The heart is called Yi [unified power] becuz when intent moves, spirit is agitated; qi is dispersed. Qi is the Mother of spirit; Spirit is the child of qi. The Mother as qi is the horse that guides/conducts the river chariot (yin spirit) in the water (yin jing). Once your mind is away from the lower Elixir Field, your Qi will be led away from it and be consumed. By gathering the Shen into the lower tan tien then the Qi follows it there. Light of eyes descend as Yang fire inner yin qi line

Thursday, April 17, 2025

Sir John Pendry Temporal Interference Asymmetric Resonator: Time-induced double slit experiment as eternal noncommutative time crystal

Co-author Professor Sir John Pendry said, "The double time slits experiment opens the door to a whole new spectroscopy capable of resolving the temporal structure of a light pulse on the scale of one period of the radiation."

Interview with the lead researcher

A light cycle of 794 femtoseconds corresponds to a wavelength of approximately 1500 nanometers, which falls within the infrared region of the electromagnetic spectrum....

Here, we find unexpected physics: many more
oscillations are visible than expected from existing theory, implying a rise time for the
leading edge estimated to be 1-10 fs, i.e. of the order of an optical cycle (4.4 fs)

a single-cycle light
pulse with a duration of 4.3 femtoseconds
in the near-infrared range.... to generate
a single-cycle pulse of light, and this could
be used as a carrier of digital information at
telecommunications wavelengths. The pulse
duration of 4.3 femtoseconds corresponds
to a potential data transmission rate of over
100 terabits per second for a single optical
fibre.

Thus the uncertainty principle, applied to the spectrum in Figure (1b) correctly predicts the length of the laser pulse..The clear prediction of Equation (4) is that every time we double the length Δt of the pulse, we will cut the energy uncertainty ΔE in half.

the obstacles to the light’s propagation were separated in time.... When it is hit with a powerful laser beam, it goes from being almost entirely transparent to briefly reflecting most of the light that hits it....the researchers used two consecutive laser pulses to turn the material reflective while also shining a less powerful “probe” laser at it. The light from the probe laser passed through the material during times when it was not reflective, and bounced back when it hit simultaneously with a laser pulse.

When they measured the light that bounced back, the researchers found similar interference patterns to those seen in the classic version of the experiment, but this time in the frequency of the light, which determines its colour, rather than in its brightness... the light enters at one frequency and comes out at many frequencies,” says Sapienza.

the rise-decay asymmetry of the time slit and the Doppler shift of the diffracted
light. Time diffraction requires a time slit modulation fast enough to develop frequency
oscillations that decay slowly, over frequencies larger than the probe bandwidth, as we show
here.

Moreover, the oscillations are very close to the asymptotic limit of an ideal time slit with a
Heaviside (infinitely fast) rise profile, for which the amplitude of the oscillations is expected
to decay as 1/(f-f0)2, where f is the frequency of oscillation and f0 the probe central frequency
(230.2 THz). This is evident when the spectrum is rescaled by the inverse frequency squared,
as its intensity is almost constant (Fig. 2C-D). The dashed purple line in Fig. 2C-D is the
asymptotic theory with two Heaviside time slits (see Fig. S2).

The number of oscillations depends on the sharpness of the material’s transition from transparent to reflective, so this means that the material was responding to the laser pulses with incredible speed – within a few femtoseconds of the pulse. One femtosecond is one-millionth of one-billionth of a second.

[Meaning because it was so sharp in time, therefore there was a broad range of frequency wave spread]

“The material response is 10 to 100 times faster than expected, and that was a big surprise,” says Sapienza. “We were hoping to see a few oscillations, and we saw many.”

That quick transition time could be useful for making time crystals, which are strange materials with moving structures that repeat over and over again.

the time slits in the new experiment change the frequency of the light, which alters its colour. This created colours of light that interfere with each other, enhancing and cancelling out certain colours to produce an interference-type pattern.

Co-author Professor Sir John Pendry said: "The double time slits experiment opens the door to a whole new spectroscopy capable of resolving the temporal structure of a light pulse on the scale of one period of the radiation."

‘Double-slit time diffraction at optical frequencies’ by Romain Tirole, Stefano Vezzoli, Emanuele Galiffi, Iain Robertson, Dries Maurice, Benjamin Tilmann, Stefan A. Maier, John B. Pendry and Riccardo Sapienza is published in Nature Physics.

https://www.nature.com/articles/s41567-023-01993-w

whereas the decay of fringe visibility in frequency reveals the shape of the time slits

Our team, led by Riccardo Sapienza at Imperial College London, fired light through a material that changes its properties in femtoseconds (quadrillionths of a second), only allowing light to pass through at specific times in quick succession.

We still saw interference patterns, but instead of showing up as bands of bright and dark, they showed up as changes in the frequency or color of the beams of light.

We had a transparent screen that became a mirror for two brief instants, creating the equivalent of two slits in time.

However, the wave nature of the process means the photon is in a sense reflected by both temporal slits. This creates interference, and a varying pattern of color in the light that reaches the detector.

The amount of change in color is related to how fast the mirror changes its reflectivity. These changes must be on timescales comparable with the length of a single cycle of a light-wave, which is measured in femtoseconds.

we can transfer concepts such as interference from the domain of space to the domain of time.

a beam of light twice gated in time produces an interference in the frequency spectrum.

inducing a fast reflectivity rise, followed by a slower decay. Separation between the time slits determines the period of oscillations in the frequency spectrum, while the decay of fringe visibility in frequency reveals the shape of the time slits.

Therefore, femto is a smaller unit than pico by a factor of 1000

https://arxiv.org/abs/2206.04362

many more oscillations are visible than expected from existing theory, implying a rise time for the leading edge of around 1-10 fs, approaching an optical cycle of 4.4 fs. This is over an order of magnitude faster than the width of the pump and can be inferred from the decay of the frequency oscillations.

The observation of temporal Young’s double-slit diffraction paves the way for optical realizations of time-varying metamaterials, promising enhanced wave functionalities such as nonreciprocity (18),

related to the rise-decay asymmetry of the time slit and the Doppler shift of the diffracted
light. Time diffraction requires a time slit modulation fast enough to develop frequency
oscillations that decay slowly, over frequencies larger than the probe bandwidth, as we show here.

The asymmetric interferogram is explained by the time evolution of the phase of the complex reflection coefficient, causing a Doppler shift of the spectrum, often dubbed time refraction

consists of a deeply subwavelength slab characterized by a time-varying dielectric function which is an aperture function A(t) defining two time slits (Fig. 1D). In this case the wave will be time-diffracted into a frequency spectrum of frequencies Aഥ(ω),

subwavelength waveguides

In contrast, the temporal analogue involves fixed momentum but changing frequency. A material in which two slits rapidly appear and then disappear, one after the other, should cause incoming waves to maintain their path in space but spread out in frequency – so-called time diffraction. The frequency spectrum would be the Fourier transform of the function describing the slits in time, with interference between waves at different frequencies

A femtosecond cycle of light refers to the time it takes for light to travel the length of a single wave cycle, which is incredibly short, around 2 femtoseconds (2 x 10^-15 seconds) for visible light. This is about the time it takes light to travel 300 nanometers, a distance comparable to the size of a virus. 300 nanometers corresponds to ultraviolet (UV) light... A single cycle of a 10 femtosecond light pulse corresponds to a wavelength of approximately 30 nanometers (30 nm). 30 nm corresponds to the X-ray region of the electromagnetic spectrum. A wave with an 800 nm wavelength λ has a period
T = λ /c of 2.67 femtoseconds.

https://www.physics2000.com/PDF/Non-CalcText/Ch33QMIIINonCalculus.pdf

Digital signals use amplitude because they represent information as discrete levels, often binary (0 or 1), where amplitude corresponds to the level or value of the signal. This is unlike analog signals which continuously vary in both amplitude and time.

be time-diffracted into a frequency spectrum of frequencies Aഥ(ω), the Fourier transform of the aperture function A(t), around the incident carrier frequency (Fig. 1E), whereas the in-plane momentum݇ ௫ will be conserved by translational symmetry (Fig. 1F).

Measuring the spectrum of the reflected probe pulses, Tirole and co-workers found that the pulses’ initial bandwidth was stretched by about a factor of ten. Crucially, that spectrum contained a series of peaks that became progressively smaller further from the pulse’s central carrier frequency. What’s more, they found that those peaks got further apart the shorter the delay between the pump pulses.

And just as the fringes in a conventional double-slit experiment become more spread out in space when the slits are closer together, so too in this experiment they got further away in frequency terms when the slits were nearer to one another in time.

While the size of the fringes closely matched theoretical predictions, their staying power came as a surprise – the peaks further from the central frequency being more pronounced than expected. This slow decay, the researchers say, indicates that the indium tin oxide responds more quickly to the leading edge of the slit pulses – taking less than 10 femtoseconds (10^-14s) to do so. This they point out is comparable with the length of one optical cycle of the infrared radiation they were using.

They achieved this by firing light through a material that changes its properties in femtoseconds (quadrillionths of a second), only allowing light to pass through at specific times in quick succession. The material responded much quicker than the team expected to the laser control, varying its reflectivity in a few femtoseconds.

The material is a metamaterial—one that is engineered to have properties not found in nature. Such fine control of light is one of the promises of metamaterials, and when coupled with spatial control, could create new technologies and even analogs for studying fundamental physics phenomena like black holes.

But he adds that the phenomenon they have observed should also be a feature of other types of waves – such as radiofrequency, terahertz or acoustic – and that as such this novel type of diffraction should “impact many technologies”.

Light can also be parceled up into "particles" called photons, which can be recorded hitting the detector one at a time, gradually building up the striped interference pattern. Even when researchers fired just one photon at a time, the interference pattern still emerged, as if the photon split in two and traveled through both slits.

In the classic version of the experiment, light emerging from the physical slits changes its direction, so the interference pattern is written in the angular profile of the light. Instead, the time slits in the new experiment change the frequency of the light, which alters its color. This created colors of light that interfere with each other, enhancing and canceling out certain colors to produce an interference-type pattern.

https://www.sciencedirect.com/science/article/pii/S0370269321003129

Emergence of a discrete time, which is one of the main points of this paper is fascinating. Its origin goes back to no less than C.N. Yang in 1947 [16], or even earlier to Levi [17] who coined the term “Chronon”. Discrete time also appeared in 2+1 gravity thanks to the work of 't Hooft [18] (see also [19]). The point of view presented here is however novel, in that it connects to deformed symmetries and a promising quantum space.
We study the kinematics of this noncommutative space using the tools developed for usual quantum mechanics, namely quantise the space associating to it an algebra of operators,

Of course α is itself periodic of period 2π. This however means that a different choice of selfadjointess domain has been made. Time translations are undeformed, and two time-translated observers will be in different, but equivalent domains. A given observer, nevertheless, can only measure quantized time intervals.

https://www.degruyterbrill.com/document/doi/10.1515/nanoph-2023-0126/html

increasing the refractive index abruptly
leads to time-refraction where the spectrum of all the waves
propagating in the medium is red-shifted, and subsequently
blue-shifted when the refractive index relaxes back to its
original value.

Time-refraction optics with single cycle modulation

Moreover, by shortening the temporal width
of the modulator to ∼5–6 fs, we observe that the rise time
of the red-shift associated with time-refraction is propor-
tionally shorter. The experiments are carried out in trans-
parent conducting oxides acting as epsilon-near-zero mate-
rials. These observations raise multiple questions on the
fundamental physics occurring within such ultrashort time
frames, and open the way for experimenting with photonic
time-crystals, generated by periodic ultrafast changes to the
refractive index, in the near future.

a sudden change in the real part of the refractive index
n(t), it undergoes two fundamental process – time refrac-
tion, and time reflection [13]. In this process of temporal
modulation of the EM properties of the medium, the energy
carried by the propagating wave (“probe”) is not conserved,
but when the medium is homogeneous the wave momen-
tum (wave-vector) is conserved (see, e.g., Ref. [14]). That is,
the time-refracted wave and the time-reflected wave have
the same wave-vector as the original wave propagating in
the medium. Consequently, when the refractive index is
increased abruptly – the spectrum of the wave undergoes
a red-shift, and when the index is decreased the spectrum
undergoes a blue-shift. This spectral shift occurs in both
time-refraction and time-reflection.

The lack of energy conservation in such
time-modulated EM media implies that the scattered wave may even be more energetic than the incident one [19], and can lead to tremendous amplification of waves by the
modulation

Red, ~ 700–635 nm, ~ 2.3–2.1 fs.

A femtosecond is equal to 1000 attoseconds, or 1/1000 picosecond.

Conventional nonlinear optics that relies on interaction between light and bound
electrons is ultrafast, but orders of magnitude too weak for observing time-reflection and PTCs.

Concatenating several time-modulations periodically can lead to the for-
mation of wide momentum gaps, and the system acts as a
photonic time-crystal (PTC) [2, 3, 29–31]. The gaps in momen-
tum of a PTC, where the temporal frequency is complex,
can lead to broadband parametric amplification, and can
interact with the emission of radiation by free electrons [32],
atoms [4] and classical dipoles [4]. All of these rely on the
ability to induce time-interfaces: very large changes in the
EM properties of materials occurring at single wave-cycle
rates.

concatenation as a sum of 2 piecewise signals. The "appended" signal is zero for the duration of the original signal.

This broad band non-resonant shift of the entire spectrum is
expected to occur when a large index change (real or imag-
inary) is induced. However, the properties of this shift and
how it evolves, especially down to the single-cycle regime,
have never been studied. Each plot in Figure 3 shows a
red-shift (increasing wavelength) and blue-shift (decreasing
wavelength). The red-shift occurs when the probe experi-
ences an increase in the refractive index which leads to
decrease in its frequency, which we measure as an increase
in the vacuum wavelength when light exits the sample.
Likewise, the blue-shift occurs when the probe experiences
a decrease in the refractive index. Interestingly, as shown
in Figure 3, there is a region of delay values where the
red-shift and blue-shift occur simultaneously for the same
probe pulse. This region of simultaneous red and blue fre-
quency shifts occurs because the probe pulse and refractive
index response have similar durations, while the time it
takes for the probe pulse to pass through the sample (on
the order of 1 fs) is much shorter. Hence, in these experi-
ments, the leading edge of the pulse experiences an increas-
ing refractive index and is therefore red-shifted, whereas
the trailing edge experiences only decreasing index and is blue-shifted. In addition, under this set of parameters, the
center of the probe pulse – which experiences both increase
and decrease of the refractive index – is negligible, and
therefore the original peak of the spectrum disappears for
these delay values.

. Those [previous experiment] suggestions were based on the argument that the relaxation mechanism relies largely on phonons...We can therefore say with high
confidence that the relaxation time of 20–30 fs has a physical origin, and is not related to the measurement system.

Vacuum wavelength refers to the wavelength of a wave, such as light, when it is traveling in a vacuum (a space devoid of matter). It is the fundamental wavelength, as it's not affected by any refractive index of a medium.

the time it takes for the probe
to pass through the sample is shorter than the rise time
of the refractive index, the spectral red-shift depends on
how much refractive index change the probe pulse experi-
ences before leaving the sample. Intuitively, we can approx-
imate the frequency shift to the ratio between the refrac-
tive index the wave experiences when it enters the sam-
ple and the refractive index it experiences when it leaves
the sample. Under this approximation, it is clear that for
thin samples (time of the probe to pass the sample < rise
time of the index) the spectral red-shift will depend on the
rise time of the index (which is related to the modulator
width through Eq. (2)). This implies that, for long modu-
lator pulses (long rise-time of the index) the probe will
experience a smaller index change while traveling through
the sample (and therefore smaller spectral red-shift) than
with short modulator pulses.

pave the way for observing photonic time crystals at optical frequencies, and many other phenomena involving time
boundaries.

https://opg.optica.org/ome/fulltext.cfm?uri=ome-14-5-1222&id=548824

For instance, wave propagation in homogeneous time-varying media conserves the momentum of light, while frequency changes [3,6], the dual with respect to wave propagation in space-varying time-invariant linear media. Moreover, an abrupt change of the medium’s properties induces the generation of reflected and refracted waves [7,8], whereas a periodic modulation of the refractive index can lead to parametric amplification effects [4,9–11]. (Interestingly, these amplification phenomena have recently been connected with parity-time symmetry and related concepts [7,12]). Scattering by finite objects with time-modulated material properties has also been recently studied [13,14], in parallel with the analysis of time-varying electric and magnetic dipoles and dipolar meta-atoms [15,16]; in these scenarios, the scattering/radiation process leads to harmonic generation via the coupling of the incident field with the Floquet dynamics of the scatterer’s time-periodic refractive index and the corrective radiation terms of the modulated dipole moments, respectively.

As in the time-invariant case, Eqs. (17)–(20) imply that the time-varying absorption losses of a temporal metamaterial are deeply related to the real part of the susceptibility and therefore to propagation/refraction properties (and their frequency dispersion), and vice versa. If the imaginary part of the temporal susceptibility is a separable function, such that , then the real part is also a separable function and has the same time dependence as the imaginary part. This means that if the time-varying absorption properties of the material (e.g., a transparent conducting oxide under an optical pump) can be represented as a separable function, then the refractive index of the material would change as quickly, and with the same temporal profile, as the dynamical change of its absorption.

Dispersion diagram (Brillouin diagram) near the first momentum band-gap of a photonic time-crystal. Solid and dotted lines represent, respectively, the real and imaginary parts of the eigenfrequency, normalized by the modulation frequency . Dashed lines correspond to the light cones for wave propagation in a time-invariant material with effective permittivity equal to eff . The parameter is the coefficient of the first harmonic of the Fourier series of . The figure is reprinted with permission from [10] © 2022 Optica Publishing Group.
These relations indicate that the real and imaginary parts of these specific nonlinear susceptibilities, for a fixed pump at or , are connected as a result of the principle of causality (and assuming again square integrability [61]). Similarly to the linear case [64], we speculate that these relations, together with relevant sum rules, could potentially be used to derive limits and trade-offs on nonlinear processes relevant for optical time-varying systems.

https://opg.optica.org/aop/fulltext.cfm?uri=aop-16-4-958&id=564632

photonic time crystals: artificial materials whose electromagnetic properties are periodically modulated in time at scales comparable to the oscillation period of light while remaining spatially uniform.

momentum bandgaps instead of energy bandgaps. The energy is not conserved within momentum bandgaps, and eigenmodes with exponentially growing amplitudes exist in the momentum bandgap. Such properties make photonic time crystals a fascinating novel class of artificial materials from a basic science and applied perspective.

In the most basic one-dimensional (1D) geometry, photonic crystals constitute a multilayer structure with a periodicity comparable to the light wavelength. In its simplest form, each period comprises alternating layers of two distinct materials characterized by permittivities and (see illustration in Fig. 1(a)).

Figure 1.

a) Schematics of a conventional 1D photonic (space) crystal where permittivity is modulated along one spatial coordinate while it is constant in time. Moreover, the crystal is uniform along the other two spatial directions. (b) Characteristic band diagram of a 1D photonic crystal. Here, the dispersion relation is shown, expressing the functional dependency of the frequency on the real part of the wavenumber that expresses the phase variation of the eigenmode along the direction of the periodic material modulation. The third coordinate axis denotes the imaginary part of wavenumber .

. (c) Schematics of a photonic time crystal where the permittivity is a periodic function of time only. Otherwise, the spatial distribution of the permittivity is uniform in all three directions. (d) Characteristic band diagram of a photonic time crystal. The third coordinate axis denotes the imaginary part of frequency . Inside the momentum bandgap, two eigenmodes are supported: one exponentially growing (shown in red) and one exponentially decaying (shown in green) in time.

Note that in (b), (c), and (d), the harmonic distribution is asymmetric with respect to the fundamental harmonic. This asymmetry is caused by the asymmetry of the matrix in Eq. (17) since ( is outside the momentum bandgap).

asymmetric band structure of amplitude

The frequencies of all the harmonics share the same imaginary part

The 1st harmonic, i.e., , possesses the same amplitude as the fundamental harmonic, i.e., . Thus, this degenerate pair of dominant harmonics has real frequencies with opposite signs. Since the two harmonics share the same momentum , their phase velocities are opposite . Therefore, this pair of dominant harmonics represents a standing wave [98] whose amplitude grows or decays exponentially over time due to the nature of the complex eigenfrequency. From Eq. (11)

By assuming that the electrons/atoms/meta-atoms interact weakly with each other, the time-dependent complex susceptibility is expressed as a product of a time-varying function, describing the change of density in time and the Lorentzian dispersion.

Further, the central frequency of the pulse is taken as . In the following, the group velocity and pulse energy of the Gaussian pulse are examined for different disorder amplitudes

the infinite group velocity of the solitons does not violate Einstein’s causality principle. This is because, in active media, the information velocity is defined by the velocity of the leading edge of the wave packet. Therefore, the group velocity, which quantifies the motion of the center of the wave packet, does not relate to the velocity at which information travels.

I emailed Professor Guenter Nimtz the above - it's his same secret!

Thus, the energy in the circuit escalates throughout one complete oscillation cycle, resulting in parametric amplification (here, the modulated “parameter” is the capacitance ). The energy growth in the circuit is exponential. One can notice that to have an energy growth without any energy decrease within each cycle of the voltage (i.e., for the time interval ), it is important to modulate the capacitance at twice the frequency, i.e.,

One can follow the same logic and consider the case when the voltage oscillation is shifted by a phase with respect to the voltage signal in the above example. Then, the power in the circuit would decrease twice per cycle (i.e., for ) and never increase, as shown in Fig. 18(d). This regime is called parametric de-amplification [161]

degenerate parametric amplification in nonlinear optics strongly depends on the relative phase difference between the signal and pump photons.

a) Difference-frequency generation process resulting in optical parametric amplification along the spatial coordinate .

requires nearly perfect phase matching since

in time crystals, the particles oscillate periodically in time in a harmonic manner, which breaks continuous time translational symmetry [22]. Time crystals represent a new phase of matter

This force keeps the system out of equilibrium. However, the system’s response to this driving force exhibits a periodicity that is different (usually an integer multiple) from that of the driving force itself. This incoherence of the particle oscillation and the external pump indicates that the oscillation of particles is mainly caused by the interactions of particles themselves rather than directly driven by the external pump. It is a kind of semi-spontaneous oscillation. The most important feature of a discrete time crystal is that it is robust to the interaction strength among particles and the imperfection in the driving pulses [167,168], showing the characteristics of a new phase of matter.

Between the subluminal and superluminal regimes, there is a special scenario that the modulation phase velocity is equal to the speed of light, which is called luminal, i.e., . This is an exceptional case where exotic wave effects can happen [223]. As shown in Fig. 33(a), the reciprocal vector (green arrow) aligns with the dispersion curve of a stationary material. The band structure of a space–time varying media is formed by folding the dispersion curve of the stationary material by reciprocal vectors. The crossing of the bands results in that all the forward-traveling states are degenerate in a broadband region and therefore strongly coupled. Therefore, luminal modulation can induce broadband nonreciprocal amplification [223].

it shifts the photon frequency to satisfy momentum conservation as opposed to the spatial case in which the wavevector changes to preserve energy (appendix A in the Supplementary Information). For time refraction, the condition ω₁n₁ = ω₂n₂ holds (where ω₁ and ω₂ are the angular frequencies before and after the time boundary and n₁ and n₂ are the indices before and after the time boundary, respectively).

https://www.nature.com/articles/s41566-025-01640-1

Recently, transparent conducting oxides (TCOs) have proven pivotal in the near-infrared region to overcome the previously stated trade-off between amplitude and speed.

These materials also lend themselves towards the realization of photonic time crystals, which can also be theoretically exploited for light amplification^23,24,25.

Therefore, the transmitted pulse is spatially split into two halves, each containing about half the overall spectral power. In addition, these two ‘fission products’ show strong spectral shifts, which are opposite in sign for both halves and centred at the near-zero-index carrier wavelength.

Time-varying metamaterials rely on large and fast changes of the linear permittivity. Beyond the linear terms, however, the effect of a non-perturbative modulation of the medium on harmonic generation remains largely unexplored. In this work, we study second harmonic generation at an optically pumped time-varying interface between air and a 310 nm Indium Tin Oxide film. We observe a modulation contrast at the second harmonic wavelength up to 93% for a pump intensity of 100 GW/cm², leading to large frequency broadening and shift. We experimentally demonstrate that a significant contribution to the enhancement comes from the temporal modulation of the second order nonlinear susceptibility. Moreover, we show the frequency-modulated spectra resulting from single and double-slit time diffraction could be exploited for enhanced optical computing and sensing, enabling broadband time-varying effects on the harmonic signal and extending the application of Epsilon-Near-Zero materials to the visible range.

https://www.nature.com/articles/s41467-024-51588-z

As pointed out in previous studies of a time-varying ITO layer^5,28, frequency shift and broadening can be respectively linked to changes in the phase and amplitude of the complex reflection coefficient of the system. Although qualitatively similar to the time-diffraction at the fundamental frequency (see Supplementary Fig. 6 for a detailed comparison), the overall shift of the harmonic spectrum is twice as large, with a much larger suppression of the peak around the unmodulated frequency.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.186902

In this study, we explore wave scattering from a time-varying interface characterized by a Lorentz-type dispersion with a steplike temporal variation in its parameters. Our findings reveal a new process: an unconventional frequency generation at the natural resonances of the system.

https://pubs.aip.org/aip/apq/article/1/2/020901/3282301

Space–time variation spoils frequency conservation and brings negative frequencies into the picture.

. In particular, we note the central role played by negative frequencies, which are an inevitable consequence of time dependence. In a rotationally symmetric system that conserves spin, direct transitions of photons from positive to negative frequency are forbidden because reversing frequency reverses spin. Access to negative frequencies is facilitated by the creation of photon pairs (“qubits”), comprising both a positive and a negative frequency, thus satisfying spin conservation but by a process that has no classical counterpart and is responsible for the radiation produced by these systems operating on the ground state.

At time t = 0, the system is set in apparent motion: this can be done without the unphysical assumption of infinite power input

Importantly in this system, neither energy nor frequency is conserved, but conservation violation comes in different forms for each. Although a positive frequency mode entering the time dependent region may emerge as a negative frequency one, this does not indicate that the final photon state has a negative energy. As discussed above, in free space, all photons have a positive energy and the quantum of energy will always be given by ℏω. Instead, as we shall see, a change in the sign of the frequency indicates a transformation of a creation operator into an annihilation operator, which, in turn, affects how we count photons. Therefore, although negative frequencies do not here imply negative energies,

The off diagonal elements represent transitions between different wave frequencies,

We shall show that such emission is essentially a quantum process associated with the creation of photon pairs (“qubits”), similar to the process Hawking pointed out in his seminal paper on radiation from black holes¹⁷ and as investigated by the analog gravity research community.^18,19 T

The interaction of light with superluminally moving matter entails unconventional phenomena, from Fresnel drag to Hawking radiation and to light amplification. While relativity makes these effects inaccessible using objects in motion, synthetic motion - enabled via space-time modulated internal degrees of freedom - is free from these constraints. Here we observe synthetic velocity of a reflectivity modulation travelling on an Indium-Tin-Oxide (ITO) interface

https://arxiv.org/pdf/2407.10809

The ability to access both
phase and amplitude modulations, in conjunction with the demonstrated high diffraction
efficiency, allows for the creation of complex and asymmetric momentum-frequency
spectra, beyond Friedel’s law27,28 which dictates that the scattering amplitude is
symmetric and is the Fourier transform of the permittivity modulation,  ~ (k, ).
Moreover, the simple space-time modulations demonstrated here can be extended, by
using complex pump beams that are structured in both space and time, to realise
programmable and complex spatio-temporal transformations, surpassing what can be
achieved by sequences of purely spatial or purely temporal modulation29.
The construction of apparent motion using discrete, stationary modulations can be
extended to study exotic and super-relativistic kinds of synthetic motions, as illustrated in
Fig.1c. This prospect of space-time control of light greatly improves upon conventional
perturbative nonlinear optical systems, where interactions with low contrast (change in
refractive index << 1) modulations require long propagation distances to accrue
significant signal – a process that introduces deleterious signals and restricts the control
of space and time independently, e.g. as in a 1D fiber.

here we investigate the fundamental question on whether it is possible to have a mirror without any spatial boundary.

https://arxiv.org/pdf/2502.13901

We demonstrate a first implementation of this approach by deflecting ultrashort laser pulses using ultrasound waves in ambient air, entirely omitting transmissive solid media. At optical peak powers of 20 GW exceeding previous limits of solid-based acousto-optic modulation by about three orders of magnitude, we reach a deflection efficiency greater than 50% while preserving excellent beam quality. Our approach is not limited to laser pulse deflection via acousto-optic modulation: gas-phase photonic schemes controlled by sonic waves

https://arxiv.org/pdf/2304.06579

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Noncommutative explains black holes/cosmology/eternal time

"We conclude noncommutativity induces entanglement" - Catarina Bastos. " iΔt represents an interactive interval of time. In the notion of time, there is an inherent clock and an inherent shift of phase that enables a synchrony, a precise dynamic beneath the apparent dynamic of the observed process. ...By starting with a discrete time series of positions, one has immediately a non-commutativity of observations, since the measurement of velocity involves the tick of the clock and the measurement of position does not demand the tick of the clock....i becomes inextricably identified with elemental time, and so the physical substitution of it for t (Wick rotation) becomes, in this epistemology, an act of recognition of the nature of time. One does not have an increment of time all alone as in classical t. One has it, a combination of an interval and the elemental dynamic that is time.... A simplest and fundamental instance of these ideas is seen in the structure of i=√−1. We view i as an iterant, a discrete elementary dynamical system repeating in time the values {⋯,−1,+1,−1,+1,⋯}. One can think of this system as resulting from the attempt to solve i2=−1 in the form i=−1/i. Then, one iterates the transformation x⟶−1/x and finds the oscillation from a starting value of +1 or −1. In this sense, i is identical in concept to a primordial time." Lou Kauffman

Relativistic Quantum physicist protege of Olivier Costa de Beauregard:

"Then comes the question: What would the de jure allowed, but de facto repressed, direct information-to-negentropy transition look like, and consist of? Well, such a phenomenon is nothing less than the one termed either 'precognition' or 'psychokinesis' in parapsychology....Why, then, if such phenomenon do exist, are they so alien to our Western culture, while, as it seems, they are alien neither to the more 'primitive' cultures nor to the elaborate cultures of the 'Far East'?..." Olivier Costa de Beauregard, protege of Nobel Physicist Louis de Broglie. "Do you know what the really brilliant piece of work here is? It's de Broglie! It's tremendous imagination. To find there are TWO oscillations where are EVERYWHERE AND IN ALL TIME IN PHASE AND YET IN DIFFERENT FREQUENCIES: THEY MOVE THROUGH ONE EACH other seemlessly - it's magnificient!" Martin van der Mark on the Law of Phase Harmony and why all matter is made of light due to 1/2 spin as Law of Phase Harmony: "the mean internal frequency of the photon will increase; simultaneously the orbital frequency of the photon will decrease due to the relativistic law of the slowing down of clocks." (see below for more details)

Orthodox Pythagorean philosophy=Daoist Neigong (noncommutative Eddie Oshins)

"However, even in this case there is a highly non-commutative world of higher order collectivity algebras B(n). This can be used to capture the geometry of rotations, like those appearing in the classical Pythagorean octave versus perfect fifth considerations." Music of Quantum Circles October 2017 DOI:10.1007/978-3-319-47337-6_11 In book: The Musical-Mathematical Mind (pp.99-110) Professor Micho Đurđevich https://www.matem.unam.mx/~micho/inde... Institute of Mathematics, UNAM, Mexico citing Alain Connes: "a non-commutative algebra naturally engenders a one-parameter group of automorphisms that makes it evolve, that makes it rotate in such a way that the passage from xy to yx corresponds to what evolution yields for the purely imaginary value t = sqrt(-1) of the parameter t of the evolution group. We must ... introduce evolution only after choosing a state in the algebra, but the evolution obtained is modified only by inner automorphisms and these are in a certain sense invisible. Here, I believe, is the key link that Hamilton sought between time and algebra. ..." In the book "Triangle of Thoughts" (American Mathematical Society, 2001) Alain Connes, Andre Lichnerowicz, and Marcel Paul Schutzenberger discuss the interrelationships among Mathematics, Physics, and Philosophy.

each zero point of geometry already has yin/yang as future (yang movement)/past (yin stillness)

As for O it is the "two emblems." O is the movement of yang. O is the stillness of yin.

The "O" will not be translated as Li included the symbol to refer to a reality at once underlying the three teachings and yet standing outside the categories of each teaching's doctrinal discourse.

p. 29

https://open.library.ubc.ca/media/download/pdf/831/1.0092419/1

PDF link on Ph.D. thesis on
Li Dao-Chun (李道純) was a 13th century Daoist Master in the line of the famous 4th generation Master of the southern Nei Dan lineage, Bai Yuchan. Li is author of the Zhōng Hé Jí (中和集) translated as Anthology on the Center and Harmony.

Resonance of Reality: Natural harmonics as natural numbers proven as Inverse Doppler Effect

Ancient Acoustic Alchemy of Pan instruments: flute, pipe, clarinet, recorder: "A fossil of flute discovered in Germany dated back to 25,000 years ago26. In contrast, it wasn’t until 1842 when the Doppler effect was first introduced to public, while the property of inverse Doppler effect may have been utilized for thousands of years. The bandwidth of conventional negative refraction metamaterials is inherently limited by the local resonance. However, the pipe instruments exhibit different negative refractive indices over a wide range of frequencies. It therefore can be used as a basic unit for designing various novel smart broadband acoustic metamaterials...This type of metamaterial is composed of Helmholtz resonators of which the group and phase velocities are opposite in direction near the resonant frequency."

Ancient Noncommutative Phase Natural Resonance proven as left-handed meta-material music

Transverse or Inverse Doppler Effect from Ancient Acoustic Alchemy music: " the theory of effective medium is only related to the size in the Y-Z plane and has no connection with the size along the X-axis. Along the Y-axis, the lattice constant (2.7 cm) of the sample is determined by the tube (0.7 cm in diameter) and the sponge substrate (2.0 cm in thickness). Along the Z-axis, there is a one-to-one correspondence between the meta-molecules with different lengths and sound waves with different wavelengths. For instance, the meta-molecule with a length of 9.8 cm corresponds to the sound wave with a wavelength of approximately 20 cm; the meta-molecule with a length of 2.9 cm corresponds to the sound wave with a wavelength of approximately 6 cm."

Tang Dynasty alchemy meditation

高上玉皇胎息經/Gaoshang Yuhuang Taixi Jing -The Most High Jade Emperor's Embryonic Breathing Classic

玉皇天尊曰:
Jade Emperor Tianzun said:

胎從伏氣中結, 氣從有胎中息。
The embryo comes from the Qi hidden away while breathing, Qi comes from having the embryo while breathing.

氣入身來謂之生, 神去離形謂之死。
Qi entering the body & arriving is called birth, Shen going & leaving the body is called death.

知神氣, 可以長生。
Knowing Shen & Qi, long life is possible.

故守虛無, 以養神氣。
Therefore, guard nothingness in order to cultivate Shen & Qi.

神行即氣行, 神住即氣住。
When the Shen moves then the Qi circulates, where the Shen stops then the Qi dwells.

若欲長生, 神氣相注。
If you desire a long life, mutually focus the Shen & Qi.

心不動念, 無來無去, 不出不入, 自然常在。
When the Xin isn't moved by thoughts, lacking coming & lacking going, without exiting & without entering, it will, naturally, always stay.

勤而行之, 是真道路。

Constantly practicing it is the true path of the Dao.

"When high energy substances of the subconscious mind emerges, they should be one's guiding force."

qigong master Yan Xin

Qigong Master Chunyi Lin on antigravity qigong levitation secret: "The essence [jing] of the metal is the sound and the essence [yuan jing] of the earth. That is from the universe [yuan qi] as the gravity when you breathe in the energy from this five elements perspective you breathe in that vibration from gravity, you feel that energy filling you up." http://springforestqigong.com

The MetaMaterial Universe - google book preview link on image

Noncommutative Phase MetaMaterial as de Broglie Law of Phase Harmony..." materials with negative refractions can induce inverse Doppler effects" A localized wave packed assembled from many plane waves can still be assigned a (four)momentum at each point. The four components of this momentum are the phase change rates in t,x,y and z given by the imaginary part of the first order derivatives in t,x,y and z. If you apply these first order derivatives on a plane wave then they'll give you the temporal and spatial frequencies of the de Broglie field. The de Broglie wavelength is simply the reciprocal of the spatial frequency. Realizing that the lag of the clock characterized oscillations inside the particle, he associated them with vibrations of the same frequency, but covering the whole space. And he showed that if an observer sees a particle in motion, then these spatial vibrations will seem to him waves propagating faster than a particle...

De Broglie Law of Phase Harmony as the Blue Light Beat Box of the Universe

Frequency is blue light from the future that moves backwards in time as an amplified subharmonic or 1/2 spin energy..."The inverse Doppler effect where an observer measures a higher frequency from a source moving away, is such an intriguing phenomenon that it has attracted substantial theoretical and experimental attention since it was first proposed... ...the energy-momentum flux will be larger in the blue shifted part than in the red shifted part....In a moving frame, they diverge: the mean internal frequency of the photon will increase; simultaneously the orbital frequency of the photon will decrease due to the relativistic law of the slowing down of clocks. Despite the difference in frequency, at any point in space-time these two oscillations must be in phase....This provides a possible physical origin for the postulated law of the "harmony of the phases" first proposed by de Broglie, which lies at the origin of quantum mechanics. ...In a head-on collision between two photons, the interaction will be essentially between the blue-shifted regions which are converging....This state may then decay back into two photons or into an electron-positron pair. Is the electron a photon with toroidal topology? J.G. Williamson and M.B. van der Mark, 1997" Realizing that the lag of the clock characterized oscillations inside the particle, he associated them with vibrations of the same frequency, but covering the whole space. And he showed that if an observer sees a particle in motion, then these spatial vibrations will seem to him waves propagating faster than a particle...

De Broglie-Einstein Law of Phase Harmony from meditation

Internal frequency during meditation is increased (blue light) while external time slows down (gets bigger) as an OM subharmonic sound of the Universe; External time speeds up (as seen by) others while their frequencies (as momentum) are decreased (to red light) in relation to meditation: Thereby maintain a constant phase coherence that is eternal Realizing that the lag of the clock characterized oscillations inside the particle, he associated them with vibrations of the same frequency, but covering the whole space. And he showed that if an observer sees a particle in motion, then these spatial vibrations will seem to him waves propagating faster than a particle...So Heisenberg Uncertainty of position and momentum is transferred into a symmetric mass measurement of particles - but what is covered up is that the position-momentum uncertainty started out, as de Broglie first discovered, with frequency as directly proportional to momentum! So that the "negative frequency" is reverse time as supermomentum or virtual photon energy-information from the future. As we recall from de Broglie: frequency is to time as momentum is to wavelength. So by relying on the wave function as amplitude squared from the wavelength then we are losing the de Broglie supermomentum as reverse time or negative frequency. As we look into a black hole, due to relativity, as the particle approaches the speed of light then the wavelength increases and time slows down. But the internal frequency, as de Broglie realized, based on quantum energy ALSO increases since the mass is due to noncommutative time-frequency (momentum). So the wavelength expands and gets bigger as the frequency of the particle as velocity increases towards the speed of light - due to relativity. But due to the music harmonics of frequency as inverse to time then since the frequency as momentum is increasing (from de Broglie) therefore if the time as wavelength is also increasing from relativity then there HAS to be a negative frequency from the future that has a reverse time. That way the quantum frequency as negative energy (virtual photons) is inverse to the negative time as EMPTINESS from the future. It is William Tiller (working indirectly with Chunyi Lin via Dr. Nisha Manek) that emphasizes the power of Yuan Qi is not from the frequency being negative as virtual photons but from the Negative TIME as negative mass! What both Alain Connes and Basil J. Hiley are emphasizing is that at each "zero point" of space there already is a 5th dimension of noncommutative time-frequency energy with the past and future overlapping. Nobel physicist Gerard 't Hooft agrees: The energy of light is due to it having a "negative refractive index" of spacetime at each zero point of space. So even though light has a zero rest mass the light is CREATING a positive mass as particles due to our own brain physical matter creating a positive refractive index that slows down the speed of light in our measurement perceptions. As Astro-physicist Paul S. Wesson realized - reality is a 5th dimension black hole such that everything is happening at the SAME time at the speed of light. So there is a definite energy to the Universe that is from the future - negentropy - and thus creates the illusion of matter due to light self-annihilating at the zero point of space. This is why H.W.L. Poonjaji and the nondualists of Advaita insist that NOTHING ever HAPPENS and that the SELF is NOT the light but rather the Shakti energy that creates the light - the OM of the light.

Goethe's "The Living-Unit of Sound" is noncommutative phase secret of alchemy

Goethe's Tone-Monad as Gurdjieff alchemy: "a contraction towards an inaudible infinite centre. We could also say that this polarity constitutes the light and darkness of the tone. Insofar as all of the undertones and overtones themselves also have their own overtones and undertones, each tone becomes a monad, i.e. a concentration or fold of the web of interwoven expansion and contraction. The audible tone is thus a product of the two forces of contraction and expansion, systole and diastole. Each tone breathes in and out and is a living audible manifestation of an inaudible force-field. This virtual field of vibration or movement weaves an infinite web of expansion and contraction"

Louis de Broglie Law of Phase Harmony visualized

From the invariance of light as the observer, a superluminal phase wave guides, from the future, the space ship (our brains): the Law of Phase Harmony of relativistic quantum 5th Dimension force. Quantum physicist Dr. Guenter Nimtz sends superluminal sound signals through the 5th dimension: ."the superluminal acoustic effect we have described is likely a ubiquitous but imperceptible phenomenon in the everyday world." Physics Professor Manfred Euler: "Binaural hearing is the acoustic analog of the interferometer or double-slit experiments. The two ears can be regarded as an acoustic interferometer, which recovers the phase difference of signals between the two ears by binaural correlation….matter waves are locally in phase with the superluminal particle clocks (de Broglie’s Law of Phase Harmony). The clock runs forever so it’s self-sustaining (consciousness-energy). It resonates with the quantum vacuum....Yet an acoustical answer can be given! Play the above mentioned infinitely rising tune and listen to a parable of scientific progress: The progress goes on but the central epistemological questions remain invariant."

The 5th Dimension is now being utilized as spin chirality of light, the hidden momentum

"Spin resonance was found to occur when the base oscillatory frequency was twice the value of the coupled frequency." This is the secret of the T'ai Chi as the Hempel Effect - 1 plus 1 does not equal 2 in noncommutative phase harmonics. The third harmonic is noncommutative to the root 1 and 2 octave. "An underlying curved space-time provides a distinct contribution to a chiral imbalance, an effect known as the mixed axial–gravitational anomal....We also show, for the first time, how to measure the magnetic spin density of light,...Black hole elasticity and gapped transverse phonons in holography" Nobel Physicist Yang: ."An electrically charged particle is affected by an electromagnetic potential (V, A), despite being confined to a region in which both the magnetic field B and electric field E are zero. If the electric charge through gauge invariance creates an electromagnetic field, wouldn't this isotopic spin also generate a field? And that is the motivation.." Nobel Laureate physicist CN Yang A single photon has such little momentum transfer so then it is amplified through a mirror feedback at the same frequency. Since sound waves are just 1 dimension, so this makes the transduction easier. The entanglement through beam splitting of the mechanical resonator enables frequency transduction while maintaining phase coherence. Total Reflection can approach Unity if Pitch is Half the Wavelength [octave], close to the qubit transition frequency [noncommutative phase]

Jing to Qi is nonlinear harmonics resonance

Raising the body temperature is synonymous with an increased immune response. Professor Abo from Japan confirmed a 40% improvement in the function of the immune system by raising the body temperature by only 1.8° Fahrenheit. Another scientist, Ishihara Yumi, PhD (Japan), established that our immune system much stronger when the body temperature is increased by 1.8°; inversely, the immune system is weakened by 30% if the body temperature is lowered by 1.8°. His statistical analyses revealed a decline in body temperature amongst the Japanese population by an average of 0.9° over the last 50 years. In his studies, Professor Hiromi Shinya, PhD (Albert Einstein College of Medicine, NY, USA) confirmed that, lowering the body temperature by only 0.9°, results in a 30% decline in enzyme and immune activity. He also discovered that cancer cells can multiply much faster at 95°F than at 98.6°F

Eddie Oshins discovers secret of non-western shamanism as quantum noncommutative phase

Nega-particles as reverse time (anti-gravity) guide light as noncommutative energy-information

The Ether-Aether-Emptiness has been Empirically Proven: Yakir Aharonov: "There is a non-local exchange that depends on the modular variable....I'm saying that I have now an intuitive picture to understand interference by saying that when a particle moves through two slits, it always goes through one slit or the other, but it knows which other slit, the slit through which it did not go, whether it is open or not, because there are nonlocal equations of motion." Finally making sense of the double-slit experiment (2017, Aharonov): The nonlocal equations of motion in the Heisenberg picture thus allow us to consider a particle going through only one of the slits, but it nevertheless has nonlocal information regarding the other slit.... The Heisenberg picture, however, offers a different explanation for the loss of interference that is not in the language of collapse: if one of the slits is closed by the experimenter, a nonlocal exchange of modular momentum with the particle occurs....Alternatively, in the Heisenberg picture, the particle has both a definite location and a nonlocal modular momentum that can “sense” the presence of the other slit and therefore, create interference...""What is the effect of this nonlocal motion?...The idea is the following then...In the beginning I certainly don't know through which slit the particle is going because I want to know the module momentum. Then I wait for the interference pattern to happen and after it happens I can check whether the particle was coming from this side [slit] or coming from that side [slit] by a future experiment." "So if I'm able to describe the situation in the present by two vectors: one coming from the future that will tell me through which path the particle went and one coming from the past that tells me that the modular momentum is definite. Then I can see, indeed, there's nonlocal phenomena and not violating causality, because I said I know only from the future through which path the particle went. This is the basic idea and now I will try to describe it more mathematically." as John Bell states: "Is it not clear from the diffraction and interference patterns, that the motion of the particle is directed by the wave?" Grant Sanderson, math/science Stanford: Unlike the doppler radar case where the ambiguity arose because waves were being used to measure an object with a definite distance and speed; what we're seeing here is the particle IS the wave - so the spread out over space and over momentum is not some artifact of imperfect measurement techniques; It's a spread fundamental to what the particle is: analogous to how a musical note being spread out over time is fundamental to what it even means to be a musical note. Grant Sanderson, Math/science degree, Stanford University

Astrophysicist Paul S. Wesson figured out the Law of Phase Harmony explained spiritual phenomenon

Professor Paul S. Wesson realized, the 4D spacetime universe exists in a holographic 5D black hole. Wesson:

...the presence of oscillations in the vacuum have the same properties as de Broglie waves....5D field equations which in 4D has the properties of a de Broglie wave....the difference can show up as a small perturbation which leads to an effect similar to quantum uncertainty...

a "wavicle" is two simultaneous realizations of flat space, one with waves and one without.

From the viewpoint of 5D field theory, waves of de Broglie type have to be considered real.So in 5D all particles behave like photons and everything in the universe is in causal contact with everything else.

an oscillatory phase, which might (if a person is so inclined) be identified with... spiritual modes of existence...separation
between points is zero, so all of the events in the world are in (5D) causal contact. In other words, everything is occurring simultaneously. There is no plausible way to avoid the conclusion that particles which can be seen moving at speeds less than c should be accompanied by waves which cannot be seen and are moving at speeds greater than c.

de Broglie waves are better understood in 5D ...characteristic of inflationary cosmology...its 5D complex generalization...as a model for de Broglie waves. A null interval admits, in a formal sense, velocities in 3D which exceed lightspeed.

a particle not as a point but a tiny ball of trapped waves. ..some of it verging on the mystical.De Broglie waves follow automatically when the expressions for the energy of a particle [E=mc squared] and a wave [E=Planck's Constant multipled by frequency] are combined.

This, admittedly, sounds strange.

Whether one believes in a model like this that straddles physics and spirituality is up to the individual....However it is remarkable that such a model can even be formulated, bridging as it does realms of experience which traditionally have been viewed as immutably separate.

"We were simply studying these circuits for the purpose of developing an amplifier, which we did," says researcher Sorin Paraoanu, a theoretical physicist at Aalto University. "But then we asked ourselves—what if there is no signal to amplify? What happens if the vacuum is the signal?"
https://www.scientificamerican.com/article/something-from-nothing-vacuum-can-yield-flashes-of-light/

Also, a simple connection between Q_M and relativity theory for the De Broglie particle/pilot wave concept shows that v_p v_w = c² is required, where the subscripts p and w refer to particle and wave, respectively. Thus, since v_p < c, always, via relativity theory, v_w> c always for the information wave components making up the De Broglie pilot wave.

http://www.entelechyjournal.com/httpdocs/billtiller.htm

"When high energy substances of the subconscious mind emerges, they should be one's guiding force."
qigong master Yan Xin

The Hempel Effect

Visually, the frequency and amplitude changes but the EAR hears no difference - both phases are the Perfect Fifth just inverted as undivided yin-yang (the Taiji). I was discussing noncommutative phase with Nobel physicist Brian Josephson - and he said that I didn't understand how octaves were a geometric logarithm - so that C to G is 3/2 yet G to C is 3/4 as the harmonic series. So I tried to point out to him that since the 2 and 4 are the SAME C as "pitch" - then in the same octave, when doubled back, you can not HAVE the same G as Both the Perfect Fifth and Perfect Fourth. Why? Because 3/4 is the reverse direction in time - so that now the "3" is the denominator as a new root tonic. And so the harmonic series assumes this is a logarithmic equation as a ratio that can be inverted - but you can not evenly divide the octave and the Perfect Fifth since 2 does not go into 3 evenly. So this means that 3/4 is actually C to F while C to G is 3/2 and the C to F was derived from doubling 2/3. So this is called the "phantom tonic" in music theory and reveals the noncommutative phase origin of the music harmonics - as Alain Connes recognizes. Let us draw up a fundamental vibration with its first and second harmonic overtones [1:2 and 2:3]….if we then shift the phase relationship, we get a totally different course of the combined curve; that is, of the pressure course [amplitude and frequency] which is apparently effective in the final analysis. When looking at both curves, one might suppose that in the two cases we should hear two sounds that are just as different. But in fact our ear does not notice any difference. biophysicist Vitus B. Dröscher states in his book, Magic of the Senses, p. 168 I defer to Cambridge University physicist R D Patterson who, in his classic academic “Psychology of Music” journal paper on the spiral pulse-stream processor—describes how period is inverse to pitch and natural integars for pitch create a free-energy transduction from the ear (sound-wave-mechanical pressure, water pressure-electromechinical transduction) to the brain. Normally period is measured in frequency—as is the case with the photoelectric effect—but since period is the inverse of pitch then the natural number integars of frequency as period can be translated back to Pythagorean Just Tuning as the Natural integar numbers of Infinite Quantum Potential. However, because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard. Therefore, subjectively, the frequency of the envelope seems to have twice the frequency

Philolaus relied on noncommutative phase, same as Daoist alchemy harmonics

Philolaus relied on noncommutative phase, same as Daoist alchemy harmonics, 4/3 (yin, C to F harmonic) within 3/2 Yang (C to G overtone) as Yang (3/2) is within yin (4/3) 0 to 8 is the 3/2 frequency (2/3 as C to F subharmonic of 0 to 12 now converted to 6/8 as 3/4 wavelength of 0 to 8 root tonic!) Professor Richard McKirahan: "So instead of taking 12:9, which is 3/4 of 12, we take 8:6, which is 3/4 of 8. And so by adding the length 12 to 8 [as geometric magnitude not wavelength!!] with the length 8 to 6, [as geometric magnitude, not wavelength!!] we get the length 12 to 6, which corresponds to the ratio 2:1." So he states: "beginning at the bottom note...and descending via another (a fifth above the bottom note)." So he says "bottom note" twice to emphasize they are symmetric and then says "via another" to HIDE that the "other" is the OCTAVE!! That is the bait and switch - and then he says - (1, 4) = (7, 5) What is (1, 4)? It is a Perfect Fourth which is the PITCH of C to F (overtone, 4/3). Anyone who actually knows how to play music would not fall for this bait and switch! What is (7, 5)? It is a Perfect Fourth which is the PITCH of C to G! "The term subcontrary may refer to the fact that a tone based on this mean reverses the order of the two fundamental musical intervals in a scale. It is believed that Archytas or one of his contemporaries gave the name "harmonic" to the subcontrary mean because....[book source: Infinite Series cover up of the noncommutative "bait and switch"]. Math professor Luigi Borzacchini: "Boethius’ text that I am going to analyze shows that the early musical theory of incommensurability was somehow known, even though it had been overcome by a sudden rupture." Professor Richard McKirahan: "The word translated epogdoic is not a musical term but a mathematical one. An epogdoic ratio is the ratio of 9 to 8. The occurrence of a mathematical term here is unexpected. It has been treated as an unimportant anomaly but in fact it is the key to the entire fragment....The word magnitude normally refers to physical size, but here it is given a new application, extending the notion of magnitude to include musical intervals." Or as Professor Borzacchini states: " These remarks raise the question of the difference between the ancient Pythagorean ‘musical’ perception as displayed in the Pythagorean idea of ‘linear number’ in Boethius [Philolaus] or in Nicomachus, and the modern ‘geometrical’ perception of the linear numerical magnitudes."

Ancient Advanced Acoustic Alchemy - free training book

Thursday, April 17, 2025

Sir John Pendry Temporal Interference Asymmetric Resonator: Time-induced double slit experiment as eternal noncommutative time crystal

Time-refraction optics with single cycle modulation

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