Contiguous & Time-Dynamic Quantum Certainty

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Rotation

Before exploring quantum spin/rotation, let us analyse rotation.

Frequency is a facet of rotation:

c = f * λ which relates to v = f * λ , where velocity and wavelength are proportional to the density or refractive index of the medium which a wave passes. From one medium to another either independent dimension must remain constant. That is frequency or wavelength must remain constant. Wavelength, λ, is a distance. It will change subject to density changes of the material medium it is passing across.

Tone, with sound, is similar to colour with light. They are the fundamental identifiers of the length of a wave. When sound moves from a one medium to a less rarified medium, the wavelength will decrease. That change as with Doppler shift - also a wavelength change, rather than a frequency change can be demonstrated in a thought experiment.

A spring will shorten its individual coil lengths when gravity accelerates on the vertically oriented spring. Gravity is an acceleration. Given that fact, lateral pulses of acceleration on a laterally and frictionlessly suspended spring will produce corresponding pulses of coil-length shortening. When air replaces the spring as the modulus and is similarly affected by percussive accelerations the tone is higher in response to higher accelerations.

For the wave to pass through the air medium, it must move at the same speed as the compressed air over time. That relationship is λ / T for which the outcome is wave velocity, v. As velocity changes while wavelength changes, frequency cannot change or its value will either be unpredictable or time evolve at a rate of the power of 2. We know that it is linear progression, so frequency is constant. That means that wavelength is the sole determinant of sound tone and light colour for any given velocity of the same.

The Calculus of the Physics

Circumference = Pi * ( 2* r)

= Pi * d

Area (circle) = Circumference (circle) in dimensions

= Pi * ( 2 *r ) ^ 2

= Pi * d ^ 2

Volume (circle) = Circumference in 3 dimensions

= Pi ( 2 * r ) ^ 3 , and not 4 * Pi * r ^3 / 3

4 * Pi * r ^3/3 is a mathematically incongruous answer

Volume = Pi * d ^ 3

Circumference (n dimensions) = Pi * (2 * r) ^ n

= Pi * d ^ n That is the more elegant and preferred expression.

Pi, Power Rule

As Pi is the measure of one full cyclical event,

Pi ^ n = Pi , where n ϵ { natural numbers} , N

Diameter is the preferred dimension of orthogonal orientation.

For waves displacement (distance evolved)

Sin ( θ + φ ) = Sin ( ω * t + φ )

ω * t + φ = rad / s * t + rad

ω * t represents a dependent dimension. All dimensions are dynamic. They all have an apparent (independent) dimension of time or concealed (dependent) dimension of which time is an independent factor. Constant dimensions are similarly dynamic - constantly dynamic, just as is the case with ω * t.

All dimensions must displace with contiguous differentiation otherwise one early point would have the same scale and properties as the next. That would place them as the same point, since there is nothing different about them. A constant wave would accommodate that perfectly. By that logic, all constant dimensional world lines are waves when they are observed with enough magnification.

Radians, rad, is a measure of rotational distance. One full rotation is Pi * d, where d = linear displacement or magnitude when using Sin ^2 ( θ ) rather than Sin ( θ ). When observing energy, there is no negative energy, so Sin ^ 2 ( θ ) is natural and Sin ( θ ) is an artificial observation, as it produces negative values and could not represent energy for that reason.

Expression Physics Units

ω * t + φ ---> rad

The expression, sin ( ω * t + φ ) measures the vertical displacement of a wave over the continuous dimension of time. ω = Pi * d ---> rad * m. Since diameter and circumference are scaled by the same Cartesian plane dimensions, the units of measurement are the same. With harmonic motion, radians is the preferred uniform unit to measure all events on the plane with, for harmonic displacement. ω * t ---> rad * rad * t , rad *1, rad.

Angular Product Rule

rad ^ n = rad

For one cycle of a unit circle,

C = Pi * d

= Pi * ( v * t )

= Pi * ( ( λ / T ) * t )

= Pi * ( ( λ * f ) * t )

= Pi * ( 1 m * 1 Hz * 1 s )

Spacetime

There can be no other value for frequency, there. As it remains constant, all frequency is 1 Hz. That implies that 1 Hz must be interpreted a 1 cycle per moment, or one cycle per unit of time. That makes perfect sense if we see on unit of time or one moment as one rotation, where time displacement is understood as rotational, harmonic or cyclical. If time is rotation (f), then distance is diameter (λ). c^2 delivers the 4 dimensions of spacetime - two of space λ ^ 2 and two of time T ^2, which is 1 / f ^2.

The equation is

spacetime = c

= λ ^ 2 / T ^2.

Quantum Field Equation

The quantum field equation is based the following relationship

A = Sin ^ 2 ( ω * t + φ ) for on state exclusively

The full field equation is (without Σ fully defined) is as follows

A = Σ Sin ^ 2 ( ω [ i ] * t + φ )

Amplification in the equation would make it relativistic. The expression above is complete. Arithmetic combination of waves or quantum dimensions is how nature combines necessarily dynamic quantum states. They are all time-dynamic. Only phase shift is constant.

Electromagnetism

Electromagnetism is the product of rotation (electron spin or time) and its magnification known as distance or revolution (photonic spin or electron). The time dimension is magnetic. The spatial dimension is electric. Quantum physics is time physics or magnetic physics. When invoking ω * t + φ , quantum physics represents predictable, quantum certainty. Werner Heisenberg's quantum probability comes to the end of an eventful shelf life, today.

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