A Planck unit Mathematical Universe Hypothesis

a model of the universe in terms of the geometry of the electron, Mass and Time
updated 28 May 2015

The following describes a Mathematical Universe model of the universe where the dimenensions of our universe are simple interlocking geometrical shapes derived from the electron frequency, from Mass M=1 and from Time T=2pi as the 3 fundamental 'Planck' dimensioned units. As the electron frequency itself incorporates MLT, it may be argued that the electron frequency is the origin of these units. The following is condensed from the book Platos Cave; the universe that isnt

The principals of this theory are:
- The dimensions MTPVLA (mass, time, sqrt of momentum, velocity, length, ampere) are interlocking geometrical shapes (M=point, T=radians, P=line, V=sphere surface, L=torus surface). PVLA are constructed from pi, Omega (dimensioned electron frequency) and alpha (the dimensionless fine structure constant).
- All valid systems of units such as the SI units are mathematical derivatives of these geometrical shapes.
- The electron frequency formula incorporates MTL in the ratio 9:11:15, the numerical solution to this ratio is invariant, i.e.: it is independent of the system of units used. Consequently the electron is a universal constant, in comparison the Planck units whose numerical values are localised constants. Arguably therefore the electron itself may be the origin of the Planck units (the dimensions of our universe).
- The electron frequency can be subdivided into (3) magnetic monopoles of ratio MLT 3:4:5 each
- Omega is constructed from pi and (log)e and so may be classified as a natural constant
- The universe is expanding in integer steps, as pi and (log)e can be constructed from integers in series, an expansion (and rotation) could therefore be the origin of Omega
- Each step adds 1 set of Planck units (mass, length, time...) to the universe and so it is more correct to write the universe is growing incrementally rather than simple expanding.
- This addition of discrete Planck units gives time, the arrow of time, the velocity of expansion = c and dark energy.
- Our universe is a black hole with a white hole twin. Dark matter may therefore be the fabric of the universe itself.
- Our universe is a 4-D time hypersphere surface or torus volume (the formulas are the same).
- As the universe expands it also rotates forming a spiral. The radius of the spiral gives the CMB temperature. The length of the spiral = universe time-line gives the size and mass.
- All particles and objects have a frequency along this time-line
- The electron is also a 4-D time hypersphere surface or torus volume
- 3D space is a human construct, in the above 4-D co-ordinate system all particles (except perhaps the neutrino) and objects travel at only 1 velocity = c, there is no relativity, only relative motion
- Wave-particle duality is an analog (non-integer) wave-state to integer mass point-state oscillation
- Particles and objects have no inherent (independent) motion, only an angle of motion relative to the universe time-line
- The sqrt of momentum P is the link between mass and charge
- Protons may be positrons trapped in a geometrical cage (buffer)
- There are no forces, instead orbitals are themselves physical entities - equivalent to photons albiet of inverse phase and so we may discuss nuclear, atomic, molecular and gravitational orbitals as actual units of momentum
- Mass is Energy as measured along the radial time-line axis (analogous to our time dimension), alternately Energy is Mass as measured along the horizontal axis (analogous to our 3D space). As both axis travel at velocity -c, we may interchange E and m via E-mc2. In terms of the universe there is no physical distinction

1. Calculating the fundamental constants
Defines the units: M = mass, T = time, P = sqrt of momentum, L = length, V = velocity in terms of these geometrical shapes

Using Ω, α and any 2 of these dimensioned units as scalars we may formulate geometrical solutions for the fundamental constants. Ω, α are constants regardless of the system of units, therefore to convert to SI units we need only 2 scalars. I have chosen here 'x' (momentum) and 'y' (velocity) as these are the most convenient to work with. As M and T do not include Omega it may be more appropriate to use mass and time.
Nobel laureate Leon Lederman once wrote: "My ambition is to see all physics reduced to a formula so elegant and simple that it will fit on a T-shirt"

Leon Lederman TOE t-shirt

Using an online calculator I demonstrate how we may solve the fundamental constants G, h, e, me, kB... as geometrical shapes with 10-12 digit precision using Ledermans t-shirt. Precision is consistent with CODATA 2014. to online calculator....

2. A magnetic monopole electron
A monopole has units ampere-meter which in this context becomes AL. Here the monopole is constructed from AL and the fine structure constant. This monopole is then used to construct the formula for the frequency of the electron.

magnetic monopole

This monopole resembles the quark of standard physics

3. Fundamental forces as anti-photon orbitals
In this model the fundamental forces (strong, electric, gravity) are replaced with standing wave orbitals (i.e.: wave functions are replaced by physical waves) resembling photons albeit of opposite phase. In other words, there is no empty space in the atom, the electron and proton are physically linked by an orbital and the moon does not orbit the earth through empty space according to a gravitational force but rather is pulled along by the momentum of gravitational orbitals, themselves extensions of molecular orbitals. Potential and kinetic energies simply reflect the degree of alignment of these orbitals. The strong force is a measure of buoyancy.
The online gravitational wave calculator calculates gravitational wave frequencies for a 1kg object lifted to height h. to online calculator...

4. Cosmological constant for expanding black-hole universe with contracting white-hole universe twin
Postulates an expanding black-hole universe linked to a contracting white-hole universe twin. Discrete units of momentum are transferred from the white-hole to the black-hole universe forcing this expansion. This gives us Planck time, the arrow of time and corresponding dark energy and the speed of expansion as the speed of light.
The black hole is a 4-D time hyper-sphere whose radius is this expansion timeline. Particles do not have their own momentum; they are instead pulled along by this expansion. Consequently there is no relativity for all particles and photons, regardless of their velocity in 3-D space, are travelling at the speed of light c, such that c is not the limiting speed of the universe, rather it is the only speed, as I type I am travelling at the speed of light in this 4-D hypersphere (the neutrino may be an exception).
Using as the only variable the age of the universe in Planck time units we may solve the CMB cosmic microwave background parameters. Solutions are consistent for a 14.6 billion year old black hole (mass density, radiation energy density, Hubble, black body peak frequency and CMB temperature). The cosmological constant becomes the age of the universe when the CMB reaches absolute zero.
The online calculator demonstrates this relationship to online calculator...


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email: maclem @ planckmomentum.com
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