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2Ð Locomotion: æ

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Introduction

Particles and waves – entropic and reproductive locomotion.

Locomotions, the 1st  Dimotions are translations in space, in which the parameter of life duration of the imprinting is minimal in adjacent motion-form/position STates.

Let us follow the procedure of other posts and study the simple, lineal motions of the Universe – hence wave motions – with the  Disomorphisms of the ECD method (experimental facts and correspondence with classic theories, enlightened further with new insights provided by the Disomorphic space-time properties of all systems of reality).

Loco-Motion studied by Physics is the simplest of all motions and the first studied by human beings, related to pure lineal motions (without entropic scattering, which decelerates a motion in time, converted into an spatial new dimension).

As such locomotion is essentially a ‘self-contained’ reproduction of information obtained by:

  • 2D: an ‘∆-ST-wave’-motion on present space-time, which reproduces its simpler form different from:
  • 4D: an ∆-1 or by a ∆+1 particle > ∆-1 field, which disorders the lowest scale in 4D ‘producing’ an expansive, backwards effect on space used by the particle ‘to glide’ over it (rocket-like motion.

In that regard the 2 forms of motion belong to two different dimensions of space-time. But we shall consider them both in this post, as the 4Dimension of entropy is more connected with its function – death; and the duality of those 2 motions compared here will give us an opportunity to compare the two fundamental states of systems:

  • Present-wave state
  • Past to future, entropy to information, potential to particle state.

∆-3 scale: Those 2 forms of locomotion are obviously more clear on the quantum scale, as it is the limit of human perception, where the reproduction of information only needs to chance or imprint the lower gravitational scale (wave reproduction) and/or its quantum potential (particle reproduction).

The first is described by Schrodinger’s wave equation.

The second past-potential>Future particle by Broglie->Bohm pilot wave theory recently proved, in which the particle moves by expanding and scattering the lower field (likely a gravitational neutrino background, with pilot wave scatters fluctuating around a c-constant).

Its analysis in detail will set the way in which locomotions occur in higher scales and more complex fluids (so locomotion in gravitational and ¥-space-time will be akin to locomotion in fluids either as waves or particles do). But we shall not introduce mathematical physics in-depth till the 4th line. So here we shall just make some insightful comments.

screen-shot-2016-12-29-at-09-13-20To start with ‘obviously’ the maximal speed of motion happens in the minimal form of information, light, as it has to imprint barely the quantum potential/gravitational invisible field to form the electromagnetic field, reason why the equation of c-speed refers to the lower quanta of magnetism and electricity that ‘order’ into a bidimensional wave form:

c² = 4π k(electric, coulomb curvature)/µ-agnetic constant

Notice how Maxwell’s equation change, as we ‘extract’ by squaring it, the ‘actual holographic c² st-wave of light, which is decomposed in the other side, passing to the numerator, the meaningless εo constant, which REALLY is, the inverse of the real ‘thing’ the k-curvature constant of electric fields. So the wave of light imprints/curves the quantum potential/gravitational field/neutrino background/dark entropy (similar concepts with slightly kaleidoscopic different views on the same theme, the ∆-1 larger scale).

Lower scales. quantum potential, infinite speed.

Now, the human being moves on electric repulsion and gravitational forces, taking advantage of the larger space and motion of the i-4 scale, below the scale of i-3 bits of perception… and for that reason the realm of ‘quantum potential forces’ is both invisible, with zero information and infinite, non-local in speed, to us: V=s/tiƒ=s/o=∞.

So we come now in full collision with the invisibility of pure time (information hold as the eidos, of platonic thought in an immortal logic immanent program of actions of all systems) and pure space (simultaneous infinite speed-distance of the invisible gravitational field, with its relative infinities), with the concept of ‘finitesimal’ (relative infinity of 0 size of ginormous size from an ∆o perceiver) and all the other questions that physicists have never properly grasped on the limits of our mental reality.

Locomotion, speed, wave and field-particle duality.

The Paradox of Galileo – ‘why if the Earth moves, we see it still?’ – is the key question to understand the meaning of dimensions, which can be generalized to all forms: ‘why we see reality still, if all what we study in the quantum scale has motion?’

The answer-  given by quantum physics that we expand to all scales – is the law of complementarity: ‘all what exists is still and has motion at the same time; all is a ‘fixed particle’ and a ‘moving wave’, but we perceive a limited quantity of information about reality – either state, but not both dual, complementary states, a motion-wave state and a still-particle state, together.

The fact is the best explanation of motion is one of reproduction of information, which requires a constant stop, reproduce your information in the next region of space-time, go… sliding and converting motion in yet another form of reproduction, which becomes then the fundamental ‘nature’ of reality – a fractal that reproduces information. And we shall return to that key insight.

In the graph, we show also 3 practical/theoretical proofs/explanations deduced of it – just a token of the ginormous number of ‘solid’ whys provided by ∆st: .

  • The complementarity wave-particle and our perception of quantum motions as a constant reproduction of the wave-form states..
  •  which means the minimal unit of reproduction, the angular momentum, h, will always be unlocalised by a unit (uncertain principle), as the process of reproduction is always between two steps…
  • A fact that solves  Achiles paradox, as motion has a finitesimal limit in the ‘bit of informative reproduction’ and its size.

C-constant speed.

Of the 5 possible points of view of the c-speed constancy, the realist view is that the speed of the observer doesn’t add because measures are taken at the ¡-3 plane of particles in their stop position

It explains also in realistic terms why c-speed is constant in relativity: TO COMMUNICATE both particles must first entangle each other in the lower scale (neutrino/gravitational/tachyon scale at ¡±4), so they HAVE no motion relative to each other… and so when we measure with human eyes or electronic eyes the speed of light that we have communicated, with other ‘locked’ entangled particle always will be measured in the stop position of both particles at constant c-speed.

But as we in the ‘human scale’ ∆o see continuous motion integrating the ‘camera-like’ stop and go perceive and move reality, to make measures of time and space in our level of reality accurately as continuous motion we need to use Einstein’s time dilation/length contraction and mass increase.

Let us then fully switch to the perspective of:

 ∆-1: Particle Steps and Stops: locomotions and information gauging.
Why particles move slower than c-waves has to do with the very essence of what is a particle – a form of in-form-ation that through the spin is able to ‘perceive’ information and needs to go through a ‘stop and go’ motion.
So particles unlike  pure waves must stop, ‘spin’ to get a ‘sense’ of ‘where it is’ and then move again.
And this duality of stop and motion slows down the particle. It HAPPENS IN ALL SYSTEMS THAT MOVE AND STOP TO PERCEIVE AS CAMERAS DO:
In the graphs above, we can see the stop and go motion of particles and antiparticles as they complete their motions and cycles of existence. On the left in the mechanism of a camera.
So how a particle moves? The answer if we want to get into the maths of it has to do with the conversion of the particle into a ‘wave state (E=mc2), in each step of its galactic motion.

And that wave state is defined by Compton’s wavelength, which is a quantum mechanical property of a particle,equal to the wavelength of a photon whose energy is the same as the mass (mass-energy equivalence) of that particle.

The standard Compton wavelength, λ, of a particle is given by λ=h/mc.

And it relates to the speed of a mass, as follows. V=s/ð, where ð is the cyclical frequency of information or mass parameter (E=mc2+e=hƒ->Mass=h/c2 ƒ.

As mass is the frequency of rotation of a cosmic time vortex:

Thus the more information a locomotion reproduces the slower it moves. And this is why the ‘frequency of the Compton wave’ that represents the mass but also the length-step where the mass must be reproduced is ‘smaller’; the mass stays longer in the position to reproduce all its information.

This step and stop motion of particles becomes then an essential feature of a ginormous number of equations of physics as a particle of higher mass must spin, stop and then move. Spin is then the parameter-clock of information of the system and so as the speed moves towards c, it becomes a limit, which the particle tries to break but can’t without loosing its own nature.

The outcome are the dilation of time (spin cycles that define our perception of time, as the minimal unit of intelligence of the Universe, are now more difficult to close as the wave constantly moves), and an increase of mass (the inertia to motion increases as the speed ‘deforms’ the particle), till finally before reaching v=c the particle explodes into entropy (the inverse of information) so the sign of Einstein’s equation changes to ‘negative mass’.

It must be understood that as motion is reproduction of form, the particle cannot advance without ‘stopping to reproduce its form in the adjacent’ part of spacetime. This is perceived as a Zitterbewegung (“trembling motion” in German), whose value is one half of the uncertainty of position, (Heisenberg principle). Since indeed as the particle reproduces itself in adjacent regions it constantly is ‘trembling’ back and forth in its ‘mitosis’ equivalent to one half of the position of the particle point.

Quantum steps and stops.

Let us now do for a change a bit of mathematical physics from the previous understanding to show how 5Ð physics differs in its interpretation of the same laws:

Virtual particles are ‘steps of reproduction’ of the particle through its locomotion paths, as they go on through that motion, each step of this motion has a value of ‘energy quanta’, which can be called in each scale an h-quanta, a Kb quanta or a C-quanta, whose ‘frequency’ is given by the ‘side’ element, frequency in one dimension, temperature in two dimensions and mass in 3 dimensions.

This simple truth has many implications in 5Ð quantum physics. Consider that all particles’ steps can only last an Energy x Time ≥ h in its printing steps on the lower plane; as that is the Unit of information it can reproduce in each step. This gives us a maximal time for each step of h/mc².

While this particle is in the wave state of motion on the other hand it can be treated as a ‘photon’ imprinting on the c-spacetime of the galaxy, given by the Compton wavelength of the particle; that  is equal to the wavelength of a photon whose energy is the same as the mass of that particle: λ=h/mc.

So the larger the mass, the shorter both in time and space of the steps the particle does imprinting the lower plane of light spacetime in its ‘2nd Ðimotion’ of locomotion. But alas! all particles can in fact if we calculate its speed, s/t = wavelength/time duration of the wave = mc² /h/mc = c, reach the speed of light in their imprinting of the background light spacetime of the galatom.

The difference being, that more massive particles do imprint much more mass-information, more ‘existential force’ as ‘stronger species’ than lighter ones.

It follows then that in the lower planes of existence the super predator is the black hole, which can move as fast as c-speed and imprint a ginormous mass in the process, albeit doing very small steps, till reaching the Planck Mass, of extremely small steps, occurring in a extremely Planck time period.

But this rule on praxis, reduces when the species are complex organisms, which have above the scale of radiation and the scale of mass or charge (which is the more proper concept to apply on them, as the vortex that is moving is normally a charge vortex of energy not a mass vortex), as it is not only a mass-radiation particle but it has to ‘redraw’ all the upper scales of ‘subtle forces’ that make up atomic interactions into molecules, cells, states of matter and so on.

In that regard, the rule of maximal c-speed occurs for what we might call the ‘minimal trace’ of information a particle can ‘send about itself’ – its existential force in terms of mass and wavelength, or ‘virtual particle’ of the being. When the entire being displaces, as it has to imprint then other types of scales of information, even a black hole star with its internal structure of heavy black atoms, the speed reproduces as the stop ‘state’ of the particle is much longer.

Now, this virtual messenger of the ‘incoming’ physical species, will also have a limited range-distance it can travel, according to mass, once the initial ‘impetus’ of its parental emitter is no longer here, based in the same ‘unit of information, h, that the parental emitter has disposed off to send the message, which is the justification of the range law of forces; which again is immediate: h/mc² (its time duration) x c (its maximal speed) =  h/mc², which is for example 10ˆ-13 for an electron. So if we consider the electron, the ‘message’ which two atoms share in a molecule, it follows that molecular ‘forces’ tend to be on that range, reason why they are so ‘tightly packed’. 

Now and here 5D physics departs sharply from current astrophysics and its ‘paralogic’ Kantian errors (which break the scientific method in the egocy of the cosmologist to have an explanation for all even when his range of perception does not allow it), there is NOT infinite range force, because ‘obviously’ the photon does HAVE energy hence it does HAVE mass, E=hƒ, so even if its mass is extremely small (and we cannot weight it as we cannot stop it, except when the electron does it, keeping it closed by its black hole-like infinite potential well that bends light into a c-speed trap, which is what the membrane of the electron is, being its nebulae a density of trapped electrons, it ‘feeds on’ as it moves with the obvious maximal probability for it to be feeding on the region of the trapped photons of maximal density (organic explanation of Born rule)…

So the range of the photon CANNOT be infinite unless we elongate its wave frequency to a limit of energy mass, in which the light is no longer light as we mean it, because it has gone to a range of size where ‘quantum effects’ are no longer meaningful as we have moved to a higher scale, on the gravitational cosmological world of galactic atoms… 

Now the light mass which can be considered the mass for simplicity of a polarized wave of a single electron, will always be mc² = h ƒ  m = ( h/ c²) ƒ…

If we add to that calculation all the other aforementioned facts, considering that the wave of light has MASS only when it is in the photon state, but that it is IN THE PHOTON state every time the wave collapses at the end of its wavelength, and that waves of ‘higher frequency’ (blue light) have both shorter wave-lengths, so it states in the photon state of mass more frequently, and have more mass when they are photons, hence their range-life existence as photons is smaller, this means in practical terms an obvious fact:

The distance-range of light is inversely proportional to the square of its frequency-mass (as there are 2 factors to consider, the time it stays in particle state, and the lesser length of its frequency).

This again of course, is the law for all vortices of time-space that ‘are exchanging virtual particles’ of information among them; which is by the Rashomon method yet another way to calculate the square mean distance law without resource to ‘geometrical means’ (the usual method we might term ‘entropic, ‘flat’ method’ as opposed to the previous one based in the opposite arrow of  curved, ‘information, form of the wave-particle’…

The falling of range of a force also extracts information about what is the use of that force for the particles involved. i.e. the strong force/gravitational strong field inside black holes decays ‘exponentially’ as it is essentially a ‘feeding force’, which is as we know always represented by an exponential equation of death-decay; in this case of particle-antiparticle mesons in the black hole star scale and its self-similar color-anticolor gluons within the nucleus of the atom.

And finally the weak force of no range, is obviously an evolutionary force that transforms quarks into larger scale masses.

Back to the 2Ð-locomotion study of light rays, its mass and range:

This aforementioned simple relationship explains a few things:

  • The inverse square law that applies to both gravitational and electromagnetic forces mediated in the galatom space-time light background (remember we are always talking locally).
  • The redshift of light coming from far away galaxies, as their blue light of higher frequencies does NOT reach us, having exhausted its virtual life
  • The existence of a limit or horizon of perception of light, as even redshifted light will finally ‘vanish’, when its ‘red frequency is so ‘huge’ in wavelength’ that no longer belongs to the scale of quantum/electronic existence in which we reside – electrons cannot longer capture them, its energy is too small and so we humans or our instruments become blacked out literally.
  • The explanation of the (no) big-bang horizon, as it is not the horizon of an explosion in the past, but a limit of our perception of light as electronic beings.

But if we were other type of mass species, much heavier, then we could ‘gravitationally shift’ and collapse the huge red-shifted waves of light, bending it around us, as black holes do at the galactic level, it is this precisely what happens with cosmic-like sized waves of light that in the presence of a galactic black hole bend such red-light giant electromagnetic waves  with its halo of strangelets, as atomic electrons do with far smaller wave-lengths, since ultimately both are self similar species.

So while we electronic humans are black out to larger distances galatom black hole stars and strangelet halos are not. They are able to communicate with far more remote distant galatoms of huge black hole masses.

What is then the limit of perception of light? As we have experimental evidence there is no need to do further calculus: Obviously the 13.5 billion light years from where red-shifted light of maximal z comes mistakingly taken as a time horizon of a supposed big-bang explosion.  

Now, if we apply the entangled, Rashomon method to this explanation, we can of course consider another points of view – from the entropic Ðimotion of light we might say that light gets ‘tired’ and dies; from the reproductive point of view of light, we might say that ‘blue short frequency light’ if entering a field of mass (another galatom) will not traverse it but will reach a reproductive ‘collapsing’ point giving birth with the extra boot of frequency to a 3Ðimotion, becoming a particle with rest mass and not traveling further; from the point of view of social evolution (5Ð) we can see this happening in huge amounts on the jets of blue light coming out of black holes, accelerated to collapse in a region in which a child irregular galaxy is born; and finally from the 1Ð point of informative perception, we have already explained those virtual particles give us the information of the emitter in terms of its Compton-wavelength and mass.

And from this fact it also follows that the further away we look, the more likely we are to find huge black star holes, as they will emit more energetic high frequency particles that will take longer time to relax in terms of the 4Ðimotion of entropy to reach us before dying into a red frequency blacked out of our perception; if they are ‘not intercepted’ by other galaxy that collapses into mass (which is what most do as obviously the galatom when emitting them tend to do so, through a twisted accelerator-like magnetic field set up first through its central kerr-singularity region in order to keep accelerating them for collapse into its seminal irregular galaxy baby, but that is another story that belongs to the study of how galaxies reproduce).

Let us then consider that some of the seminal flows produced by the galatom escape with a wider angle of emission the magnetic field set up as an accelerator trap by the father black hole. Those then will start is relaxation travel… And here is where the magic 10¹°-¹¹ number common to all structures of nature, both in space-populations/distances in time-frequencies/durations and in scale/masses kick in.

This is the number that gives us the mean life of stars, and the mean life of its minimal light space-time ‘unit’ of information, and the mean mass of the largest black holes from far away distances measured in terms of the mean star mass our sun, and the mean distance of the black out horizon of the big-bang.

So of course in 5 Ð, as we know the Universe is eternal, the big bang does not exist, and we have far more sound logical and epistemological and experimental proofs to explain everything.

On the other hand Big Bang theorists are at increasing pains with better telescopes to explain why the densest, largest black hole galaxies in the Universe are found to be born at larger distances, earlier ages of the Universe, when all theories imply they are very slow growing and appear latter in time. The largest black hole found is also the oldest, as it is the furthest, and it was supposed to be born in 500 million years after the big-bang when only some re-ionization of light hydrogen atoms has happened.

It then takes the pain of creationist dogma and believers to tinkle with all the equations and models we have to feed computers till some simulation of very extremal conditions very unlikely to happen can give us some bizarre model that might explain how on the hell, in just 500 million years a black hole of the size of 66 billion suns appeared in the middle of a perfectly formed gargantuan galaxy. Rational answer BECAUSE THERE WAS NOT BIG-BANG.

Simplest proof. Such a black hole will live 10¹ºº years ad minimal (counting that there is black hole evaporation, another no-no error we explain in our 5Ð study of black holes)…

So by mere statistical probability, we exist within the supposed life of the Universe which we can at least elongate to the life of that galactic black hole in the absolute infancy of the Universe, more or less in the 0.00000000000000000000000000000000000…. keep adding 90 000001% of its life span, and the probability that we exist in that moment without any other data, is similarly 0.0000000……..(keep adding 90 zeros)1 % chance.

The big-bang as we shall show in so many pages of this blog is the very proof not of the birth of the Universe but of the ‘common nature’ of all huminds, scientific or religious: dogma and belief is always higher in the esteem of the majority of humans of any profession than truth and reasoning.

Or as Landau put it: ‘cosmologists are seldom right but never in doubt’

Other hypothetical entropic forms of motion.
In that sense particles can’t move faster without having to go through the slow motion of becoming a wave to achieve reproduction, and the very slow process of reproducing upwards, through all of its planes all its information.
At best, they can just clean up the field ahead by ‘warping space-time’ expanding behind the lower scales into an entropic explosion, very much like a rocket does externally but ‘intrinsically’, producing an expansive entropic wave in its lowest possible scale.
This kind of reproduction is what physicists call a warp drive, which we compare with a similar concept, AN EM DRIVE THAT uses the quantum potential to that aim.

screen-shot-2016-12-29-at-09-10-40 screen-shot-2016-12-29-at-09-11-22

In the graph particles move by adjacent reproduction of its minimal form, communicated to simple ∆-1 beings, which acquired the wave packet form.  But particles of higher ∆+1 order would have a very slow hard time reproducing all its forms ‘again’ from zero, onto the lower field, so what they actually do is ‘tear’ the fabric of the ∆-2 scale, (remember that systems do exist only as ∆±1 ternary elements), like if it was ‘tense’ rubber band, so they expand entropically, scattering its back region and ‘compress’ its frontal region, on the ‘limits’ of c-speed provoking an alternate expansion slightly above c of the wave behind and a contraction slightly below c in front. In this manner Broglie’s theory recently proved right by the EM engine, explains the general different motion of a particle, that ‘breaks’ the fabric of space-time ∆-2 scales below to move, faster, denser informative particles, which if moving as a ‘wave’ would take eons to reproduce its form.

One all this is said we can consider locomotion in aspects not treated by classic physics, from the point of view of the fundamental concept involved, the ratio of S/T energy/information, entropy/form that determines the speed at which a system reproduces in space-time adjacent regions as waves or particles that ‘tear’ the fabric of the lower scale, scattering and leaving a ‘vacuum’ through which it moves.

Its fundamental constant of action is ‘speed’, which appropriately relates, the 2 other dimensional parameters in its simplest forms (lineal space and lineal time):

V(i-4)=S/T=∂S/∂T

Indeed, while we move due to the gravitational forces caused ultimately by the black holes of the Universe and its gravitational pull in the i+4 scale beyond which perception is meaningless, we neither see black holes nor gravitational forces. 

We shall thus deal in this scale of reality in 3 sections:

  • In this post we will consider the action of motion in different species, and how it follows the toroid steps of energy functions. Indeed, when we consider the duality of ‘spatial distances’ vs. ‘lineal, toroid motions’, motion is the action of toroid limbs and fields, perceived not statically but as a flow.
  • In the posts of physics and forces of the 10 Dimensional scales perceived by man, we shall deal with the standard laws of gravitational forces and the laws of motion of physics, enlightened by the knowledge of ∆ST theory which will allow us to demonstrate the ‘non-local nature of gravitation’, consider the 3 ‘ages of evolution of gravitational theory and its validity (Newton, poison, Einstein) and many of the fundamental principles of physics.
  • In the study of the i-4 dimension of ‘force’, we shall study forces from the scalar perspective of their interaction with the i+4 Universe. And the ultimate paradox of motion as the reproduction of a scale of points with minimal form and maximal energy.

SUMMARY

2D-3D: Locomotion of present waves. 

1D-4D: Locomotions of past to future particles.

5D: Complex Locomotions of  ∆±i organisms.

2D-3D motion: WAVES

Motion is natural to waves, which are thin covers of new information, ∆º imprinted on a lower ∆-1 relative plane of the 5th dimension and as such waves are the fastest, most enduring motions, as the quantity of information they print is always minimal. 

The wave is a ‘fleeting’ motion that hardly changes the form of the lower scale it imprints with its motion. As such is the ideal ‘form’ to study the simplest $t-eps of reality, and the constant ‘switch’ between motion and form.

Strictly then we consider the wave the simplest information possible, even if paradoxically species transmit information through waves. But it is a ‘communicative information’, NOT a genetic, generational information. Waves do NOT transmit the o-1Dimensional seed of the being, which must be regarded as a ‘particle, still state’, but communicate the ‘thinner ‘envelope’ of the system.

Thus waves are more connected to the external membrane than to the singularity, and do NOT transfer much internal vital energy, but rather peels a sensorial cover of the system, ‘re-forming’ with it the underlying ∆-1 quanta of the medium, which therefore must be ‘affine’ to the point/membrane in which the wave of information started its motion:

In the graph the simplest creative motion, is the creation of a wave of form by a sinusoidal function, which contracts the ∆-1 medium provoking an inverse distension of space in the lower substrata to reach an ∆º-1 balance between both planes.

This inverse motion of the whole ‘generator’ of the wave (the cyclical or SHM element) is the key reason why waves do happen, in inverse fashion between the ∆º plane of the ‘fermion’ that generates the ‘boson wave’ in the lower ∆-1 plane, ordering it as a ‘shallow’ whole, where the envelop of the wave is a loose ‘membrane’ imitation of the cyclical, reinforced one (as it passes through the x²+y²=1 unit circle constantly, creating a cyclical inertial form that the wave ‘looses’ as soon as the vibration ends. 

The existence of such waves proves that ultimately in the lowest strata of reality there is a quantum potential/gravitational field of non-local action at distance, which is ‘pure motion and the vibrating particle uses to imprint the first form, light, as a boson wave that transfers ‘shallow’ basic informative communication with other particles at the extreme of the wave, which will collapse closer to its ∆+1 plane into a ‘density’ micro particle (photon) absorbed as information by the other electron/particle, entagled initially through a neutrino≈graviton:

We deal with the ‘special’ aspects of the c-constant light wave in relativity revis(it)ed born as the case of the special nature of quantum particles, of the fact that it is one of the two extremes of virtual perception of the humind (the larger scale in the c-case) and so we do NOT perceive the interaction between the quantum potential and the wave of light, at the ∆-i level and the wave of light and the gravitational plane in the ∆+i level.

Let us then instead of making it too complicated go straight forward to the study of waves in which we do see both ∆±i scales.

A perfect one-dimensional traveling wave follows the equation:

ψ (s, t)  = A cos (ks -ωt +φ)  where:

s is position in space, t is time cycle, ψ (a function of s and t) is the disturbance describing the wave (for example, for an ocean wave,
ψ  would be the excess height of the water, or for a sound wave,  ψ would be the excess air pressure).
A is the amplitude of the wave (the peak magnitude of the oscillation),
φ is a “phase offset” describing how two waves can be out of sync with each other,
ω is the temporal angular frequency of the wave, describing how many oscillations it completes per unit of time, and related to the period
T  by the equation: ω = 2 πT
k is the spatial angular frequency (wavenumber) of the wave, describing how many oscillations it completes per unit of space, and related to the wavelength by the equation  k = 2 πλ.
This wave travels in the +s direction with speed (more specifically, phase velocity)  ω(t) /k (S) = λ/T= λ (s) x ƒ (ð).

So we see immediately THE FUNDAMENTAL QUALITY OF A WAVE and its perfect illustration of the parts of T.œs and the steps of all Universal motions in 5D²:

The time and space elements are absolutely symmetric to each other, ks, wt; but inverse through a perpendicular symmetry, which under the ‘cosine operator’ appears as a ± symbol. The inversion in lineal time however becomes a product in cyclical time, where each wave is a step of a time sequence of frequency motions.

 So motion is a constant S≈T≈Step, in which the system transforms itself as it reproduces its forms along the path of motion from S-tate to T-ate:  $<t>$<t… for a lineal reproductive motion as the one-dimensional simplest wave is.

Finally as a system the wave has the 3 , 1,2,D components OF A PRESENT FORM:

1D: The singularity that vibrates as an SHM around a central point of balance:

2D: the envelope of the wave, which can be seen lineally as the wave travels along its path o cyclically, as an angular momentum reproduced by the combination of the ‘particle’ in ∆+1 and the ∆-1 lineal motion which feeds the wave, and WISHES to be, moulded in form as a…

3D: vital energy transferred by the wave, as it GIVES form to the more lineal motion of the ∆-1 quanta of the wave; and it is defined by the amplitude of the wave, but in most cases ‘squaring it’ to have a bidimensional or three-dimensional volume of energy, giving us the intensity (or in the quantum formalism, the probability) of the energy wave.

But why the points accept to mold their motion as form? Ah, my friend that is the mystical part of it that no abstract ‘scientist’ with its arrogant anthropomorphism and dog-eat-dog ‘capitalist’ aberrant view of reality – culture is science – will accept:

THERE IS A CONSTANT, NATURAL TENDENCY-DIMENSION OF ACTION IN ALL BEINGS, WHICH ARE IDENTICAL – TO LOVE EACH OTHER WISHING TO COME CLOSER AS IDENTIAL BEINGS IN TIGHTER HERD AND EVOLVE SOCIALLY INTO ORGANISMS. This 4th i-logic postulate of non-Æ geometry is the key to MOST actions of the Universe, either perpendicular≈darwinian or parallel≈social. In the case of the wave, as it is a disturbance up and down, IT IMITATES in parallel up and down, in each micro-particle, of the path of the wave, the UP AND DOWN, motion of the larger original SHM singularity that started the wave. All wish to ‘dance up and down’ in parallel to the ‘macro point’ that initiated the wave, and so they transmit up and down, and as the flow moves left to right, we see this synchronic social love as a wave of information from the particle in SHM to the receiver at the end of the wave. The mathematical description being simple, and well-known, it is not worth to repeat it.

Group and phase velocity. A sample of the application of the 3 ‘methods of knowledge’ 

Let us now consider a ‘sample case’ on how I work with the Ðisomorphic method. We always start from the generator, and try to define the 3 x3+0 elements, and find its main disomorphisms contrasted with experimental events. Obviously we just make a sample of the whole process here. Then once the Ðisomorphic method is applied, we contrast our findings with the classic scientific language, which in the case of waves is mathematical, to see if our first deductions are corrected, and if not try to harmonise properly the 3 legs of a isomorphic method, which are the 1) Experimental method: scientific facts and events to describe 2) Disomorphic, organic method: its interpretation with the most general ∆st laws of ‘stience’ (T.œ ternary parts, 5D”, generator, disomorphisms)  & 3) Classic, ‘correspondence’ definition in human ‘sciences’ (scientific method), in the precise language huminds have used, which can be anything from musical scores, to mathematical equations, to verbal logic, to color theory in a painting, to poetry homologies…

AS anything can be enlightened by adding T.œ laws. So let us apply the 3 legs of the E->D->S to wave speed.

Another important element of waves is then to connect its different speeds with the 3 elements of the wave. The wave as  a T.œ IS the group velocity, which has a constant form, maintained by the envelope, responds to T.œ laws – most likely made of 3 (5)> 9 (11) waves in ternary packets, which are then the ‘vital energy within the outer envelope’, and seemingly NO singularity, as waves are essentially present forms of minimal complexity and singularity particles extend through multiple ∆±1 planes. But in closer look, the singularity can be considered to exist at the front of the wave, in the point in which the wave ‘collapses’ its form; travelling within the wave at faster speed from the back to the front of the wave, tracing its inner form, protected in a relative stillness within the envelop, and this is the faster phase velocity of the wave.

Mathematically, though, we can refine our analysis as a second layer of study, after we interpret the space-time event/form with T.œ ternary generator laws:

The group velocity vg is classically defined by the equation: Vg =  ∂ω/ ∂ k where ω is the wave’s angular frequency (usually expressed in radians per second), and k is the angular wavenumber (usually expressed in radians per meter). The phase velocity is:  vp = ω / k.

As per our article on analysis, since a derivative is a ‘quanta’ of space-time of a whole. Yet the group velocity is in this case surprisingly not the whole, but the quanta of the phase velocity…

Alas! As our description must correspond, we must have made an error of interpretation in the novel Disomorphic analysis… As obviously the group velocity is ONLY the envelope (a derivative quanta), WHICH IS not MAINTAINING a synchronous stable inner world together, hold as in a super organism all the parts in synchronicity with the membrane. 

We reinterpret then our analysis and with a little bit of thought it becomes then obvious that indeed, the internal region of the wave does NOT move, but vibrates up and down in connection with its parallelism with the ∆+1 SHM particle.

The energy is then definitely that up and down ‘amplitude of the wave’, which is NOT ideally damped because IT APPEARS by synchronous resonance between parallel particles-forms, imitating the previous form, trying to maintain its ‘relationship’ as the wave advances. And this up and down motion is what travels as individual quanta-momentum, integrated into ‘energy’ (form of the particle with up and down SHM motion). Then the group velocity is merely an accessory to this energy, which we call in ∆st the ‘ideal wave velocity’, when BOTH are synchronised in speed, as ONLY then the wave is a ‘T.Œ’ (Where always the 3 parts limbs/potentials<wave-bodies>particle-heads are synchronised).

Is this new interpretation correct, in experimental/mathematical models? There is a wave in which both phase and group, energy provided by the phase, and form provided by the envelope are synchronised, and do respond such wave to the PERFECT S=t SYMMETRIES of REAL T.œs?

The ternary classification of waves. 

S=T: Indeed, there is such a wave. Since when  ω(t) is directly proportional to k (s), and hence S≈T is a perfect symmetry the group velocity is exactly equal to the phase velocity. A wave of any shape will travel then undistorted at this velocity.

So this is the ideal wave that harmonises EDS, the experimental isomorphic and classic scientific language of wave (mathematical mirror).

All other waves are not perfect wave-organisms, imperfect T.œs without the proper synchronicities of the parts of the whole and as such should be studied. And the possibilities are as follows:
T≈S: If ω is a linear function of k, but not directly proportional (ω=ak+b), then the group velocity and phase velocity are different. The envelope of a wave packet (see figure on LEFT) will travel at the group velocity, while the individual peaks and troughs within the envelope will move at the phase velocity.The clocks of the body and membrane of the wave differ; but at least as both are in a lineal≈stable proportionality, the wave will maintain its form.
T≠S: If ω is not a linear function of k, the envelope of a wave packet will become distorted as it travels. Since a wave packet contains a range of different frequencies (and hence different values of k), the group velocity ∂ω/∂k will be different for different values of k. Therefore, the envelope does not move at a single velocity, but its wavenumber components (k) move at different velocities, distorting the envelope.

Entropic motion

The general law of T.œ applied here being the 4th postulate of parallelism=equality and perpendicularity=dissimilarity, which increases the entropic disorder and ultimately makes the wave a disturbance with no relevant information but ‘noise’; which is a good introduction to study the second type of movement, the scattering motion of particles, which leave an expansive wave of destruction behind that seem to move the particle faster (as entropy is initially faster), but IT WILL NOT BE A MAINTAINED MOTION, as the distortion affects the underlying ∆±1 world, and finally will ‘tear’ topologically the ∆-1 stretching/compressing backwards/forwards direction, ‘snapping’ exhausted halting the motion-impulse of the particle and ‘potential field’ around it; which again in physics is expressed with laws of potentials and work, and so we shall study those themes in the 4th line, if I ever come to reorder my 11 annotated notebooks on Lindau’s awesome encyclopaedia of physics, where the whole EDS method is applied to every equation of physics… enough for today though… we shall return

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