David Harness: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=13598
en-us2022 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 17 Jan 2022 07:46:29 GMTMon, 17 Jan 2022 07:46:29 GMTNew applications published by David Harnesshttps://www.maplesoft.com/images/Application_center_hp.jpgDavid Harness: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=13598
4D Spatially-Extended Photon and Electron Quantum Mechanical Observables For All Wavelengths and Energy Levels
https://www.maplesoft.com/applications/view.aspx?SID=154590&ref=Feed
4D Einstein-Maxwell energy density analysis initiates with the fact the quantum composed in the total field formal frame of the electromagnetic stress tensor T𝜇𝜈 of the Einstein equations, requires the negative outward pressure -Pa of quantum energy, e.g., as calculated by Baez and Tatom in "What's the energy density of the vacuum?", to have some nonstandard basis for the missing 4D quantum volumetric wavelength 𝜆 parameterization -- beyond the zero-dimensional (0D) Dirac delta functional 𝜹 imaginary-invisible mathematical point particle QED-Standard Model representations of the quantum mechanical observables. Accordingly, the present nonstandard 4D photon string-like cylindrical coordinate transverse lemniscate expansion of the Poynting energy flux vector over one wavelength renders for all 𝜆 the photon energy and angular momentum ℏ observables. Likewise, a 4D electron spherical coordinate expansion parameterized by the Bohr radii renders for all energy levels n the electron rest mass and angular momentum ℏ/2 observables.<img src="https://www.maplesoft.com/view.aspx?si=154590/4DPhotonElectron_11_4.gif" alt="4D Spatially-Extended Photon and Electron Quantum Mechanical Observables For All Wavelengths and Energy Levels" style="max-width: 25%;" align="left"/>4D Einstein-Maxwell energy density analysis initiates with the fact the quantum composed in the total field formal frame of the electromagnetic stress tensor T𝜇𝜈 of the Einstein equations, requires the negative outward pressure -Pa of quantum energy, e.g., as calculated by Baez and Tatom in "What's the energy density of the vacuum?", to have some nonstandard basis for the missing 4D quantum volumetric wavelength 𝜆 parameterization -- beyond the zero-dimensional (0D) Dirac delta functional 𝜹 imaginary-invisible mathematical point particle QED-Standard Model representations of the quantum mechanical observables. Accordingly, the present nonstandard 4D photon string-like cylindrical coordinate transverse lemniscate expansion of the Poynting energy flux vector over one wavelength renders for all 𝜆 the photon energy and angular momentum ℏ observables. Likewise, a 4D electron spherical coordinate expansion parameterized by the Bohr radii renders for all energy levels n the electron rest mass and angular momentum ℏ/2 observables.https://www.maplesoft.com/applications/view.aspx?SID=154590&ref=FeedMon, 18 Nov 2019 05:00:00 ZDavid HarnessDavid HarnessQuantum Electromagnetic Radiation Pressure Spectrum
https://www.maplesoft.com/applications/view.aspx?SID=154576&ref=Feed
Electromagnetic transverse wave energy density radiation pressure spectrum loglogplot of -Pa vs wavelength λ. Annotations indicate shorter λ are compressive of central cosmological constant vacuum energy density pressure Λ and longer λ rarefactive of Λ. Present 4D Einstein-Maxwell energy density analysis, of the computationally dualistic total field units of energy density and mass density pascals, introduces a nonstandard basis for the missing photon volumetric λ parameterization − missing in the zero-dimensional (0D) Dirac delta functional imaginary-invisible mathematical point particle QED-Standard Model representations of the photon. Equations (1-4) introduce a basis for quantum gravity renormalization, in terms of 4D spacetime curvature via quantum energy density computational duality with quantum mass density.<img src="https://www.maplesoft.com/view.aspx?si=154576/EMtransverseRadPaSpectrumGIF_10_15.gif" alt="Quantum Electromagnetic Radiation Pressure Spectrum" style="max-width: 25%;" align="left"/>Electromagnetic transverse wave energy density radiation pressure spectrum loglogplot of -Pa vs wavelength λ. Annotations indicate shorter λ are compressive of central cosmological constant vacuum energy density pressure Λ and longer λ rarefactive of Λ. Present 4D Einstein-Maxwell energy density analysis, of the computationally dualistic total field units of energy density and mass density pascals, introduces a nonstandard basis for the missing photon volumetric λ parameterization − missing in the zero-dimensional (0D) Dirac delta functional imaginary-invisible mathematical point particle QED-Standard Model representations of the photon. Equations (1-4) introduce a basis for quantum gravity renormalization, in terms of 4D spacetime curvature via quantum energy density computational duality with quantum mass density.https://www.maplesoft.com/applications/view.aspx?SID=154576&ref=FeedFri, 15 Nov 2019 05:00:00 ZDavid HarnessDavid HarnessSimulated Reality Hologram Matrix State Space (click-through calibration check)
https://www.maplesoft.com/applications/view.aspx?SID=95142&ref=Feed
<p>Free PDF:</p>
<p><a href="http://consc.net/online/8.3a">Simulated Reality Hologram Matrix State Space</a></p>
<p>Abstract</p>
<p>New holographic principle approach achieves spacetime, gravitational, electromagnetic uniﬁcation via Maxwell-Einstein gravitoelectromagnetic total stress energy (mass) density tensor Hilbert (4D ± 4Di) hologram interference ﬁeld stationary state domain of universal wave function. S-matrix in-states/out-states eigenvalue range, features (moment of inertia x angular velocity) <strong>SO</strong>(1, 3)<sub>ij</sub> self-adjoint operator integrations, generating Dirac-Noether conserved angular momentum observables in <em>material coordinates</em>. Fundamental quantum continuum equation returns gravitoelectromagnetic spectrum photon <strong>SO</strong>(1, 3)<sub>yy</sub> principle spin axis eigenvalues in units of Maxwell stress tensor pascals. New origin of electron-positron wave-particle mass-charge via energization of <strong>SO</strong>(1, 3)<sub>zz</sub> principle spin axis angular momentum, invariant throughout inertial dynamics of electromagnetic and gravitational ﬁelds being inversely compressive/dispersive of cosmological constant vacuum energy density tensor pressure, according to principle quantum number <em>n</em>. In thought experiment test vs. general theory via <em>pp</em>-waves microlensing problem, wherein light-to-light gravitational attraction is four times matter-to-matter attraction, hypothesis predicts null microlensing result in area general theory known to break down on microscopic scale.</p><img src="https://www.maplesoft.com/view.aspx?si=95142/278203\SRHMSScalSpin2.gif" alt="Simulated Reality Hologram Matrix State Space (click-through calibration check)" style="max-width: 25%;" align="left"/><p>Free PDF:</p>
<p><a href="http://consc.net/online/8.3a">Simulated Reality Hologram Matrix State Space</a></p>
<p>Abstract</p>
<p>New holographic principle approach achieves spacetime, gravitational, electromagnetic uniﬁcation via Maxwell-Einstein gravitoelectromagnetic total stress energy (mass) density tensor Hilbert (4D ± 4Di) hologram interference ﬁeld stationary state domain of universal wave function. S-matrix in-states/out-states eigenvalue range, features (moment of inertia x angular velocity) <strong>SO</strong>(1, 3)<sub>ij</sub> self-adjoint operator integrations, generating Dirac-Noether conserved angular momentum observables in <em>material coordinates</em>. Fundamental quantum continuum equation returns gravitoelectromagnetic spectrum photon <strong>SO</strong>(1, 3)<sub>yy</sub> principle spin axis eigenvalues in units of Maxwell stress tensor pascals. New origin of electron-positron wave-particle mass-charge via energization of <strong>SO</strong>(1, 3)<sub>zz</sub> principle spin axis angular momentum, invariant throughout inertial dynamics of electromagnetic and gravitational ﬁelds being inversely compressive/dispersive of cosmological constant vacuum energy density tensor pressure, according to principle quantum number <em>n</em>. In thought experiment test vs. general theory via <em>pp</em>-waves microlensing problem, wherein light-to-light gravitational attraction is four times matter-to-matter attraction, hypothesis predicts null microlensing result in area general theory known to break down on microscopic scale.</p>https://www.maplesoft.com/applications/view.aspx?SID=95142&ref=FeedThu, 15 Jul 2010 04:00:00 ZDavid HarnessDavid HarnessRelativistic Medium From Unified Energy Vector
https://www.maplesoft.com/applications/view.aspx?SID=1765&ref=Feed
A photon is postulated to be a wavetrain having a coherence length equal to one wavelength. The wavepulse is analyzed for a unified flux distribution, in its own inertial frame, based on the symmetric addition to the Poynting-Heaviside energy vector S of a gravitational cross product, as an alternative to that first proposed by Heaviside. From the mutual restoring force of the cross products a relativistic medium emerges, wherein there is no string, presenting an alternative to string/M-theory.
Maple 10 is used to analyze the symmetric three dimensional electric, magnetic, and gravitational flux distribution of the quantum on a similar basis to static charged rest mass electron-proton flux distributions in their own inertial frame. Eddington's detection of the deflection of light by the sun, and Tolman's detection of a gravitational component to electromagnetic radiation, previously attributed to spacetime curvature, are re-interpreted. The quantum's spacecurve flux distribution is shown in pair production to gain a spin moment, an added degree of freedom, through the interaction with the field of a nuclei, enabling the spherical expansion of the quantum into the electron and positron flux configurations.
Please download the .zip file to get both worksheets for this application.<img src="https://www.maplesoft.com/view.aspx?si=1765/thumb.jpg" alt="Relativistic Medium From Unified Energy Vector" style="max-width: 25%;" align="left"/>A photon is postulated to be a wavetrain having a coherence length equal to one wavelength. The wavepulse is analyzed for a unified flux distribution, in its own inertial frame, based on the symmetric addition to the Poynting-Heaviside energy vector S of a gravitational cross product, as an alternative to that first proposed by Heaviside. From the mutual restoring force of the cross products a relativistic medium emerges, wherein there is no string, presenting an alternative to string/M-theory.
Maple 10 is used to analyze the symmetric three dimensional electric, magnetic, and gravitational flux distribution of the quantum on a similar basis to static charged rest mass electron-proton flux distributions in their own inertial frame. Eddington's detection of the deflection of light by the sun, and Tolman's detection of a gravitational component to electromagnetic radiation, previously attributed to spacetime curvature, are re-interpreted. The quantum's spacecurve flux distribution is shown in pair production to gain a spin moment, an added degree of freedom, through the interaction with the field of a nuclei, enabling the spherical expansion of the quantum into the electron and positron flux configurations.
Please download the .zip file to get both worksheets for this application.https://www.maplesoft.com/applications/view.aspx?SID=1765&ref=FeedThu, 20 Jul 2006 04:00:00 ZDavid HarnessDavid Harness