The "Jerusalem Cube" and "Jerusalem Square" fractals were first put online by the author in 2011,... more The "Jerusalem Cube" and "Jerusalem Square" fractals were first put online by the author in 2011, and have since gained a degree of popularity. This paper documents the background to their discovery.
Variations in massenergy density due to the presence and relative motion of particulate matter mu... more Variations in massenergy density due to the presence and relative motion of particulate matter must, //on principle//, involve deviations from flat spacetime, and velocity-dependent changes in geometry due to moving masses must then be associated with deviations from Minkowski spacetime, and from the equations of special relativity. Since special relativity's Doppler equations are relativistically unique in being time-symmetrical, //any// Lorentzlike deviation from these equations, //no matter how small//, will introduce time-asymmetry while retaining compliance with the PoR. Any consistent general theory of relativity is therefore required to be asymmetrical with respect to time.
It has been widely assumed that the "arrow of time" problem is a general one, and appears in all ... more It has been widely assumed that the "arrow of time" problem is a general one, and appears in all classical models. A previous paper has shown that the problem does not appear in C19th Newtonian theory. We now show that, within the range of potential relativistic solutions, the "arrow" problem //only// arises with special relativity.
It is widely assumed that the predictions, equations, and descriptions of Newtonian and Einsteini... more It is widely assumed that the predictions, equations, and descriptions of Newtonian and Einsteinian physics are symmetrical with respect to time, prompting the question of how it is that known real-world asymmetries can result from time-symmetrical equations. We identify a fundamental time-asymmetry in the Newtonian Doppler equations, and explore its consequences. The "arrow of time" problem now appears solved for Newtonian theory, but not for theories based on special relativity.
According to the Einstein Equivalence Principle (EEP), any classical curved-spacetime geometrical... more According to the Einstein Equivalence Principle (EEP), any classical curved-spacetime geometrical theory of gravity must reduce to the physics of special relativity over small regions. However, the existence of null solutions means that a flat-spacetime //geometry// does not always equate to a flat-spacetime //physics// - in the "Cliffordian" acoustic-metric counterexample, particles and particle interactions have associated curvatures, the resulting equations are inherently non-SR, and the "flat limit" instead represents the disappearance of any physical objects and observers with which to attempt physics. Any thorough review of relativity theory therefore needs to also consider non-SR solutions.
As demonstrated by Columbia University's "Proto-CIRCUS" plasma containment device, a flexible "Vi... more As demonstrated by Columbia University's "Proto-CIRCUS" plasma containment device, a flexible "Villarceau torus" – an array of interlocking rigid Villarceau-circle coils with adjustable or flexible mountings – can be used to create toroidal fields with variable geometry. We review some basic results relevant to Villarceau circles and fixed and variable Villarceau coils.
Under current theory, Einstein's 1916 general theory of relativity applies the Doppler equations ... more Under current theory, Einstein's 1916 general theory of relativity applies the Doppler equations of special relativity to motion shifts and gravitational shifts, while cosmological shifts are thought to obey a different shift law. However, geometrical considerations require these arguments and equations to be interchangeable. If this geometrical argument is correct, either the cosmological shift law and/or the core relationships of general relativity will need to be modified.
One of the greatest challenges of quantum gravity is the resolution of the black hole information... more One of the greatest challenges of quantum gravity is the resolution of the black hole information paradox, a disagreement between classical and quantum theory as to whether and how massenergy and information can escape a gravitational horizon. The disagreement appears when a classical physics based on Minkowski spacetime is compared to the predictions of quantum mechanics, but does //not// arise with the Newtonian Doppler relationships, or with acoustic metrics. Examining the range of other potential relativistic solutions that might allow classical information-escape across a gravitational horizon, we find that the Newtonian solution appears unique.
When a gravitational source moves, gravitoelectromagnetic effects alter the energy and momentum o... more When a gravitational source moves, gravitoelectromagnetic effects alter the energy and momentum of nearby light, causing the body's motion-shift characteristics to depart from those of special relativity. Since wave theory requires identical equations of motion for “gravitational” and “non-gravitational” bodies, a full gravitational theory cannot reduce perfectly to the physics of special relativity.
Einstein wrote in 1950 that he no longer believed that general relativity should include an enfor... more Einstein wrote in 1950 that he no longer believed that general relativity should include an enforced reduction to flat-spacetime physics. The behaviour of velocity-dependent distortions around a “moving” gravitational source is explored using the principle of relativity, with the resulting descriptions and principles suggesting a more general agreement between the general principle of relativity and the behaviour of particulate-matter physics and quantum mechanics than is normally assumed, evoking W.K. Clifford's concept of “all physics as curvature”. The removal of special relativity from general relativity and the substitution of its Minkowski metric with a relativistic acoustic metric replaces the current layered approach – SR, GR1916, quantum gravity – with a single set of more powerful principles, giving enhanced compatibility (and perhaps even duality) between a suitably revised general theory and quantum mechanics.
This is a basic 3D render of the shape described in "The Koch curve in three dimensions"... more This is a basic 3D render of the shape described in "The Koch curve in three dimensions". The shape is a network of identical edge-connected six-sided polyhedra, each of with can be repeatedly divided into smaller and smaller copies.
A downloadable 3D model of the basic six-faced building block (and bounding polygon) for the &quo... more A downloadable 3D model of the basic six-faced building block (and bounding polygon) for the "Koch curve"-based "Delta" fractal. This is for the benefit of anyone who wants to build the fractal themselves in a 3D modelling program, but would like a ready-made model of the basic unit to get them started. The file is in .stl format, which should load into most 3D modelling and/or rendering programs (click the "View" button on the right to get to the download link).
Isaac Newton is usually associated with the idea of absolute space and time, and with ballistic l... more Isaac Newton is usually associated with the idea of absolute space and time, and with ballistic light-corpuscle arguments. However, Newton was also a proponent of wave/particle duality, and published a "new" variable-density aether model in which light and matter trajectories were either bent by gravitational fields, or deflected by an aether density gradient. Newton's (flawed) aether model can be considered as an early attempt at a curved-space model of gravity.
A downloadable 3D model of the "Koch curve"-based "Delta" fractal, eleventh i... more A downloadable 3D model of the "Koch curve"-based "Delta" fractal, eleventh iteration. The file is in .stl format, which should load into most 3D modelling and/or rendering programs, memory permitting (click the "View" button on the right to get to the download link). I think that the number of triangles in this model should be 6×3^11, so ... somewhere around a million facets? The file's about fifty Meg, but you might find that some programs have trouble building it if your PC has less then four Gig of RAM.
A page from "Alt.Fractals". This diagram demonstrates that starting with a tetrahedron ... more A page from "Alt.Fractals". This diagram demonstrates that starting with a tetrahedron and repeatedly adding half-scale daughter tetrahedra to the free faces doesn't produce a "Koch Snowflake"-type shape, but instead creates a solid whose shape converges on a cube.
Contenido: Parte I Repaso de física: 1) La velocidad del la luz; 2) Gravedad, energía y masa; 3) ... more Contenido: Parte I Repaso de física: 1) La velocidad del la luz; 2) Gravedad, energía y masa; 3) Espacio y tiempo curvos; 4) Relatividad; 5) Catástrofe newtoniana. -- Parte II Doble efecto en movimiento relativo: 6) Cambios dopler; 7) Aparente cambio de longitud en cuerpos en movimiento; 8) Aberración de ángulos; 9) Arrastre de luz de los cuerpos en movimiento. -- Parte III Límites de observación: 10) Mecánica cuántica y observabilidad; 11) Estrellas oscuras y agujeros negros. -- Parte IV Actualizaciones teóricas estándar: 12) ¿Qué tiene de erróneo la Relatividad General?; 13) Matemáticas horribles. -- Parte V Espacio-tiempo plano y Relatividad Especial: 14) Teoría de la Relatividad Especial de Einstein; 15) Y, que hay de erróneo en la Teoría Especial; 16) Evidencia experimental de la Relatividad Especial. -- Parte VI Física del futuro: 17) Cosmologías; 18) Problemas de agujeros de gusano; 19) Ingeniería métrica y trama de unidades. -- Parte VII El factor humano: 20) Limitaciones de...
A downloadable 3D model of the "Koch curve"-based "Delta" fractal, third iter... more A downloadable 3D model of the "Koch curve"-based "Delta" fractal, third iteration. The file is in .stl format, which should load into most 3D modelling and/or rendering programs (click the "View" button on the right to get to the download link).
When an information-carrying lightbeam is (legally) swept across a surface at more than c, simple... more When an information-carrying lightbeam is (legally) swept across a surface at more than c, simple signal-propagation arguments allow the observed behavior of the moving image (or "sprite") to include time-reversal and pair-production effects. A pair-production description also arises if we try to impose some common assumptions of general relativity onto the physics of an indirectly-radiating Eighteenth-Century "dark star". This result seems suspiciously similar to the modern concept of "Hawking radiation".
The "Jerusalem Cube" and "Jerusalem Square" fractals were first put online by the author in 2011,... more The "Jerusalem Cube" and "Jerusalem Square" fractals were first put online by the author in 2011, and have since gained a degree of popularity. This paper documents the background to their discovery.
Variations in massenergy density due to the presence and relative motion of particulate matter mu... more Variations in massenergy density due to the presence and relative motion of particulate matter must, //on principle//, involve deviations from flat spacetime, and velocity-dependent changes in geometry due to moving masses must then be associated with deviations from Minkowski spacetime, and from the equations of special relativity. Since special relativity's Doppler equations are relativistically unique in being time-symmetrical, //any// Lorentzlike deviation from these equations, //no matter how small//, will introduce time-asymmetry while retaining compliance with the PoR. Any consistent general theory of relativity is therefore required to be asymmetrical with respect to time.
It has been widely assumed that the "arrow of time" problem is a general one, and appears in all ... more It has been widely assumed that the "arrow of time" problem is a general one, and appears in all classical models. A previous paper has shown that the problem does not appear in C19th Newtonian theory. We now show that, within the range of potential relativistic solutions, the "arrow" problem //only// arises with special relativity.
It is widely assumed that the predictions, equations, and descriptions of Newtonian and Einsteini... more It is widely assumed that the predictions, equations, and descriptions of Newtonian and Einsteinian physics are symmetrical with respect to time, prompting the question of how it is that known real-world asymmetries can result from time-symmetrical equations. We identify a fundamental time-asymmetry in the Newtonian Doppler equations, and explore its consequences. The "arrow of time" problem now appears solved for Newtonian theory, but not for theories based on special relativity.
According to the Einstein Equivalence Principle (EEP), any classical curved-spacetime geometrical... more According to the Einstein Equivalence Principle (EEP), any classical curved-spacetime geometrical theory of gravity must reduce to the physics of special relativity over small regions. However, the existence of null solutions means that a flat-spacetime //geometry// does not always equate to a flat-spacetime //physics// - in the "Cliffordian" acoustic-metric counterexample, particles and particle interactions have associated curvatures, the resulting equations are inherently non-SR, and the "flat limit" instead represents the disappearance of any physical objects and observers with which to attempt physics. Any thorough review of relativity theory therefore needs to also consider non-SR solutions.
As demonstrated by Columbia University's "Proto-CIRCUS" plasma containment device, a flexible "Vi... more As demonstrated by Columbia University's "Proto-CIRCUS" plasma containment device, a flexible "Villarceau torus" – an array of interlocking rigid Villarceau-circle coils with adjustable or flexible mountings – can be used to create toroidal fields with variable geometry. We review some basic results relevant to Villarceau circles and fixed and variable Villarceau coils.
Under current theory, Einstein's 1916 general theory of relativity applies the Doppler equations ... more Under current theory, Einstein's 1916 general theory of relativity applies the Doppler equations of special relativity to motion shifts and gravitational shifts, while cosmological shifts are thought to obey a different shift law. However, geometrical considerations require these arguments and equations to be interchangeable. If this geometrical argument is correct, either the cosmological shift law and/or the core relationships of general relativity will need to be modified.
One of the greatest challenges of quantum gravity is the resolution of the black hole information... more One of the greatest challenges of quantum gravity is the resolution of the black hole information paradox, a disagreement between classical and quantum theory as to whether and how massenergy and information can escape a gravitational horizon. The disagreement appears when a classical physics based on Minkowski spacetime is compared to the predictions of quantum mechanics, but does //not// arise with the Newtonian Doppler relationships, or with acoustic metrics. Examining the range of other potential relativistic solutions that might allow classical information-escape across a gravitational horizon, we find that the Newtonian solution appears unique.
When a gravitational source moves, gravitoelectromagnetic effects alter the energy and momentum o... more When a gravitational source moves, gravitoelectromagnetic effects alter the energy and momentum of nearby light, causing the body's motion-shift characteristics to depart from those of special relativity. Since wave theory requires identical equations of motion for “gravitational” and “non-gravitational” bodies, a full gravitational theory cannot reduce perfectly to the physics of special relativity.
Einstein wrote in 1950 that he no longer believed that general relativity should include an enfor... more Einstein wrote in 1950 that he no longer believed that general relativity should include an enforced reduction to flat-spacetime physics. The behaviour of velocity-dependent distortions around a “moving” gravitational source is explored using the principle of relativity, with the resulting descriptions and principles suggesting a more general agreement between the general principle of relativity and the behaviour of particulate-matter physics and quantum mechanics than is normally assumed, evoking W.K. Clifford's concept of “all physics as curvature”. The removal of special relativity from general relativity and the substitution of its Minkowski metric with a relativistic acoustic metric replaces the current layered approach – SR, GR1916, quantum gravity – with a single set of more powerful principles, giving enhanced compatibility (and perhaps even duality) between a suitably revised general theory and quantum mechanics.
This is a basic 3D render of the shape described in "The Koch curve in three dimensions"... more This is a basic 3D render of the shape described in "The Koch curve in three dimensions". The shape is a network of identical edge-connected six-sided polyhedra, each of with can be repeatedly divided into smaller and smaller copies.
A downloadable 3D model of the basic six-faced building block (and bounding polygon) for the &quo... more A downloadable 3D model of the basic six-faced building block (and bounding polygon) for the "Koch curve"-based "Delta" fractal. This is for the benefit of anyone who wants to build the fractal themselves in a 3D modelling program, but would like a ready-made model of the basic unit to get them started. The file is in .stl format, which should load into most 3D modelling and/or rendering programs (click the "View" button on the right to get to the download link).
Isaac Newton is usually associated with the idea of absolute space and time, and with ballistic l... more Isaac Newton is usually associated with the idea of absolute space and time, and with ballistic light-corpuscle arguments. However, Newton was also a proponent of wave/particle duality, and published a "new" variable-density aether model in which light and matter trajectories were either bent by gravitational fields, or deflected by an aether density gradient. Newton's (flawed) aether model can be considered as an early attempt at a curved-space model of gravity.
A downloadable 3D model of the "Koch curve"-based "Delta" fractal, eleventh i... more A downloadable 3D model of the "Koch curve"-based "Delta" fractal, eleventh iteration. The file is in .stl format, which should load into most 3D modelling and/or rendering programs, memory permitting (click the "View" button on the right to get to the download link). I think that the number of triangles in this model should be 6×3^11, so ... somewhere around a million facets? The file's about fifty Meg, but you might find that some programs have trouble building it if your PC has less then four Gig of RAM.
A page from "Alt.Fractals". This diagram demonstrates that starting with a tetrahedron ... more A page from "Alt.Fractals". This diagram demonstrates that starting with a tetrahedron and repeatedly adding half-scale daughter tetrahedra to the free faces doesn't produce a "Koch Snowflake"-type shape, but instead creates a solid whose shape converges on a cube.
Contenido: Parte I Repaso de física: 1) La velocidad del la luz; 2) Gravedad, energía y masa; 3) ... more Contenido: Parte I Repaso de física: 1) La velocidad del la luz; 2) Gravedad, energía y masa; 3) Espacio y tiempo curvos; 4) Relatividad; 5) Catástrofe newtoniana. -- Parte II Doble efecto en movimiento relativo: 6) Cambios dopler; 7) Aparente cambio de longitud en cuerpos en movimiento; 8) Aberración de ángulos; 9) Arrastre de luz de los cuerpos en movimiento. -- Parte III Límites de observación: 10) Mecánica cuántica y observabilidad; 11) Estrellas oscuras y agujeros negros. -- Parte IV Actualizaciones teóricas estándar: 12) ¿Qué tiene de erróneo la Relatividad General?; 13) Matemáticas horribles. -- Parte V Espacio-tiempo plano y Relatividad Especial: 14) Teoría de la Relatividad Especial de Einstein; 15) Y, que hay de erróneo en la Teoría Especial; 16) Evidencia experimental de la Relatividad Especial. -- Parte VI Física del futuro: 17) Cosmologías; 18) Problemas de agujeros de gusano; 19) Ingeniería métrica y trama de unidades. -- Parte VII El factor humano: 20) Limitaciones de...
A downloadable 3D model of the "Koch curve"-based "Delta" fractal, third iter... more A downloadable 3D model of the "Koch curve"-based "Delta" fractal, third iteration. The file is in .stl format, which should load into most 3D modelling and/or rendering programs (click the "View" button on the right to get to the download link).
When an information-carrying lightbeam is (legally) swept across a surface at more than c, simple... more When an information-carrying lightbeam is (legally) swept across a surface at more than c, simple signal-propagation arguments allow the observed behavior of the moving image (or "sprite") to include time-reversal and pair-production effects. A pair-production description also arises if we try to impose some common assumptions of general relativity onto the physics of an indirectly-radiating Eighteenth-Century "dark star". This result seems suspiciously similar to the modern concept of "Hawking radiation".
ISBN 0955706831: "With over two hundred and fifty diagrams and additional thumbnails giving const... more ISBN 0955706831: "With over two hundred and fifty diagrams and additional thumbnails giving constructional details, Alt.Fractals is a fascinating browsing experience for the newcomer, a key resource for anyone interested in fractal design, and an essential bookshelf reference for the expert."
A fresh look at relativity theory from first principles, with special emphasis on potential non-S... more A fresh look at relativity theory from first principles, with special emphasis on potential non-SR solutions.
In a two-body problem, special relativity allows us to select an unoccupied exactly intermediate ... more In a two-body problem, special relativity allows us to select an unoccupied exactly intermediate frame for the propagation of light, for which there is no relative Lorentz time dilation or length contraction between object and observer. This gives the standard SR physical outcomes purely as a result of signal-propagation effects. The approach still requires the use of the SR velocity-addition formula.
Special relativity is often presented as making qualitatively novel predictions. We show that the... more Special relativity is often presented as making qualitatively novel predictions. We show that the physical relationships of the 1905 special theory are not radically new: they are necessarily the exact geometric mean of the effects predicted by simple signal-propagation arguments. The "aberration redshift" effect is briefly compared to SR's "transverse redshift" effect.
The idea of unseen "dark matter" is commonly invoked to explain the stronger-than-expected gravit... more The idea of unseen "dark matter" is commonly invoked to explain the stronger-than-expected gravitational properties of galaxies. Despite serious experimental efforts, no independent detection of dark matter is yet considered to have been unambiguously successful. With experimental data failing to confirm more and more dark matter candidates, it is suggested that these "undetected" particles may simply not exist. Instead, a mechanism is proposed, linking expansion with timeflow, that produces similar behaviours without requiring new forms of matter.
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Papers by Eric Baird