Discussion

These observations correspond with my belief that physical reality is fundamentally spectral and random in origin. The traditional approach to this subject has been through analysis and therefore uniqueness. Notions of smoothness may be the wrong language to use here, with the Zeta function. For instance many phenomena in nature are fractal. As like the branches of a tree, they may exhibit glint, spikes or flash. Signals may be Analog or Digital, so signal processing provides a very general language and does not necessarily require a classical spatial continuum in its description. Indeed, Weierstrass, the father of modern day analysis postulated a continuous function that is no-where differentiable. A recent paper by S. C. Woon has indicated that Riemann Zeta function is a fractal and that through Voronin's Univerality encodes The Sum of All Theorems.

Everything maybe reduced to Signal-to-Noise ratio – light, heat and sound are perceptions of waves and our brains are in fact wave-sensing devices. I suspect the total number of photons has to do with allowing the different features in scale to be seen from Quantum (very small) to Euclidean (in everyday experience) to Cosmological (very large). This includes the large-scale modulation (large wavelengths) that we simply don’t notice. It maybe that a critical amount of quanta is needed – Googol =10^100 say, to cause this as seen on the Dyson-Montgomery information curve. THERE IS NOTHING MAGICAL IN ALL OF THIS IN THAT IT IS ONLY THE AMOUNT OF POSSIBLE INFORMATION IN THE UNIVERSE THAT GIVES RISE TO ITS FEATURES OF SCALE - THAT IS ALL THAT THERE IS. The modulated Rice function is just an information curve – of all possible information. The primes represent unique ‘infon’ states albeit through a complicated relationship to the encoded Zeta function. The primes represent the minimal bit length of possible information that can be compressed¹⁹ as they can't be factored down into smaller integers (otherwise they would eventually be broken down to nothing).

Zeta effectively simulates the ensemble of all physical reality, and the reality is itself quantal, although our brains are not consciously aware of this level of reality.

The RICE distribution contains a Modified I0 Bessel functions (of the 1st kind – zeroth order) multiplied by the Rayleigh density, and my modification is extended to be RICE distribution multiplied by a combinatorial sum which is the sum of all possible signals.

Computation in Zeta may not have yet revealed the cosmological characteristics (viz. the Rice modulation of all combinations of signals) in the statistics of the Montgomery-Dyson curve, because of the current limits to bit capacity, and that bit itself is deterministic (quantum computing is still in its infancy).

The cosmological implication to all of this could be that the ‘Big Bang’ is still happening but only at larger scales; the spike could be that of dark energy – the missing 73% or so that pushed out (area under the spike). The outgoing information 'shock wave' carries on for eternity. The dark matter are seen as ripples in the Montgomery-Dyson curve, and imprinted as the gravitational rotation curves (Reference Vera Rubin) associated within the space curvature across large scale galactic structures. Galaxies may have super massive black holes at their centers, such as 'The Great Annihilator' at the center of our Milky Way. They have the mass of millions of suns, and it has even been suggested are the gateways to other universes (via Rosen-Einstein bridge) by forming a neutral force ring between the central singularity and centrifugal rim. These lead to some important questions: Are black holes described by thermal phenomena limited to the left hand side of the curve? Could it be that black holes, as well as physically essential to stability, are demanded to logically exist?

What we see in our observable Universe is the small-scale debris left behind after a massive ‘shock wave’. If we increase our field of view looking out on the cosmos using some super telescope, SNR increases on the Dyson information curve (where the mean signal-to-noise ratio is normalised; <SNR>=1). A constant position in scale in an expanding universe implies eventual thermodynamic ‘heat death’ as the noise-limited case is approached in time (increasing entropy), while the farthest reaches are seen to be accelerating away (negative tangent beyond the singularity at π/2). For 'Sum of all Possible Signals + Noise' , read as 'Sum of All Possible Universes'. This may help explain Hawking's 'No boundary' proposal.

This negative pressure field may represent the inflationary phase of the universe where matter and radiation were not yet separated, but the universe become transparent when crossover occurred to positive pressure, and gravity started to cluster mass objects. The Casimir Effect may affect the energy of the vacuum to be actually manifested in the resonances of the Riemann Zeta function in the far limits up the Critical Line.

Thus in effect:

The sum of all signals, where each signal is noise modulated with infinite detail, gives rise to physical reality.

Zero point energy is seen at these higher cosmological scales with some infinite bandwidth by Fourier transforming) from an unlimited information/energy tap from the ‘big bang’ spike in the ‘time' domain. This originates from the modulated tangent in the RICE probability density function and it may be the means why our Universe evolved from ‘Nothing’ (d –d =0).

BULLET POINTS

In recent months, I've had time to further reflect on some fundamental and probably unanswerable metaphysical questions within our present language. Partly based on my findings, I've put these in as bullets for discussion and allude to some of them:

Prime numbers code the fundamental units of information. Information is the fundamental unit of Physics.
A final theory must not be concerned with continuous fields, not even with spacetime, but rather with information exchange among physical processes.
Can a prime number spectral analyzer ever be built? What is the impact on key encryption?
Mean Signal-to-Noise ratio SNR. With no restriction, S £ N or S > N equally likely so mean [S/N] or A²/2σ² = <SNR>= 1 in the MRice⁴ distribution. Incredibly, mean signal-to-noise ratio of unity gives stable, flat infinite bandwidth in the Montgomery graph. All other values not equal to one are unstable.
Array processing techniques such as beam forming and replica correlation (against original signal) are not only analogous, but physical manifestations of techniques that operate on elements within random matrices.
The relationship with prime numbers makes the essential information invariant whatever the information processing. An analogy is the same film recorded on both DVD and Video VCR. The format of the data, and the way the data are processed is completely different with each of these platforms, although the viewer would watch and experience pretty much the same film (within variations of sampling and picture quality).
The information paradigm provides a description of MIND + MATTER - The Mind-Body problem. Can thoughts and dreams be described within a signal processing framework? Is the brain a quantum computer, and could it ever be replicated by machine? It has been suggested (Roger Penrose - The Emperors New Mind & Shadows of the Mind) that neurons contain special microtubule structures that perform transmissions and quasi-computations within the intermediate scale between classical and quantum mechanics.
The Universe appears to contain fractal structures repeated randomly at all scales like branches of a tree, down to a level of quantisation, below which the reality is impenetrable. Is the quantisation²⁰ seen as pure coherent signal in the energy levels of atoms at whole numbers of level spacing? Compare the Montgomery -Dyson curve at the lower levels in Section 5. Do the teeth look like the Balmer Series²¹ in Hydrogen atoms? First glint at x=0.16~(1/2p) 2x free space value, relative distance down to next glint = 0.03/0.16 = 0.1875. No surprise that stars are made of Hydrogen in their purest form.
Take the square root of the ratio of the mass of a neutron to the mass of a electron = 3/[Öj - z(3)]. This is an interesting relationship (Eaglemann Prize) between physical atomic constants that involve the Golden Ratio j ((Ö5+1)/2~1.618..) and the Riemann Zeta function evaluated at 3. The former involves fractals, continued fractions (Ramanujan-Rogers identities?) and aesthetic geometry; the latter encodes prime numbers. Is this numerology or meta-mathematics?
Do massive galactic black holes look like atoms when observed from the vantage of larger scale? Do they emit dark matter i.e. ripple outward space.
Does information processing negate String Theory? What of the Standard Model?
The Big Bang is an eternal process, at ever increasing scale in a universe with no boundary coming through as a 'point of light' of all information contained. Can the Big Bang ever be reconciled with a kind of Steady State of never ending expansion - with scale invariance rather than length invariance? Can we ever surf the information wave or will 'heat death' ultimately prevail and we slide back relatively on the curve?
Can new technology - anti-gravity, flying saucers, spaceships, spinning magnetic fields harness the energy of the vacuum ? Could this provide the unlimited thrust to travel to the outer reaches of our universe and allow us to escape this fate? UFOs, electrogravitic propulsion?
Are rotating black holes sources of (unlimited) dark energy? Black holes may in fact be dark energy stars as they require an infinite time to form, but actually theoretically evaporate in a finite time.
Does the Riemann Hypothesis relate (indirectly) to Loop Quantum Gravity (Lee Smolin)? One-to-Many map of Mathematics-to-Physics.
Hologragphy in black holes that give information on the outside 2-d surface mapping one-to-one the 3-d (+gravity) on the inside depending on one's relative position on the "God prime spike" within an AdS/CFT framework. Does the singularity at p/2 in the tangent function represent some kind of a "cosmological horizon" between the inside and outside of our universe.
Are such discontinuity man-made due to our partitioning pieces of nature's jigsaw to manage concepts such as mass, energy and momentum? Does signal processing describe a more fundamental level of physical reality? These are loaded questions. Does the sum of all possible signals, set our universe uniquely - Probability to Actuality across the singularity by analytic continuation?
The Yang-Mills Mass Gap. Does light have mass? Both, YES or NO, 1 or 0. It dwells in the Sum of all possible signals. LHC?
Gravity is non-baryonic in origin - it leaks into our universe; in parallel but distinct from the electro-weak and nuclear forces associated with matter. The modeling of energy levels in atoms has no 'handle' for gravity; is this the missing Higgs particle? l ® ¥ gravity modulates space as a carrier wave as seen in the ripples. Gravity becomes weaker (in time) and cannot brake the accelerating universe.
Big Bang as an eternal process and expansion outside requires less instruction than all the processes that go on inside - is there any kind of analogy with serial and parallel computation respectively as suggested by Seth Lloyd/Y. Jack Ng? Is the information lost at (and beyond) the event horizon? Is the transfer of information, and therefore determinism, always limited by the speed of light?
Is physics described by an information interface of relationships between physical processes rather than the physical entities themselves?
Black holes are associated with stupendous amounts of entropy. Is this a natural connection to the primes?
Are the sum of all Signals + Noise really random?
Is dark matter the imprint of the side lobe ripple formed from the God spike discontinuity? (Note, the sidebands are features of what is known as the Gibbs phenomenon, due to the Fourier Transform over a discontinuity, in this case the God prime spike).
Are formations of galaxies explained by unraveling the ensemble of all signals and noise around their central massive rotating back hole.
Are galaxies the residue at the back-end of the God spike?
Are these Boltzmann spikes the 'boot-up' of reality and the 'kick start' of life in our own internal model of the world when we are born. The laws of Physics serve as approximations and models of reality but NOT reality itself. At its most fundamental level, reality must be information-based down at some Level X (whatever X may be), and not the compartmentalized world-view of General Relativity or Quantum Mechanics which contain only some of the essential elements.
In the semi-classical limit h ® 0, the transition from quantum to classical chaos description is highly singular. Does this represent the crossing of the 'Boltzmann' God spike from signal (finite bandwidth) to chaotic (infinite bandwidth) respectively? The Planck signal A = n.h becomes diminished so the God spike ® Rice (S+N) ® Rayleigh distribution (noise-limited) as the SNR becomes zero. Does this come out as thermal noise in our universe as an event, when the 'dice has been set', rather than one of an infinite set of probable outcomes in the multiverse?
Semi-classical limit. Decoherence and the effect of decoupling the environment, h ® 0 with emergent phenomena at the macroscopic level.
The End of Time T ® ¥ is when the outside observer sees the object (the unfortunate astronaut say) crossing (or rather hovering at the asymptotic limit of) this singularity at the event horizon and increasingly becoming red-shifted; leaving our universe to the multiverse of all possible signal plus noise. This is a transition from classical chaos to the realm of probability (quantum theory). (In his own private frame of reference, the astronaut will cleanly cross the event horizon within what appears to be normal finite time, without noticing anything unusual assuming he survives and is not fried by heat or radiation). Is the asymptotic limit T ® ¥ at the boundary of the cosmological horizon looking in at the multiverse.
Is the Universe the logical consequence of observership? Is observation essential to its existence, as opposed to the Platonic view point?
How is common experience shared through differing perception? Are these perceptions as real as physical objects such as tea cups, rocks, dust, stars and galaxies?
Consciousness passes through us sentient beings. Maybe it passes through, but not from the Big Bang, forever as a loop singularity. Is this the Sum of All Possible Signals plus Noise?
Is there a place for God, are the primes God-given - or does it pass all understanding? Is our universe the only anthropic one from all the multiverse. Or is there some cosmic fine tuning involved σ=1 in Rice⁴ distribution for stability, averaged over all possibilities? Was it constructed for our benefit? Are the properties of the Riemann Zeta function that special?
Does the optimal packing of information (namely the Sum of all possible Signals) emerge as our Universe? I conjecture that the % of mass/energy that is dark energy = FCC packing efficiency (~74.04%). This is discussed in the next section on the Kepler Conjecture.

"I am Alpha and Omega, the beginning and the ending,.." (Revelation 1:8)

Adrian Rifat

A special acknowledgement goes to my friend Ron Mantay who helped me construct this website. The pioneers of the internet have enabled an ordinary person like myself to disseminate my own findings and experience from a different subject perspective, that may be of interest to others. I am especially grateful to Matthew Watkins for including my paper to his site which is an audacious enterprise to connect Number Theory with Physics.

I have made 'clear blue water' between myself and the mathematical community for at least two years. I passionately believe that mathematical knowledge is for everybody and nobody owns it. There is a real hunger for understanding of the deep fundamental questions by people not necessarily associated with traditional academia, but who have equally worthy contributions from their own professions and experiences especially in subject areas such as engineering and information science that may overlap. Often they can be easily dismissed and tarnished with the same brush as other 'nutters' or 'cranks' . Consequently the use of the internet is replacing traditional refereed journals and everything is now 'up for grabs'.

Also I would also like to thank Professor Sir Michael V. Berry and Professor E. B. Davies (Kings College London) for their advice and direction.

I would also like to thank my parents, particularly my Father, friends, my wife, Portia, and family for their patience and trying not to appear bored with my mutterings.

More importantly, mathematics should be fun, and we should never be afraid to test new, unfamiliar ideas even if they turn out to be wrong. For a hundred duff ideas, one may hit the jackpot. We should care about fundamental questions, but care less about what others may think, think for ourselves, be bold and challenge old assumptions otherwise we don't move on. Even experts can delude themselves that they are always right. Whatever the outcome of such theorems, one thing that is certain is that if they are to be resolved, it will be in a manner that is both controversial and unexpected.

All material on this site is property of Adrian Rifat.