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～THE PERFECT SOLUTION of R.H. (by a new right light theory)～
[Preface]
The existing (light)quantum has specifically (peculiarly) physical property of wave-particle duality by nature.
Most people would not know well why its elementary particle (particularly photon) could have caused spontaneously such (what) a strange physical phenomenon….
But fortunately, it will be able to (re)solve this important matter and the other unsolved problems incl. the greatest (deepest) mystery of the quantum entanglement etc .. indeed without difficulties,
especially by utilizing the Riemann zeta function’s “…”….~~
~~~~~
First of all, it would have been shown that the pair correlation between pairs of zeros of the Riemann zeta function is the same as the pair correlation function of random Hermitian matrices by Montgomery’s pair correlation conjecture as the following mathematical formula (an extract).
That is, intervals of every nontrivial zero of the Riemann zeta function could have been equal to energy level(s) spacing of atomic nucleuses….
The above energy levels would have taken discrete values….
The discrete energy levels should have been primarily related to Planck’s quantum hypothesis (the Planck’s law).
E = (n)hv n : natural (integral) number
It’d be having mainly the existing physical characteristics of the quantum fluctuation that would have been repeating the pair production and the (pair) annihilation by a (virtual) particle & an anti-particle with a very short period of time (incl. theoretically Planck time)….
Just the next expression on the mechanical energy including the kinetic energy (except the potential energy) which would be convertible into the light (thermal) energy for one pair of the two particles with same masses… particularly considered a spot of completely inelastic collision as a point collided at that time of the annihilation…
1/2(m +m) v2 = 1/2(m +m)⋅02 = 0
The above equation would have resembled closely the following formula(e).
ζ(0) =-1/2 0=1/2+it (it=-1/2)
By the way,
The value ζ(0) = −1/2 is not determined by the functional equation, but is the limiting value of ζ(s) as s approaches zero.
In other words, the value (zero) of ζ(0) =-1/2 is extremely near zero, not just 0….
- Note : Refer to the following paragraph [The Complement] for the reason why it is not fixed from the Riemann zeta functional equation…
As for the above numerical quantity (… amount) approached perfect zero on the nontrivial zeros of the Riemann zeta function,
it is not suitable to apply mainly the rest energy amount of the particle (an electron) and/or its anti-particle (a positron).
But, it could (should) be allotted as the zero point energy for the fundamental particle (a … photon).
So, it may apply the lowest energy for a virtual photon (not a real particle) of quantum vacuum fluctuation.
Although the existing visible light comprises each photon with a different wavelength (energy level), no one would ever know how to emit its various photons together at the same time (moment)….
- Note : According to the established definition of single photon sources, it has not yet been determined the (root) cause of the single photon with the varied wavelengths….
We should think about this issue that is based on its lowermost energy : Evp for the (uniformly) virtual photon at first and the (visible) light which combines varied photon energy levels with each luminous flux by various multiple (not common multiple) of a basic wavelength upon Evp would have been derived from its luminous source (newly named “Initial Photon : IP”)….
- The related (simplified) expression for the visible light (from violet to red in the spectral colors)
(a+b+c+…)λ1 = W1+W2+W3…W7
(bλ1 =)W2: Wavelength of photon energy level (amount) for the blue color
(The rest of them are omitted.)
(a+b+c+d+e+f+g)λ1=W1+W2+W3+W4+W5+W6+W7
(a+b+c…≠0)
And then, a sure curve line(s) just like some waveform between each zero point along mainly t axis (and so on) in the related graphs of Riemann zeta function would have shown mathematically (theoretically) a (random) locus of the above virtual photon (energy) with the recurring annihilation of the quantum fluctuation.
- See the graphs below.
And also, after calculating the number of all the nontrivial zero points per second, regarding t axis as the timeline (time axis) with the units of Planck time etc,
(see the below description/account on the imaginary part for that reason of its applicable time…)
it may obtain (determine) an arithmetical mean (average) value of the above waveforms (sine wave) from (half-)cycles among the zeros which plural red & blue lines cross there….
That is (must be) a certain (net) waveform of the virtual (initial) photon per (every) second.
- Note1 : A virtual
photon (ene