two fundamental definitions suitably and fundamentally lead to the well-known expression for rest energy, , without invoking electromagnetism, but they require verification or falsification by the suggested experiment. If the experiment verifies the Wave Surfing Theory, then possible future studies include the full relativistic version of the theory with all its details, its relationships with Quantum Field Theory (particularly on annihilation and creation of particles) and the Standard Model, dark matter, particle entanglement and dark energy.
Transformation: An International Journal of Holistic Mission Studies, 2006
Transformation: An International Journal of Holistic Mission Studies, 2008
The paper examines the emphasis on knowing the inner life of Jesus by a prominent 19th century Li... more The paper examines the emphasis on knowing the inner life of Jesus by a prominent 19th century Liberal Protestant, and Albert Schweitzer's decisive blow to the Life of Jesus movement at the beginning of the 20th century. It gives critiques to both the former and the latter, and identifies the approach of the Liberal Protestants as ‘subjective’ in two senses. While the subjectivity of an interpreter can pose problems in the interpretation of Jesus, it is maintained that the possibility of knowing some aspects of the subjectivity of Jesus cannot be ruled out a priori. A method of correlation is suggested to give a more objective and connected interpretation of Jesus' outer words/actions and his mind.
Quarterly Journal of the Royal Meteorological Society, 2007
ABSTRACT The two-dimensional dynamics of multicell and unicell squall lines are examined using a ... more ABSTRACT The two-dimensional dynamics of multicell and unicell squall lines are examined using a numerical model. Both types feature a convective jump updraught with extensive, deep, rearward-extending anvils. the multicell case contains travelling convection cells and is unsteady but persistent, whereas the unicell case is quasi-steady.In the multicell case, an extensive density current is produced by the evaporation and drag of rain falling from a succession of convection cells which travel rearwards relative to the density current head. the circulation within the density current is complex and consists of three mutually interactive branches: a rotor, a cold downdraught, and a subsidence region.In the unicell case, a density current is not produced and the updraught is forced by a propagating wave of elevation, generated as an interaction between the updraught, water loading and evaporation in a very localized area.The squall line structure is compared with other models and it is shown that certain propagating two-dimensional tropical and mid-latitude squall lines are dynamically similar, their detailed structure being controlled by the inflow wind profile.The multicell case is compared with a quasi-two-dimensional West African squall line which occurred on 22 June 1981 during the Convection Profonde Tropicale (COPT 81) experiment performed in the northern part of the Ivory Coast. Good agreement is found between the model and the observations, and hence the dynamics of the observed squall line is quantified. the unicell case, in which a density current and conventional downdraughts are absent, has yet to be identified in atmospheric observations.
Journal of the Atmospheric Sciences, 1990
Based on a relativistic model for a quantum particle, the paper proposes a new definition of ener... more Based on a relativistic model for a quantum particle, the paper proposes a new definition of energy which takes into account the additional localised surfing motion of the particle on its phase surface which is perpendicular to its translational motion. The conventional relativistic formula for energy is found to be a limiting case for this new definition of energy when the characteristic parameter in the new energy formula is set to zero. For a particle at rest translationally, the two formulae yield the same energy, but in general for the same non-zero translational velocity they yield different energies, the difference being dependent on the value of the characteristic parameter. A certain kinetic energy range has been theoretically identified where the performances of the conventional formula and the new formula of energy can be best tested against experimental data. The new definition of energy prompts a definition of rest mass, m, which is the surfing momentum of the particle ...
The paper presents an interpretation of quantum mechanics in which a particle’s motion is inheren... more The paper presents an interpretation of quantum mechanics in which a particle’s motion is inherently non-deterministic while it has definite unambiguous momentum and position whose existence is independent of measurement. It is therefore distinct from the Copenhagen Interpretation while it is also distinct from the pilot wave theory in that this interpretation is inherently non-deterministic. This paper paves the way for rigorous investigation into the spins of particles in the succeeding paper.
The preceding paper [1] proposed an alternative interpretation of quantum mechanics which is dist... more The preceding paper [1] proposed an alternative interpretation of quantum mechanics which is distinct from the Copenhagen Interpretation and the pilot wave theory. This alternative interpretation and its associated non-deterministic velocity component are tested here with reference to particle spins. A mechanism for generating particle spins is rigorously identified for the case of a free particle and the case of the hydrogen electron. The mechanism can be generalised for electrons in other atoms and other particles. The incomplete nature of the Schrödinger equation with regard to its inability to incorporate particle spin is demonstrated. The adoption of Born’s rule by the physicist community for interpreting the probability density is seen as implicitly acknowledging the mechanism for generating particle spin but this mechanism was far from being made explicit by that rule. The crucial question of the need for sensitive non-deterministic information input to maintain particle spin...
Wave-Particle Duality, Spin, Mass and Energy1 Damon Wai Kwan So2 Oxford Centre for Mission Studie... more Wave-Particle Duality, Spin, Mass and Energy1 Damon Wai Kwan So2 Oxford Centre for Mission Studies, Woodstock Road, Oxford OX2 6HR. Abstract A previous paper [1] proposed an alternative interpretation of quantum mechanics which is distinct from the Copenhagen Interpretation and the pilot wave theory. This alternative interpretation and its associated nondeterministic surfing velocity on the S (phase) surface are applied here to model point-like entities (particles and photons) with non-deterministic trajectories in the one-slit experiment and the two-slit experiment. The diffraction integral for these point-like entities, as a solution to the Helmholtz equation, is in the same form as the diffraction integral found in optical studies so that the mathematical results in optical studies regarding diffraction and interference patterns can be readily applied to the point-like entities modelled here. The nonrelativistic model for slowly moving particles and the relativistic model for fas...
This book presents a dynamic picture of Jesus in his majestic Lordship and freedom, his humble se... more This book presents a dynamic picture of Jesus in his majestic Lordship and freedom, his humble servanthood and obedience, his compassion for needy humanity in his public ministry, his courageous entry into Jerusalem and his sacrificial love revealed in his death there, his resurrection from the dead and his universal reign. This dynamic picture is related closely to Jesus’ fundamental and underlying relationship with his Father through the Holy Spirit. The concrete expression of that Trinitarian relationship in Jesus’ life, ministry, death, and resurrection is presented in a unified manner, avoiding the pitfall of majoring on only one of these aspects. This holistic and dynamic picture of Jesus in intimate fellowship with his Father through the Spirit gives the readers a valuable glimpse into the mystery of the Trinity and invites them to reflect on what it means to follow Jesus as individuals and as communities in the context of the twenty-first century with its many challenges. Je...
The Benjamin (1968) analysis of a two-fluid density current is extended to include the effect of ... more The Benjamin (1968) analysis of a two-fluid density current is extended to include the effect of vorticity within the current. In the case of constant vorticity, the density-current depth is shown to lie between the limits of half and two-thirds of the channel depth. More general vorticity distributions are also considered, namely those that have : (i) a maximum in the upper and lower regions of the density current ; and (ii) a maximum in the middle of the density current. In the former, as in the case of constant vorticity , density-current structures exist, whereas in the latter, deep overturning circulations predominate which can cause a ' blocking ' of the upstream inflow. A generalized propagation formula which includes the effects of finite depth and rear inflow into the density current is established and the uniqueness issue is considered. The analysis is further extended to a three-fluid system, composed of physically distinct component flows, namely, a density current, an overturning updraught region in upper levels ahead of the density current and an updraught in which the fluid ascends without overturning to its outflow level. Two types of behaviour are identified. First, a symmetric mode in which the density current and the overturning updraught have the same depth and, second, an asymmetric mode with solutions restricted to a certain parameter range. A special case in which the fluids have the same density illustrates the basic dynamics of the problem and also the nature of the vertical transport of momentum.
The datasets by Bertozzi [9] and by Lund and Uggerhøj [10] show that an electron with kinetic ene... more The datasets by Bertozzi [9] and by Lund and Uggerhøj [10] show that an electron with kinetic energy (normalised with respect to its rest energy) near to or greater than 2 is underestimated by Einstein’s generalised formula for the energy of a moving object/particle. Also, the datasets show that the highest kinetic deficit in Einstein’s formula occurs at the data point with the highest kinetic energy or highest speed. This energy deficit or anomaly becomes evident when energy is plotted again speed. It is not so evident vice versa, as is often the case; hence the anomaly was not identified. A new definition of energy incorporating the surfing momentum of a particle on its phase (S) surface is proposed. This new definition predicts or explains the observed energy deficit in Einstein’s generalised formula and can further our understanding of the nature of rest mass, rest energy and massless particles. Using the criterion of least squares, it is shown that the new formula performs bett...
Transformation: An International Journal of Holistic Mission Studies
Based on a relativistic model for a quantum particle, the paper proposes a new definition of ener... more Based on a relativistic model for a quantum particle, the paper proposes a new definition of energy which takes into account the additional localised surfing motion of the particle on its phase surface which is perpendicular to its translational motion. The conventional relativistic formula for energy is found to be a limiting case for this new definition of energy when the characteristic parameter in the new energy formula is set to zero. For a particle at rest translationally, the two formulae yield the same energy, but in general for the same non-zero translational velocity they yield different energies, the difference being dependent on the value of the characteristic parameter. The new definition of energy prompts a definition of rest mass, m, which is the surfing momentum of the particle on its phase surface divided by c. The surfing energy of the particle is its surfing momentum multiplied by c. The surfing energy is therefore given by mc2 which has been conventionally understood as the rest energy. The theoretical analysis therefore shows from the new definition of energy how the link between surfing momentum and mass, and the link between surfing momentum and surfing energy (rest energy), lead to the well known relationship between rest mass and rest energy, without invoking electromagnetism. Surfing energy, though identical to rest energy, affords a more physically intuitive understanding than rest energy because it can be visualised. Surfing energy, validly understood as an internal kinetic energy of the particle, can be converted into other forms of energy which is accompanied by a reduction of the particle’s rest mass due to a simultaneous reduction in its surfing momentum. A certain kinetic energy range has been theoretically identified where the performance of the conventional equation linking energy and velocity (by Einstein) and the performance of the corresponding new equation can be best tested against experimental data. The dataset provided by Lund and Uggerhøj [13] has been used to demonstrate that, for the energy range given by the dataset, the proposed new relationship between kinetic energy and translational velocity is more consistent with the dataset than Einstein’s equation, if one allows for a systematic error in the ToF measurement. More experiments to be performed at the critical energy range will further clarify the comparison. Verification of the new theory will have significant implications for our understanding of dark matter and other questions in physics.
This paper tackles the problem of superposition and the associated paradox of the Schrödinger's c... more This paper tackles the problem of superposition and the associated paradox of the Schrödinger's cat by proposing a theoretical model in which an ontologically discrete free particle in non-deterministic motion with a real trajectory can fulfil the statistical expectation of Born's rule. The suggested expressions or constraints for a set of three orthogonal velocity components of the particle in this model are consistent with these observations: de Broglie's relation between wave length and momentum, particle spin and Born's rule. Two of these velocity components are deterministic but the third component is non-deterministic and is subjected to the overall statistical constraint of Born's rule. These three consistencies with observations give credibility to these velocity components and the theoretical model. Energy is defined by including the quantum potential term and it satisfies the observed Planck-Einstein relation, hence giving credibility to this definition. Superposition is understood as an illusionary phenomenon as a result of the process of averaging the presence of the particle over multiple instants. Just as Richard Feynman commented in his lecture on the two-slit experiment that the average family of America had two and a half children-and such a fictitious family is merely the result of an averaging process and is therefore not real, the spread-out presence of a particle in space at a single instant is merely the result of an averaging process where the multiple pictures of the particle at multiple positions over multiple instants are averaged over those multiple instants to yield an average picture of the particle per instant but the instant in 'per instant' is a fictitious instant which is not a real instant. As the family in '2.5 children per family' is not a real family, so the superposition of the particle per instant is not physically real (because the instant in per instant is fictitious). This understanding of superposition dissolves the paradox of the Schrödinger's cat. The proposed theoretical model of a free particle with three orthogonal velocity components also provides a possible and consistent mechanism for the generation of particle spin which therefore supports the model. An experiment to further verify or falsify the theoretical model will be proposed in a later paper. A crucial difference between the textbook treatment of a free particle and the theoretical model here is that the former artificially and unnecessarily only allows the Laplacian in the Schrödinger equation to operate in the translational direction (thus generating plane waves) while the treatment in this paper allows the Laplacian to operate fully and therefore properly in all three dimensions. The theoretical model, when verified by experiment, can lead to a new interpretation of quantum mechanics.
This paper tackles the problem of superposition and the associated paradox of the Schrödinger's c... more This paper tackles the problem of superposition and the associated paradox of the Schrödinger's cat by proposing a theoretical model in which an ontologically discrete free particle in non-deterministic motion with a real trajectory can fulfil the statistical expectation of Born's rule. The suggested expressions or constraints for a set of three orthogonal velocity components of the particle in this model are consistent with these observations: de Broglie's relation between wave length and momentum, particle spin and Born's rule. Two of these velocity components are deterministic but the third component is non-deterministic and is subjected to the overall statistical constraint of Born's rule. These three consistencies with observations give credibility to these velocity components and the theoretical model. Energy is defined by including the quantum potential term and it satisfies the observed Planck-Einstein relation, hence giving credibility to this definition. Superposition is understood as an illusionary phenomenon as a result of the process of averaging the presence of the particle over multiple instants. Just as Richard Feynman commented in his lecture on the two-slit experiment that the average family of America had two and a half children-and such a fictitious family is merely the result of an averaging process and is therefore not real, the spread-out presence of a particle in space at a single instant is merely the result of an averaging process where the multiple pictures of the particle at multiple positions over multiple instants are averaged over those multiple instants to yield an average picture of the particle per instant but the instant in 'per instant' is a fictitious instant which is not a real instant. As the family in '2.5 children per family' is not a real family, so the superposition of the particle per instant is not physically real (because the instant in per instant is fictitious). This understanding of superposition dissolves the paradox of the Schrödinger's cat. The proposed theoretical model of a free particle with three orthogonal velocity components also provides a possible and consistent mechanism for the generation of particle spin which therefore supports the model. An experiment to further verify or falsify the theoretical model will be proposed in a later paper. A crucial difference between the textbook treatment of a free particle and the theoretical model here is that the former artificially and unnecessarily only allows the Laplacian in the Schrödinger equation to operate in the translational direction (thus generating plane waves) while the treatment in this paper allows the Laplacian to operate fully and therefore properly in all three dimensions. The theoretical model, when verified by experiment, can lead to a new interpretation of quantum mechanics.