Essay Abstract

Using a baseline sine function, the structure of prime numbers reveals itself in the form of a standing waves amongst the integers, creating a scaling based on the prime number and its associated waveform relative to the baseline sine function. The baseline sine function produces a sine wave in which the arrow of time manifests when compared with a non-zero acceleration - a prime standing wave. Using multiple sine functions, across up to one hundred iterations, several other properties emerge that are observationally verified. When applying the waveform to real-world structures related to acceleration, energy, and time, behaviors first proposed by Albert Einstein's Theories of relativity; to include structure of black holes, the Schwarzschild radius ( ), mathematical singularities, and even galactic-scale structures - most exciting is the emergence of a double-helix structure from the fabric of space. All behaviors emerge from the same geometric proportions exhibited by the singularities that exist at the nodes of prime number standing waves. Base ten, two dimensional, two variable equations are used due to limited computing power and exponential complexity.

Author Bio

I'm an independent researcher, when it comes to topics like my essay. My day job consists of, when I'm not herding my daughters, research and development on ultra-low friction targeting stabilization systems, for high resolution data at large distances. I love all things nature, especially wood. Look closely at knots, fibers, and branches - you will see many structures related to fluids... occurring in a solid, what is solid, really? Relative rate of entropy. What a beautiful Universe.

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I am amazed at the range and depth of talent these forums attract; truly a humbling experience to be able to offer musings to such a talented group.

To those that read the essay, a couple things:

Check out various nebulae, starting with the red square. It exhibits strikingly similar structures to those observed in the complexity arising out of simple sine waves.

To see another interesting behavior, use graphing software to model the following:

Z=sin(pi*x*n)+cos(pi*x*n). The emerging geometry closely follows both the hyperbolic steucture leading to Schwarzchild, and the interference pattern generated by Schroedinger's wave equation. Use two separate numbers, say n=3 and n=5, overlay z of 3, and z of 5, and adjust the scale, which changes the amplitudes at different rates. The resultant geometry is spectacular mimics behaviors observed on macro and micro scales.

David Pfender Chapman, it's possible that you like to look at the sky, and it seems to you an empty endless space in which you see the sine function in all its manifestation. According to the principle of the identity of space and matter of Descartes, space is matter that moves. When Copernicus began to assert that the Earth revolves around the Sun, he had, according to Descartes, to add that along with the Earth around the Sun, the entire circumsolar space rotates. Space is what the whole world is built of. Space is a superposition of sine functions. Look at my essay in which I showed how radically the physics can change if it follows this principle. Rate and leave your comment there.

Sincerely, Dizhechko Boris Semyonovich.

Mr. Semyonivich,

Thank you for your comment. I agree with you completely. I took a look at your essay and will read it closely this evening. I also believe all of space is rotating around any massive body. In fact, something I didn't have room to elaborate was how I arrived at the Schwarzchild solution. In short, it was based off of the derivative and anti-derivative of 1/x. If we use natural units, 1=c^2, thus, E=c^2/x, or E=c^2/r, using polar coordinates. What's interesting is the ability to use Bernoulli to account for the pressure gradient that exists due to relative E. This is potentially why the continuity equation works as a function of the conservation of energy.

I will comment on and rate your essay later today. Thank you for the feedback!

    Dear David Pfender Chapman,

    FQXi.org is clearly seeking to confirm whether Nature is fundamental.

    Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

    All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

    Only the truth can set you free.

    Joe Fisher, Realist

    12 days later

    Hi Prof David P Chapman

    Your OP ... "Using a baseline sine function, the structure of prime numbers reveals itself in the form of a standing waves amongst the integers, creating a scaling based on the prime number and its associated waveform relative to the baseline sine function........" is a very nice idea, Best wishes to your paper... by the way ....

    Here in my essay energy to mass conversion is proposed................ yours is very nice essay best wishes .... I highly appreciate hope your essay ....You may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

    Some of the Main foundational points of Dynamic Universe Model :

    -No Isotropy

    -No Homogeneity

    -No Space-time continuum

    -Non-uniform density of matter, universe is lumpy

    -No singularities

    -No collisions between bodies

    -No blackholes

    -No warm holes

    -No Bigbang

    -No repulsion between distant Galaxies

    -Non-empty Universe

    -No imaginary or negative time axis

    -No imaginary X, Y, Z axes

    -No differential and Integral Equations mathematically

    -No General Relativity and Model does not reduce to GR on any condition

    -No Creation of matter like Bigbang or steady-state models

    -No many mini Bigbangs

    -No Missing Mass / Dark matter

    -No Dark energy

    -No Bigbang generated CMB detected

    -No Multi-verses

    Here:

    -Accelerating Expanding universe with 33% Blue shifted Galaxies

    -Newton's Gravitation law works everywhere in the same way

    -All bodies dynamically moving

    -All bodies move in dynamic Equilibrium

    -Closed universe model no light or bodies will go away from universe

    -Single Universe no baby universes

    -Time is linear as observed on earth, moving forward only

    -Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

    -UGF (Universal Gravitational Force) calculated on every point-mass

    -Tensors (Linear) used for giving UNIQUE solutions for each time step

    -Uses everyday physics as achievable by engineering

    -21000 linear equations are used in an Excel sheet

    -Computerized calculations uses 16 decimal digit accuracy

    -Data mining and data warehousing techniques are used for data extraction from large amounts of data.

    - Many predictions of Dynamic Universe Model came true....Have a look at

    http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

    I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

    Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

    In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

    I request you to please post your reply in my essay also, so that I can get an intimation that you replied

    Best

    =snp

    9 days later

    Dear David

    If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don't rate them at all. Infact I haven't issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to gain.

    Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me and my essay in questioning this circumstance?

    My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. And again, how lucky we are! for if they didn't then gas accumulation wouldn't be halted and the star would again be led to collapse.

    Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?

    For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.

    My essay is attempt of something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up a potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond formation activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemistry processes arose.

    By identifying atomic forces as having their origin in space, we have identified how they perpetually act, and deliver work products. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might explain for intricate structure and complexity within universal physical systems.

    To steal a phrase from my essay "A world product of evolved optimization".

    Best of luck for the conclusion of the contest

    Kind regards

    Steven Andresen

    Darwinian Universal Fundamental Origin

    8 days later

    Is mathematics a natural or man-made phenomena? Mathematics is a mostly man-made discipline. Mostly because now we have computer-made mathematics as well. E.g. new theorems are being proved by machines.

    A wave isn't a quantumm field.

    Figures only some resemble the objects they are claimed to represent. E.g. F11 is not really an electron cloud.

    EQ11 is not valid near a horizon. Moreover, gravitational potential energy is negative not positive, which also implies KE-U has to be changed to KE+U, but this Newtonian expression for Energy is not valid near horizons.

      a month later

      Dear Juan,

      I do appreciate your critique, regarding my essay. I do, however, disagree with many of your arguments.

      Citing computer-generated mathematics is not proof of the origins of mathematics - in fact, that is circular logic. Computers operate on laws requiring an initial A=B statement - that was supplied by humans, which was derived by observing and quantifying behaviors and patterns in nature. The relationships exist, we quantified them and drew logical conclusions. Therefore, it is my position that the relationships defined by the symbolic language of mathematics existed in nature and were discovered. We created the symbolic structure, not the structure itself.

      The claim isn't that 'a wave' is a quantum field... that was to illustrate a concept. It works wonders for quantifying waveform dynamics. The field exists as this equation, in a z=x(-y) plane. This plane propagates with geometry related to 1/r and 1/r^2. I didn't have time to include that in my essay, as it was a last minute decision to submit it. I don't understand how someone who loves mathematics cannot see the beautiful complexity.

      Other than the electron cloud, which was a stretch, I don't see any other claims that are only 'claimed to represent'. Do you not see a standing waveform, quite clearly, in several of them? Are the characteristics of Special Relativity not visible in others? It's a bit abstract, but isn't a stretch to see the behavior.

      I'm sorry for my laziness regarding the U term. Seeing as it is the total energy equation, I figured I'd combine a single step to save space. Generally, I prefer the integral form - which implies a negative U value.

      Nobody can make the claim that anything isn't valid near the horizon of a black hole. We have mathematical evidence of several possibilities, in that odd region of space and time. Using Fourier transforms (and inverse), really interesting behaviors are seen at the Schwarzchild radius, which can be proven mathematically - including the equation structure of 1/r. Setting GMm to a constant value, using natural units, gets us there.

      E=nhw/2pi=E/2pi=mc^2/2pi=[(sin((pix)/2))(-cos(4(piy))]

      =KE=-U

      n*hbar*v/F=r=E/F

      n*hbar*w=E=mc^2

      Thank you for your time.

      ***See attachment (apologize) for chicken scratch - I've got two young girls and time is in short supply.

      Scalar field structure. Quasi-periodic with hints of Penrose tiling.

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