Number theory derivation from infinity; speculations on equations that are derived in terms of the Field

NTuft · May 22, 2022

Here are pages 239-241 of McQuarrie, cited earlier, for educational purposes:

We then proceed to use the Hamiltonian that has been derived from the Harmonic Oscillator. In doing so we've eliminated an 'imaginary unit', i term; I do not know here if i is a stand-in for "time", a la Relativity, or why this is used in QM equations. I am reading Relativity. I am not sure we can eliminate this term, and then go on to try and shoe-horn the Harmonic Oscillator's derived Hamiltonian to fit by Linear-Combinations-of-Atomic-Orbitals that can explain experimental data. It seems like something is simplified and lost, and there is a breakdown in being able to describe more complex multi-nucleon/electron atoms or even basic molecules, because we have to iterate out so much to describe each electron configuration. I do not think I understand and I need to review; I do not even know $svg.image?\left%3Cbra|%20%20|ket\right%3E$ s .

I for one do not agree that we can square the normalized Psi modulus as $svg.image?\left|%20\psi%20%20\right|\left|%20\psi%20%20\right|%20=%20\left|%20\psi%20^{2}%20\right|$ . This is I think what constitutes the "Born probabilistic interpretation." From Shpenkov, pg. 3 (see pg. 1 for "Physical meaning of imaginary unit, i", link to paper), it's noted:

Quote

Looking at the squaring (2), we see that the result of this action is a removal of the "imaginary" azimuthal function $svg.image?\hat{\Phi}_{m}(\varphi)$ with its imaginary unit i = $svg.image?\sqrt{-1}$ from the solutions of the wave equation, because, $svg.image?{\hat{\Phi}_{m}(\varphi)=e^{im\varphi}$ and $svg.image?{\hat{\Phi}_{m}(\varphi){\hat{\Phi}^{*}_{m}(\varphi)=1$ . This step, consisting, thus, in elimination of inconvenient functions $svg.image?{\hat{\Phi}_{m}(\varphi)$ from consideration, and resulting in getting rid of the independent variable $svg.image?\varphi$ , caused a series of the inevitable contradictions and of principle problems of QM.

The main result of all this "solution" is that Born's idea, becoming a principal postulate of QM, made it absolutely impossible to imagine and conceive the real structure of individual atoms, which are three-dimensional structures. The removing of the third coordinate $svg.image?\varphi$ from the trio of spherical polar coordinates (r, $svg.image?\theta$ , $svg.image?\varphi$ ) is unjustified step invalid for any reason [4]. [emphasis added]

Shpenkov posits $svg.image?\hat{\Psi%20}%20,%20\hat{\Psi%20}%20%20=%20\Psi%20_{k}%20+i\Psi%20_{p}$ , for k=kinetic energy and p=potential energy.

Also, using the classical wave equation for sound, with a constant value for the wave number, k = ( $svg.image?\omega$ /c), instead of a variable (as in the wave number k in the Schrödinger equation). Please see:

anyflip.com link to: Important Results of Analyzing Foundations of Quantum Mechanics. Kreidik, L.G.; Shpenkov, G.P.;

Shpenkov's wave model is apparently able to predict a periodic table of elements that closely aligns with the current table, and has other favorable results from his models but I have not read enough.

--

From chalmers.se:

Mathematical discovery could shed light on secrets of the Universe

the paper: Emergent Sasaki-Einstein geometry and AdS/CFT

from the write-up:

Quote

“The challenge is to describe how gravity arises as an ‘emergent’ phenomenon. Just as everyday phenomena – such as the flow of a liquid – emerge from the chaotic movements of individual droplets, we want to describe how gravity emerges from quantum mechanical system at the microscopic level,” says Robert Berman, Professor at the Department of Mathematical Sciences at Chalmers University of Technology.

In an article recently published in the journal Nature Communications, Daniel Persson and Robert Berman, together with Tristan Collins of MIT in the USA, showed how gravity emerges from a special quantum mechanical system, in a simplified model for quantum gravity called the ‘holographic principle’.

“Using techniques from the mathematics that I have researched before, we managed to formulate an explanation for how gravity emerges by the holographic principle, in a more precise way than has previously been done,” explains Robert Berman.

Ripples of dark energy
The new article may also offer new insight into mysterious dark energy. In Einstein's general theory of relativity, gravity is described as a geometric phenomenon. Just as a newly made bed curves under a person's weight, heavy objects can bend the geometric shape of the universe. But according to Einstein's theory, even the empty space – the ‘vacuum state’ of the universe – has a rich geometric structure. If you could zoom in and look at this vacuum on a microscopic level, you would see quantum mechanical fluctuations or ripples, known as dark energy. It is this mysterious form of energy that, from a larger perspective, is responsible for the accelerated expansion of the universe.

This new work may lead to new insights into how and why these microscopic quantum mechanical ripples arise, as well as the relationship between Einstein's theory of gravity and quantum mechanics, something that has eluded scientists for decades.

“These results open up the possibility to test other aspects of the holographic principle such as the microscopic description of black holes. We also hope to be able to use these new connections in the future to break new ground in mathematics,” says Daniel Persson.

The scientific article, Emergent Sasaki-Einstein geometry and AdS/CFT, is published in Nature Communications and is written by Robert Berman, Tristan Collins and Daniel Persson at Chalmers University of Technology, Sweden, and Massachusetts Institute of Technology, USA.

From the paper (which is way beyond me in technical expertise) I have gathered that they've employed a complex cone in order to describe this emergent gravity mathematically. The proper placement of a negative fractional exponent (-(1/6), if I read it) allowed this to jibe with their calculations.

Edited May 22, 2022 by NTuft
i as a stand-in for time may be part of the Lorentz transformation, and not Einstein's idea; I don't remember.

NTuft · June 1, 2022

Reformulation:

I don't even think I'm shaking the apple cart...

We're coming down from what I would call the "compactified/enfolded/stacked" (undifferntiable?) 5th through 10th dimension of string theory within AdS/CFT. Coming from 5th I'm saying there is a number set, i', comprising the square roots of prime numbers. This is a subset that should exist as an algebra or conceptual geometry: it is a subset of irrational quadratics as mapped by the Minkowski ?(x) function.

Here, with the set of sq. rt's of primes we can not SQR, as that is a non-linear operation, but I will say can multiply by self-same so as to obtain: i'*i' obtains the prime no.; i'*i'*i' yields the prime to the 3/2 power; i'*i'*i'*i' completes the prime squared: using these numbers we can define our natural or real numbers by the Fundamental Theorem of Arithmetic. (Conjecture) Similar to how i, the imaginary unit as sq. rt. of -1 serves as an "irremovable discontinuity", here, too, the i' sets can serve as objects for complex math. I also posit that the members of the set can be equated to Quantum Mechanical states normally comprised by the four quantum numbers by way of boundary conditions, perhaps specifically helical boundary conditions.

I speculate that co-efficients for Energy equations are difficult to assign arbitrarily, but that yes we could borrow them wholesale from Classical Mechanics. Here, a series of differentiation operations on i' yield dyadic ratios (see ?(x) function) that can align with Kinetic Energy (1/2), Potential Energy (-1/4), and on further (3/8 , 15/16, divergence...); to various exponents, which may also relate (admittedly only by the appearance of similar numbers) to 1/2-integer assignments elsewhere. I think we can assume that if we are examining a QM system for description these variables can be added, as it's rather "open-frame".

Yet, this is in AdS/CFT frame-work: constant, negative Gaussian curvature space. We go down through hyperbolic space: we map this with a complex hyperbolic graph that can be scaled by i' mappings, and the shapes we use are hyperbolic->conic sections, as needed, to form our geometry (I want molecular orbitals here). We are using quaternions, octonions, sedenions : these have various iterations of imaginary numbers: better our 'imaginary numbers' comprise rather the set of square roots of primes, because to split the prime by approximation presupposes we know both the signs of the multiplicator and multiplicand, which we cannot take for granted, or so I think. Again, now I want to be able to quantize a QM system by assigning 4 quantum numbers as defined by a helical boundary condition such as the mapping of a certain magnitude of i' to the complex graphing possibilities that describe the state in total.

For emergent quantum gravity at 1D level, we have negative curvative arising from initial symmetry breaking of the stretching of the string, the seperation of the point charges, the ejection of two mass bodies): we go into 2D hyperbolics for consistency in negative curvatuve. So, 2 "gravitons" comprise our system that is now 2-bodied: the gravitational force between the bodies an inverse square of the distance (being able to be described by an i' value); for emergent quantum gravity.

Edited June 1, 2022 by NTuft
edited introduction. Please, address boundary conditions.

NTuft · June 16, 2022

addenda:

4 pages of maths

Please address helical (4-or-more parts of quantum numbers quantized by) boundary conditions and conic section mapping around hyperbolic complex plane, a la atomic and molecular orbitals comprising discrete and oppositely possible 4 vector translations and spin 1/2-integer states (i.e. discrete locations dictated in space to carve a sphere while maintaining +1/2 or -1/2 spin on either half ; divisions of n/7, with n= 1-7: .857142... sphere carving around central "complex cone" or center of gravity, C.o.G ). Find bounds for elliptical asymptote through quadratic roots with hyperbolic trigonometry scaling sinh and cosh as averages of natural exponentiation; apply to other harmonic functions making use of natural logs.

5-7-22-6-1-22.pdf

NTuft · June 16, 2022

studiot · June 16, 2022

Perhaps you should recast your speculation ?

I can't see the remotest correspondence between number theory and all this physics, speculatory or otherwise.

NTuft · June 17, 2022

On 6/16/2022 at 4:13 AM, studiot said:

Perhaps you should recast your speculation ?

I can't see the remotest correspondence between number theory and all this physics, speculatory or otherwise.

Please allow me to leave the elegance to the Tailor (L.B.)

The quantum harmonic oscillator on the sphere and the hyperbolic plane: 𝜅-dependent formalism, polar coordinates, and hypergeometric functions
J. Math. Phys. 48, 102106 (2007); https://doi.org/10.1063/1.2795214
José F. Cariñenaa) and Manuel F. Rañadab)
Departmento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
Mariano Santanderc)
Departamento de Física Teórica, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid, Spain

I cannot access this paper yet except for the abstract.

Perhaps not an authoritative source, but:

Quote

https://www.quora.com/What-math-does-string-theory-actually-require

Ali Abdulla
professor of physicsAuthor has 15.6K answers and 4.5M answer views6y
The String theory main concept is based on avery small(close to Planck dimention)string,open or closed or a type of brane,which osccillate,their modes osccilataions represent particles,therefore, the math, required is the math used in the problems of simple harmonic motions, type of differentail equations with all kind and their possible solution ,free and damped one.This is in general,of course the theory is dealing with a quantum vacuum field,so, the quantum mechanics principles are used with the Math of quantization,and the creation and anihhilation operators.All that is through the solution of Shrodinger equation which is mathematically is a type differential equation.

I do not know of those two operators specifically.

However, the Schrödinger equation as adapted by the Born probability interpretation and modified by operators , seems to break down in explanatory power when we generalize the 1-D(particle in a box)->2-D(Hooke spring) harmonic oscillator further.

"5.4 The Harmonic Oscillator Approximation Results from the Expansion of an Internuclear Potential Around Its Minimum".

What I'd call Fourier transformations for analysis or modelling are useful for approximating the simple harmonic oscillator to a higher dimensional space or reducing space/time functions to vibrational spectra. For improved accuracy anharmonic correction is added from my limited reading..
However, mathematicaly, the virial theorem does not hold even for the simplest di-atomic molecule, and so corrections have to be made, and it is accepted as a way of making approximations.

Why? Because we do think we have a handle on molecular orbitals... I concur. These are very much spherical harmonic oscillator solutions apparently -- as exemplifying the tendency toward lowest energy configurations they are our basis for modelling Q.M. on 4 quantum numbers -- but again, "the spherical solution of Schrödinger equation does not agree w/any experiment"..

So there is a gap in the explanatory power. Q.M. interpretations need to account for wave-particle duality, uncertainty(I'm not sure), and quantization, but I don't think it has to be as 'nebulous' as what the probabilistic interpretation leads to (chop up the Copenhagen interpretation).
It makes sense to me that squaring the Psi modulus in the wave-function removes a complex-valued part of the azimuthal function; removing this discontinuity makes the probabilistic distribution of a 1-D oscillator extensible as probabilistic interpretations of position in space or momentum in higher dimension space by extending the wave-propagation along a string (sinusoidal) to higher dimension (string theory..).

i think we need a complex-valued 2-D or 3-D harmonic oscillator reverse engineered from molecular orbitals, and it likely needs to use hyperbolic geometry and trigonometry. Euclidean geometric extension from 1-D oscillator to map 'spheres' via Fourier analysis (limited understanding) may have a wrong assumption.

If "bonding+anti-bonding" orbital maps can be represented with hyperbolic mathematics that may mean something. It may be more like positive or negative roots, solutions to a quadratic equation. It may mean the space-time has curvature and it's indeterminate as to why (i.e. we deduce the curvature is present from the models that work and can now geometer) as in we don't have to resort to presume there is a pervasive gravity field...

-----
using WolframAlpha:

$svg.image?f(x)=\frac{1}{2\sqrt{x}}$

$2}}$

The f(x) appears to be an odd function: maps from (+,+)Q1->(-,+)Q4 on reflection across Y. However, when I add in the complex graph (and it looks like a hyperbola), WA throws it over to quadrant 3 (-,-)[reflection across y=-x] which seems equivalent to Q1(+,+) in my mind. Anyway, not sure it's even valid when it wants to do a complex number there. I'd like it to be a complex graph but I haven't figured how to get that done.

f'(x) appears odd as well: maps from Q2(+,-)->Q3(-,-): when I add in the complex on WA it mirrors it across the y-axis to Q3.

however, the derivative of an odd function is even, and the derivative of an even function is odd. So one is odd and one is even, or neither is... Both converge as a limit towards 0.
image.gif.3a7081333fc80408d5d69f4275dc4614.gif
If anyone can tell me anything about these things to characterize them, I'd appreciate it.

Thank you

Edited June 17, 2022 by NTuft
not sure f(x) or f'(x) even or odd, doesn't cross origin. changed infinity to 0 as limit, y=-x.

**swansont** · June 17, 2022

1 hour ago, NTuft said:

Why? Because we do think we have a handle on molecular orbitals... I concur. These are very much spherical harmonic oscillator solutions apparently -- as exemplifying the tendency toward lowest energy configurations they are our basis for modelling Q.M. on 4 quantum numbers -- but again, "the spherical solution of Schrödinger equation does not agree w/any experiment"..

Where do your quotes come from?

NTuft · June 17, 2022

38 minutes ago, swansont said:

Where do your quotes come from?

I'm actually quoting myself there from my notes. I will have to re-source the paper, but it was on the Shpenkov wave equation and was written by a Victor Christianto, a researcher from the Phillipines, IIRC. I'm aiming for intellectual honesty but I know that's not always realistic.
From the start of Ch. 8, Approximation Methods, in McQuarrie's Quantum Chemistry (after introducing Douglas Hartree and Vladimir Fock):

Quote

We ended the previous chapter by saying that the Schrodinger(sic) equation cannot be solved exactly for any atom or molecule more complicated than a hydrogen atom. At first thought, this statement would appear to certainly deprive quantum mechanics of any interest to chemists, but, fortuneately, approximation methods can be used to solve the Schrodinger(sic) equation to almost any desired accuracy."

appendix on hyperbolic math:

Quote

ed.:Hyperbolic triangle::Standardized Gaussian curvature:
In terms of the (constant and negative) Gaussian curvature K of a hyperbolic plane, a unit of absolute length corresponds to a length of

$\sqrt{-K}$

:Hyperbolic law of cosines::Relativistic velocity addition via hyperbolic law of cosines: ...relativistic rapidities.

:Complex hyperbolic space: ...symmetric space associated with the Lie group $svg.image?\mathrm{SU}(n,1)$ . Constructed by giving a metric on the unit ball in $svg.image?\mathbb{C}^{n}$ . Characterized by being the only simply connected Hermitian[odd OR even f(x)?] manifold whose holomorphic sectional curvature which is constant equal to -1.
:Unit hyperbola::Parametrization:

A direct way to parameterizing the unit hyperbola starts with the hyperbola xy = 1 parameterized with the exponential function: $svg.image?(e^{+t},e^{-t})$
This hyperbola is transformed into the unit hyperbola by a linear mapping having the matrix A:

$svg.image?A=\frac{1}{2}\begin{pmatrix}1%20&%201%20\\1%20&-1%20\\\end{pmatrix}$ :
$svg.image?(e^{+t},e^{-t})A=(\frac{e^{+t}+e^{-t})}{2}%20,%20\frac{(e^{+t}-e^{-t})}{2})=(cosht,%20sinht)$

This parameter t is the hyperbolic angle[rapidity?], which is the argument of the hyperbolic functions.

One finds an early expression of the parametrized unit hyperbola in Elements of Dynamic (1878) by W. K. Clifford. He describes quasi-harmonic motion in a hyperbola as follows:

Quote

"The motion $svg.image?\rho=\alpha%20cosh(nt+\epsilon)+\beta%20sinh(nt+\epsilon)$ has some curious analogies to elliptic harmonic motion. ... The acceleration $svg.image?\ddot{\rho}=n^{2}\rho$ thus it is always proportional to the distance from the centre, as in elliptic harmonic motion, but directed away from the centre."

As a particular conic, the hyperbola can be parametrized by the process of addition of points on a conic.

Sourced from HandWiki reference manual: Topic::sub-topic

Edited June 17, 2022 by NTuft
idea cloud

NTuft · June 18, 2022

On 5/10/2022 at 2:25 PM, uncool said:

…no, NTuft, that is not why e^(i pi) = -1. Your blind substitution is not correct.

You are claiming that e^(x*i*pi) = x cos(pi) + i x sin(pi) = -x, if I’ve remade your equations correctly. This simply isn’t true. It has nothing to do with the actual justification of the original equation (which has to do with McLaurin series), and is self-contradictory with a bit of thought.

Hi @uncool,
I've got a few pages from yesteryear on that Taylor/Maclaurian(sic) series.

Is it because it's a summation(or integral) of the rectangular hyperbola $svg.image?y=\frac{1}{x}$ ¹ that you say the Taylor series (McLaurin centered at 0) series is justification of the original equation?

Quote

"We have defined the natural logarithm as an integral, an 'area' under the rectangular hyperbola:

[...]
Then we can define number e as the positive number at which log(e)=1:
[...]
If we remember the geometric interpretation of the log as the area under the curve 1/x, this means that e is the number such that the area between 1 and e is equal to 1.
[...]
By the theory of the derivatives of the inverse function, we know that the function exp es differentiable and[...]
http://www.matematicasvisuales.com/english/html/analysis/expolog/edosdef.html

I think also, by an inversion of some sort, $svg.image?e^{x}$ falls down or up on a hyperbola? Or did these guys figure it out from series/sums beforehand somehow.. I will look to read at above reference some more.

Do you have any other thoughts??
¹WolframAlpha: y=(1/x) (ty)

Quote

"cont'd Taylor series

Let f(x) be infinitely differentiable at x=c
f^(n)(c) exists for every n
Taylor series of f(x) at x=c

$svg.image?\sum_{n=0}^{\infty}\frac{f^{(n)}(c)}{n!}(x-c)^{n}$
Taylor series of f(x) at x=0 is Maclurin[sic] series

ex_| $svg.image?f(x)=e^{x}$
Maclaurian[sic] series

$svg.image?f^{(n)}(x)=e^{x}$

$svg.image?f^{(n)}(0)=e^{0}=1$
$svg.image?\sum_{n=0}^{\infty}\frac{1}{n!}x^{n}$
= $svg.image?\sum_{n=0}^{\infty}\frac{x^{n}}{n!}$

ex_|f(x)=cos(x) f(0)=1
f'(x)=-sinx f'(0)=0
f''(x)=-cosx f''(0)=-1
f'''(x)=sinx f'''(0)=0
f''''(x)cosx f''''(0)=1

f(x)=cos(x)=> $6!$

ex_|f(x)=sinx
=> $svg.image?\sum_{n=0}^{\infty}(-1)^{n}\frac{x^{2n+1}}{(2n+1)!}=x-\frac{x^{3}}{3}+\frac{x^{5}}{5}$

Taylor/Maclaurian[sic] series converge to their function (cosx, sinx); these are analytic functions.
[...]
Maclaurin(!) series_|
$svg.image?f(x)=e^{x^{2}}$
$svg.image?\sum_{n=0}^{\infty}\frac{(x^{2})^{n}}{n!}=\sum_{n=0}^{\infty}\frac{x^{2n}}{n!}$

$svg.image?f(x)=\frac{e^{x}-1}{x}$
${n!})-1}{x}=\sum_{n=0}^{\infty}\frac{x^{n}}{(n+1)!}$

f(x)= sin(x^2)

$svg.image?\sum_{n=0}^{\infty}(-1)^{n}\frac{(x^{2})^{2n+1}}{(2n+1)!}=\sum_{n=0}^{\infty}(-1)^{n}\frac{x^{4n+2}}{(2n+1)!}$ "

some math

Edited June 18, 2022 by NTuft

NTuft · June 18, 2022

Quote

In geometry, the Braikenridge–Maclaurin theorem, named for 18th century British mathematicians William Braikenridge and Colin Maclaurin,^[1] is the converse to Pascal's theorem. It states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line L, then the six vertices of the hexagon lie on a conic C; the conic may be degenerate, as in Pappus's theorem.^[2]

The Braikenridge–Maclaurin theorem may be applied in the Braikenridge–Maclaurin construction, which is a synthetic construction of the conic defined by five points, by varying the sixth point. Namely, Pascal's theorem states that given six points on a conic (the vertices of a hexagon), the lines defined by opposite sides intersect in three collinear points. This can be reversed to construct the possible locations for a sixth point, given five existing ones

https://en.wikipedia.org/wiki/Braikenridge–Maclaurin_theorem

In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus. For example, many asymptotic expansions are derived from the formula, and Faulhaber's formula for the sum of powers is an immediate consequence.

The formula was discovered independently by Leonhard Euler and Colin Maclaurin around 1735. Euler needed it to compute slowly converging infinite series while Maclaurin used it to calculate integrals. It was later generalized to Darboux's formula.

https://handwiki.org/wiki/Euler–Maclaurin formula

@exchemist,

Of course we know 6. A box and two? Nucleons paired by exclusion (proto-neutro), but some such at vertices pi, or on elliptic interior. To a ring of course 6₆ and any of our iterations of C O N H; like sugar. Yee-haw, saddle up. Seriously, something at the vertices of the solids.

exchemist · June 18, 2022

1 hour ago, NTuft said:

@exchemist,

Of course we know 6. A box and two? Nucleons paired by exclusion (proto-neutro), but some such at vertices pi, or on elliptic interior. To a ring of course 6₆ and any of our iterations of C O N H; like sugar. Yee-haw, saddle up. Seriously, something at the vertices of the solids.

I’m afraid it looks very much as if your hovercraft is full of eels.

NTuft · June 18, 2022

24 minutes ago, exchemist said:

I’m afraid it looks very much as if your hovercraft is full of eels.

Egads man.. Oh, well. Dam up the river build a smokehouse and start a farm.

Maybe some other more formalized manner? Or if you're remote viewing and I have parasites send me a P.M.

NTuft · June 18, 2022

At the 5th dimensional to 10th or 26th silly string standard model let's say the set of square roots of prime numbers, positive and negative, exists as part of all algebras and geometry.

At 4th dimensional derivative level we have a 1/2 Kinetic Energy term, which is complex (time-dependent) because of the need to accrue momentum
At 3rd dimensional derivative level we have a -1/4 Potential Energy term, and we want to restrict Potential Energy interactions to 3-D models for electrostatics

At 2nd dimensional level we have a 3/8 term, normally omitted from the Kinetic Energy terms; we'll call it the gravitational interaction at 2-D level: like basic former electrostatics.

At 1st string we have 15/16 = planck length of some kind => extension implicit in the string stretch or whatever @StringJunky

NTuft · June 21, 2022

Continuation:

Ergo, gravity and Magnetism are synonymous, acting along lines of force. And electricity is circling radially around these lines, giving an alternative to the transverse EM wave. See Schrödinger wave equation visualization.

Edited June 21, 2022 by NTuft
undlaut

**swansont** · June 21, 2022

6 hours ago, NTuft said:

gravity and Magnetism are synonymous

They are decidedly not.

NTuft · June 23, 2022

On 6/21/2022 at 3:44 AM, swansont said:

They are decidedly not.

This could be evidence that gravity can be explained from geometry and charge seperation alone:
Electro-gravity via geometric chrononfield
Eytan H. Suchard 2017 J. Phys.: Conf. Ser. 845 012019

Quote

Abstract. In De Sitter / Anti De Sitter space-time and in other geometries, reference submanifolds from which proper time is measured along integral curves, are described as events. We introduce here a foliation with the help of a scalar field. The scalar field need not be unique but from the gradient of the scalar field, an intrinsic Reeb vector of the foliations perpendicular to the gradient vector is calculated. The Reeb vector describes the acceleration of a physical particle that moves along the integral curves that are formed by the gradient of the scalar field. The Reeb vector appears as a component of an anti-symmetric matrix which is a part of a rank2, 2-Form. The 2-form is extended into a non-degenerate 4-form and into rank-4 matrix of a 2- form, which when multiplied by a velocity of a particle, becomes the acceleration of the particle. The matrix has one U(1) degree of freedom and an additional SU(2) degrees of freedom in two vectors that span the plane perpendicular to the gradient of the scalar field and to the Reeb vector. In total, there are U(1) x SU(2) degrees of freedom. SU(3) degrees of freedom arise from three dimensional foliations but require an additional symmetry to exist in order to have a valid covariant meaning. Matter in the Einstein Grossmann equation is replaced by the action of the acceleration field, i.e. by a geometric action which is not anticipated by the metric alone. This idea leads to a new formalism that replaces the conventional stress-energy-momentum-tensor. The formalism will be mainly developed for classical physics but will also be discussed for quantized physics based on events instead of particles. The result is that a positive charge manifests small attracting gravity and a stronger but small repelling acceleration field that repels even uncharged particles that have a rest mass. Negative charge manifests a repelling anti-gravity but also a stronger acceleration field that attracts even uncharged particles that have rest mass.

1. Introduction The motivation of this theory is to show that matter can be put into correspondence with an acceleration field. There are two ways that measurement of proper time by a physical clock between events will be shortened: either by gravity in which the clock moves along geodesic curves but in curved space-time or by other interactions that prevent the clock from moving along a geodesic curve. These two approaches have to appear in the equation of gravity in order to describe Nature by a fully geometric model. The latter is not anticipated by the metric tensor alone and therefore it requires a new approach.

...

5. Energy density by an acceleration field – Reeb vector at the classical non-covariant limit

The acceleration in (25) is dauntingly small and very difficult to measure. It requires an immense field of 1 million volts over 1 millimetre to expose an acceleration of uncharged clocks, which is about 8.61cm/sec^2, less than 0.01 g, providing that there are no other fields that cancel out this acceleration. In fact, we will see below that charge also generates gravity and that for the choice8πKin (23), the acceleration will be about 4.305 cm/sec^2. By the principle of parsimony, the fact that this acceleration field stores energy, i.e $svg.image?Energy-Density=\frac{a^{2}}{8\pi%20K}$

means that this acceleration is aligned with the electric charge, electro-static field curves because this can explain the electric charge attraction and repulsion by simply, increasing or decreasing the energy stored in such a weak acceleration field. As we shall see, if instead of 8π K we develop this theory such that 4π K divides the square norm of acceleration, no acceleration of neutral particles will be measured within a homogeneous electrostatic field. This is because, we will develop the Euler Lagrange equations of the Ricci scalar plus (11) and see that charge also generates gravity and not only inertial mass does.

...
7. Vaknin’s theory We quote here one of the four models of Vaknin [14] as follows: This work contains a possible realization of space-time as an ideal geometric object that becomes physically accessible only where a wave function which is called “chronon” collapses. The physical model is therefore of events and not of particles. This paper offers the idea that matter occurs where the Reeb vector is not zero. Showing consistency of this model with Quantum Mechanics is a very difficult task although it is possible to show that the energy of an electric field is stored in an acceleration field by replacement of the electromagnetic tensor with the anti-symmetric acceleration field.
Vaknin's description of the realization of event is as follows:"Time as a wave function with observer mediated collapse. Entanglement of all Chronons at the exact "moment" of the Big Bang. A relativistic QFT with Chronons as Field Quanta (excited states.) The integration is achieved via quantumsuperpositions".
The main difference between Vaknin’s approach and the author’s approach is that Vaknin’s approach is algebraic where the author’s approach is geometric. Thus, the outcome is two different theories that discuss a similar idea. We now show the simplest implementation of Vaknin’s model as a quantization idea of time by collapsible events,...
...
8. General Relativity for the deterministic limit By General Relativity, we have to add the Hilbert-Einstein action [16][17][18] to the negative sign of the square curvature of the gradient of the scalar field in order to replace the energy-momentum tensor in the Einstein’s field equations. ...
Rµν is the Ricci tensor and Rµν Rg µν 2 1 − is the Einstein tensor [18].In general, by (27) and σ = 8π (33) can be written as ...
...

9. electro-gravity –unexpected gravity inducedby electric charge
In comparison, ... looks like an energy momentum tensor of a perfect fluid and in contrast, Z P Pνµ consists of the unit vector k PkP P Z Pµ µ = which points to a perpendicular direction to Uµ . ...
This property means that this term does not behave like as expected from an ordinary Energy – Momentum tensor. From (26) and from Einstein – Grossman’s equation in vacuo ...

This means that charge can cause gravity or anti-gravity and its sign is opposite to the acceleration field around the charge. A more general form is
$svg.image?M_{Charge-Gravitational-Mass}=\frac{\pm%20Q}{\sqrt{2\sigma%20K\varepsilon%20_{0}}$ where $svg.image?\sigma=8\pi$ , $svg.image?K$ is Newton's gravity, and $svg.image?\varepsilon%20_{0}$ is permittivity of vacuum. ...

Conclusion An upper limit on measurable time from each event backwards to the "big bang" singularity as a limit or from a manifold of events as in de Sitter or anti - de Sitter, may exist only as a limit and is not a practical physical observable because it can only be theoretically measured. Since more than one curve on which such time can be virtually measured intersects the same event - as is the case in material fields which prohibit inertial motion, i.e. prohibit free fall - such a time can't be realized as a coordinate. Nevertheless, using such time as a scalar field, enables to describe matter as acceleration fields by using the gradient of the scalar field and it allows new physics to emerge by a replacement of the stress-energy-momentum tensor. One arrives at electro-gravity as a neat explanation of the Dark Matter effect and the advent of Sciama's Inertial Induction, which becomes realizable by separation of high electric charge. This paper totally rules out any measurable Biefeld Brown effect in vacuum on Pico-Farad or less, Ionocrafts due to insufficient amount of electric charge [20]. The electrogravitational effect is due to field divergence and not directly due to intensity or gradient of the square norm. Inertial motion prohibition by material fields, e.g. intense electrostatic field, can be measured as a very small mass dependent force on neutral particles that have rest mass and thus can measure proper time. The non-gravitational acceleration should be from the positive to the negative charge. The electro-gravitational effect which is opposite in direction and half in intensity, requires large amounts of separated charge carriers and acts on the entire negative to positive dipole.

Appendix B – Planck Area Gravity – Based on a lecture by professor Seth Lloyd of the M.I.T combined with the Geometric Chronon model and its correlation with sub-atomic particle

...

The problem is that there is no stable charged particle without spin and therefore our discussion could mean a temporary decomposition of electrically neutral Bosons into two energy states, one temporarily behaving like a negative charge and one like a positive one. The reasoning behind such a claim is that if matter is expressible by a weak acceleration field and the weak acceleration field energy is the energy of an electric field, then elementary neutral particles, even with zero magnetic momentum and with zero electric dipole, should have an internal electric field. The question is how to infer such a structure. The idea is that area changes are relative to energy ratios even if they are changes due to charge electro-gravity and not due to inertial mass. It is a manifestation of a holographic principle [23], [24]. Our modest test will be to divide the Higgs energy by 2 and then either by 192.005150...,or by 62.6395393... . That is by Beta = 384.010301743200560 or by Alpha =125.279078679349110. For example: 125 GeV / 125.279078679349110 ~= 0.9977 GeV which should be a Baryonic energy state. Another energy is 125 GeV / 384.01030174320056 ~= 325.5 MeV This energy is the model dependent vacuum constituent Quark energy according to Zhao Zhanget. al. [25]. According to this paper, no neutral particle can avoid having an internal structure, otherwise, the particle would not be able to manifest an acceleration field as energy. This leads to the possible model of BS Meson, Z Boson and Higgs Boson as either oscillating + and – charge such that both the magnetic and electric dipoles are zero, or as spinning + and - charge such that both magnetic and electric dipoles vanish. The problem is the Z and the Higgs bosons which are considered elementary particles. The Z boson mass is 2 .91 1876 ± .0 0021 GeV / C . If we split this mass into two charges, then 1/ 192.00515087160028 of area around the negative charge will be added, which is considered as proportional to mass [23]. But that portion is of half of the mass that splits to two charges, so we seek1/384.00258393161619 of the mass of the Z boson as having a physical meaning. 91 .1876 GeV /( 384.0103) = 237.4613 MeV (B.8) which is the energy difference between the Phi (previously Eta) and Omega Mesons!

...

By the Checkered Board Model and EMS [26] the mass of the up Quark deviates from the Standard Model’s 2 ~ 2.3 MeV/C and is 2 237.31 MeV/C according to that very same model, the down Quark is 2 42.39Mev/C unlike the S.M. 2 ~ 4.8 MeV/C . The Z boson can contribute to mass fluctuations through half of its mass by area fluctuations around a positive charge too but that yields 727.87572MeVand there is no known 727.876 MeV resonance in the particles world. Here is a summary of the electro-gravity energy in the Planck scale around a positive and a negative charge that split an elementary boson and by this, these energies are beyond the Standard Model.

...

@Markus Hanke

**swansont** · June 23, 2022

11 hours ago, NTuft said:

This could be evidence that gravity can be explained from geometry and charge seperation alone:
Electro-gravity via geometric chrononfield
Eytan H. Suchard 2017 J. Phys.: Conf. Ser. 845 012019

"There could be evidence" is not "there is evidence"

Let's discuss credibility of sources for a moment:

The paper is based on someone's thesis from 1984 - not on peer-reviewed articles or experiment that's been done. That should be a red flag.

Citing ArXiv links and preprints, rather than journal articles when the ArXiv/preprint is from several years preceding suggests the papers never made it through peer review. That's a red flag.

Youtube videos as a citation is yet another red flag.

All of that together screams that this is not a serious proposal - it's built on a rather shaky foundation, much of which has not entered mainstream science.

Meanwhile, gravity and magnetism have distinct differences. Newtonian gravity (i.e. what GR reduces to when you don't have really strong gravity) not having a repulsive component, and monopoles vs dipoles as the default configuration are two of the main points of difference.

NTuft · June 23, 2022

8 hours ago, swansont said:

Meanwhile, gravity and magnetism have distinct differences. Newtonian gravity (i.e. what GR reduces to when you don't have really strong gravity) not having a repulsive component, and monopoles vs dipoles as the default configuration are two of the main points of difference.

Condensed matter experiments mapping electric and magnetic fields.

The paper is in a peer-reviewed journal, do you know it? I will look at the references. Do you have any thoughts on the math? I cannot verify what that all is, but someone reviewed this paper who does differential geometry.

**swansont** · June 23, 2022

2 hours ago, NTuft said:

Condensed matter experiments mapping electric and magnetic fields.

What is this supposed to mean?

You can’t just link to material because it has a few buzzwords that show up in a search.

2 hours ago, NTuft said:

The paper is in a peer-reviewed journal, do you know it? I will look at the references. Do you have any thoughts on the math? I cannot verify what that all is, but someone reviewed this paper who does differential geometry.

Peer reviewed journal that appears to report conference papers, which are generally not peer reviewed.

“conference organisers act as editors managing the peer review process”

https://publishingsupport.iopscience.iop.org/questions/iop-conference-series-publication-procedure/

So the peer review is only as rigorous as the conference wants it to be, and if it’s not backed up by experimental confirmation, you can’t present it as valid support for anything.

NTuft · June 23, 2022

11 hours ago, swansont said:

Meanwhile, gravity and magnetism have distinct differences. Newtonian gravity (i.e. what GR reduces to when you don't have really strong gravity) not having a repulsive component, and monopoles vs dipoles as the default configuration are two of the main points of difference.

22 hours ago, NTuft said:

The formalism will be mainly developed for classical physics but will also be discussed for quantized physics based on events instead of particles. The result is that a positive charge manifests small attracting gravity and a stronger but small repelling acceleration field that repels even uncharged particles that have a rest mass. Negative charge manifests a repelling anti-gravity but also a stronger acceleration field that attracts even uncharged particles that have rest mass.

So the Journal of Physics saw this through, and from reading it is being applied in specific industries. There appear to be as many solid references to what the author is doing with math as there are questionable ones. Or they're blowing smoke. But the math formalism I deduce is valid, or do you think JoP has this out for open access as a diversion of some sort?

Perhaps you will find this acceptable to credibility standards:

Quantum asymmetry between time and space Joan A. Vaccaro Published:01 January 2016 https://doi.org/10.1098/rspa.2015.0670

It may not be entirely related, but I think it is (vis a vis quantized time, chronons), and I think it was written in anticipation of time crystals. I have not reviewed the references.

43 minutes ago, swansont said:

What is this supposed to mean?

You can’t just link to material because it has a few buzzwords that show up in a search.

Outside of our condensed atmosphere we are talking about plasma jetting around untangling magnetic lines, sending them off with force. This isn't seen in classical derivations of electro magnetic induction, as far as I understand. I can't speak towards magnetic monopoles or dipoles yet. Believe it or not I was already familiar with this concept: electrogravitation.

Edited June 23, 2022 by NTuft
grammar

**swansont** · June 24, 2022

11 hours ago, NTuft said:

But the math formalism I deduce is valid

Science is more than credible math. That's one necessary condition. But you have to compare the theory with experiment.

IOW, y = x^2 is credible math. But if the phenomenon you are modeling doesn't follow a quadratic, the theory is incorrect. If these chronons (on which the paper is based) don't exist or behave as advertised, then the paper is built on a poor foundation.

The paper is based on a thesis from almost 30 years ago. Not on a peer-reviewed paper that was published based on the idea. No other references. One is compelled to ask why that is.

Quote

Perhaps you will find this acceptable to credibility standards:

Quantum asymmetry between time and space Joan A. Vaccaro Published:01 January 2016 https://doi.org/10.1098/rspa.2015.0670

It may not be entirely related, but I think it is (vis a vis quantized time, chronons), and I think it was written in anticipation of time crystals. I have not reviewed the references.

Just because there are key words in common with another paper does not mean they are related in any meaningful way.

Science is also more than "take this idea and run with it" and also more than "post a whole bunch of references without making the connection to the question before us" (reminiscent of the Gish gallop)

It's up to YOU to explain why you think a monopole and a dipole behave the same way, when clearly they don't. And why an only attractive force is the same as one that is both attractive and repulsive.

NTuft · June 25, 2022

17 hours ago, swansont said:

But if the phenomenon you are modeling doesn't follow a quadratic

What I am proposing is electric field lines that do not form a barrier of an asymptote between charges, but rather extend to infinity as they pass into another dimension. Upon extension of 1-D mass charge to 2-D we have curvature to space having moved into time. The paper from the Royal Society publication I cited has "coarse granulation" of time co-ordinate to account for Time Reversal symmetry violation in making the quantum Hamiltonian.

From the prior paper on geometrization accounting for a tensor of stress-energy-momentum given acceleration, we are equating general relativity as it is formulated as either a pervasive gravity field upon inertial masses = gravitational masses to a uniformly accelerated frame, from which it is indistinguishable. The paper's author produces the tensor that would emerge from charge seperation, accounting possibly for weak, stong, and electro -+ "gravitic|magnetic" -- 4 charge!~seperation force phenomena -- in the context of a constant positive cosmological constant (de Sitter space, which is equatable or equally explainable in Anti-de Sitter space of constant negative curvature for the cosmological constant).

The Royal Society paper demonstrates a problem with the quantum treatment of time. The chronon paper treats time as theoretical quantiziation issue wherein frame of measurement when made and frame of measurement being assumed cannot necessarily be correlated, as far as I get it, and so we must quantize time to have differential physics equations for description given conditions; the explanation is a uniformly accelerated universe with self-interactions from charge seperation accounting for gravitic forces: both a stronger gravitic force and a weaker anti-gravitic force if I understand it (net gravity on geodesic lines of least energetic falling). The Royal Society paper proposes a different mechanism for Hamiltonian (time evolution Energy description) formulation due to violation or accord with Time reversal symmetry (I think it is saying that the normal quantum interpretation implies time evolution, an Arrow of Time, but what they find necessitates a Symmetric Arrow of Time).

Please read the Chronon paper through, and account for what the geometer is deriving as an equivalency to the stress-energy-tensor, and how this could have implications for an alternate basis for G.R..

17 hours ago, swansont said:

It's up to YOU to explain why you think a monopole and a dipole behave the same way, when clearly they don't. And why an only attractive force is the same as one that is both attractive and repulsive.

Examine the electric field lines collapsing. Instead, let them run off to a point off the graph (or into an asymptote on a 2-D hyperbolic map); electric charge seperation and resulting 3-D spin and 4-D momentum generation induces self-referential forces of inductance, and magnetic field inductance, which magnetic field lines are malleable as lines of force, as demonstrated in the plasma furnace. See Alfven waves.

Edited June 25, 2022 by NTuft
last point on plasma. Hooray for benchtop machines. ITER Tokamak slots.

NTuft · June 25, 2022

@swansont,

I drink

18 hours ago, swansont said:

Science is also more than "take this idea and run with it" and also more than "post a whole bunch of references without making the connection to the question before us" (reminiscent of the Gish gallop)

I'm not going to look it up.

Comments on the math here? How can we make half roots equal cosh(x) for hyperbolic Pythagorean theorem $svg.image?cosh(c)=cosh(a)cosh(b)$

sinh(x)
$svg.image?sinh(x)=\frac{e^{+x}-e^{-x}}{2}$

cosh(x)

$svg.image?cosh(x)=\frac{e^{+x}+e^{-x}}{2}$

We take

cosh^2 (x) − sinh^2 (x) = 1

and extend the complex plane to 4 quadrants by negative real access and "negative imaginary" 3rd and 4th quadrant access as positive square roots of primes. More legitimate complex plane by tetrapartite roots.
++ --

+- -+

**swansont** · June 25, 2022

7 hours ago, NTuft said:

What I am proposing is electric field lines that do not form a barrier of an asymptote between charges, but rather extend to infinity as they pass into another dimension

And how is that related to your claim that gravity and magnetism are “synonymous”?

Your posts contain far too many tangents. They need to be much more concise, coherent and relevant.

studiot · June 25, 2022

1 hour ago, swansont said:

Your posts contain far too many tangents. They need to be much more concise, coherent and relevant.

Especially relevant. +1

I stopped bothering with this thread since it left the title subject of number theory far behind.

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