Academia.eduAcademia.edu

Figure 28 – uploaded by James (Jim) E Beichler

See full PDFdownloadDownload figure
oat causing a wake at its forefront. The wake would contribute increased the inertia of the particle (the nertial points absorbed by the particle would raise the overall internal that constitutes the particle higher und steeper in the fourth dimension) as each point in the wake (external space) is overrun by the advancing yarticle/boat. This would be similar to Higgs’ analogy for describing how a Higgs boson is transferred to a sarticle from the Higgs field to increase the mass of the particle while the particle moves point-by-point through space.

Figure 28 oat causing a wake at its forefront. The wake would contribute increased the inertia of the particle (the nertial points absorbed by the particle would raise the overall internal that constitutes the particle higher und steeper in the fourth dimension) as each point in the wake (external space) is overrun by the advancing yarticle/boat. This would be similar to Higgs’ analogy for describing how a Higgs boson is transferred to a sarticle from the Higgs field to increase the mass of the particle while the particle moves point-by-point through space.

Related Figures (49)

But the particle cannot be physically reduced to a point, so the measurement taken as the vice closes on tl particle would be the smallest measurable ‘unit of change’ associated with any given experiment. True uncertainty would go to zero when that outer extended boundary of the particle or the ‘unit of change’ is reached. The radius of that boundary would be proportional to h/4z since we would have a situation whe the surface area of the sphere around the origin point of the axes is 4ar*. This would yield the relationship 4nr’ = kh where k is an as yet unspecified constant of proportionality that would differ for each and every experimental situation. Of course, the quantity of h/4z is already, if not coincidentally, expressed in the uncertainty equations. At that point, the outer boundary of the particle or object being measured would b equal to the smallest possible measure by which the particle or object size could be determined real rather than a true quantum which would appear as a dimensionless point at the axis of a space-time diagram representing the quantum or measuring event. On the other hand, as Ax—0 in this case the corresponding uncertainy Ap—infinity by mathematical Reruns J Reins Peet YOR een, eet ey 8 The quantity Ax—0 actually means that the measuring device being used (a high-energy collision experiment) closes in on the outer material limits of the extended object being measured, rather like a vice clamping down tight on a hard round ball (2e. a proton), rather than implying that the particle itself (the target) occupies or is reduced to a point. If the object beng measured could be reduced to a point, then tha point would represent the center of a space-time axis or diagram and no mote, but in reality the particle is extended aorund the pnojnt.
But the particle cannot be physically reduced to a point, so the measurement taken as the vice closes on tl particle would be the smallest measurable ‘unit of change’ associated with any given experiment. True uncertainty would go to zero when that outer extended boundary of the particle or the ‘unit of change’ is reached. The radius of that boundary would be proportional to h/4z since we would have a situation whe the surface area of the sphere around the origin point of the axes is 4ar*. This would yield the relationship 4nr’ = kh where k is an as yet unspecified constant of proportionality that would differ for each and every experimental situation. Of course, the quantity of h/4z is already, if not coincidentally, expressed in the uncertainty equations. At that point, the outer boundary of the particle or object being measured would b equal to the smallest possible measure by which the particle or object size could be determined real rather than a true quantum which would appear as a dimensionless point at the axis of a space-time diagram representing the quantum or measuring event. On the other hand, as Ax—0 in this case the corresponding uncertainy Ap—infinity by mathematical Reruns J Reins Peet YOR een, eet ey 8 The quantity Ax—0 actually means that the measuring device being used (a high-energy collision experiment) closes in on the outer material limits of the extended object being measured, rather like a vice clamping down tight on a hard round ball (2e. a proton), rather than implying that the particle itself (the target) occupies or is reduced to a point. If the object beng measured could be reduced to a point, then tha point would represent the center of a space-time axis or diagram and no mote, but in reality the particle is extended aorund the pnojnt.
high) would go to infinity.
high) would go to infinity.
The incomplete nature of the non-Riemannian fix
The incomplete nature of the non-Riemannian fix
Reactions of EM and Gravitation to the duality of space ¢ cal = In reality, this duality in the fundamental concept of space and time is or should be reflected in all yhysical theories of nature that involve differentials in space and/or time. The metric represents an -xtended line between two centers of mass or gravity, while the non-symmetric (skew- or anti-symmettic) ortion represents the center of rotation of motion (Clifford’s twist or the later concept of torsion based o1 lis twist) at a point in space. So point and extension differ in the fundamental concept of a rotation. In fact here are two and only two real points or locations in space that naturally emerge in all of physical reality, he centers of mass (gravity) and rotation.
Reactions of EM and Gravitation to the duality of space ¢ cal = In reality, this duality in the fundamental concept of space and time is or should be reflected in all yhysical theories of nature that involve differentials in space and/or time. The metric represents an -xtended line between two centers of mass or gravity, while the non-symmetric (skew- or anti-symmettic) ortion represents the center of rotation of motion (Clifford’s twist or the later concept of torsion based o1 lis twist) at a point in space. So point and extension differ in the fundamental concept of a rotation. In fact here are two and only two real points or locations in space that naturally emerge in all of physical reality, he centers of mass (gravity) and rotation.
If the velocity ‘v’ goes to zero and the mass ‘m7’ is just falling due toward ‘M’ due to gravity, then the Heaviside term goes to zero and does not contribute at all to gravity. Within a more modern context the equation can be rewritten as
If the velocity ‘v’ goes to zero and the mass ‘m7’ is just falling due toward ‘M’ due to gravity, then the Heaviside term goes to zero and does not contribute at all to gravity. Within a more modern context the equation can be rewritten as
Assume each intersection is a dimensionless point in 3-D space and there is no space between points. At each dimensionless point in 4-D space-time a perpendicular line called an A-line extends into the 5th- D and closes back into the point in 4-D space-time. Each A-line or loop is equal and constant length. Since all of the loops are are of equal size in the 5th-D and parallel to each other, they form a cylinder (A-cylindricity) of sorts in the higher dimension. The 5th-D of space-time is not itself closed with respect to 4-D space-time, but each individual point is closed in the higher dimension with respect to 4-TD snace-time. length and each A-line exited three-dimensional space and returned to that some point in three-dimensional space to form a closed loop.
Assume each intersection is a dimensionless point in 3-D space and there is no space between points. At each dimensionless point in 4-D space-time a perpendicular line called an A-line extends into the 5th- D and closes back into the point in 4-D space-time. Each A-line or loop is equal and constant length. Since all of the loops are are of equal size in the 5th-D and parallel to each other, they form a cylinder (A-cylindricity) of sorts in the higher dimension. The 5th-D of space-time is not itself closed with respect to 4-D space-time, but each individual point is closed in the higher dimension with respect to 4-TD snace-time. length and each A-line exited three-dimensional space and returned to that some point in three-dimensional space to form a closed loop.
Furthermore, if the non- or anti-symmettic tensor represents a secondary and unsuspected effect of gravity due to the dualistic nature of space itself, how can electromagnetism and gravity be unified into a single theory? Actually this structure simplifies the unification because gravity-gravnetism is now symmetric with electricity-magnetism. So despite the fact that everything points to a higher fourth dimension of space as well as the (point/extension) duality of space, no one has either attempted or even suspected combining the two methods to unify physics. Yet by recognizing the promise and validity of the hyperspatial model, some scientists have seen it instead as a way t to unify gravity and the quantum. i. re 7 T od as < wt rT>- 1 5 171 . 1 a a ~ Ge In reality, the gravnetic (gravitational) vector potential and the magnetic vector potential A are not intrinsic to the curvature at discrete points in space (in the non-Riemannian-like and tangent space-like fashion), but rather imply that curvature must be extrinsic in a higher dimensional embedding manifold ot space-like structure, thus implying the necessity of a five-dimensional embedding manifold.
Furthermore, if the non- or anti-symmettic tensor represents a secondary and unsuspected effect of gravity due to the dualistic nature of space itself, how can electromagnetism and gravity be unified into a single theory? Actually this structure simplifies the unification because gravity-gravnetism is now symmetric with electricity-magnetism. So despite the fact that everything points to a higher fourth dimension of space as well as the (point/extension) duality of space, no one has either attempted or even suspected combining the two methods to unify physics. Yet by recognizing the promise and validity of the hyperspatial model, some scientists have seen it instead as a way t to unify gravity and the quantum. i. re 7 T od as < wt rT>- 1 5 171 . 1 a a ~ Ge In reality, the gravnetic (gravitational) vector potential and the magnetic vector potential A are not intrinsic to the curvature at discrete points in space (in the non-Riemannian-like and tangent space-like fashion), but rather imply that curvature must be extrinsic in a higher dimensional embedding manifold ot space-like structure, thus implying the necessity of a five-dimensional embedding manifold.
The Evolution of Classical Unified Field Theories a a eS “oe Wilson nat Flint sbylously noticed éhe value of the ‘five- dimensional model for incorporating the quantum into relativity very early on in the development of the quantum theory. Wilson even stated that doing so was the only way forward for physics. Yet this strategy for advancing physics has been downplay by almost all other scientists over the past century. How could this have been? Quite simply, this group c English scientists did not accept the Copenhagen Interpretation of the quantum and quantum mechanics. So their work implied that the quantum and relativity could be easily unified if the Copenhagen Interpretation, which puts up synthetic barriers between the quantum and relativity (discrete versus continuity and determinism versus indeterminism) that cannot be easily overcome as well as discourages attempts to do so. So if the Copenhagen Interpretation is disregarded, the unification of the quantum and relativity should not be that difficult although it should be made within a five-dimensional framework of space-time.
The Evolution of Classical Unified Field Theories a a eS “oe Wilson nat Flint sbylously noticed éhe value of the ‘five- dimensional model for incorporating the quantum into relativity very early on in the development of the quantum theory. Wilson even stated that doing so was the only way forward for physics. Yet this strategy for advancing physics has been downplay by almost all other scientists over the past century. How could this have been? Quite simply, this group c English scientists did not accept the Copenhagen Interpretation of the quantum and quantum mechanics. So their work implied that the quantum and relativity could be easily unified if the Copenhagen Interpretation, which puts up synthetic barriers between the quantum and relativity (discrete versus continuity and determinism versus indeterminism) that cannot be easily overcome as well as discourages attempts to do so. So if the Copenhagen Interpretation is disregarded, the unification of the quantum and relativity should not be that difficult although it should be made within a five-dimensional framework of space-time.
These lines would normally remain parallel in the fourth direction and equidistant apart no matter how far they are extended, which is a direct violation of the very concept of the non-Euclidean geometries that were developed to take into account the possibilities presented by the failed parallel postulate and which does nothing to verify the possible physical reality of the three-dimensional space. by-point) was analyzed, but continuity was not ‘proven’ between any individual points in the three- dimensional extension emanating from a line extending in the fourth direction or between individual discrete points and other such points in the three-dimensional extensions. A first step was made though by Einstein’s proving that the physics in every parallel three-dimensional space displaced along the line in the fourth direction of space would be the same, which is also important. It is only necessary now to prove tha discrete points can be used to construct the continuity of three-dimensional space. © Wee gloss ee oes wee 2 lowe = 2 eee mes Bee esol ve eee wee ela ws lee cm BK Tee eee gee chee Poxeeeet: hie ees ll
These lines would normally remain parallel in the fourth direction and equidistant apart no matter how far they are extended, which is a direct violation of the very concept of the non-Euclidean geometries that were developed to take into account the possibilities presented by the failed parallel postulate and which does nothing to verify the possible physical reality of the three-dimensional space. by-point) was analyzed, but continuity was not ‘proven’ between any individual points in the three- dimensional extension emanating from a line extending in the fourth direction or between individual discrete points and other such points in the three-dimensional extensions. A first step was made though by Einstein’s proving that the physics in every parallel three-dimensional space displaced along the line in the fourth direction of space would be the same, which is also important. It is only necessary now to prove tha discrete points can be used to construct the continuity of three-dimensional space. © Wee gloss ee oes wee 2 lowe = 2 eee mes Bee esol ve eee wee ela ws lee cm BK Tee eee gee chee Poxeeeet: hie ees ll
Each point is equidistant from its contiguous neighbor point
Each point is equidistant from its contiguous neighbor point
and related theories. This problem is ubiquitous such that all of physics and mathematics suffers from this same problem in one form or another, but it is especially crucial for the standard model of the quantum, which is basically a non-geometrical theory that defaults to a Euclidean flat pseudo-geometrical structure for space-time.
and related theories. This problem is ubiquitous such that all of physics and mathematics suffers from this same problem in one form or another, but it is especially crucial for the standard model of the quantum, which is basically a non-geometrical theory that defaults to a Euclidean flat pseudo-geometrical structure for space-time.
* 4 . The halo forms around the galaxy to maintain three-dimensional integrity of the whole and continuity with the rest of the universe. But only local variations from the spherical universe are allowed, thus we ‘observe’ galaxies as part of our three-dimensional surface with the added ‘halos’. cy So in essence, or perhaps ‘quintessence’, when the matter in the galactic rim extends into the fourth dimension it is gaining DE in the form of inertial momentum (my) without the corresponding gain in mass from the universe as a whole as represented by the global curvature. DE, or the gravitational vector potential, exists everywhere in empty space, but when it is bound or restricted inside a particle it becomes or rather ‘is’ active inertia. However, when the DE is constrained or bound into a material particle by spatial cutvature (under quantum conditions) it becomes ot ‘is’ passive inertia. Within one context, DE supplies the extra speed to the stars and systems in the galactic rim, but within another it is extra inertia because it is constrained within the body of the galaxy (local curvature relative to global curvature) by the matter in the
* 4 . The halo forms around the galaxy to maintain three-dimensional integrity of the whole and continuity with the rest of the universe. But only local variations from the spherical universe are allowed, thus we ‘observe’ galaxies as part of our three-dimensional surface with the added ‘halos’. cy So in essence, or perhaps ‘quintessence’, when the matter in the galactic rim extends into the fourth dimension it is gaining DE in the form of inertial momentum (my) without the corresponding gain in mass from the universe as a whole as represented by the global curvature. DE, or the gravitational vector potential, exists everywhere in empty space, but when it is bound or restricted inside a particle it becomes or rather ‘is’ active inertia. However, when the DE is constrained or bound into a material particle by spatial cutvature (under quantum conditions) it becomes ot ‘is’ passive inertia. Within one context, DE supplies the extra speed to the stars and systems in the galactic rim, but within another it is extra inertia because it is constrained within the body of the galaxy (local curvature relative to global curvature) by the matter in the
The halo is like a shadow or mirror image of the galactic core due to the centrifugal force (equal and opposite) of the gravity of the rest of the universe represented by This dependence is exactly what is observed as shown in the graph below. It should be quite clear from this equation that the contribution of the global curvature to the total force in the form of the kinetic energy (applied dark energy) increases as a function of the radius and the slowing of gravitationally derived speed from the central body or local curvature (gravitational field). As each star or star system is added to the galaxy and orbits the galactic core, it has a component of gravitationally derived velocity as well as an extra component that corresponds to the four-dimensionality of the galactic plane. This dependence is exactly what is observed as shown in the graph below. The curves representing the scalar and vector potential contributions to energy add to give the speed curve for the Andromeda galaxy, as shown. The kinetic energy gained from the vector potential graphs as a straight line running from the zero point (galactic center) to the edge of the galactic rim, supplying exactly the kinetic energy needed to explain the constant speeds of stars and star systems around the galactic core. Nearer the galactic core, the vector potential correction to speed is masked or dominated by the stronger
The halo is like a shadow or mirror image of the galactic core due to the centrifugal force (equal and opposite) of the gravity of the rest of the universe represented by This dependence is exactly what is observed as shown in the graph below. It should be quite clear from this equation that the contribution of the global curvature to the total force in the form of the kinetic energy (applied dark energy) increases as a function of the radius and the slowing of gravitationally derived speed from the central body or local curvature (gravitational field). As each star or star system is added to the galaxy and orbits the galactic core, it has a component of gravitationally derived velocity as well as an extra component that corresponds to the four-dimensionality of the galactic plane. This dependence is exactly what is observed as shown in the graph below. The curves representing the scalar and vector potential contributions to energy add to give the speed curve for the Andromeda galaxy, as shown. The kinetic energy gained from the vector potential graphs as a straight line running from the zero point (galactic center) to the edge of the galactic rim, supplying exactly the kinetic energy needed to explain the constant speeds of stars and star systems around the galactic core. Nearer the galactic core, the vector potential correction to speed is masked or dominated by the stronger
Given the calculated value of the halo curvature, the amount of curvature at the center of the galaxy could then be found by simple triangulation.
Given the calculated value of the halo curvature, the amount of curvature at the center of the galaxy could then be found by simple triangulation.
No anti-particles (oppositely directed bumps and hills) are created while the creation of protons and electrons slows expansion enough to end the inflationary period
No anti-particles (oppositely directed bumps and hills) are created while the creation of protons and electrons slows expansion enough to end the inflationary period
The quantum nature of the universe is reflected in the first equation as a fundamental property of the space-time continuum, but exactly how to apply the quantum concept to the single field and space-time curvature still needs some explanation. Klein had the right idea when he tried to quantize Kaluza’s five- dimensional extension of general relativity. If you quantize the extension along the fifth direction of space-
The quantum nature of the universe is reflected in the first equation as a fundamental property of the space-time continuum, but exactly how to apply the quantum concept to the single field and space-time curvature still needs some explanation. Klein had the right idea when he tried to quantize Kaluza’s five- dimensional extension of general relativity. If you quantize the extension along the fifth direction of space-
ime (or the fourth direction of space), then the lower four dimensions of space-time (or three dimensions of space) will also be quantized. However, since Klein was working with the Kaluza model, which was vast »ver-restricted in its application of a higher embedding geometry, Klein’s model was subsequently over- estricted. The fact that what happens along the extra dimension of space also affects the lower three limensions of space is also implied in the Einstein-Bergmann model of Kaluza’s work, although they did 1ot apply this to the quantum as did Klein. Instead, Einstein added a footnote that he and Rosen had ittempted to explain particles, unsuccessfully, on the basis of the Einstein-Rosen Bridge. If instead, we go back to the Heaviside equation or its modern equivalent, quantization becomes a very ~~ “ am The implications of this simple quantization are quite profound. First of all, the dark matter halo round galaxies, represented by the second term in the equation, can now be viewed as a wave interactio: superposition of outgoing quantized gravity waves from the core mass due to the changes in velocity of 1 orbiting masses interacting with the incoming gravity wave (represented by I in “/sec”’ units). In this cas he quantity TP could be likened to David Bohm’s concept of the quantum potential field which is a yackeround field consisting of all possible quantum waves. Secondly, this equation indicates that the stat sravity view of F = mg cannot be quantized in any normal way within the three-dimensional space wher 10rmal gravity acts. This implies that gravity can only be quantized within the higher embedding dimenst “rom a purely static point-of-view, normal gravity is purely structural in our world while the quantum mmediately invokes an interaction which is wholly dynamical and non-structural except in the fact that i changes structure through the interaction.
ime (or the fourth direction of space), then the lower four dimensions of space-time (or three dimensions of space) will also be quantized. However, since Klein was working with the Kaluza model, which was vast »ver-restricted in its application of a higher embedding geometry, Klein’s model was subsequently over- estricted. The fact that what happens along the extra dimension of space also affects the lower three limensions of space is also implied in the Einstein-Bergmann model of Kaluza’s work, although they did 1ot apply this to the quantum as did Klein. Instead, Einstein added a footnote that he and Rosen had ittempted to explain particles, unsuccessfully, on the basis of the Einstein-Rosen Bridge. If instead, we go back to the Heaviside equation or its modern equivalent, quantization becomes a very ~~ “ am The implications of this simple quantization are quite profound. First of all, the dark matter halo round galaxies, represented by the second term in the equation, can now be viewed as a wave interactio: superposition of outgoing quantized gravity waves from the core mass due to the changes in velocity of 1 orbiting masses interacting with the incoming gravity wave (represented by I in “/sec”’ units). In this cas he quantity TP could be likened to David Bohm’s concept of the quantum potential field which is a yackeround field consisting of all possible quantum waves. Secondly, this equation indicates that the stat sravity view of F = mg cannot be quantized in any normal way within the three-dimensional space wher 10rmal gravity acts. This implies that gravity can only be quantized within the higher embedding dimenst “rom a purely static point-of-view, normal gravity is purely structural in our world while the quantum mmediately invokes an interaction which is wholly dynamical and non-structural except in the fact that i changes structure through the interaction.
Each loop is not connected to the other loops outside of the normal three-dimensional point-to-point connection mistakenly assumed and thus afforded by the intrinsic nature of the space-time continuum. In other words, Kaluza utilized a higher embedding dimension, but mysteriously retained the intrinsic nature of space-time curvature. Thus he used a fundamentally flawed mixed intrinsic/extrinsic model of physical reality. Klein’s idea that quantification in the fifth-direction of space will quantize the lower four- dimensional space-time is valid, but only under the newly specified geometrical conditions that render our normal three-dimensional space real. Quantizing surfaces point-by-point into the single field
Each loop is not connected to the other loops outside of the normal three-dimensional point-to-point connection mistakenly assumed and thus afforded by the intrinsic nature of the space-time continuum. In other words, Kaluza utilized a higher embedding dimension, but mysteriously retained the intrinsic nature of space-time curvature. Thus he used a fundamentally flawed mixed intrinsic/extrinsic model of physical reality. Klein’s idea that quantification in the fifth-direction of space will quantize the lower four- dimensional space-time is valid, but only under the newly specified geometrical conditions that render our normal three-dimensional space real. Quantizing surfaces point-by-point into the single field
Each intersection represents a dimensionless point in 3-D space and there is no space between points
Each intersection represents a dimensionless point in 3-D space and there is no space between points
The geometrical points in space or space-time about which the quantum would then be considered action or actionable points in space around which the fundamental unit of change determined the quantized three- dimensional ‘sheet’ that is our experiential material world.
The geometrical points in space or space-time about which the quantum would then be considered action or actionable points in space around which the fundamental unit of change determined the quantized three- dimensional ‘sheet’ that is our experiential material world.
Since the higher dimension is extended to at least as great a distance as the other three dimensions of space (the Einstein radius of the universe), the final quantum number would be nearly infinity in this case. The normal laws and theories of physics that apply in three-dimensional space would be strictly limited to the three-dimensional ‘sheets’. However, the only three-dimensional ‘sheet’ that is characterized by curvature is the primary or fundamental ‘sheet’ (quantum ground state of n=1) so while the theories and laws of physics influence only three-dimensional extension within the ‘sheets’, the laws must be modified for non-ground This quantizes the space-time curvature and unifies the space-time continuum of general relativity and the quantum world. The fundamental ‘sheet’ where the single field is on average densest would account for the n=1 quantum state or ground state of a static universe defined by its static curvature, T,, = G,,. However, higher quantum states can be attained dynamically on a point-by-point basis. Higher quantum states, for n=2 to n = nearly infinity, would appear like pages in a book stacked one on top of the other both above and below the primary n=1 ‘sheet’.
Since the higher dimension is extended to at least as great a distance as the other three dimensions of space (the Einstein radius of the universe), the final quantum number would be nearly infinity in this case. The normal laws and theories of physics that apply in three-dimensional space would be strictly limited to the three-dimensional ‘sheets’. However, the only three-dimensional ‘sheet’ that is characterized by curvature is the primary or fundamental ‘sheet’ (quantum ground state of n=1) so while the theories and laws of physics influence only three-dimensional extension within the ‘sheets’, the laws must be modified for non-ground This quantizes the space-time curvature and unifies the space-time continuum of general relativity and the quantum world. The fundamental ‘sheet’ where the single field is on average densest would account for the n=1 quantum state or ground state of a static universe defined by its static curvature, T,, = G,,. However, higher quantum states can be attained dynamically on a point-by-point basis. Higher quantum states, for n=2 to n = nearly infinity, would appear like pages in a book stacked one on top of the other both above and below the primary n=1 ‘sheet’.
This is why Kaluza’s cut-transformation which is the mathematical equivalent to cutting a splice across the three-dimensional ‘sheet’ perpendicular to the fourth direction (and thus around the particles three- dimensional boundary) yields electromagnetism. a strain in the three-dimensional space surrounding the particle that science observes and interprets as the electrical field.
This is why Kaluza’s cut-transformation which is the mathematical equivalent to cutting a splice across the three-dimensional ‘sheet’ perpendicular to the fourth direction (and thus around the particles three- dimensional boundary) yields electromagnetism. a strain in the three-dimensional space surrounding the particle that science observes and interprets as the electrical field.
Whereas points through the surface from point-to-point between such bound like particles would be quite weak even though it transmits the point-by-point ‘stress’ of stretching in the higher expanded fourth dimension of space to the outer surface of the particle in three-dimension space. Obviously, these two internal forces that are the geometrical or structural equivalents to the outer forces of strains associated with the gravity and electric fields are just the strong nuclear force (or field) and the weak nuclear force (or field). This structural switch of roles, whereby the external weak force (gravity) becomes the internal strong force and vice versa, explains exactly how and why the internal weak nuclear force has become associated with the stronger external force of electricity and recast as the electro-weak force in earlier unification schemes. However, a great deal more physics is now implied by the geometrical structure of space-time curvature. Within the particle, the surface of curvature and the point-by-point stretching stress due to expansion in the fourth direction change roles in a sense. The internal particle ‘force’ due to the surface tension becomes by far the stronger of the two internal particles ‘forces’. While a particle is outwardly spherical in three-dimensional space, it is inwardly three-dimensional surface an exponentially curved in the fourth direction of space which would form a strong surface to surface ‘force’ of attraction with another like patticle.
Whereas points through the surface from point-to-point between such bound like particles would be quite weak even though it transmits the point-by-point ‘stress’ of stretching in the higher expanded fourth dimension of space to the outer surface of the particle in three-dimension space. Obviously, these two internal forces that are the geometrical or structural equivalents to the outer forces of strains associated with the gravity and electric fields are just the strong nuclear force (or field) and the weak nuclear force (or field). This structural switch of roles, whereby the external weak force (gravity) becomes the internal strong force and vice versa, explains exactly how and why the internal weak nuclear force has become associated with the stronger external force of electricity and recast as the electro-weak force in earlier unification schemes. However, a great deal more physics is now implied by the geometrical structure of space-time curvature. Within the particle, the surface of curvature and the point-by-point stretching stress due to expansion in the fourth direction change roles in a sense. The internal particle ‘force’ due to the surface tension becomes by far the stronger of the two internal particles ‘forces’. While a particle is outwardly spherical in three-dimensional space, it is inwardly three-dimensional surface an exponentially curved in the fourth direction of space which would form a strong surface to surface ‘force’ of attraction with another like patticle.
in free space these four-dimensional extensions become the magnetic vector potentials, Dark Energy and shotons depending on the characteristics of any given situation, but when packaged under the metric curvature surface they become inertia and the stress source of the magnetic field strength that manifests in ither moving or stationary particles. If a frve-dimensional space-time continuum representing the single ield is used to interpret Einstein’s equation then no additional term is necessary for Dark Matter, since it 1: ncorporated into the anti-symmetrical portion of the complex tensor. The additional anti-symmetric term iso results in a ‘twist’ in each dimensionless point in three-dimensional space as opposed to the symmetric erm of the tensor which represents the normal Riemannian metric or extension-based geometry of space- ime curvature in the higher embedding dimension of space. vs oa | te, ie ye oF sas a a Y a | te, a cf TT. 1m . Pa 7 The additional or anti-symmetric term — Einstein called it a non-symmetric form in his final attempt to develop a unified field theory — represents a point-geometry as opposed to the normal Riemannian metric, which is an extension-geometry. This point-geometty can account for Dark Energy, inertia, the magnetic vector potential and photons, all of which are represented as points in three-dimensional space extended in the fourth dimension of space as one-dimensional lines (Kaluza’s A-lines).
in free space these four-dimensional extensions become the magnetic vector potentials, Dark Energy and shotons depending on the characteristics of any given situation, but when packaged under the metric curvature surface they become inertia and the stress source of the magnetic field strength that manifests in ither moving or stationary particles. If a frve-dimensional space-time continuum representing the single ield is used to interpret Einstein’s equation then no additional term is necessary for Dark Matter, since it 1: ncorporated into the anti-symmetrical portion of the complex tensor. The additional anti-symmetric term iso results in a ‘twist’ in each dimensionless point in three-dimensional space as opposed to the symmetric erm of the tensor which represents the normal Riemannian metric or extension-based geometry of space- ime curvature in the higher embedding dimension of space. vs oa | te, ie ye oF sas a a Y a | te, a cf TT. 1m . Pa 7 The additional or anti-symmetric term — Einstein called it a non-symmetric form in his final attempt to develop a unified field theory — represents a point-geometry as opposed to the normal Riemannian metric, which is an extension-geometry. This point-geometty can account for Dark Energy, inertia, the magnetic vector potential and photons, all of which are represented as points in three-dimensional space extended in the fourth dimension of space as one-dimensional lines (Kaluza’s A-lines).
we Each time the curvature in the fourth direction of space drops by the ‘effective width’ of three-dimensional space (it experiences a quantum drop of ryx or about r,/137) such an equilibrium position is established. This structure turns the continuously sloping curvature into energy ‘steps’ on which the electrons move up and down the curvature as they absorb and emit energy in the form of electromagnetic waves. These equilibrium positions occur at distances of n°R, from the center of the nucleus where n=1, 2, .3 and so on. The quantity R, is the Bohr radius of the hydrogen atom and is equivalent to h/2xm,ca or 5.29 x 107" meters. These orbital positions or steps end when the curvature from the nucleus merges with the collective The prescribed — allowed or restricted — electron orbits already exist structurally in the space (along the urvatute) surrounding the nucleus before the electron jumps into (or out of) another orbital position. In ne sense the positions are etched into the curvature in the local space near nuclei by the quantum onditions of existence, but in another sense they are the product of a physical negotiation between the ucleus and the orbiting electrons. Otherwise, they are virtual until an electron falls into any particular orbit. ‘his point would never have been made with regard to previous theories or theoretical models of the orbits, yhich Bohr only defined after the fact by electromagnetic and quantum considerations alone. The positions where the orbits occur are gravitational (curvature) equilibrium positions between the en |e | a ae ae a: cn fe) a ae ae a) ee ae ee oe Te ae en (i rn i es) erie, a ae
we Each time the curvature in the fourth direction of space drops by the ‘effective width’ of three-dimensional space (it experiences a quantum drop of ryx or about r,/137) such an equilibrium position is established. This structure turns the continuously sloping curvature into energy ‘steps’ on which the electrons move up and down the curvature as they absorb and emit energy in the form of electromagnetic waves. These equilibrium positions occur at distances of n°R, from the center of the nucleus where n=1, 2, .3 and so on. The quantity R, is the Bohr radius of the hydrogen atom and is equivalent to h/2xm,ca or 5.29 x 107" meters. These orbital positions or steps end when the curvature from the nucleus merges with the collective The prescribed — allowed or restricted — electron orbits already exist structurally in the space (along the urvatute) surrounding the nucleus before the electron jumps into (or out of) another orbital position. In ne sense the positions are etched into the curvature in the local space near nuclei by the quantum onditions of existence, but in another sense they are the product of a physical negotiation between the ucleus and the orbiting electrons. Otherwise, they are virtual until an electron falls into any particular orbit. ‘his point would never have been made with regard to previous theories or theoretical models of the orbits, yhich Bohr only defined after the fact by electromagnetic and quantum considerations alone. The positions where the orbits occur are gravitational (curvature) equilibrium positions between the en |e | a ae ae a: cn fe) a ae ae a) ee ae ee oe Te ae en (i rn i es) erie, a ae
This equation readily implies a quantum structure for the orbits such that
This equation readily implies a quantum structure for the orbits such that
The ‘sheet’ which serves as our common three-dimensional space is represented by principle quantum number one. The ‘sheet’ curves spherically in the macroscopic domain to render the Riemannian curvature of our three-dimensional universe as a whole as proposed by general relativity, while there are three basic forms of curvature in the smallest possible local portions of the ‘sheet’ at the quantum level. They define the primary elementary particles.
The ‘sheet’ which serves as our common three-dimensional space is represented by principle quantum number one. The ‘sheet’ curves spherically in the macroscopic domain to render the Riemannian curvature of our three-dimensional universe as a whole as proposed by general relativity, while there are three basic forms of curvature in the smallest possible local portions of the ‘sheet’ at the quantum level. They define the primary elementary particles.
No anti-particles (oppositely directed bumps and hills) are created while the creation of protons and electrons slows expansion enough to end the inflationary period
No anti-particles (oppositely directed bumps and hills) are created while the creation of protons and electrons slows expansion enough to end the inflationary period
Under those special conditions where a gamma ray of the correct energy comes close to a nucleus (or other object corresponding to sharply curved space) and actually surrounds the nucleus (touches all sides of the nucleus simultaneously) the quantum stress in the space-time continuum creates the particle and its anti- particle. Of course the last condition is having the proper energy to create the curvature in the ‘sheet’, so curvature packages energy in a sense. This process occurs because the ‘photon’ which is equivalent to an ‘A. line’ or longitudinal portion of the light wave cannot exist at two different places in three-dimensional space simultaneously, such as both sides of the nucleus simultaneously. So, pair production could not have occutred before the inflationary period ended with the creation of elementary particles and can only occur afterwards when the proper quantum and geometrical conditions are met. vn wal El Sd a | - fe = Pe og 7 * oe 7 <: 1 , 2 Wa ca | Pe lost as gamma rays that have no curvature. The annihilation works like opposing wave pulses traveling in opposite directions along a single tightly stretched string. The only difference is that the two pulses in the string cancel each other only momentarily and the energy that they carry continues as before and the pulses reemerge after the collision still traveling as they were before they collided. Annihilation is the same as the oppositely directed pulses cancelling out, however, unlike the pulses in the string the particles covert to energy when they make contact and thus disappear. Pair production creatino anti-narticle/narticle naires onerates in the onnosite wav and could not have
Under those special conditions where a gamma ray of the correct energy comes close to a nucleus (or other object corresponding to sharply curved space) and actually surrounds the nucleus (touches all sides of the nucleus simultaneously) the quantum stress in the space-time continuum creates the particle and its anti- particle. Of course the last condition is having the proper energy to create the curvature in the ‘sheet’, so curvature packages energy in a sense. This process occurs because the ‘photon’ which is equivalent to an ‘A. line’ or longitudinal portion of the light wave cannot exist at two different places in three-dimensional space simultaneously, such as both sides of the nucleus simultaneously. So, pair production could not have occutred before the inflationary period ended with the creation of elementary particles and can only occur afterwards when the proper quantum and geometrical conditions are met. vn wal El Sd a | - fe = Pe og 7 * oe 7 <: 1 , 2 Wa ca | Pe lost as gamma rays that have no curvature. The annihilation works like opposing wave pulses traveling in opposite directions along a single tightly stretched string. The only difference is that the two pulses in the string cancel each other only momentarily and the energy that they carry continues as before and the pulses reemerge after the collision still traveling as they were before they collided. Annihilation is the same as the oppositely directed pulses cancelling out, however, unlike the pulses in the string the particles covert to energy when they make contact and thus disappear. Pair production creatino anti-narticle/narticle naires onerates in the onnosite wav and could not have
The collision thus results in an inward pressure of -1/3 along the direction of motion and outward stresses of +2/3 and +2/3 of the electrical charge along the remaining two dimensions or directions of space inside the target proton. This configuration thus accounts for the —1/3, +2/3 and +2/3 electrical charge of ‘quarks’ from which the proton is constructed according to the Standard Model. This dimensional model of ‘quarks’ also explains why ‘quarks’ can never be found outside of the particles and nuclei in which they reside, solving one of the major dilemmas associated with ‘quark’ theory. TH: 2d so anche: bon ldbin “SAaandél? Bimdel weedbizre Geneiinwe méetendiimnd wl the donde ohEo I ole rteien| -~-Lhnéene
The collision thus results in an inward pressure of -1/3 along the direction of motion and outward stresses of +2/3 and +2/3 of the electrical charge along the remaining two dimensions or directions of space inside the target proton. This configuration thus accounts for the —1/3, +2/3 and +2/3 electrical charge of ‘quarks’ from which the proton is constructed according to the Standard Model. This dimensional model of ‘quarks’ also explains why ‘quarks’ can never be found outside of the particles and nuclei in which they reside, solving one of the major dilemmas associated with ‘quark’ theory. TH: 2d so anche: bon ldbin “SAaandél? Bimdel weedbizre Geneiinwe méetendiimnd wl the donde ohEo I ole rteien| -~-Lhnéene
Yet how can this be so? Quite beyond the obvious question of what is a one-dimensional string and how could it vibrate (?) within the one dimension that it supposedly occupies, the Calabi-Yau bundles fill ‘discrete’ points in space for which no simple connection or connecting property has ever been defined. That is why there are literally millions upon millions of possible different superstring theories. You can put
Yet how can this be so? Quite beyond the obvious question of what is a one-dimensional string and how could it vibrate (?) within the one dimension that it supposedly occupies, the Calabi-Yau bundles fill ‘discrete’ points in space for which no simple connection or connecting property has ever been defined. That is why there are literally millions upon millions of possible different superstring theories. You can put
The distance does not really seem to matter, big or small, since its only purpose is to weaken the effect of the gravitons traveling between the two branes. The bulk seems to have no other purpose than the convenience it affords the model by accounting ‘or the distance between the two branes. The bulk seems to be no more than a mathematical device that w only mandated to justify the distance between the two branes. The branes themselves have no other featur han the fact that they are platforms upon which to place material reality, at least in the case of the primary ot real-world brane. Unlike a normal membrane in three-dimensional space, the branes seem to be one- sided and the single side of each brane is facing the other at a constant distance. In one version of the Randall-Sundrum (RS) Braneworld, dubbed RS-1, the branes are a few centimeters apart, while they are -xtremely distant, but not quite infinitely far apart, in RS-2. In still another version, the RS-1 branes are a rety large distance from one another and infinitely far apart in RS-2.
The distance does not really seem to matter, big or small, since its only purpose is to weaken the effect of the gravitons traveling between the two branes. The bulk seems to have no other purpose than the convenience it affords the model by accounting ‘or the distance between the two branes. The bulk seems to be no more than a mathematical device that w only mandated to justify the distance between the two branes. The branes themselves have no other featur han the fact that they are platforms upon which to place material reality, at least in the case of the primary ot real-world brane. Unlike a normal membrane in three-dimensional space, the branes seem to be one- sided and the single side of each brane is facing the other at a constant distance. In one version of the Randall-Sundrum (RS) Braneworld, dubbed RS-1, the branes are a few centimeters apart, while they are -xtremely distant, but not quite infinitely far apart, in RS-2. In still another version, the RS-1 branes are a rety large distance from one another and infinitely far apart in RS-2.
The bulk can then be closed and defined as a single-polar Riemannian embedding manifold. If curvature is then returned to the primary ‘sheet’, the Randall-Sundrum model corresponds quite nicely with the single field model which has been developed within this paper. This correlation is important because it demonstrates that other scientists, even when they are working from false premises, are slowly approaching the same model as here proposed. ptt 17 wine oe
The bulk can then be closed and defined as a single-polar Riemannian embedding manifold. If curvature is then returned to the primary ‘sheet’, the Randall-Sundrum model corresponds quite nicely with the single field model which has been developed within this paper. This correlation is important because it demonstrates that other scientists, even when they are working from false premises, are slowly approaching the same model as here proposed. ptt 17 wine oe
Related topics:
Mathematical PhysicsGeometry And TopologyAlgebraic GeometryNon Euclidean GeometryPhysicsTheoretical PhysicsElementary Particle PhysicsNuclear PhysicsQuantum PhysicsStellar Astrophysics
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved