Rome is the centre of the universe'

1
? Derek Eastham, 2007
1
Your vision of the universe depends on your point
of view and, as we see later, your energy.
It may be hot here but the orbits of the planets
are ellipses from where I am standing.
Rome is the centre of the universe. The strange
motion of the planets is Gods will.
The centre of scientific thought moved to
northern protestant Europe in the 17th C. Newton
invents the modern scientific method-logic
supported by mathematics which relate to
measurable quantities.
The force of attraction between two bodies is
Here is my law of gravitation which explains
these ellipses!
And, as we shall need later, the potential energy
of a body mass, m, at a distance R from body
mass, M, is
The motion of astronomical bodies can be
predicted with extreme accuracy using this law
and Newtons laws of motion especially if we
allow for the increase in mass predicted by
special relativity
Later we show that the electrons and positrons in
the vacuum can be viewed from different energies
where the laws of physics must be the same but
the different viewpoints show the true nature of
space (the vacuum).
2
? Derek Eastham, 2007
2
General Relativity in a space-ship
The general theory of relativity is based
completely on the principle of equivalence so
that it is impossible to tell the difference
inside an accelerating space-ship and one in a
gravitational field of strength g.
Beam of light generated in space ship
(1)Time or space only-is what you would get in
Newtonian theory because light must fall at
g like any massive object-as Galileo
demonstrated and the space-ship shows.
This bending is Extremely Exaggerated!
(2)Time and space (which is defined by light)
must both change equally (see below) so that
light appears to fall at 2g which agrees with
the experiment below
We show later that only time dilates and yet
light falls at 2g!
If the velocity of light is constant (in a
vacuum) then since vs/t then, if time dilates,
space must expand accordingly so as you always
measure c.

This is the length2 in space time
The famous metric of space-time in a spherically
symmetric system published by Scwartzchild
shows that space-time must be curved if the
vacuum is completely empty. Dont be fooled by
the hard algebra-this result can be deduced from
the space-ship gerdanken experiment.
The experiment showed that the bending of light
was proportional to2g-the event horizon of a
black hole, when time stops and space expands
infinitely, is when
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3
? Derek Eastham, 2007
Red shift and time dilation in a gravitational
field
Infinity


Photon of energy 2m0c2E0
A photon of energy 2m0c2falls to a point R, in a
gravitational field where it produces an electron
and a positron. Its energy increases by an amount
?E which must be equal to the kinetic energy of
the pair.
?E
Gravitational potential energy GM2m0c2/Rc2GM?E/
Rc2
Energy conservation means that ?Er.h.s.
expression so
R
Potential energy of Mass?E/c2
Potential energy of 2m0
Since the energy of a photon is
then time dilates as
These results only agrees with GR in a weak
gravitational field
R
4
4
When equivalence breaks down for light
There is only one way to explain the difference
between the gerdanken experiment and GR and that
is if the electrons and positrons in the vacuum
have structure (contain Coulomb energy) and this
structure changes in a gravitational field which
affects the path of light.
1) This is due to light falling at g, as
expected of Newtonian gravity. This causes time
to dilate according to the previous equation.
A quantum lattice of electrons and positrons. The
spacing is only a few times the diameter of a
proton. The lattice dimension changes in a
gravitational field. This lattice has no mass and
is therefore invisible.
2) The bending of light is explained as due to
the changes in the optical properties of the
vacuum which give a total effect equal to 2g.
We show later that the optical properties change
because the phase velocity of light increases
in a gravitational field.
The unequivocal conclusion is that space does
not expand and gravity waves are not
oscillations of the dimension of space.
5
5
Electromagnetism and QED
This is not a tutorial it is just a few small
facts from a big subject. To get a better
background I recommend starting with (of
course!) the book Atomic Physics of lasers by D
A Eastham. (from Amazon)
We put all constants 1
This is the same form as gravity but has a much
much shorter range. We can substitute this into
Schrodingers quantum mechanical equation and
get the structure of a hydrogen atom fairly
accurately. If the electric field in an
electromagnetic plane wave is then one can
calculate how this wave interacts with the
electrons in an atom using equations from
elementary quantum theory
Coulomb potential energy
Schrodingers eqn.
This is a semi-classical approach because we use
the classical equation for light from Maxwells
equations. The proper theory of the interaction
of electrons and photons is known as quantum
electrodynamics. It is the most complete theory
in all physics and the interactions between the
quanta can be visualised by Feynman diagrams.
This allows you to consider all possibilities.
t
The Coulomb potential is generated by exchange
photons (wiggly line). This one is the repulsive
potential of like charges.
x
In this way we can consider possibilities which
are not apparent in semi-classical theory and
below we show the three contributions to the Lamb
shifts -very small shifts in the electron energy
levels in atoms, principally the s states.
The exchange interactions
e
p
p
e
The photon, spin 1, can be generated by the
electron and reabsorbed causing a spin flip of
the electron.
The exchange photon can form an electron and
positron for very short times.
Electron mass renormalization The electron
interacts with the zero-point photons in the
vacuum.
Anomalous magnetic moment. This is small
contribution to the Lamb shift in atoms but a
rather larger change in the magnetic moment.
Vacuum polarization
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6
The electron-positron, quantum lattice of space
The simplest solution for the empty universe is
that it is the lowest energy isolated state of
an infinite number of electrons and positron
which make a cubic lattice in which each lepton
is bound by its own mass. Note it can also be
any lepton as discussed later in slide 16.
There is no contribution to the energy from
static dipole-dipole interactions.
Charge of lepton in units of e.
Part of the infinite cubic lattice. This can only
have no kinetic energy if it is infinite. It has
no dipole moment because the dipole moment of
each positron is in the opposite direction to
each electron.
We put all the constants equal to one until we
need to calculate something!
or
Lattice spacing in free space. d0 is about 2x
diameter of a proton.
The energy of the vacuum is zero and so it has no
kinetic energy. It is invisible and massless.
This should be contrasted with the current idea
that the leptons in the vacuum have negative
kinetic energy! Here the lattice only has Coulomb
energy which can be negative or positive
depending on your viewpoint.
Mass of lepton
I cannot measure the structure of this lattice
at all. It has no mass and no kinetic energy.
It is -in effect- the quantization of space itself
Lab-frame man
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7
How a gravitational field is generated from the
quantization of space.
Immerse a body of mass M in the infinite
lattice-this happens at the big bang! The lattice
will relax (lower its energy) to its lowest
state which is again E0 by the lattice
contracting around the body so that the decrease
in the total Coulomb energy is equal to Mc2.
The lattice cannot make a perfect crystal-it is a
quasi crystal and the lattice dimension at R,
only defines a local frame of reference.
This lattice is invisible-it has no mass and is
really a quantization of space which contains
only Coulomb energy
M
R d
infinity d0
We must have that the gravitational energy is
equal to the change in the lattice binding energy
so
The previous conception of the vacuum with no
structure would not work here because the mass
of the leptons would change with gravitational
field!
Equivalence principle or Galileos balls says all
masses behave the same.
Gravitational potential energy of lepton
Potential energy- gravitational or Coulomb
Emec2 (any R)
This is Newtonian gravity if time is constant.
Coulomb potential energy of lepton in lattice
This gap must be the same or me would change in
a gravitational field.
8
8
The quantum lattice is the origin of the quantum
field
First consider that a photon is generated by the
transverse displacement of an electron and an
adjacent positron. We can then work out the
harmonic oscillator constant, K, which can be
used to calculate the speed of light by inserting
this into the well-know expression for the
velocity of (sound) waves in an atomic lattice.
Consider a single line of leptons along the axis
of the lattice,
n3/2
The phase velocity for these (transverse) waves
is the well known expression
and K is (see paper for details) where EB is the
binding energy in the lattice.
In quantum field theory a photon corresponds to
the transition from the n3/2 to n1/2 level in
an harmonic oscillator potential.
This equation is only true for low frequencies
but since Maxwells equation must apply then it
is true for all frequencies as long as we are
sure these photons are the same as Maxwells!
C
This is the velocity in free space (no M) since
here EBE0
Thus the solution for eµ1 (edielectric
constant) is not empty space but is quantized
space and we can state that the origin of
the quantized field is the quantized lattice.
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9
Photons generated by lattice vibrations
Lattice vibrations have the same energy as the
photons in the lab-frame but the dipole is
invisible it has no mass in the lab-frame so
the only conclusion is that the photons are the
same! and a plane wave is the same as you would
get at a distance from a dipole. i.e.
An oscillating dipole dd0(?t) produces a wave
of frequency ? containing photons with energy

This is what I measure.
I can just generate photons from the vacuum
with my magic quantum operator wand.
Lab-frame man Anything with mass must be in the
lab-frame.
Lattice vibrations generate photon with
energy and mass zero
The lab-frame where we are condemned to exist
because we have mass.
Em0c2
Quantum field theory wizard
The zero-point energy of photons in the lattice
frame-see later.
The lattice (vacuum) frame or the dark underworld
which controls the working of the universe.
E0
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10
The trajectory of light in the vacuum
The light travels in the lattice and its path can
be calculated from the previous equations for the
phase velocity and time dilation (see gerdanken
experiment). Notice that the gerdanken
expt. works even with no lattice.
The solution if time varies as above
The weak field solution
The solution if time is constant
This is the refractive index of space in a weak
gravitational field.
This is the phase velocity squared of light in a
weak gravitational field which can exceed c in
a crystal. It determines the path of light and
we see that it gives the same answer as GR, and
measurements, even though space remains constant.
The big conclusion is therefore that space and
time are separate and are not created together
at the big bang. Infinite space existed before
the big bang and was defined by the quantum
lattice. Time started with the (a) big bang! This
gets rid of some embarrassing things in
cosmology such as the notion that the space
between galaxies expands but the galaxies
themselves do not! (You can measure the size of
the galaxies and they are all the same even at
large distances in the early universe.)
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11
A very crowded slide-to absorb it properly will
take some time.!
The empty universe is simply light!
The nature of the vacuum must be reconciled with
QED since this theory is exact as far as we
know. Below we compare the current model of the
vacuum with that based on a quantum lattice.
The current concept of the vacuum consistent with
Diracs single particle equation. Only consistent
with QED with vacuum fluctuations.
The vacuum based on the solution to the many
particle equation but also consistent
with Diracs equation and QED
Lab-frame
Lab-frame
Em0c2
E0
He is truly invisible!!
Vacuum fluctuations mean that leptons and
photons can randomly exist in the lab-frame for
times less than
Zero-point energy light at m0c2
1 N
Lattice frame
E0
-m0c2
Massless lattice-man measures the Casimir
force.
The leptons have no kinetic energy in the lattice.
The zero-point energy photons smear out the
position of the electron by about 0.1 Fermi which
is 5 of d0. This can be thought of as the
electrons in the atom interacting with the
lattice. Although there is no average field the
electron experiences a continuous acceleration
and de-acceleration at extremely high frequencies
causing a jitter.
In pair production 2m0c2 of the photons energy is
converted to the rest mass of the leptons
and the vacuum remains unaltered i.e. no holes
are produced. In vacuum polarization the
exchange photon can become a pair (from the
vacuum if you like) for a time
How deep?
The electrons and positrons occupy an infinity of
states with negative ? kinetic energy. The vacuum
contains photons presumably at E-m0c2.
Electron mass renormalization-contribution to
Lamb shift
Since the energy of the vacuum is zero there are
no vacuum fluctuations and the vacuum is always
self-healing i.e. we never produce holes in the
vacuum from pair production! And the zero-point
energy is in the lab-frame and consists of
stationery waves.
12
12
The big summary so far

• The gerdanken experiment gives results which do
  not agree with GR except in the weak field. This
  can only be reconciled if the electrons and
  positrons in space have quantum structure which
  affects the trajectory of light in a
  gravitational field.

2. The lowest state of an infinite ensemble of
electrons and positrons (or any other
leptons), where the kinetic energy of the
leptons vanishes, is a quantum lattice in
which each lepton is bound in by an amount
equal to its mass. The vacuum contains only
Coulomb potential energy which manifests
itself as zero-point electromagnetic
radiation.
3. The lattice can generate photons in the
lab-frame which have zero mass and velocity c
in free space.
4. A gravitational field is easily generated by
lattice relaxation so that the gravitational
potential energy of a lepton at any position
is equal to the change in its Coulomb binding
energy in the lattice.
Newtonian Gravity in flat space-time
5. The phase velocity of light generated by the
lattice shows that light bends in the
weak-field exactly as measured and (predicted
by GR).
13
Feynman type diagrams for the e-p lattice
Feynman diagrams cannot strictly be used for a 3D
array of particles!
13
This shows the Feynman diagram for the vacuum
(lattice) where only nearest neighbours
interact. The exchange photons have no arrows.
e
Feynman diagrams were not invented to include an
array of particles. We can represent the exchange
photons by counter propagating phase-locked
beams-that is standing waves. The sum of all the
waves represents the zero-point energy in the
electromagnetic field. We only show the
interaction between adjacent leptons here.
Standing waves are stationary states
e
e
You can do a real laboratory experiment where you
trap charge particles in an array of nodes
generated by standing waves generated using
laser beams. In a lepton lattice this is
automatically assured because the leptons have
zero-kinetic energy and cannot escape. In the
laboratory experiment you have to cool the
particles down to temperatures close to absolute
zero if they are to be held in by the electric
fields in the laser beam.
Elep mlep 0
e
e
Note that the particles in the vacuum array are
at antinodes not nodes
The n3/2 excitation of the harmonic oscillator
moves along the lattice and is effectively a
photon of energy shown by the heavy
line i.e. we can put arrows on it because it is
propagating and transporting energy. The
oscillation of the leptons is shown by a dotted
line.
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14
Normalizing the renormalization-beyond QED
NG
QED
The lattice generates the zero-point field which
is the same as QED but there is no need for
renormalization because the (E0) lattice
provides a classical framework to relate the
Coulomb energy (the zero-point field) to the
mass in this lattice. (You have found the hidden
structure implied by renormalization.) Also
there is no need for vacuum fluctuations as well.
The Feynman diagram for calculating
the self-energy or mass of the electron is the
interaction of the zero point radiation
field with the electrons. The idea being that the
e-ps create the photons so that the
self-energy must be the interaction of the
electron charge with the field
The lattice therefore defines mass and links it
to charge and space.
The result you get is infinity which is
renormalized to the mass of the electron. This
works since it goes on to correctly calculate the
Lamb shifts etc.
Of course this must be the correct interpretation
since it goes on to show how the Coulomb
interaction can generates a gravitational field
and the true nature of the neutrino. (And dark
matter and dark energy!)
Therefore, renormalization and vacuum
fluctuations are not necessary if the leptons in
the vacuum are structured into a cubic quantum
lattice such that each one is bound in by an
amount equal to its own so that the lattice
energy E0.
Notice that you would never get through this
barrier and unify gravity and the
electro-weak by mathematics alone! You actually
need to jump from algebra to real geometry.
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15
To come later part (a)- The lattice or
quantisation of space makes 3 further
important predictions which agree with
measurements

• What is dark matter?
• If you solve the problem of the lowest
  energy state of a finite number of electrons and
  positrons you again get
• a cubic lattice but now the solution has a
  finite zero-point kinetic energy, and hence mass,
  which is in the form
• of coherent oscillations. The calculations
  show that these bosons (spin zero) are stable and
  have no
• electromagnetic interactions showing that
  they are almost certainly dark energy. They can
  however produce
• annihilation radiation when in collision
  with energetic cosmic rays and this has been
  observed coming from
• the galactic bulge exactly where one
  might expect the highest concentration of dark
  matter. The oscillations
• do not generate any electromagnetic fields
  because there is no motion where the electrons
  and positrons separate to create an oscillating
  dipole i.e. the electrons and positrons are in
  phase rather than anti-phase. This type of motion
  is identical to that in gravitons or dark energy
  so that dark energy and dark matter interact and
  this causes the increased rate of expansion of
  the universe

2) What is dark energy? The lattice has
other modes of vibration besides those which
generate photons. These modes are identical
to the modes of oscillation of dark matter and
do not generate oscillating electric and magnetic
fields i.e. photons. Instead they create
(or are equivalent to) gravitons. You can now
have monopole and quadrupole gravitons and
neither interact with atoms-they are undetectable
unless you have a detector made from dark matter!
They can be likened to optical sound waves
in a solid which are generated by the electron
clouds around the atoms oscillating against
each other. When the lattice undergoes an
enormous relaxation at the big bang it looses a
huge amount of energy very quickly and this
is the origin of both dark energy and dark
matter.
16
16
To come later part (b)- The lattice or
quantisation of space makes 3 further
important predictions which agree with
measurements
3) What are neutrinos? Although group
theory shows that the weak interaction and the
electromagnetic interaction both belong to a
higher symmetry group it is an incomplete theory
and cannot reveal the nature of the neutrino or
its mass. However you notice an important
point that the whole of NG theory up to now
(including the gerdanken experiment) is invariant
in the lepton mass so could also apply to muons
or taus. There is no point in asking which
lattice the photons are in they are all
indistinguishable and only characterised by their
energy.
The principle of equivalence is implicit in the
way you generate a gravitational field from the
lattice! Mathematically the mass disappears from
both sides of the equation implies equivalence.
So now you can speculate that neutrinos are some
form of spin wave in the lattice which would have
zero-mass in the lab-frame just like photons and
gravitons. You just need to calculate the
harmonic dipole-dipole coupling by analogy with
photons.
Dipole moment of lepton
Energy of spin wave of lepton
Spin of lepton
The same for all lattices
Mass of lepton
Lattice spacing
So the energy of the electron, muon and tau
neutrinos are the same but they have a different
dipole moment and so are distinguishable by their
interactions unlike photons. Neutrino
oscillations have a simple explanation without
requiring that the neutrinos has mass.
Nuetrinos continued over
17
Neutrinos are part of the electro-weak
interaction and they are produced in the beta
(electron) decay of nuclei. The model of the
neutrino derived from the lattice is shown below.
It is a photon (electro-part) coupled to a spin
flip wave (weak- because the dipole-dipole
interaction is much smaller than the Coulomb
interaction) generated when the electron (or
positron) flips its spin and is phase locked to
the photon -the spin flip travels along the
lattice but the leptons do not move. Notice the
similarity between this and the anomalous
magnetic moment Feynman diagram in slide 5.
17
More about neutrinos
An electron neutrino
Note that the spins are not as shown. They are
orthogonal to the displacement of the leptons.
Think of the spin wave as a surfer riding the
magnetic field of the photons.
Const. 1
In the lattice frame you see just leptons
oscillating and flipping their spin. In the
lab-frame you see and would measure the
oscillating field of the photon coupled to the
field of a travelling dipole of the lepton which
is different for each lepton. The field is
therefore quite different to an electromagnetic
wave as described in slide 5.
NB. You dont use the measured (anomalous lab-fram
e) dipole moment here.
Energy of neutrino irrespective of type.
There are 6 types of neutrino Neutrinos (i.e.
electron-spin flip) Antineutrinos (i.e. positron
spin flip) Dipole moments µe
µµ µ? Electron Muon
Tau
Caution The classical model above may
need tweaking to be in line with below but see
next slide.
The spin of the neutrino is thus 1
1/2 1/2, 3/2 but model above And its mass0
suggests only ½
possible.
Standard Electro-weak Theory Integer Spin
Group?1/2Integer Spin Group Spin 1 ?Spin1/2
etc.etc.
Note that neutrinos cannot interact with atoms
Standard electro-weak theory is incomplete and
cannot tell you what the nature of the neutrino
really is. One might guess that since it has ½
integral spin it might be a particle and thus
have mass. Then if the mass is the same for all
neutrinos this might explain neutrino
oscillations . However, with one
noticeable exception the measured mass is zero!
Now NG shows why!
Important point-The generality of this theory is
overwhelming since it explains so much! with no
new axioms! It not only explains how to unify
gravity and electromagnetism it also unifies the
weak interaction-LONG LIVE THE LATTICE Space is
quantized.
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18
How classical models are essential
The lesson of NG in the advancement of physics
clearly shows that classical models are
essential and is illustrated throughout these
slides and we choose three examples to show this.
Neutrinos Electro weak theory tells you that the
weak and electromagnetic fields are part of a
higher group but one cannot get from it, except
possibly by divine inspiration, the proper
nature of the neutrino and its mass. The true
test of the overwhelming nature of NG is that
it provides a model for the neutrino which
predicts that its mass is zero and that one can
have neutrino oscillations. In essence we have
therefore incorporated the weak interaction into
our unification as must be the case if we have a
correct theory.
QED We showed earlier that the lattice spacing
provided a physics explanation for
renormalization so that one could relate the
self energy of the electron to its mass if the
electrons and positrons were bound in a lattice
by the Coulomb interaction by an amount equal to
their own mass. There is no possible way to move
forward from QED to unify it to gravity without
some model. In this case the model is essential
because it rectifies the incorrect assumption
about the nature of the vacuum which was derived
from a single particle equation.
Dark Matter and Dark Energy It is, at first,
quite astonishing that these can be explained by
a classical model but the lesson is that this
theory joins up the classical and quantum worlds.
Gravity is no longer an outsider. The only
explanation of dark energy has been that it is
the cosmological constant but when one uses the
old vision of the vacuum you arrive at an
embarrassing 10121 times larger value that is
needed to explain the cosmic acceleration. Now of
course the explanation is that the interaction of
dark energy with dark matter is pushing the dark
matter apart along with normal matter and so is
acting like antigravity. Unrealistic ideas like
an antigravity field are clearly absurd and one
does not have to invoke any unphysical concepts
such as variation of the inverse square law of
gravity. (Incidentally there are some
observations which show that dark matter does
not fall at g in a gravitational field which is
completely explained by this. We will review
these measurements along with those which confirm
the nature of dark matter from the observation
of annihilation radiation for the galactic bulge
in the second paper refs. 1 in paper 1.)
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19
Here we use Schrodingers equation to show that
the lattice is the lowest energy solution for an
infinite number of leptons
Solving Schrodingers equation for the vacuum-the
universe
We first reduce the many body problem to a single
body one by noting that each lepton is identical
and has the same single particle Hamiltonian.
SE
This is a trial solution method. You would
never get this this answer directly from SE!!
We use the state function for a single electron
interacting with the zero-point energy field
.
We insert a trial solution which is a product of
a stationary lepton in the lattice ( a ?
function) and the zero-point radiation modes.
The wave fn for a single lepton in the
zero-point radiation field
is the probability amplitude for finding a
photon in mode i.
The particle wave fn which is a ? Function at a
lattice site
The photons must be stationary states like this
and if we evaluate the rhs of SE then we get a
sum of terms which are all zero if the zero-point
energy is at zero in lab frame. All Ei 0 and
this preserves the concept of a photon as a
lattice vibration. See slide 11.

This is the Hamiltonian for a stationary particle
in a field with vector potential A. (See
fantastic textbook mentioned earlier p48)!
Combining all the equations to get the lhs of
SE gives
Sum of all the Feynman diagrams for lepton
mass renormalization-slide 14

See paper 1 for a full mathematical treatment
The lattice is defined by this.
So we conclude that if the zero-point energy for
all modes are at zero-energy in the lab frame
then the lhs S is equal to the lepton mass. So
NO RENORMALIZATION and NO VACUUM FLUCTUATIONS are
necessary. We have found a solution of SE for the
vacuum.
WE HAVE FOUND THE TRUE SOLUTION FOR THE VACUUM OR
THE UNIVERSE

• D A Eastham, December 2007
• to be submitted for .publication
• separately.

20
20
Some Important Physics about the Quantum Lattice
It is very important to understand that the
quantum lattice is completely invisible and its
structure cannot be measured in any way. It is
the point where the kinetic energy of each lepton
vanishes and so does its mass in the lab-frame.
The only manifestation of the lattice is the
zero-point field which has measurable effects
such as the Lamb shifts, spontaneous emission
and the Casimir effect.
THIS MEANS THAT IT CANNOT BE DISCREDITED BECAUSE
IT BREAKS SOME CONSERVATION LAW OR SYMETTRY
RULE BASED ON ITS STRUCTURE.

• The lattice is therefore the origin of
• The static gravitational field
• The quantum field which includes photons,
  gravitons and neutrinos
• Dark energy or monopole gravitons
• Dark matter or monopole bosons or lattice
  fragments where the zero-point energy is in
  coherent
• monopole oscillations