First of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens tha...First of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining, is variation in δgtt. The metric tensor variations given by δgrr, δgθθand δgϕϕare negligible, as compared to the variation δgtt. Afterwards, what is referred to by Barbour as emergent duration of time δtis from the Heisenberg Uncertainty principle (HUP) applied to δgttin such a way as to be compared with ΔxΔp≥ℏ2+γ˜∂C∂Vwith V here a volume spatial term and γ˜a complexification strength term and ∂C∂Vinfluence of complexity of physical system being measured in order to obtain a parameterized value for the initial value of an inflaton which we call V0.展开更多
We look at early universe space-time which is characterized by a transition from Pre-Planckian to Planckian space-time. In doing so we also invoke the geometry of Octonionic non-commutative structure and when it break...We look at early universe space-time which is characterized by a transition from Pre-Planckian to Planckian space-time. In doing so we also invoke the geometry of Octonionic non-commutative structure and when it breaks down. Doing so is also equivalent to a speculation given earlier by the author as to the kinetic energy of Pre-Planckian space-time being significantly larger than the Potential energy, which is the opposite of what happens after the onset of Inflation, with the assumption as to how this is justified given in a (Pre- Planckian) Hubble Parameter set as of Equation (16), and we close with a comparison of this proposal with string cosmology, as represented in the 2nd reference in this paper.展开更多
This paper is to address using what a fluctuation of a metric tensor leads to, in Pre Planckian physics, namely . If so then, we pick the conditions for an equality, with a small , to come up with initial temperature,...This paper is to address using what a fluctuation of a metric tensor leads to, in Pre Planckian physics, namely . If so then, we pick the conditions for an equality, with a small , to come up with initial temperature, particle count and entropy affected by initial degrees of freedom in early Universe cosmology. This leads to an initial graviton production due to a minimum magnetic field, as established in our analysis. Which we relate to the inflaton as it initially would be configured and evaluated.展开更多
The quantum gravity problem that the notion of a quantum state, representing the structure of space-time at some instant, and the notion of the evolution of the state, does not get traction, since there are no real “...The quantum gravity problem that the notion of a quantum state, representing the structure of space-time at some instant, and the notion of the evolution of the state, does not get traction, since there are no real “instants”, is avoided by having initial Octonionic geometry embedded in a larger, nonlinear “pilot model” (semi classical) embedding structure. The Penrose suggestion of recycled space time avoiding a “big crunch” is picked as the embedding structure, so as to avoid the “instants” of time issue. Getting Octionic gravity as embedded in a larger, Pilot theory embedding structure may restore Quantum Gravity to its rightful place in early cosmology without the complication of then afterwards “Schrodinger equation” states of the universe, and the transformation of Octonionic gravity to existing space-time is explored via its possible linkage to a new version of the HUP involving metric tensors. We conclude with how specific properties of Octonion numbers algebra influence the structure and behavior of the early-cosmology model. This last point is raised in Section 14, and is akin to a phase transition from Pre-Octonionic geometry, in pre-Planckian space-time, to Octonionic geometry in Planckian space-time. A simple phase transition is alluded to;making this clear is as simple as realizing that Pre-Octonionic is for Pre-Planckian Space-time and Octonionic is for Planckian Space-time. We state that the Standard Model of physics occurs during Planckian Space-time. We also argue that the Standard Model does not apply to Pre Planckian Space-time. This is commensurate with the Octonion number system NOT applying in pre-Planckian space-time, but applying in Plankian space-time. And the last line of Equation (54) gives a minimum time step in pre-Planckian space-time when we do NOT have the Standard Model of physics, or Octonionic Geometry.展开更多
In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. ...In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. the solution in 2012 was that the author stated that quantum measures in 4 dimensions would not work, mandating, if measure theory were used, imbedding in higher dimensions was necessary for a singularity. The idea was to use the methodology of String Theory as to come up with a way out of the impasse if higher dimensions do not exist. We revisit this question, taking into account a derived HUP, for metric tensors if we look at Pre-Planckian space-time introducing a pre-quantum mechanical HUP which may be a way to ascertain a solution not mandating higher dimensions, as well as introducing cautions as to what will disrupt the offered solution. Note that first, measurable spaces allow disjoint sets. Also, that smooth relations alone do not define separability or admit sets Planck’s length, if it exists, is a natural way to get about the “bad effects” of a cosmic singularity at the beginning of space-time evolution, but if a development is to be believed, namely by Stoica in the article, about removing the cosmic singularity as a breakdown point in relativity, there is nothing which forbids space-time from collapsing to a point. Without the use of a Pre Planckian HUP, for metric tensors, the quantum measures in four dimensions break down. We try to ascertain if a Pre Planckian HUP is sufficient to avoid this pathology and also look at if division algebras which can link Octonionic geometry and E8, to Quark spinors, in the standard model and add sufficient definition to the standard model are necessary and sufficient conditions for a metric tensor HUP which may remove this breakdown of the sum rule in the onset of the “Big Bang”.展开更多
We will first of all reference a value of momentum, in the early universe. This is for 3 + 1 dimensions and is important since Wesson has an integration of this momentum with regards to a 5 dimensional parameter inclu...We will first of all reference a value of momentum, in the early universe. This is for 3 + 1 dimensions and is important since Wesson has an integration of this momentum with regards to a 5 dimensional parameter included in an integration of momentum over space which equals a ration of L divided by small l (length) and all these times a constant. The ratio of L over small l is a way of making deterministic inputs from 5 dimensions into the 3 + 1 dimensional HUP. In doing so, we come up with a very small radial component for reasons which due to an argument from Wesson is a way to deterministically fix one of the variables placed into the 3 + 1 HUP. This is a deterministic input into a derivation which is then First of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining, is variation in δg<sub>tt</sub>. The metric tensor variations are given by δg<sub>rr</sub>, δg<sub>θθ</sub> and δg<sub>φφ</sub> are negligible, as compared to the variation δg<sub>tt</sub>. From there the expression for the HUP and its applications into certain cases in the early universe are strictly affected after we take into consideration a vanishingly small r spatial value in how we define δg<sub>tt</sub>.展开更多
This document will from first principles delineate the degree of flatness, or deviations from, in early universe models. We will, afterwards, make comparison with recent results we have looked at concerning metric ten...This document will from first principles delineate the degree of flatness, or deviations from, in early universe models. We will, afterwards, make comparison with recent results we have looked at concerning metric tensor fluctuations and comment upon the role of what early universe gravitational energy may play a role in the presumed deviation from flat space results. Note that N~S<sub>initial(graviton)</sub>~10<sup>37 </sup>will be tied into the presumed results for initial state density, in ways we will comment upon, leading to observations which are supporting the physics given by Equation (26) of this document as with regards to Gravitational waves, from relic conditions. The deviations from flat space may help confirm the conclusions given by Buchert, Carfora, Kolb, and Wiltshire allegedly refuting the claim by Green and Wald that “the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects”, as well as give additional analysis appropriate for adding detail to expanding experimental procedures for investigating non FLRW models such as the Polynomial Inflation models as given by Kobayashi, and Seto, as well as other nonstandard cosmologies, as brought up by Corda, and other researchers. As well as improve upon post Bicep 2 measurements which will avoid GW signatures from interstellar dust, as opposed to relic GW. We hope that our approach may help in the differentiation between different cosmology models. Most importantly, our procedure may help, with refinement of admissible frequency range, avoid the problem of BICEP 2, which had its presumed GW signals from presumed relic conditions identical to dust induced frequencies, as so identified by the Planck collaboration in reference [25] which we comment upon in the conclusion.展开更多
We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration do...We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration does as to the HUP previously derived. In doing so, we will be trying it in our discussion with the earlier work done on the HUP. not equal to zero, constant, but large would frequently imply which would have three dissimilar real valued roots. And the situation with not equal to zero yields more tractable result for which will have implications for the HUP inequality in Pre-Planckian space-time, and buttresses an analysis of a 1 dimensional “time” mapping for emergent VEV (vacuum expectation values).展开更多
文摘First of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining, is variation in δgtt. The metric tensor variations given by δgrr, δgθθand δgϕϕare negligible, as compared to the variation δgtt. Afterwards, what is referred to by Barbour as emergent duration of time δtis from the Heisenberg Uncertainty principle (HUP) applied to δgttin such a way as to be compared with ΔxΔp≥ℏ2+γ˜∂C∂Vwith V here a volume spatial term and γ˜a complexification strength term and ∂C∂Vinfluence of complexity of physical system being measured in order to obtain a parameterized value for the initial value of an inflaton which we call V0.
文摘We look at early universe space-time which is characterized by a transition from Pre-Planckian to Planckian space-time. In doing so we also invoke the geometry of Octonionic non-commutative structure and when it breaks down. Doing so is also equivalent to a speculation given earlier by the author as to the kinetic energy of Pre-Planckian space-time being significantly larger than the Potential energy, which is the opposite of what happens after the onset of Inflation, with the assumption as to how this is justified given in a (Pre- Planckian) Hubble Parameter set as of Equation (16), and we close with a comparison of this proposal with string cosmology, as represented in the 2nd reference in this paper.
文摘This paper is to address using what a fluctuation of a metric tensor leads to, in Pre Planckian physics, namely . If so then, we pick the conditions for an equality, with a small , to come up with initial temperature, particle count and entropy affected by initial degrees of freedom in early Universe cosmology. This leads to an initial graviton production due to a minimum magnetic field, as established in our analysis. Which we relate to the inflaton as it initially would be configured and evaluated.
文摘The quantum gravity problem that the notion of a quantum state, representing the structure of space-time at some instant, and the notion of the evolution of the state, does not get traction, since there are no real “instants”, is avoided by having initial Octonionic geometry embedded in a larger, nonlinear “pilot model” (semi classical) embedding structure. The Penrose suggestion of recycled space time avoiding a “big crunch” is picked as the embedding structure, so as to avoid the “instants” of time issue. Getting Octionic gravity as embedded in a larger, Pilot theory embedding structure may restore Quantum Gravity to its rightful place in early cosmology without the complication of then afterwards “Schrodinger equation” states of the universe, and the transformation of Octonionic gravity to existing space-time is explored via its possible linkage to a new version of the HUP involving metric tensors. We conclude with how specific properties of Octonion numbers algebra influence the structure and behavior of the early-cosmology model. This last point is raised in Section 14, and is akin to a phase transition from Pre-Octonionic geometry, in pre-Planckian space-time, to Octonionic geometry in Planckian space-time. A simple phase transition is alluded to;making this clear is as simple as realizing that Pre-Octonionic is for Pre-Planckian Space-time and Octonionic is for Planckian Space-time. We state that the Standard Model of physics occurs during Planckian Space-time. We also argue that the Standard Model does not apply to Pre Planckian Space-time. This is commensurate with the Octonion number system NOT applying in pre-Planckian space-time, but applying in Plankian space-time. And the last line of Equation (54) gives a minimum time step in pre-Planckian space-time when we do NOT have the Standard Model of physics, or Octonionic Geometry.
文摘In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. the solution in 2012 was that the author stated that quantum measures in 4 dimensions would not work, mandating, if measure theory were used, imbedding in higher dimensions was necessary for a singularity. The idea was to use the methodology of String Theory as to come up with a way out of the impasse if higher dimensions do not exist. We revisit this question, taking into account a derived HUP, for metric tensors if we look at Pre-Planckian space-time introducing a pre-quantum mechanical HUP which may be a way to ascertain a solution not mandating higher dimensions, as well as introducing cautions as to what will disrupt the offered solution. Note that first, measurable spaces allow disjoint sets. Also, that smooth relations alone do not define separability or admit sets Planck’s length, if it exists, is a natural way to get about the “bad effects” of a cosmic singularity at the beginning of space-time evolution, but if a development is to be believed, namely by Stoica in the article, about removing the cosmic singularity as a breakdown point in relativity, there is nothing which forbids space-time from collapsing to a point. Without the use of a Pre Planckian HUP, for metric tensors, the quantum measures in four dimensions break down. We try to ascertain if a Pre Planckian HUP is sufficient to avoid this pathology and also look at if division algebras which can link Octonionic geometry and E8, to Quark spinors, in the standard model and add sufficient definition to the standard model are necessary and sufficient conditions for a metric tensor HUP which may remove this breakdown of the sum rule in the onset of the “Big Bang”.
文摘We will first of all reference a value of momentum, in the early universe. This is for 3 + 1 dimensions and is important since Wesson has an integration of this momentum with regards to a 5 dimensional parameter included in an integration of momentum over space which equals a ration of L divided by small l (length) and all these times a constant. The ratio of L over small l is a way of making deterministic inputs from 5 dimensions into the 3 + 1 dimensional HUP. In doing so, we come up with a very small radial component for reasons which due to an argument from Wesson is a way to deterministically fix one of the variables placed into the 3 + 1 HUP. This is a deterministic input into a derivation which is then First of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining, is variation in δg<sub>tt</sub>. The metric tensor variations are given by δg<sub>rr</sub>, δg<sub>θθ</sub> and δg<sub>φφ</sub> are negligible, as compared to the variation δg<sub>tt</sub>. From there the expression for the HUP and its applications into certain cases in the early universe are strictly affected after we take into consideration a vanishingly small r spatial value in how we define δg<sub>tt</sub>.
文摘This document will from first principles delineate the degree of flatness, or deviations from, in early universe models. We will, afterwards, make comparison with recent results we have looked at concerning metric tensor fluctuations and comment upon the role of what early universe gravitational energy may play a role in the presumed deviation from flat space results. Note that N~S<sub>initial(graviton)</sub>~10<sup>37 </sup>will be tied into the presumed results for initial state density, in ways we will comment upon, leading to observations which are supporting the physics given by Equation (26) of this document as with regards to Gravitational waves, from relic conditions. The deviations from flat space may help confirm the conclusions given by Buchert, Carfora, Kolb, and Wiltshire allegedly refuting the claim by Green and Wald that “the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects”, as well as give additional analysis appropriate for adding detail to expanding experimental procedures for investigating non FLRW models such as the Polynomial Inflation models as given by Kobayashi, and Seto, as well as other nonstandard cosmologies, as brought up by Corda, and other researchers. As well as improve upon post Bicep 2 measurements which will avoid GW signatures from interstellar dust, as opposed to relic GW. We hope that our approach may help in the differentiation between different cosmology models. Most importantly, our procedure may help, with refinement of admissible frequency range, avoid the problem of BICEP 2, which had its presumed GW signals from presumed relic conditions identical to dust induced frequencies, as so identified by the Planck collaboration in reference [25] which we comment upon in the conclusion.
文摘We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration does as to the HUP previously derived. In doing so, we will be trying it in our discussion with the earlier work done on the HUP. not equal to zero, constant, but large would frequently imply which would have three dissimilar real valued roots. And the situation with not equal to zero yields more tractable result for which will have implications for the HUP inequality in Pre-Planckian space-time, and buttresses an analysis of a 1 dimensional “time” mapping for emergent VEV (vacuum expectation values).
