Energy Model

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Energy as Electromagnetic (EM) Radiation (aka Light in all its frequencies, including visible colors, radio waves, microwaves, x-rays, and the rest) propagates in 3D space over time at the speed of light, called 'c', which is constant uninfluenced (as in a complete vacuum or outer space).  Spins in 3D space project onto 2D planes, like graph paper and oscilloscopes, as an oscillation (see the picture above).

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Rotational Symmetry of Rate

The GEMSTone model of Energy adds a symmetry not found in traditional physics - rotation at rate c as the limit achieved by Light as the translation limit achieved by Light is also c.

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Complex Equation of Light

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This 2D graph shows the general form of the complex equation of GEMLight for EM radiation where the gold curve is the Imaginary number part (using i = sqrt(-1)) and the blue curve is the Real number part.​  The imaginary part represents the time-phase aspect of light while the real part represents the spatial component of light.  These curves dissipate with distance or time, since c=dx/dt means either distance dx or time dt can use used since they are fixed multiples of each other, as c*dt = dx, and dt = dx/c, per the inverse square relationship observed for EM radiation.  

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In 'Cradians', the maximum slope models the maximum velocity in the X-Y plane, so c = pi/2 Radians (thus the name, Cradians).  

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​Spin Model

As was mentioned, these 2D plots are projections of a 3D spin onto a flat plane.  These pi-spaced oscillations in 2D represent 3D spins in space.  What is Frequency in an oscillation interpretation is the number of central axis crossing per unit distance.  As the Frequency increases, the curves pack more tightly together.  In the GEMSTone model, the distance between the real and imaginary curves relates to the wavelength of the energy as a spinning filament with the general form as shown by the curve - so as the Frequency increases, the wavelength as distance-between-curves decreases, and this is visualized as the energy filament getting narrower.  A higher oscillatory Frequency is a more tightly wrapped 3D spin of thinner filament width which more completely fills the volume of space in which the energy filament spins - this equivalent to more dense matter more completely filling its volume.

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Cross Products and Gyroscopic Stability

Notice that these curves are projections of spin about the Y-axis which represents Time (dt), where the X axis represents Distance (dx).  Since velocity v = dx/dt, when v = c, dx/dt = pi/2 Radians.  A spin at rate c does 2 things simultaneously: First, it induces gyroscopic stability about the central axis, in this case stability about the Time vector as the vertical Y-axis; second it causes some spatial indeterminism since the spin about Time occurs in space.  This accounts for observations of non-locality such as quantum tunneling.  

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The GEMSTone model of matter/antimatter interaction, as electron and positrons in this context, follows the Law of Assembly: The waveform of the electron and the waveform of the positron under coherent alignment engage in constructive superposition.  The Feynman view of a positron being treated as an electron going backwards in time is maintained in the GEMSTone model.  The mechanism in GEMSTone is the opposite cross-products of the opposite spin directions of the electron and positron at c about the Time axis.  The cross product of the electron spin at c points 'forward' in our view of the passage of time, while the cross product of the positron at spin -c points 'backward' in our view of the passage of time.  The spin differential between them is |c*-c| = c*c = c^2 (meaning c-squared).  

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The photon is the region of constructive interference over an electron/positron wavelength, which results in these velocities (+dx/+dt) + (-dx/-dt) producing dx/dt → 0/0 = c.  This is seen as the relatively "flat" spot around the origin in the curves.  As soon as that state is achieved, the invariant speed c is obtained by the superposed wavelength and the assembly as EM Radiation with electron-lobe and positron-lobe with Photon as the superposition propagates linearly at c.

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The inverse square dispersion of the energy filament starts from its peak Amplitude of brightness, and diminishes from there.  For scale, an Amplitude of 1 decreases to below the minimum ionization energy of an electron at about c meters (1 light second) from the origin.  Energy and photons are not point size particles - they have extent as shown by the equations of the waveform.  Objects do not interact at regions comparable to their size, ever.  Note that Any two rigid spheres of Any size interact at exactly 1 point.  Arbitrary curves in opposite directions interact at a singe point.  A photon is the length of an electron/positron wavelength.  The EM radiation is attached continuously to the photon region of the waveform and dissipates with distance according to its initial amplitude.

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Net Spin Cancellation

Remember that in math, when the Left-Hand-Side (LHS) is equal to the Right-Hand-Side (RHS) of an equation, as in LHS = RHS, each side is equivalent to the other, by definition of equals (=). Where E=m*c^2, Energy exchange of 'E' terms is equivalent to m*c^2 interaction.
 

The opposite-spin electron and positron counteract each other's inertia, and the net inertia (mass) is 0 for Light.  The time vectors are opposite and cancel leaving no stability about the Time axis.  The negative electron charge as e- is opposite to the positive positron charge as e+ and these cancel leaving the Photon with 0 charge.  Charge is a measure of spin about the Time vector axis.

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The dual-spin system itself spins about the origin, and that cross product creates the direction of propagation of the photon, orthogonal to the electron and positron lobe propagation directions.  These symmetric spins at the same rate propagate in 3D space, and the lobe extents form a spherical shell in space - and this is the source of the inverse square dispersion of Force over distance.

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These plots of GEMLight show two complementary waveforms containing photons in superposition. The central photon regions are net-zero in amplitude and do not engage in constructive interference, since any waveform added to zero retains its original value. This structural non-interaction explains why multi-colored light — including white light — can be decomposed into its constituent photons: they coexist within the superposition without altering each other’s geometry. Each filament retains its twist density and frequency, allowing diffraction or filtering to reveal the individual components.

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If the Light decouples its superposition interaction between the electron and positron, these opposite spins no long counterbalance, and the electron's spin at c give it stability in that orientation of Time while the positron's relative spin at -c  give it stability in that opposite orientation of Time, and each inertia is present as the mass of matter (electrons) and antimatter (positrons).  

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GEMSTone Expansions

So the conversion from the Energy state to the Mass state depends on the opposite spins whose spin differential is c^2, so the ratio for the GEMSTone expression is E/m = c^2 - or in the more familiar form, E = m*c^2.  We know c=dx/dt, and in the GEMSTone Cradian measure c=pi/2, and pi = C/D.  Thus all these forms are interchangeable:

E/m = v^2, v=c

E/m = (dx/dt)^2 = dx^2/dt^2, c=dx/dt

E/m = pi^2/4 = C^2/4*D^2, c=pi/2, pi=C/D

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This GEMSTone meme shows the invariant ratios, from left to right: C/D=pi, E/m=c*c, dx/dt=v.

Note that these invariant ratios produce invariant ratios, as (E/m) / (C/2*D) = dx/dt = c.

​Potential Energy

In the GEMSTone expansion E/m=C^2/4*D^2, an increase in Energy requires an increase in the geometric ratio on the right-hand side. For a fraction to grow, the numerator must increase faster than the denominator. Thus, increasing E corresponds to the Circumference term C growing more rapidly than the Diameter term D. Geometrically, this means the Filament’s overall twist length increases faster than its width, tightening the rotational strain. This twist tightening is the structural mechanism by which a Filament stores higher potential energy.

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​Subluminal Form

Objects with mass like electrons have v < c and appear as an angle between 0 and pi/2 radians.

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GEMSTone Kinetic Energy

KE/m = v/2 x C/2*D

This expression arises from the mixed GEMSTone Energy form:

E/m = dx/dt x C/2*D with the substitutions:

• c=dx/dt

• c=pi/2 in Cradians

• pi =C/D

The GEMSTone form reproduces the standard mechanical result:

KE = 1/2 * m*v^2

but reveals why the one‑half factor appears.

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​The one-half term is applied to v because in Cradians, the velocity angle is:

omega = arctan(v)

and the velocity-fraction angle is:

nu = arctan(v/c)

so the maximum slope when v = c is pi/2 radians, while the maximum slope of velocity fraction is v=c at c/c = 1 at pi/4 radians. Thus the velocity‑fraction angle reaches only half the maximum slope of the velocity angle. This is the geometric origin of the familiar 1/2 factor in kinetic energy:

the halving comes from the angular geometry of velocity, not from the structure of space.

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When Force is added to a structure with v<c it can manifest as velocity increase, geometric deformation, or a combination.  In the limit, a rigid structure transfers all Force into increased velocity as acceleration, while a sufficiently non-rigid structure transfers all Force into increased geometric distortion before the structural renormalization results in a velocity difference at the CM of the structure, where velocity is characterized for a massive object.  When the geometry of the waveform twist loosens, the effect is increased velocity.

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Force, Rigidity, and Subluminal Response

When Force acts on a structure with v < c:

1. Velocity Increase (Rigid Response)

A highly rigid structure cannot absorb much twist strain.
Thus nearly all applied Force manifests as increased translation:

F → Delta_v

This is the classical “acceleration” regime.

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2. Geometric Deformation (Non‑Rigid Response)

A less rigid structure absorbs Force as increased twist strain:

F → Delta_Twist

Only after the structure renormalizes does the center‑of‑mass velocity change.

This is the Curvature–Translation Amplification Principle in action.

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3. Mixed Response

Most real systems lie between these extremes, partitioning Force into both:

• twist strain (as stored potential energy)

• translation (kinetic energy of linear velocity of motion)