Move over or tap on either image to activate (may take a few seconds to load)
Synchronized field or path integral:
V(Φ) = ⎰ | ∏ cos(f0∙rsn + θtp) | dx
V(Φ) = integral vacuum potential
f0 = nominal rate or frequency (=1)
rs = scaling ratio (producing scale-invariant wave set)
Θtp = phase propagation (in parametric time)
In other words, each factor Φn = fn(θtp) is a functional of the phase propagation, so that:
V(Φ) = ⎰ | Φ0(θtp)Φ1(θtp)Φ2(θtp) etc.. | dx
So far it has numerically been shown that for rs=φ (Golden Ratio, 1.618..), n=0..2 and x/L0 >>1:
V(Φ) = ⎰ | ∏ Φn(θtp) | dx ≅ A + B cos (2∙θtp)
With L0 being the wavelength of f0. This means that the synchronized field produces an external (“2-theta”) oscillation with twice the frequency of the internal, nominal phase wave. In physics terms, this breaks the symmetry of the field.
The amplitude (top-top) of the 2-theta oscillation, B, is apprx. 4% of the ground level A. The latter in physics is hypothized to be the Vacuum Expectation Value (VEV).
Note: the standard use of the letter Phi for the field as well as for the Golden Ratio is mere coincidence. Either way the uppercase Φ refers to the field, and lowercase φ refers to the scaling ratio.
The individual phase waves Φ0, Φ1 and Φ2 are shown at the bottom, with the absolute value of the composite wave ∏Φn above it.The purpose of the model is to show the synchronized field’s “2-theta” wave A + B cos (2∙θtp) in a glance. For that purpose the ground level A is filtered out, and gain B is normalized, say from 0 to 1, so that the synchronized V(Φ)norm ≅ cos (2∙θtp). In the animation this is the total white area under the curve of the composite wave.
The model can be seen as a purely manual spherical projection of ∏Φn "seen from above”, whereby lighter colors indicate higher peak levels. The final rendering merges the composite wave with the integral potential through the multiplication ∏Φn∙V(Φ)norm, for each ∆x.
The sinusoïdal segment left from the centre traces the ideal “2-theta” wave, for easy verification and comparison.
Waterfall power spectrum of the "2-theta" wave generated out of the synchronized field, for axiomatic scaling ratio's ranging from apprx. 1.5 to 1.7. Exactly at Golden Ratio the spectrum peaks, proving the unique resonance point.