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# Extending Newton’s law from nonlocal-in-time kinetic energy

A novel framework for applying Newton's laws by J.A.K. Suykens

https://www.sciencedirect.com/science/article/abs/pii/S0375960109001480

"The solution to the extended Newton equation also admits a quantization of the nonlocality time extent, which is determined by the classical oscillator frequency. The extended equation suggests a new possible way for understanding the relationship between classical and quantum mechanics."

R A El‑Nabulsi is trying to corner the market on this formulation, writing quite a few papers on the topic in the last few years.

Jerk in Planetary Systems and Rotational Dynamics, Nonlocal Motion Relative to Earth and Nonlocal Fluid Dynamics in Rotating Earth Frame

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edited December 2020

Suykens paper is a good patchwork extension of Classical Mechanics, essentially meeting Bohmian Mechanics halfway. The Copenhagen Interpretation may amount to Bohr's fatalistic nihilism over the slaughter of WWI and Death of Strindberg. Such reanalysis involves rejiggering Planck's Constant to be non-dimensional, to allow a Quantum of Action to be defined at any scale or frequency. :-B

El-Nabulsi ends his paper with an increasingly common sort of Analogue-QM claim, in this case for non-local effects at atmospheric-scale:

"The main conclusion of this paper is that nonlocality has significant effects on classical laws of fluid dynamics even at large spatial scale and which could be measured experimentally. It will be interesting to explore the impacts of nonlocality-in-time in strongly turbulent media like the Earth’s oceans and atmospheres among them being Rossby waves "

Indeed. The general idea is that "quantum weirdness" is resolving as "realism" of extended classical ideas. Entanglement can be generally understood as synchronized clock-like processes "connected" by shared reciprocal qualities.

Comment Source:Suykens paper is a good patchwork extension of Classical Mechanics, essentially meeting Bohmian Mechanics halfway. The Copenhagen Interpretation may amount to Bohr's fatalistic nihilism over the slaughter of WWI and Death of Strindberg. Such reanalysis involves rejiggering Planck's Constant to be non-dimensional, to allow a Quantum of Action to be defined at any scale or frequency. :-B El-Nabulsi ends his paper with an increasingly common sort of Analogue-QM claim, in this case for non-local effects at atmospheric-scale: "The main conclusion of this paper is that nonlocality has significant effects on classical laws of fluid dynamics even at large spatial scale and which could be measured experimentally. It will be interesting to explore the impacts of nonlocality-in-time in strongly turbulent media like the Earth’s oceans and atmospheres among them being Rossby waves " Indeed. The general idea is that "quantum weirdness" is resolving as "realism" of extended classical ideas. Entanglement can be generally understood as synchronized clock-like processes "connected" by shared reciprocal qualities.
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It's a bit simpler that that if I understand their premise. Consider an object oscillating as x ~ sin(wt). This will have a velocity, an acceleration, but also all the higher-order derivatives such as jerk, snap, crackle, pop, etc. None of these will ever disappear since a sinusoid is forever differentiable, and even more obviously for rotating systems subject to gravity such as the Earth.

So, they are asking whether these higher-order terms are being accounted for properly when solving e.g. Navier-Stokes of a rotating fluid. This figure in the linked El-Nabuski paper caught my eye because they were showing phases-space plots such as the following:

Similar to what I am finding in the wave equation models for ENSO and QBO:

https://forum.azimuthproject.org/discussion/comment/22443/#Comment_22443

This characteristic phase-space is related to the Mach-Zehnder-like modulation that I'm calculating re the analytical solutions to the LTE simplification of Navier-Stokes. Curious on what the deeper connection since the solution is replete with the nonlocal-in-time higher-order jerk, etc terms.

Comment Source:It's a bit simpler that that if I understand their premise. Consider an object oscillating as x ~ sin(wt). This will have a velocity, an acceleration, but also all the higher-order derivatives such as jerk, snap, crackle, pop, etc. None of these will ever disappear since a sinusoid is forever differentiable, and even more obviously for rotating systems subject to gravity such as the Earth. So, they are asking whether these higher-order terms are being accounted for properly when solving e.g. Navier-Stokes of a rotating fluid. This figure in the linked El-Nabuski paper caught my eye because they were showing phases-space plots such as the following: ![](https://imagizer.imageshack.com/img924/6432/wB7bzU.png) Similar to what I am finding in the wave equation models for ENSO and QBO: https://forum.azimuthproject.org/discussion/comment/22443/#Comment_22443 ![](https://imagizer.imageshack.com/img922/3835/F6Yfjt.png) This characteristic phase-space is related to the Mach-Zehnder-like modulation that I'm calculating re the analytical solutions to the LTE simplification of Navier-Stokes. Curious on what the deeper connection since the solution is replete with the *nonlocal-in-time* higher-order jerk, etc terms. 
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edited December 2020

Yes, Paul, I think your phase plot match is good. Those corners must be your anti-entropy filtering. Amusing how they add a bit of low frequency entropy in removing high frequency noise.

"Nonlocal-in-time" is a very awkward expression. Newtonian time began nonlocal by presuming a single uniform time across the universe. Relativity properly undermined this assumption. We are now redefining time to be inherent oscillation as such. That waves are integer-countable make them QM at any scale or frequency.

Wilczek has proposed that time-symmetric oscillations may be defined as "time crystals". While this began as exotic nanoscopic QM, it serves as well for Galileo's Pendulum, or any orderly periodic wave-form, including atmospheric oscillations.

Lets posit "conservation of time" (and space), in that one may locally dilate or compress time, but the spacetime field does not gain or lose time overall; there is opposite and equal time warpage when things fly apart.

We need not insist any physics ideas are fundamental truths, merely effective interpretations to ponder.

Comment Source:Yes, Paul, I think your phase plot match is good. Those corners must be your anti-entropy filtering. Amusing how they add a bit of low frequency entropy in removing high frequency noise. "Nonlocal-in-time" is a very awkward expression. Newtonian time began nonlocal by presuming a single uniform time across the universe. Relativity properly undermined this assumption. We are now redefining time to be inherent oscillation as such. That waves are integer-countable make them QM at any scale or frequency. Wilczek has proposed that time-symmetric oscillations may be defined as "time crystals". While this began as exotic nanoscopic QM, it serves as well for Galileo's Pendulum, or any orderly periodic wave-form, including atmospheric oscillations. Lets posit "conservation of time" (and space), in that one may locally dilate or compress time, but the spacetime field does not gain or lose time overall; there is opposite and equal time warpage when things fly apart. We need not insist any physics ideas are fundamental truths, merely effective interpretations to ponder.
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"Those corners must be your anti-entropy filtering. "

No, it's just kindergarten-level connect the dots

"Nonlocal-in-time"

It has some commonality to a non-stationary time-series.

Take a look at this YT video that I created several weeks ago. The wave appears to be moving to the right but then reverses direction. It thus appears to be non-stationary.

https://youtu.be/wGP65xm9jZs

More clarification here where I show how my LTE formulation allows reversing traveling waves. :

https://geoenergymath.com/2020/10/07/reversing-traveling-waves/

My thinking is that what is being ascribed to a chaotic wave behavior is more likely just a consequence of non-linear math in Navier-Stokes that has not been fully explored. None of the conventional approaches such as Fourier series will work on these kinds of waveforms, which is why many people looking at real time-series hit a dead-end and just assume it's a chaotic property.

--

Today I was cleaning up a massive model comparison between the Pacific ocean's ENSO time-series and the Atlantic Ocean's AMO time-series. My premise is that the tidal forcing is essentially the same in the two oceans, but that the standing-wave configuration differs. So the approach is to maintain a common-mode forcing in the two basins while only adjusting the Laplace's tidal equation (LTE) modulation.

If you don't know about these completely orthogonal time series, the thought that one can fit even one, let alone two time-series simultaneously is unheard of (Michael Mann doesn't even think that the AMO is a real oscillation based on reading his latest research article).

This is the latest product

Read this backwards from H to A.

H = The 2 tidal forcing inputs for ENSO and AMO -- differs really only by scale and offset

G = The constituent tidal forcing spectrum comparison of the two -- primarily the expected main constituents of the Mf fortnightly tide and the Mm monthly tide, amplified by an annual impulse train which creates a repeating Brillouin zone.

E&F = The LTE modulation for AMO, essentially one strong high-wavenumber modulation as shown to the right

C&D = The LTE modulation for ENSO, a strong low-wavenumber that follows the El Nino La Nina cycles and then a higher modulation

B = The AMO fitted model modulating H with E

A = The ENSO fitted model moduating H with C

Ordinarily, this would take eons of machine learning compute time to determine, but with knowledge of how to solve Navier-Stokes, it's a tractable problem.

Comment Source:> "Those corners must be your anti-entropy filtering. " No, it's just kindergarten-level connect the dots > "Nonlocal-in-time" It has some commonality to a non-stationary time-series. Take a look at this YT video that I created several weeks ago. The wave appears to be moving to the right but then reverses direction. It thus appears to be non-stationary. https://youtu.be/wGP65xm9jZs More clarification here where I show how my LTE formulation allows reversing traveling waves. : https://geoenergymath.com/2020/10/07/reversing-traveling-waves/ My thinking is that what is being ascribed to a chaotic wave behavior is more likely just a consequence of non-linear math in Navier-Stokes that has not been fully explored. None of the conventional approaches such as Fourier series will work on these kinds of waveforms, which is why many people looking at real time-series hit a dead-end and just assume it's a chaotic property. -- Today I was cleaning up a massive model comparison between the Pacific ocean's ENSO time-series and the Atlantic Ocean's AMO time-series. My premise is that the tidal forcing is essentially the same in the two oceans, but that the standing-wave configuration differs. So the approach is to maintain a common-mode forcing in the two basins while only adjusting the Laplace's tidal equation (LTE) modulation. If you don't know about these completely orthogonal time series, the thought that one can fit even one, let alone two time-series simultaneously is unheard of (Michael Mann doesn't even think that the AMO is a real oscillation based on reading his latest research article). This is the latest product ![](https://imagizer.imageshack.com/img924/6379/2rf9vM.png) Read this backwards from H to A. H = The 2 tidal forcing inputs for ENSO and AMO -- differs really only by scale and offset G = The constituent tidal forcing spectrum comparison of the two -- primarily the expected main constituents of the Mf fortnightly tide and the Mm monthly tide, amplified by an annual impulse train which creates a repeating Brillouin zone. E&F = The LTE modulation for AMO, essentially one strong high-wavenumber modulation as shown to the right C&D = The LTE modulation for ENSO, a strong low-wavenumber that follows the El Nino La Nina cycles and then a higher modulation B = The AMO fitted model modulating H with E A = The ENSO fitted model moduating H with C Ordinarily, this would take eons of machine learning compute time to determine, but with knowledge of how to solve Navier-Stokes, it's a tractable problem. 
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edited December 2020

PaulP wrote: "kindergarten-level connect the dots"

What dots?? How does the hexagonal pattern emerge?

Still trying to understand what "non-local in time" should mean. Perhaps "not close in time" just as non-local "action at a distance" is understood. Therefore, in a Chaotic System, "sensitivity to initial conditions" is increasingly non-local the longer time has elapsed.

[Mann et al, 2020] is simply asserting that we have not yet certainly identified cycles longer than ENSO frequency, because the data is so noisy. The cool part is predicting such cycles for future confirmation. Its a reasonable conjecture that they exist, under harmonic and complexity theories.

For example, the Ice Age Cycle is surely an oceanic and atmospheric oscillatory motion cycle, not just molecular-scale temperature oscillation. There are thus probable harmonic overtones between ENSO and Ice Ages hidden deep in the data sets, despite great differences in frequency and amplitude.

https://www.nature.com/articles/s41467-019-13823-w

Comment Source:PaulP wrote: "kindergarten-level connect the dots" What dots?? How does the hexagonal pattern emerge? Still trying to understand what "non-local in time" should mean. Perhaps "not close in time" just as non-local "action at a distance" is understood. Therefore, in a Chaotic System, "sensitivity to initial conditions" is increasingly non-local the longer time has elapsed. [Mann et al, 2020] is simply asserting that we have not yet certainly identified cycles longer than ENSO frequency, because the data is so noisy. The cool part is predicting such cycles for future confirmation. Its a reasonable conjecture that they exist, under harmonic and complexity theories. For example, the Ice Age Cycle is surely an oceanic and atmospheric oscillatory motion cycle, not just molecular-scale temperature oscillation. There are thus probable harmonic overtones between ENSO and Ice Ages hidden deep in the data sets, despite great differences in frequency and amplitude. [Mann et al, 2020] link- https://www.nature.com/articles/s41467-019-13823-w
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Thought you were referring to the angularity of the plot lines -- the data is only monthly sampled so the connecting lines are not smooth. The parallelogram shape is a hysteresis lag effect as described in the link. This will be seen in typical lissajous patterns

The multidecadal cycles that Michael Mann thinks are phantoms likely come about from the closeness of the the strongest tides Mf and Mm, which have values when aliased against the annual cycle of 3.8 years and 3.9 years. This creates a longer term beat cycle, which is the aliased Mt cycle in which ~40 cycles fit into a year. It's not exactly 40, but about 39.99 which means that the strength of the Mt tide on the annual impulse only gradually changes from year to year, giving rise to the multidecadal character of AMO. ENSO doesn't have that character, likely because Mf is incrementally stronger.

see the comment after the blog post: https://geoenergymath.com/2020/12/22/overfittingcross-validation-enso→amo/#comment-2245

when the aliased Mm approaches aliased Mf then the slow modulation gets stronger

Comment Source:Thought you were referring to the angularity of the plot lines -- the data is only monthly sampled so the connecting lines are not smooth. The parallelogram shape is a hysteresis lag effect as described in the link. This will be seen in typical lissajous patterns ![](https://i.stack.imgur.com/XhxSo.png) The multidecadal cycles that Michael Mann thinks are phantoms likely come about from the closeness of the the strongest tides Mf and Mm, which have values when aliased against the annual cycle of 3.8 years and 3.9 years. This creates a longer term beat cycle, which is the aliased Mt cycle in which ~40 cycles fit into a year. It's not exactly 40, but about 39.99 which means that the strength of the Mt tide on the annual impulse only gradually changes from year to year, giving rise to the multidecadal character of AMO. ENSO doesn't have that character, likely because Mf is incrementally stronger. see the comment after the blog post: https://geoenergymath.com/2020/12/22/overfittingcross-validation-enso%e2%86%92amo/#comment-2245 when the aliased Mm approaches aliased Mf then the slow modulation gets stronger ![](https://imagizer.imageshack.com/img923/3978/FJhQRI.png) 
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edited December 2020

Those pointy corners rather trochoidialize the "typical lissajous". Its apparently a data-reduction modeling artifact.

Coherent periodic series do appear in "lucky" bursts in stochastic sequences. These can be hard to rule out. In fact, many physicists think our universe is a very lucky accident. Transient deterministic resonances also occur locally in chaos.

The ultimate test of geophysical conjecture is to predict the future. Peak Oil miscalculations offer a cautionary case from the Geoenergymath case-base (the effective limit to Oil Extraction based on fracking and tar-sands is the collapse of civilization, not depletion). To falsify [Mann et al, 2020], nothing better than a correct and repeatable multidecadal forecast.

Slide-1 stratigraphy on the page-link below seems to record decadal-multidecadal climate oscillations, never mind if they do not happen to match any specific claim made from modern observations.

https://www.slideshare.net/gauravhtandon1/stratigraphy

Geoharmonics relentlessly vary with tectonic shifts on the geologic-timescale, and surely for many causes on the (multi) decadal scale.

Comment Source:Those pointy corners rather trochoidialize the "typical lissajous". Its apparently a data-reduction modeling artifact. Coherent periodic series do appear in "lucky" bursts in stochastic sequences. These can be hard to rule out. In fact, many physicists think our universe is a very lucky accident. Transient deterministic resonances also occur locally in chaos. The ultimate test of geophysical conjecture is to predict the future. Peak Oil miscalculations offer a cautionary case from the Geoenergymath case-base (the effective limit to Oil Extraction based on fracking and tar-sands is the collapse of civilization, not depletion). To falsify [Mann et al, 2020], nothing better than a correct and repeatable multidecadal forecast. Slide-1 stratigraphy on the page-link below seems to record decadal-multidecadal climate oscillations, never mind if they do not happen to match any specific claim made from modern observations. https://www.slideshare.net/gauravhtandon1/stratigraphy Geoharmonics relentlessly vary with tectonic shifts on the geologic-timescale, and surely for many causes on the (multi) decadal scale. 
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"Those pointy corners look more typical trochoid than "typical lissajous". What calculation artifact corresponds to a line wheeled-over to form a trochoid loop? Not sure "hysteresis" explains this best."

I'm creating that phase-space waveform myself through a solution to a differential equation so know exactly what is causing the shape, which is a sample-and-hold lag integrator with a delta spike that is incommensurate with the clock frequency.

This is not difficult, especially considering that this is the kind of stuff that shouldn't be a problem to reverse engineer -- since the time variable is missing from the phase plot.

Consider this guy asking what's causing a similar pattern on stack exchange

https://scicomp.stackexchange.com/questions/10493/fit-my-data-to-lissajous-curve-in-matlab

Everyone tries to be so helpful, but the questioner should realize that he could figure it out himself if he left the time-scale in his data acquisition and plotted y(t) vs t (i.e. potential) and dy/dt vs t (i.e. current) side-by-side. Then he would see it is just a square wave, with likely some noise on the top.

Comment Source:> "Those pointy corners look more typical trochoid than "typical lissajous". What calculation artifact corresponds to a line wheeled-over to form a trochoid loop? Not sure "hysteresis" explains this best." I'm creating that phase-space waveform myself through a solution to a differential equation so know exactly what is causing the shape, which is a sample-and-hold lag integrator with a delta spike that is incommensurate with the clock frequency. ![](https://imagizer.imageshack.com/img924/9426/dMpqsD.png) ![](https://imagizer.imageshack.com/img922/4291/UUwE0h.png) This is not difficult, especially considering that this is the kind of stuff that shouldn't be a problem to reverse engineer -- since the time variable is missing from the phase plot. Consider this guy asking what's causing a similar pattern on stack exchange https://scicomp.stackexchange.com/questions/10493/fit-my-data-to-lissajous-curve-in-matlab ![](https://i.stack.imgur.com/2wCQY.png) Everyone tries to be so helpful, but the questioner should realize that he could figure it out himself if he left the time-scale in his data acquisition and plotted y(t) vs t (i.e. potential) and dy/dt vs t (i.e. current) side-by-side. Then he would see it is just a square wave, with likely some noise on the top. 
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This is the wavenumber vs frequency dispersion spectrum for MJO-style equatorial waves. If the spectrum is perfectly symmetric, it is a standing wave, i.e. exp(-ikx)+exp(ikx) ~ cos(kx). See the red lines in the lower right.

But if one side is unbalanced, then the wave starts to travel in one direction. The higher frequency MJO waves are known to travel more than the lower frequency ENSO, which are usually represented as standing waves.

Comment Source:This is the wavenumber vs frequency dispersion spectrum for MJO-style equatorial waves. If the spectrum is perfectly symmetric, it is a standing wave, i.e. exp(-ikx)+exp(ikx) ~ cos(kx). See the red lines in the lower right. ![](https://imagizer.imageshack.com/img922/3598/gPALOp.png) But if one side is unbalanced, then the wave starts to travel in one direction. The higher frequency MJO waves are known to travel more than the lower frequency ENSO, which are usually represented as standing waves. 
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edited January 3

Here is a fascinating paper bearing on Newtonian and Relativistic limits, equivalent Photon and Phonon Physics, and a burning Relativistic QM controversy over Super-Luminal Tunneling Velocity-

On virtual phonons, photons, and electrons Gunter Nimtz 2018 Physikalisches Institut, Universtat zu Koln

https://arxiv.org/pdf/0907.1611.pdf

Based on previous literature study and experimental phonon work, I think the faster-than-c observations are a subtle combination of relativistic illusion and poorly understood tunneling dynamics, best detailed in related topics.

This paper also involves Virtual Particles; an interesting comparison to Quasiparticles. All Particles are increasing seen as extended (non-local) Field Excitations, and its not proven any particle is truly fundamental.

Comment Source:Here is a fascinating paper bearing on Newtonian and Relativistic limits, equivalent Photon and Phonon Physics, and a burning Relativistic QM controversy over Super-Luminal Tunneling Velocity- On virtual phonons, photons, and electrons Gunter Nimtz 2018 Physikalisches Institut, Universtat zu Koln https://arxiv.org/pdf/0907.1611.pdf Based on previous literature study and experimental phonon work, I think the faster-than-c observations are a subtle combination of relativistic illusion and poorly understood tunneling dynamics, best detailed in related topics. This paper also involves Virtual Particles; an interesting comparison to Quasiparticles. All Particles are increasing seen as extended (non-local) Field Excitations, and its not proven any particle is truly fundamental.
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edited January 4

More substantiation that sample-and-hold behavior occurs in atmospheric dynamics behavior. Consider the model of QBO generated by modulating the draconic (or nodal 27.212 day cycle) lunar forcing with a hemispherical annual impulse generating a lagged response. It should have the following predicted frequency response peaks:

Caption: From section 11.1.1 Harmonics of MathematicalGeoEnergy

The 2nd, 3rd, and 4th peaks listed (at 2.423, 1.423, and 0.423) are readily observed in the power spectra of the QBO time-series. When the spectra are averaged over each of the time series, the precisely matched peaks emerge more cleanly above the red noise envelope — see the bottom panel in the figure below (click to expand).

Caption: Power spectra of QBO time-series — the average is calculated by normalizing the peaks at 0.423/year.Each set of peaks is separated by a 1/year interval.

The inset shows what these harmonics provide — essentially the jagged stairstep structure of the semi-annual impulse lag integrated against the draconic modulation.

It is important to note that these harmonics are not the traditional harmonics of a high-Q resonance behavior, where the higher orders are integral multiples of the fundamental frequency — in this case at 0.423 cycles/year. Instead, these are clear substantiation of a forcing response that maintains the frequency spectrum of an input stimulus, thus excluding the possibility that the QBO behavior is a natural resonance phenomena. At best, there may be a 2nd-order response that may selectively amplify parts of the frequency spectrum.

Comment Source:More substantiation that sample-and-hold behavior occurs in atmospheric dynamics behavior. Consider the model of QBO generated by modulating the draconic (or nodal 27.212 day cycle) lunar forcing with a hemispherical annual impulse generating a lagged response. It should have the following predicted frequency response peaks: ![](https://geoenergymath.files.wordpress.com/2021/01/image.png) Caption: From section 11.1.1 Harmonics of MathematicalGeoEnergy The 2nd, 3rd, and 4th peaks listed (at 2.423, 1.423, and 0.423) are readily observed in the power spectra of the QBO time-series. When the spectra are averaged over each of the time series, the precisely matched peaks emerge more cleanly above the red noise envelope — see the bottom panel in the figure below (click to expand). ![](https://imagizer.imageshack.com/img923/9562/rWNeH3.png) Caption: Power spectra of QBO time-series — the average is calculated by normalizing the peaks at 0.423/year.Each set of peaks is separated by a 1/year interval. The inset shows what these harmonics provide — essentially the jagged stairstep structure of the semi-annual impulse lag integrated against the draconic modulation. It is important to note that these harmonics are not the traditional harmonics of a high-Q resonance behavior, where the higher orders are integral multiples of the fundamental frequency — in this case at 0.423 cycles/year. Instead, these are clear substantiation of a forcing response that maintains the frequency spectrum of an input stimulus, thus excluding the possibility that the QBO behavior is a natural resonance phenomena. At best, there may be a 2nd-order response that may selectively amplify parts of the frequency spectrum. 
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edited January 5

Two dynamic similarity cases to Earth QBO physics-

Jupiter’s Equatorial Stratospheric Oscillation (JESO) https://astronomycommunity.nature.com/posts/monitoring-jupiter-s-atmospheric-heartbeat-over-three-decades

A mechanical similarity-case https://en.wikipedia.org/wiki/Balance_wheel

Regarding non-local spacetime extension of Newtonian physics: Newton's observer is akin to a radically simplified Laplace Demon. Even Einstein's point-observer is as unphysical as Newton's point-mass, 350 years on. All point-idealizations disregard Heisenberg Uncertainty.

Comment Source:Two dynamic similarity cases to Earth QBO physics- Jupiter’s Equatorial Stratospheric Oscillation (JESO) https://astronomycommunity.nature.com/posts/monitoring-jupiter-s-atmospheric-heartbeat-over-three-decades A mechanical similarity-case https://en.wikipedia.org/wiki/Balance_wheel ---------- Regarding non-local spacetime extension of Newtonian physics: Newton's observer is akin to a radically simplified Laplace Demon. Even Einstein's point-observer is as unphysical as Newton's point-mass, 350 years on. All point-idealizations disregard Heisenberg Uncertainty.