2-Dimensional (entropy and momentum) Planck unit Mathematical Universe
2pi, fine structure constant alpha, omega - pi^e/e^(e-1) and the sqrt of Planck momentum sqrt(kg.m/s)
updated 12 Nov 2014

This is a model of a 2-D (2 dimensional) universe; these 2 dimensions are entropy and momentum. It is a Planck unit theory albiet the fundamental Planck units are; Planck time tp and Planck temperature Tp (dimension a = entropy) and Planck momentum (dimension b = momentum). There is also a dimensionless state (all dimensions cancel) which would be characterised as a magnetic monopole, the electron frequency formula is given as an example.

The universe at the Planck level reduces to the geometry of 2pi, the fine structure constant alpha = 137.03599... and Omega = pi^e/e^(e-1). The dimensions (SI units M,L,T,A,K) and numerical solutions to the fundamental constants of physics G, h, e, c, me, mu0 (vacuum permeability), kB (Boltzmanns constant)...      can be derived by the use of 2 dimensioned scalar variables a and b. We may debate whether these scalar variables exist at the universe level or are instead human constructs given that the above listed physical constants themselves may be constructs... in other words, our universe may simply be a dimensionless magnetic monopole - and if our universe lacks physical dimensions then it must be defined as a Mathematical Universe.

The model is divided into 4 parts:
1. The fundamental physical constants are defined in terms of the geometry of 2pi, the fine structure constant alpha, omega and the 2 dimensioned scalars a and b.
2. Postulates a magnetic monopole as a geometrical shape formed from the Ampere AQ and Planck length. The electron becomes a monopole cubed (AQ.lp)3, the monopole thereby resembles a quark.
3. The 4 forces are replaced with physical orbitals (nuclear, atomic, molecular, gravitational).
4. Postulates an expanding black-hole universe with a white-hole universe twin. Parameters for a 13.575 billion year old black hole agree with observations from the the CMB (cosmic microwave background).

A non-technical discussion of the concepts and philosophy can be read online (chapter 2).
"Platos Cave: a model of the universe in terms of the geometry of momentum"     

1: Postulates a 2-D Planck universe from a dimensionless magnetic monopole.
time: tp = 2pi.a6
velocity: c = 2pi.Ω2.b3/a
length: lp = 2pi2Ω2.a5b3
mass: mP = 1.ab5
charge: A = 64pi3Ω3/(α.a3b3)

The online calculator demonstrates this relationship.

download paper: 2-D Planck unit Mathematical Universe update pending

2: Electron as a standing wave magnetic monopole
Proposes a formula for a magnetic monopole (quark) from Planck time tp, -e, -c and alpha. Uses this monopole to solve the mass of the electron and the Rydberg constant. Results consistent with CODATA 2010. Suggests a temperature particle, the 'kelvon'. read more...

download paper: Spherical electron as 'quark' magnetic monopole
download paper: Fine structure constant alpha and the sqrt of Planck momentum

3: GUT Unified Field Theory: the 4 forces as physical standing wave orbitals
Replaces the 4 fundamental forces (strong, electric, gravity) with standing wave orbitals (wave functions are treated as physical waves, essentially photons albiet of opposite phase). This offers a rationale for the empty space within an atom, how electrons jump between orbitals in the atom, what is gravitational potential and kinetic energy, quantum entanglement, the relationship between nuclear binding energy, ionisation energy and escape velocity...

download paper: Unified Field Theory of Anti-photon Orbitals (nuclear, atomic, molecular, gravitational)

The online gravitational wave calculator calculates gravitational wave frequencies for a 1kg object lifted to height h. to calculator...

4: Cosmological constant and expanding black-hole universe with contracting white-hole universe twin
Proposes an expanding rotating charged black-hole universe with a contracting white-hole universe twin. Units of Planck momentum are transferred in discrete steps from the white-hole universe to our black-hole universe. Derives mass domain parameters from 3-D sphere volume and charge (electromagnetic) domain parameters (i.e.:Stefan-Boltzmann constant) from 4-D sphere surface area. Offers solution to CMB (cosmic microwave background) mass density, radiation energy density and temperature. Suggests a cosmological constant based on a temperature particle, the 'kelvon'.

The online calculator demonstrates this relationship to calculator...

download paper: Time, Dark Energy and the Black-hole White-hole Universe update pending
download paper: Fine structure constant alpha and the sqrt of Planck momentum

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

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email: maclem @ planckmomentum.com
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