# BEAUTIFUL UNIVERSE:

## TOWARDS
RECONSTRUCTING PHYSICS

FROM NEW FIRST
PRINCIPLES

By Vladimir F. Tamari

4-2-8-C26 Komazawa, Setagaya-ku, Tokyo Japan 154-0012

(First published on this website and circulated by email from 10 July 2005. Material related to the Compton Effect and Dark Energy in sections 2.6 and 2.11 was added in November 2010)

**ABSTRACT**

* A proposal to reconstruct physics from simple
physically realistic
first principles is outlined using a Beautiful Universe model. Only one
type of
‘building block' is used: a spherically-symmetrical charged node
spinning with
angular momentum in units of Planck’s constant (h). Rotating
nodes become
magnetized and self-assemble as a regular face-centered cubic lattice
to form
the vacuum, radiation and matter. Non-spinning nodes make up dark
matter. Three
space and one time dimension are derived from the lattice and node
interactions.
Mutual repulsion between nodes making up the vacuum accounts for the expansion of the
universe and for the pressure of 'dark matter'. A
spinning node transfers its angular momentum to adjacent nodes by
rotating on
an orthogonal axis, thus creating an electromagnetic field with forward
momentum. The spin rate of the node receiving the momentum, its
‘density’
determines the rate c _{v} at which it receives the radiation.
In a
vacuum c_{v} is the maximum, c_{0} the velocity of
light. Two
or more adjacent nodes locked together through a tensegrity of
attractive (+ -)
and repulsive electrostatic forces form as matter. The
surrounding nodes
orient their axes to form magnetic, gravitational or electrostatic
fields. The
inverse-square law and E=mc_{0}^2 are derived from the
resulting
geometry. Motion of matter is a self-convolution of an energy
pattern in the
lattice. This links the concepts of Newtonian force and mass with in
units of h,
whereby a collision causes a Heaviside contraction of an object’s
length. Doppler
shifts in the signals used by an outside observer to measure the moving
object
causes a further contraction in the estimated length, similar to the
effects of
a time dilation. The two effects explain a result of Special Relativity
in
classical terms. Using the Hamiltonian Analogy and the idea of a node
index of
refraction n=c_{o}/c_{v} General Relativity is reduced
to the
dynamics of energy transport along streamlines made up of nodes of
different spin.
Variable velocity along curved streamlines is acceleration and hence
gravity.
Quantum probability is derived from the electric field of a dipole wave
in the
lattice. Heisenberg’s uncertainty relations emerge naturally from the
resulting
geometry. Cosmological inflation, but not a Big-Bang singularity would
result
from initial conditions of nodes in their closest proximity to each
other. The
outline of a discrete calculus needed to describe the model’s
interactions is
presented. Some experiments are proposed to test various aspects of the
model. *

*Key
words:** Physical Theory. *Theory of everything. TOE .
Special Relativity,
General Relativity. Node. Lattice. Quantum Mechanics. Uncertainty
relations.
Discrete Calculus. Ether, Heaviside. Planck’s Constant. EPR. Expanding
Universe. Inflation. Anomaly.

**1.
THE BEAUTIFUL UNIVERSE (BU) MODEL**

**1.1
THE
NEED FOR REALISTIC THEORIES CLOSE TO NATURE **

Nature
is now complex, but is believed to have evolved systematically over
billions of
years, following simple processes. This is the lesson of the theories
of evolution[1],
of fractal equations[2],
cross-stitch embroidery[3],
digital philosophy[4],
and of Wolfram’s book *A New Kind of Science*[5]:
A very simple effect, principle, rule or algorithm applied repeatedly
leads to
a very rich and complicated outcome. In their efforts to discover
the laws of
nature, however, philosophers and physicists in different eras and
belonging to
different cultures were guided not only by their own thoughts and
chance
discoveries, but also by the intellectual baggage of their time: the
accumulated
knowledge , preconceived ideas, and even theological
concepts.

It is no wonder then that present-day physics is a hodge-podge of complicated ideas that do not always work well together, if at all. For example the theory describing gravity on a large scale, General Relativity (GR)[6] and the theory describing atomic and nuclear processes, Quantum Mechanics (QM)[7], speak different ‘languages’ describing what in the end must be the same phenomena. Moreover both (GR) and (QM), although extremely successful in predicting experimental results, both use non-intuitive ideas that seem far from reality. As with the preceding classical physics of Galileo and Newton, these theories describe the behavior of space, mass, time, or gravitation, but give no inkling of what these entities are. A lack of a self-consistent physical model of nature at its most basic level has allowed physicists to accept almost without question some of the more bizarre conclusions of (QM) such as instantaneous interaction at cosmic distances. This contradicts a basic premise of Special Relativity (SR)[8] that signals cannot travel faster than the speed of light.

Such confusion is possible because vastly different mathematical models to describe the same physical phenomena can be derived: even within (QM) itself, Schrödinger’s wave equation[9] was found to be exactly equivalent to a very different mathematical model, Heisenberg’s matrices[10]. But if a model is not ‘true to nature’ its very success distracts from other possibilities, blocking further progress. That happened with Ptolemy’s concept of the Earth staying still while the Sun and the planets rotated around it in complicated circular epicycles[11]. The system ‘worked’ even succeeding in predicting eclipses, because relative to an observer on Earth that is how the planets seemed to move. However it was not until Copernicus[12] put the Sun at the center that Kepler[13] could discover the much simpler elliptical orbits for the planets, paving the way for Newton’s law of gravitation[14] and modern physics.

Similarly, although the concept of flexible spacetime ‘works’ in (SR) and (GR), and that of probability waves ‘works’ in (QM), they are just mathematical ideas that must be discarded if better models closer to nature can be found. This is more than just a way to seek more elegant theories: understanding nature at its own level is a necessary step to pave the way for further theoretical, experimental and technological discoveries. The human brain evolved over millions of years in organisms that interacted directly, causally and locally with inanimate nature on a molecular scale[15]. Is it too much to ask now that our understanding of Mother Nature should also be as simple, direct and realistic as possible?

**1.2
A
NEW START**

There
is a widely recognized need to ‘start all over’[16],
using the hard-won results of 20^{th} Century physics, but
reconstructing them
out of a few basic self-consistent premises.

In the last few decades a great number of papers and books introduced new starting points at various levels of sophistication and completeness: Twistor Theory[17], various theories based on an ether particle[18], Quantum Gravity[19] and many others. String Theory[21] represents such a new start but it creates even more complications with ten or more dimensions using new mathematics, making the theory unlikely to be true to nature in the sense discussed above.

The ideas behind Beautiful Universe (BU), the model presented here, derived from my discovery that a classical dipole’s electromagnetic potential field and its streamlines form a miniature united field from which can be derived many of the known phenomena of (SR), (GR), and (QM)[22]. (BU) theory describes a whole universe made up of charged particles spinning as dipoles, (including regions of dark matter where the particles have no spin). In the following sections, the (BU) model will be presented from first principles. In Section 2 an attempt will be made to show that the experimental results, but not the assumptions or all the methods of Newtonian physics, (SR), (GR) and (QM) and related cosmological theories may eventually be derived simply and directly from (BU). In Section 3 experiments that may prove the correctness of the (BU) approach are proposed. The (BU) presented here is incomplete, and the treatment is qualitative and elementary. The aim is to gain a sure physical understanding of the proposed model’s basic concepts, leaving to future work the necessary but more abstract task of describing it systematically, quantitatively and mathematically.

**1.3
A NETWORK OF CHARGED NODES CREATES SPACE
AND TIME**

It is hypothesized that the entire universe is made up of an ordered lattice of identical spherically-symmetric charged nodes that are smaller than the smallest known nuclear particle, but are on a similar scale to it. This network of nodes creates space itself, so it is meaningless to speak of the shape of an individual node, neither of the material it is made of, or its behavior nor of any space between nodes. Nevertheless to facilitate our understanding, a node can be thought of as being spherical, capable of spinning freely in place around any axis passing through its center. Either at cosmological initial conditions or during the universe’s later development, volumes of nodes rotate and interact with other volumes rotating in an opposite direction (FIG. 1).

This cosmic angular momentum is acquired by individual nodes, and can be transmitted to neighboring nodes without friction, but will never disappear, conserving angular momentum locally and in the universe as a whole. Again, we can use the terms of classical physics here only as an analogy, but having like charge, the nodes repulse each other and create an expanding universal space. It is theorized that individual nodes all over the universe spin in the same direction around their own axis.

**FIG. 1. An
imagined
scenario for the creation of spin in nodes. (a) Two volumes of charged
particles
impinge on each other, as each volume rotates in the opposite
directions. Their
interaction causes individual nodes to acquire spin.(b) The
resulting
volume of spinning magnetized nodes self-assemble to creates an
expanding space.
There is also the possibility that the nodes exist within other
undetected
dimensions D (dashed outline).**

Spin plays a central role in (BU) and both the physical situation and the terms used should be clear. There is first the ‘rotation’ of vast volumes of nodes without the individual nodes spinning on their axis (FIG. 1). A dark-matter node is one without spin (FIG. 2a).

**FIG. 2 the
three
possible states of nodes (a) basic charged node. (b) Spinning around
one axis,
with angular momentum in units of Planck’s constant h. (c) Spinning
around two axes
creates forward momentum (large arrows).**

‘Spin’ is when an individual node rotates around its axis so that it becomes a magnetic dipole (FIG. 2 b) with angular momentum in units of (h) without affecting adjacent nodes. ‘Forward momentum’ is when the magnetic dipole spins on another axis orthogonal to the dipole axis. The word ‘forward’ is used because such spin causes adjacent nodes to rotate, as follows:

When
spinning, a node becomes a magnetic dipole and
generates Coulomb-like interactions[23] between neighboring dipoles. In a static field of adjacent spinning
nodes the (+
+) and (- -) poles *repulse* each other until an all the nodes
are so
oriented that a state of equilibrium is reached, even though each node
continues to spin around its own fixed axis. When a node acquires
forward spin, additional
angular momentum in multiples of Planck’s constant[24] (*h* = 6.626068 × 10^{-34} m^{2} kg / s) is
generated, (FIG.
2c) and this momentum (p) is passed on completely without ‘friction’
and
distributed to the immediately adjacent nodes in the forward direction.
When
this occurs the magnetic dipole axis of the recipient node will twist
according
to the amount of momentum it received.

When
two or more spinning nodes in a field are forced to lock
in place with opposite poles *attracting*, (+ -) or (- +) static
structures
of matter are created (FIG. 3).

**FIG. 3 A simple particle forms when two
spinning nodes
change their orientation and are ‘locked’ because of the attraction of
(+ -) poles.
The orientation angles of the node axes,, and
their polyhedral arrangements define the possible ‘quantum spin’ states
of the
particle. **

This in turn sets the spin orientation and energy of all other surrounding nodes. It is suggested that the term ‘quantum spin’ be used when referring to spin as it is now used in (QM). ‘Quantum spin’ does not define a rotation around an axis, but the possible symmetries of a particle in space.

Everything in (BU), space, energy, radiation, matter is just patterns of nodes rotating in place and forming the universal lattice. Apart from this rotation around various axes sharing fixed centers, it is assumed that a node never rolls freely in space, bounces against matter, collides with other nodes like billiard balls, or flows like a grain in shifting sand A vast volume of nodes might conceivably slide, shearing from an adjacent volume, leaving an inhomogeneous ‘fracture’ in the lattice. This will not be considered here, where it will be assumed that node centers are always fixed, and only angular momentum is transferred from one node to its neighbor.

The (BU) interactions described above may be all the necessary and sufficient premises needed to describe all of the known phenomena of physics at its most basic level.

**1.4
RADIATION IN VACUUM**

Coulomb-like repulsion and attraction between the spinning magnetized nodes and self-assembly create a minimum-energy arrangement of nodes in equilibrium that we know as the vacuum. All the nodes forming the vacuum have identical spin

(1)
s_{o}=h

The
square-face Kepler packing was recently proven to be
the densest packing possible for spheres[25] (FIG. 4), and Gauss proved that the face-centered cubic (FCC) packing
is the
densest lattice possible[26].
The (FCC) occurs in nature, for example ZnS, or zinc blende, has a
face-centered cubic arrangement of sulfide ions with zinc ions in every
other
tetrahedral hole. An FCC and its tetrahedral components are shown in
(FIG. 4).

**FIG. 4 Self-assembly of magnetic dipole nodes
oriented
in the same direction as a Kepler packing. Each unit of the packing
forms a
cube with a node at each corner, with another node where the cube’s
diagonals
cross. The smallest regular volume made up of four nodes would be a
tetrahedron
(shaded). **

To maintain this state of minimum energy, the axes of the nodes in vacuum are in static equilibrium and as nearly parallel as possible. On the other hand, there exists the possibility that besides their usual rotation about their spin axis, the axis itself is also rotating about its center, so that all nodes in the universe are in synchronous rotation around two axes at once unless disturbed. Such rotation in unison would prevent the + and – poles of adjacent nodes in vacuum from clumping up because of the attractive Coulomb forces.

The cubic symmetries of the node packing are responsible for the three dimensions of space. It is unnecessary here to speculate whether the nodes are set in yet one or more other hidden dimensions, causing their assumed behavior. This possibility, however, would raise the question of the universe having a center, with unequal distance and time scales in radial or tangential directions as shown in Fig. 36 below.

Electromagnetic
waves are created when an arrangement of matter
loses equilibrium and forward angular momentum is released successively
from
node to neighboring node in a falling-domino effect. A given node
now
possesses spin s_{v} in integral multiples of (*h)*.

(2)
s_{v}=
j s_{o} =jh
(j=1,2,3…)

creating
a magnetic effect and capable of forward momentum. In a process similar
to magnetic
induction, each node transfers all of its momentum to the handful of
nodes in
‘front’ of it in the lattice dividing its energy between them as in
(FIG. 5).

** FIG. 5 Forward momentum (large arrows) is
transferred
from node A to neighboring nodes. B gains most of the momentum, since
it shares
the plane (shaded) in which contains both of their spin axes. This gain
in angular
momentum causes B to twist by an angle . Lesser twisting is experienced by
node D
whose axis
is normal to that of the forward momentum of A. Other nodes such as C
in diagonal directions from A, twist at even
lesser
angles.**

This transfer is complete and lossless, and when two or more pulses arrive at a given node simultaneously, they superpose and interfere, adding their momentum linearly as vectors (FIG. 6).

**FIG. 6. Two modes contributing their
momentums to the
adjoining node to the right. The momentums add vectorially and
interfere
according to their phases.**

All
the momentum of the donor node is passed to the
adjacent nodes and propagates forward and outwards, spreading from node
to node
within the lattice (FIG. 7). How much momentum each node receives
and in what
direction requires careful analysis: a node directly aligned with the
momentum vector
will get more forward momentum than that located diagonally to the
side. As a
result of these interactions the nodes in free space acquire different
amounts
of spin and align themselves in various orientations. The resulting
fields will
have equipotential surfaces _{constant} where the change of angle between neighboring nodes is constant. Normal
to _{constant },
the field streamlines are
the paths along which the energy of the field is initially propagated.
If the
field is in equilibrium the nodes settle in unchanging orientation,
and indicate the field curvature. If momentum is continually being
transferred a
radiation field is the result as in (FIG. 7).

As
each charged node spins it creates its own magnetic **B** and electric **E** fields *within itself*. These effects only
appear
when the spinning behavior of adjoining nodes is affected. The
use of the B
and E terms here is assumed *ad hoc*, and is only justified by
what we
know of the macroscopic behavior of radiation, and not from basic
principles.
On the scale of the nodes, it is not possible to speak of a continuous
streamline line joining three or more congruent nodes, because of the
step-like
geometry of the packing. However, along a line of successive
nodes the spin
axis changes direction in a harmonic motion similar to that of (FIG. 8)

**FIG. 7.
Fields in (BU)
can be in equilibrium (a), (b), (c), or time varying radiation fields
(d). In
all cases equipotential surfaces () are where
node-to-node orientation is constant. Streamlines
(S) are normal to (). (d) The nodes in
a
radiation field transfer angular momentum along (S) so that nodes on
successive
() have different phase angles at various times t0,t1,t2,…**

**FIG. 8. Nodes transferring their spin
and forward momentum
as part of an electromagnetic pulse radiating along a streamline S in
the z direction.
The Magnetic (B) component of the nodes’ rotation creates the electric
field and
Electric components (E) create the electric field. Any component of the
rotation
in the xy plane creates polarization. The strength of (E) and
(B), hence the
intensity, is determined by the node spin. The colors are a graphic aid
and have
no physical significance.**

**1.5
VELOCITY OF INTERACTION, SPACE AND TIME**

There
is no time dimension presupposed in (BU) theory, only
successive ‘instantaneous’ local states of the universe. Spatial
directions, i.e.
dimensions, do not have an inherent reality either, but result from the
geometry of the node packing. Distances exist because signals traverse
different numbers of nodes in succession. However for convenience, and
to keep
track of the various states of a local volume of space involving many
nodes, a
minimum unit of time t_{0 }is defined using a hypothetical
separation d_{0} between nodes, whereby angular momentum in a vacuum free from and far
away from
matter, is transferred from node to node with a velocity c_{0}.
This
is the *maximum* speed of light c in vacuum c= c_{o }= 2.99792458 times 10^8 meters per second.

(3)
c_{o} = d_{o} / t_{o}

If
the nodes to which the forward momentum is transferred
have a spin s_{1}>s_{0}, then the pulse will be
delayed, and
will travel over a smaller number of nodes, i.e. a distance, as
compared to one
in vacuum, where nodes have spin s_{o} (FIG. 9).

**FIG. 9 radiation travels at a maximum speed
of c _{0} in a vacuum free of matter, but at lesser speeds where the potential is
higher, i.e. the nodes are denser, spinning at a higher than the vacuum rate s_{o}**

Assuming that the relationship between the velocity of transfer depends linearly on the inverse of the spin of the node receiving the momentum and its orientation,

(4)
_{}

where
M is a geometrical inclination factor depending on the direction in the
lattice
between the donor node and the node receiving the momentum as will be
explained
in section 2.2 below. When the direction is orthogonal to the faces of
the FCC
M=1, and √3 when it is diagonal. The
pulse
velocity c_{v <} c_{o }is measured by the distance
it travels
compared to an adjacent pulse traveling in vacuum. Straight-line
distances are
measured by the number j of nodes a signal traverses:

(5)
d_{o}=j
Md_{o}
(j= 1,2,3…)

A local index of refraction of space n or its inverse can now be defined:

(6)

Angular momentum spreads as energy in the lattice as light would in a transparent medium having a variable index of refraction such as the atmosphere with variable density gradients[27], or in a gradient index GRIN lens[28] as in (FIG. 10).

FIG. 10 (a) A light wave radiates in vacuum of index of refraction n

_{o}=1 (b) In an inhomogeneous potential field of variable index of refraction the wave is distorted accordingly by refraction. Particles (not shown) having the same momentum and traveling in the same media would be similarly ‘refracted’ (large arrows).

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