1 advanced quantum theory in pi-space · pdf file1 advanced quantum theory in pi-space in this...

1 Advanced Quantum Theory In Pi-Space

In this chapter, we’ll discuss how to represent Physics in terms of waves and waves within

waves. The Standard Model is reverse engineered into this format. Before that is done, I’ll

show how to model Simple Harmonic Motion and the Pendulum. Also mass is modeled as

waves within waves and this later ties into the Higgs Boson.

1.1 Defining Mass Next, we need to discuss the Advanced Quantum Theory in Pi-Space. Here we’ll define in

more detail the non-local wave function and its properties. In the earlier sections, I talked

about disturbances to the Gravity and Electric field. I also stated that the Gravity and Electric

field were in the non-local plane. Also, there is the issue of what is mass? It is typically seen

a value which is applied to the equations but where does it come from. We know for

example that it creates a Gravity field for example.

Let’s first define what mass is in Pi-Space. In the Advanced Quantum Theory, mass forms

the non-local plane and is wave based.

This is a simple but crucial concept before moving forward.

Let’s draw a wave function with mass and then without mass.

In Pi-Space, mass is the non-local wave within the local wave. The higher the amplitude of

the non-local wave the more mass it has. For now, we will not concern ourselves with the

Mathematics around it. This is the concept. Mass is simply the non-local wave within the

local-wave. Therefore Mass has a wave component. I will drill down into the specifics later.

Here we have a mass carrying wave. The local wave is simply Sin[x]. The non-local wave is

the addition. The specifics of the function itself is not important rather the addition of two

waves in this fashion.

Also, we can have a local wave with no non-local wave. This is a massless wave like light.

This is the first rudimentary concept of Advanced Quantum Pi-Space. The fact that mass is a

wave within a wave means we can start visualizing reality as a symphony of vibrating waves

within each other. Some are long, some are short, some curve, some do not and so on. From

this simple idea, we can start talking about Strings and String Theory in more detail. From

this idea we can spring to Strings.

1.2 Simple Harmonic Motion Strings are based on Simple Harmonic Motion so let’s define this using the Pi-Space

formulas. First we show how it’s currently solved.

kxF

and

tkAtmvtKE 222 sin2

1

2

1)(

Also

tkAtkxtU 222 cos2

1

2

1)(

We can calculate the period T as well

k

mT 2

Let’s use the Pi-Space formulas now

*,,,*,,,2

2

2

NonLocalLocal

trc

hr

GM

trtrc

vArcSinCostr

c

p

trtrc

vArcSinCos

We’re dealing with two local field effects of a Spring and a moving mass. Let’s add KE and

PE.

Localtrkxtrtrc

vArcSinCosm

,

2

1,, 2

The interesting point to note is that the PE can also be represented by a KE representation.

Localtrtrc

xArcSinCosktrtr

c

vArcSinCosm

,,,,

The single wave functions cancel out, so we’re left with just Cosine functions and some

constants.

0,,

tr

c

xArcSinCosktr

c

vArcSinCosm

We can solve for the KE of the mass

tr

c

xArcSinCos

m

ktr

c

vArcSinCos ,,

If the wave function is constant, the representation simplifies (we drop them)

c

xArcSinCos

m

k

c

vArcSinCos

This can also be represented in the other way in terms of the spring.

c

xArcSinCos

c

vArcSinCos

k

m

The period of Cosine is 2 times the constant Pi. Also these values are the area calculations.

So if we want a diameter calculation we have to square root it. Also from my work on

Special Relativity (see the Introduction to Pi-Space Theory) I showed that time is a diameter

calculation. Please review this if you are unsure.

So it turns out that Period can be calculated as

k

mT 2

Note: In case you are wondering how can the two representations (Pi-Space and traditional

are similar / equivalent), there is a simplification of the Cos squared function as follows.

xCosxCos 22

1

2

12

Also

xCosxSin 22

1

2

12

This would give us something like

1*2

121*

2

12 22

c

xArcSinCosk

c

vArcSinmCos

Drop the -1 and we get

c

xArcSinCosk

c

vArcSinmCos *

2

12*

2

12 22

Drop the 2

c

xArcSinCosk

c

vArcSinmCos *

2

1*

2

1 22

If we compare this with the Classical value, we get a similar formulation.

tkAtkxtU 222 cos2

1

2

1)(

And

tkAtmvtKE 222 sin2

1

2

1)(

According to the Pi-Space Theory, these String equations should therefore be relativistic.

c

xArcSinCos

m

k

c

vArcSinCos

And

Simple Harmonic Motion in Pi-Space, Energy Eqn

0

c

vArcSinmCos

c

xArcSinkCos

If we use amplitude instead of x, we get

0

c

vArcSinmCos

c

AArcSinkCos

Multiply the result by C^2 to get back to Newtonian

values

1.3 Simple Harmonic Motion solving for v using x and A

Energy Conservation for Harmonic Oscillator

222

2

1

2

1

2

1mvkxkA

Solving for v classically

22 xAm

kv

At x=A, velocity is 0

At x=0, velocity is maximum

We can solve the equations in the traditional fashion.

Harmonic Velocity, Amplitude A, position x, Spring force k, mass m.

c

c

x

c

AArcSinCos

m

kv *

2

1

2

11

2

2

2

2

Worked example

A=5 meters , x=2.5 meters, k=1 kg ,m=2 kg

Classic

Sqrt[(1.0/2.0)*((5.0*5.0) - (2.0*2.0))]

Result is 3.24037 m/s

Pi-Space

Sqrt[(1.0/2.0)]*

(

Cos[ArcSin[1 -

(

(

((5.0*5.0*0.5) - (2.0*2.0*0.5))/(299792458*299792458)

)

)

]]

*299792458

)

This produces a result of 3.15883 m/s. This is not the same as the classical result.

Pi-Space maintains that is a more “accurate” result.

To make the result match the Classical Result, we just need to make Speed of Light less

accurate (incorrect!) e.g. 2997924

Let’s redo the calculation

Sqrt[(1.0/2.0)]*

(

Cos[ArcSin[1 -

(

(

((5.0*5.0*0.5) - (2.0*2.0*0.5))/(2997924*2997924)

)

)

]]

*2997924

)

This produces a result of 3.24038 m/s so they match.

This would need to be verified by experimentation. I do not have the equipment for this.

1.4 Pendulum Described in Pi-Space We can solve the equations in the usual Hamiltonian way. We use the small angle idea which

is part of the proof normally. However for Pi-Space, we don’t need to but let’s do it this way

anyway.

Potential Energy of a Pendulum is

2

2

1mgL

LocaltrmgLtrtrc

vArcSinCosm

,

2

1,, 2

And

2

2

2

1

2

1

L

xmgLmgL

Which gives us

2

2

1x

L

gm

Represent Pendulum as KE formulation and we get

Localtrtrc

xArcSinCos

L

gmtrtr

c

vArcSinCosm

,,,,

Dropping m and the wave function

c

xArcSinCos

L

g

c

vArcSinCos

This is the same as the Harmonic Solution.

We can solve for v

Harmonic Velocity

cc

xArcSinCos

L

gv *

2

11

2

2

And the other way

cc

vArcSinCos

g

Lx *

2

11

2

2

And Period T is

g

L

1.5 The Smallest Local Wave It’s important to describe the scale of things. In our reality, the smallest local wave is the

Planck Length. This is not the smallest wave, this is the smallest local wave. In the Pi-Space

Theory, the smallest local wave and objects made up from larger wave lengths can carry mass

waves or what I call non-local waves. The Planck Length is 10^-35.

3c

Gl p

So how do we make larger local waves? In the Pi-Space Theory, this is achieved for example

by moving upwards in a Gravitational Potential.

1.6 Why Particles Have Discrete Mass? A valid question to ask is why do certain elementary particles have fixed mass? The answer

in Pi-Space is that the Mass carrying local wave has a specific amplitude and wavelength that

limits the amount of mass that it can “carry”.

A local wave of a certain amplitude can only carry so many non-local waves of another

amplitude. The non-local wave amplitudes are what we call Mass in Classical physics

according to Pi-Space. Therefore we must have exact masses for particles with certain

amplitudes like say an electron.

Pi-Space Rule of Thumb: Mass is carried by the Local Wave. It can only carry a fixed

number of Non-Local waves.

In my Quantum Doc, I showed how when one falls into a Black Hole all that is left in the

formula is the Mass wave functions (which are the non local ones)

trm ,*

1.7 Why The Fine Constant Exists (Ratio of Local to Non Local) Also what follows from this is the Fine Structure constant which falls out from this which is

the ratio of the local wave to the non local wave namely the coupling constant characterizing

the strength of the electromagnetic interaction. The formula is

Pi-Space Rule of Thumb: The Fine Constant is the ratio of the local wave to the non local

wave.

h

ce

2

02

Note: EM (Magnetic piece) and Gravity are non local waves in Pi-Space. Recall in the

Quantum Section that the EM wave is out of phase with the Gravity Wave. This is how they

can both travel on the same local wave.

1.8 Explaining Why The Non Local Waves (aka Strings) always perpendicular to the direction of motion

It is assumed to be quite mysterious why Strings or (what I call) non Local waves are

perpendicular to the direction of movement. In Pi-Space, it’s pretty straightforward how to

explain this. Take a look at the diagram and look at the non local waves. They are always

perpendicular to the direction of movement.

Non local waves carry the non local Mass waves which ultimately generate the Gravity field

proper. As described already, the minimum size of these local waves is the Planck Length

and maximum speed of light. Importantly, Maxwell also discovered the perpendicular

relationship between electricity and magnetism and this was formalized by Heaviside using

the Cross Product (which is another way to describe perpendicular behavior). Therefore, in

the Pi-Space Theory both the Mass and the Magnetic Field waves are non local and out of

phase with one another.

1.9 Simple Proof Why 10 Dimensions Describes Gravity, EM and Our Reality

Consider a local wave with maximum velocity c and which has a three dimensional reality

plus time. This is three dimensions plus one equaling four.

Consider two other properties of this reality which is the magnetic field and the gravity field

which are non local.

Both EM and Gravity are out of phase with one another.

Squaring the amplitudes for each effect produces a tiny compressed Pi-Shell which String

Theorists could call curled up dimension.

The size of these theoretical Pi-Shells are smaller than the Planck Length but are part of the

Local Wave whose smallest size is the Planck Length.

If we add up the total number of “dimensions” if we choose to use this concept, then we get 3

+ 1 for the local wave and 3 + 3 for the non local wave.

It’s a matter of debate whether these are really “dimensions” as in other realities but in Pi-

Space, it is completely valid to model them as tiny curled up dimensions as was described by

Kaluza Klein.

1.10 Unifying String Theory with Pi-Space Gravity To Complete The Gravity Work (Very Large to Very Small)

To unify String Theory with Pi-Space all one needs to do is take the current Pi-Space

formulas derived for Navier Stokes and Classical Gravity and add the String Theory

Harmonic String in place of the Mass component of Newton’s Gravity.

Using this approach we have an initial complete Theory of Gravity which combines Newton,

Einstein’s Relativity and String Theory.

Therefore, we have the very large to the very small.

*,,,*,,,2

2

2

NonLocalLocal

trc

hr

GM

trtrc

vArcSinCostr

c

p

trtrc

vArcSinCos

In String Theory, we know what M^2 is a Harmonic Oscillator based on the Regge and

Chew-Frautschi Plot. All we need to do is replace solved for M with this. Therefore String

Theory in the Newtonian Analogue describes the Mass component of Gravity. Later, I’ll

flesh this out some more. However, for any engineering student trying to understand how to

fit String Theory into Gravity this is where it fits into the Pi-Space Equations for Gravity.

Quantum Gravity lies in the non local wave and is determined by the Mass value using the

classical analogue.

1.11 Adding a Wave Within a Wave In Pi-Space Using A Mass String

I’ve stated already that String Theory in Pi-Space is about defining the non local wave. In

particular, these waves within waves explain the Gravity due to mass and the EM (Magnetic)

effect.

Let’s do the math!

We need a wave within a wave formula.

*,,,*,,,2

2

2

NonLocalLocal

trc

hr

GM

trtrc

vArcSinCostr

c

p

trtrc

vArcSinCos

We’re only interested in the non local part, so we drop the local piece for this example.

*,,,*2

2

NonLocal

trc

hr

GM

trtrc

vArcSinCos

The mass is the non local part, so we define mass as a String. This is taken from A First

Course In String Theory by Barton Zwiebach.

L

EnergyForceT 0

We have Tension and we have mass per unit length

202

0 vvL

MT

This becomes

02

2

0

0

2

2

t

y

Tx

y

Which is a Harmonic Oscillator

I’ve done these before (see earlier). This gives us.

0,, 00

tr

c

xArcSinCosTtr

c

vArcSinCos

According to the Pi-Space Theory this is the relativistic version.

Note that this is the Energy version of the String which represents Mass in terms of the Local

Wave.

2

00 ,, Mtrc

xArcSinCosTtr

c

vArcSinCos

Now if we want to plug this into the Local Wave formula for Gravity where the non local

wave (or String even representing Mass) creates a Gravity field in the classical sense, we

need to determine the amplitude of this wave. Recall in Pi-Space, that the Gravity field is

created by a Mass based area change to the atoms in the Gravity field. Gauss described this

as an area change to a volume. Einstein called this a warping on Space Time and using the

Equivalence it altered the Mass Density of an atom. So these Mass waves alter the area of a

Pi-Shell (atom). Later, I’ll formalize Einstein “Space Time Fabric” but for now, I’ll show a

formula for a non local wave inside a local wave which is quantized.

We solve for x which maps to the amplitude of the mass string in Pi-Space.

'*2

11

2'

2'

0

0 cc

vArcSinCos

TxM

Note that this is the non local speed of light, which just means the maximum speed that this

wave can travel in the non local frame. From the perspective of the local frame, speed here is

“infinite” (infinite frame) because it’s already at the speed of light.

We’ll add an additional dash ‘ notation to express the fact that this is not the local max speed

of light or local velocity v.

tr

c

hr

cc

vArcSinCos

TG

trtrc

vArcSinCos ,

'*2

11

,,*2

2

2'

2'

0

0

All I’ve done is replace Mass with the String Theory version of Mass. This is a Wave Within

a Wave Formulation.

And this is what it looks like.

Note: I'll explain how Pi-Space sees Speed of Light in terms of a non local wave.

1.12 Spooky Action At A Distance / Quantum Entanglement

The wave within wave formula contains the description of defining the non local wave and

how it’s part of the mass wave which generates the Gravity field. The inner wave is non

local. The non local wave operates within the local wave which has maximum speed of light.

It is generated first and to an observer in the local reality based on the local wave, any

updates to a non local wave will appear instant! However, the key point to make is that this

does not violate cause and effect. The non local wave is generated first, then the local wave

(>= Planck length) is created from the non local waves. The ordering ensures that cause and

effect are protected, so a wave which is perceived to travel > local wave speed C does not

cause weird time effects. Also Quantum Entanglement is related to EM properties. The

Magnetic component of EM is also non local waves as I’ve shown before. I’ll cover this

later. This is one of the meanings of Mass as a String in the Pi-Space Theory.

tr

c

hr

cc

vArcSinCos

TG

trtrc

vArcSinCos ,

'*2

11

,,*2

2

2'

2'

0

0

1.13 Basic Concept of The Higgs Field In Pi-Space and Fields In General

Let’s just define the basic concepts initially. One of the consequences of the wave within

wave formulation is that we can map the non local wave to the Standard model Higgs Field

which is the “mass giver”. In Pi-Space we consider free space with no particles or energy to

be made from just non local waves. In the Pi-Space Theory, free space is seen as a “sea” of

non local waves. Therefore it is not empty. Some of these non local waves may carry atoms

(what I call Pi-Shells) and the non local waves form the mass component. A light wave for

example which carries no mass is a “pure local wave”. See my earlier post on a massless

wave. Also, what arises from this sea of non local waves are particles which can appear and

disappear momentarily. Therefore, virtual particles are created by interacting non local

waves. Also, this leads us into the Einstein Space Time fabric idea. At the simplest level, the

gravitational fabric in Pi-Space is made from these non local space time waves interacting

with the atoms non local mass wave component. Also, the fact that non local waves complete

before local waves provides us with fields which are always in place around us. For example,

we do not see a Gravity field partially constructed or a magnetic field (N S pole) partially in

place. They are always there fully formed. This was one of the puzzles which Newton

accepted as unsolved in his work but focused on the local wave formulas (energy, velocity

and force) which we use today. This was sufficient because we operate primarily in “local

wave” space with maximum speed of light C as Einstein pointed out in his SR work.

Note: There are exchange particles in Pi-Space which I will cover later but some are non

local.

1.14 Quantum Spin States

Let’s map the idea of Spin states to Pi-Space next. Pauli and Dirac produced unique Spin

states for EM and Gravitons. Electrons and Fermions have spin +1/2 and spin -1/2.

Gravitons have Spin 2. Let’s show how this can be mapped to the Pi-Space approach. In Pi-

Space, we extend the idea of the pure probability approach to have two orthogonal waves

combining with one another. If you are unsure of this please read the Quantum Doc. There

is the EM case and the Gravity wave case which is the product of Mass waves which I have

mapped to String Theory strings. Essentially, Magnetic and Gravity fields are both created

by Non Local waves which are waves within local waves. So when two orthogonal local

waves combine to form the diameter of an observable particle, they are also carrying non

local Mass waves and EM charge.

The unit of length of a local wave is the Planck Length with max speed C. First, we cover the

EM case. Here we draw the Local wave only. I do not draw the Non Local wave so I draw

the local part only. I indicate where 1 Planck Length is.

Spin Down (-½)

Spin Up (+½)

ElectroMagnetic Field E + M in two Axes.

Spanning 1 Planck Length Carried on Local

Wave Max Speed C

Max Amplitude Case 1


-yA

xis

E

-zAxis M

+yA

xis

E

+zAxis M

M

E

y=sinx, x∊[0,2π]

y=-sinx, x∊[0,2π]

O

1

-1

π/2 π2π

3π/2

y

x

y=sinx, x∊[0,2π]


O

1

-1

π/2 π2π

3π/2

y

x

Spin Up +½

M

E

Spin Down -½

M

1 Planck Length

M

E

E M

From this one can see one can fit either a spin up or a spin down inside on Planck length. It

is analogous to a Cosine wave (starts at 1)

Using the Pauli/Dirac Matrices notation, this is

10

01,

0

0,

01

10

i

i

From this he derived the Eigenvectors and Eigenvalues. I won’t go into the full detail of this

now, rather the concept of the mapping to a local wave.

e.g.

1

1

2

1

Next we take a look at the local wave which carries the Mass. The EM wave is analogous to

a Cosine wave where it’s starting point is 1 and then it goes to 0. In the case of the local

wave, this is analogous to a Sine wave, which starts at 0. It spans 2 wave functions (2 Planck

lengths) which gives it equivalent Spin 2. The wave function just covers one axis but both

axes form three dimensions.

Mass Carrying Wave Creating 3D Space



-yA

xis

-zAxis

+yA

xis

+zAxis



E

y=sinx, x∊[0,2π]


O

1

-1

π/2 π2π

3π/2

y

x

Mass Carrying Wave

(Graviton) Spin 2

1 Planck Length

E

We can see using the Pi-Space approach, the Mass carrying wave has spin 2 (2 Planck length)

and is like a Sine wave. The Non Local Mass it is carrying is modeled as a String Theory

String. (See earlier work). Running alongside this is a EM field local wave carrying charge

which is analogous to a Cosine wave and has Spin +1/2 and -1/2.

1.15 Evolution Of Ideas So Far

Let’s cover the ideas so far to get to this point.

Concentrate on a sphere in terms of its diameter and area.

Formalize the mapping of velocity to the diameter change and area to the energy of the

sphere.

Define the Square Rule mapping velocity to energy

Define the observer and relativity.

Show a new Proof for Pythagorean Theorem based on Spheres

Total compressed Pi-Shell means traveling at speed of light.

Potential Energy is area gain.

Kinetic Energy is area loss.

Reverse Engineer existing Special Relativity and Newtonian Gravity work to show it works. Mainly

use diagrams.

Call this sphere a Pi-Shell and not just an atom because a planet can be modeled like this and

also String Theory extra dimensions.

Map the total area of a Pi-Shell to Einstein’s formula.

Derive a new Kinetic Energy formula where at V=C we get E=MC^2 as opposed to infinity.

Derive a new version of Lorentz Fitzgerald Transformation which returns same values based

on Trig

Use the same Newtonian logic to derive Potential Energy formulas and equivalent Newtonian

style formulas.

Produce a document showing formulas and calculations which match Newton's values

Derive a general solution for Orbits

Explain how a Black Hole works

Move onto Quantum Theory

Extend the Probability approach to show that what is missing is Non Local waves.

Provide a “Schrödinger’s Wish” formula where we deal with waves and not just probabilities.

Use Hamiltonians for each wave plane

Formalize Non Local waves

Explain Quantum Entanglement as Non Local behavior

Solve for Local and Non-Local waves which are orthogonal

Show how Pi-Space is compatible with Gaussian Gravity

Solve for Bernoulli

Solve for Navier Stokes explaining where Turbulence comes from

Begin work on Advanced Quantum Theory.

Reverse Engineer Harmonic Motion.

Explain ten dimensions

Formalize the Non Local waves. Show how they are String Theory Strings.

Produce a new formula Very Big to Very Small Gravity formula (Newton, Quantum,

Relativity, String for Mass)

Begin work reverse engineering Charge and the Standard Model

…

I just want to write this for the record about probabilities and Pi-Space.

Pi-Space does not say that the probabilities approach is wrong! Probabilities are correct

experimentally. All that Pi-Space says is that we have not modeled the Non-Local waves in

the equations for these events (which would explain the percentage of one result over

another).

Because Physics doesn't currently believe there are Non Local waves, we are forced to use

Probabilities.

I realize this goes against Orthodoxy but this is Pi-Space.

If we can successfully model the Non Local waves interaction with Local waves we won't

need Probabilities is what Pi-Space says, or even help explain why it’s happening...

BTW: The Math for the Non Local waves is the same as the Local Wave. It's how they

interact which produces one result over another.

1.16 Modeling Charge In Pi-Space

Charge is another example of waves within waves.

Conventional Physics models charge as positive and negative. When like charges come

together, they repel. Unlike charges attract.

Pi-Space can explain why this happens using the wave within wave design pattern.

Coulomb and Newton are similar

2r

GMmFg

2r

QqKFc e

There are three distinct cases.

1. + and – charges attract.

2. -- repel

3. ++ repel

The Pi-Space rule of Thumb for movement is that a Pi-Shell or particle will move towards the

place where the Non Local waves are the smallest. This is how Gravity works in Pi-Space.

Mass moves towards the Center of Gravity where the Non Local mass waves are the smallest

and the Pi-Shell become smaller. This is the Principle of Least Action.

Recall that Mass waves are Non Local and carried on the Local Wave.

Charge is also Non Local in Pi-Space. It is carried on the EM wave. At present, we model

the Charge as a Non Local wave on the Electric wave.

In this case, we can see that we can model the Force between Charge and Mass using the

same formula. This is why the Newtonian and Coulomb formula match.

However, this does not explain Positive and Negative Charge and why there is attraction and

repulsion.

To explain this we need to add another set of waves within the Non Local. For the purposes

of this discussion we can call this the “Charge Type Waves”.

Therefore we can define two charge type waves within the Non Local charge.

The Charge Type waves are out of Phase with one another (Sine and Cosine).

We arbitrarily choose the Sine wave as the Positive Charge Wave and the Cosine wave as the

Negative wave. We could define this the other way around if we wanted. The point is that

they define the two Charge states of Positive and Negative.

Therefore we have

Electric Wave (Local) =>(carries) Charge Quantity (Non Local) =>(carries)

Positive/Negative Charge Type Wave (Non-Non Local)

We can define a simple notation called N(x)

N(0) = Local Wave (Electrical)

N(1) = Non Local Wave (Charge Quantity)

N(2) = Non Non Local Wave (Charge Type, Positive, Negative)

Let’s draw the Charge Type Wave

For Positive Charge (we use N(2) Sine wave). Note the three terms in the formula below

indicating N(0), N(1) and N(2).

For Negative Charge (we use N(2) Cosine wave)

So, let’s consider what happens when we combine two of these diagrams.

There are three cases.

We can think of N(2) Sine as +-+-+-+- and Cosine as -+-+-+-

Case (1) Positive and Negative Charge combine. Both N(2) Sine and Cosine cancel

+-+-+-+- -+-+-+-+ = 0

Thefore N(2) cancels and we end up with the a Gravity style Mass Non Local Diagram.

The + and - charges attract. Moving towards one another, the Non Local waves become the

smallest. If they move away, the Positive and Negative N(2) charges grow stronger so the

particle does not want to move in this direction. This is the Principle of Least Action.

Case(2) Positive and Positive N(2) charges combine. Two Sine waves combine and the

amplitude of the N(2) charges increases.

+-+-+-+- +-+-+-+ = N(2) amplitude 2

The two positively charge particles will repel as their Non Local waves become larger. So as

they move away from one another, they become smaller. Once again the Principle of Least

Action.

Case(3) Negative and Negative N(2) charges combine. Two Cosine waves combine and the

amplitude of the N(2) charges increases.

-+-+-+-+- -+-+-+-+ = N(2) amplitude 2

The two negatively charge particles will repel as their Non Local waves become larger. So as

they move away from one another, they become smaller.

So as we can see it is reasonably simple to model Charge in Pi-Space. We map various

attributes like charge to the Waves Within Waves Pi-Space design pattern. Also we don’t

need to add any new concepts. We are reusing the same ideas over and over again and from

this we can derive the attribute of charge and its behavior.

1.17 Modeling Size of Mass and Charge Using The Pi-Space Notation

At the present time, using the notation we can model Mass and Charge. We can also model a

positive and negative charge and explain where there is attraction and repulsion. Next, I’ll

explain how we can model quantity of charge or mass. We say something has more mass or

less mass, or more charge or less charge.

Pi-Space uses what I call a “pack mule” design pattern. Waves are inside waves but waves

also can be said to “carry” other waves. Some particles are heavier which means that there

are more waves carried either by the EM waves or the Mass wave.

In the example diagrams we have the wave function, for example Cosine or Sine. Inside it

are the parameters which detail the number of waves.

Outside it is the amplitude of the wave. In Pi-Space, the changing amplitude changes the size

of the particle or wave amplitude. This is related to energy and I’ll talk about that later.

Newtonian Mass is a combination of the Number of Non Local waves which are carried

times their amplitude which is measured under Gravity.

Typically, we talk about the Rest Mass. In Pi-Space, this refers to the number of Non Local

waves carried by Local wave. For the most part, the number of waves remains constant

except for fusion or fission which is how they are altered.

Charge is also the measured in the same way, except for the N(2) waves which produce the +

and – charge.

1. Zero Charge/Mass (0 mass/charge waves)

2. Increasing Mass/Charge (10 mass/charge waves)

3. Greater Mass/Charge (50 mass/charge waves)

Note that the number of N(1) waves (traditionally called Mass or Charge) carried determines

how strongly or otherwise the particle interacts and alters the field(s) around it.

1.18 Modeling A Quark In Pi-Space

I’ve already modeled the Charge Type Carrying wave. Typically for an electron this is

charge -1 and for a Proton it’s +1. Murray Gell-Mann showed up how the Quark creates the

+1 charge using +2/3 and -1/3. In Pi-Space, the reason why we tend to have triples is the

nature of the wave states. We have min amplitude, max amplitude and the case where the

two waves cancel each other out which I’ll call zero amplitude. Typically this are three

states. Carried on each waves are two inner waves which are out of phase with one another

equivalent to a positive and negative charge carrier wave. See earlier work on modeling

charge. Combined, they form a simple addition and subtraction mechanism which the

Quarks take advantage of next.

Now, a Quark is therefore a way of breaking down the charge carrier wave as modeled in Pi-

Space.

Let’s draw both Quark types. (+2/3 and -1/3)

+2/3 Quark (We model +2/3 as 0.666 of the Sin wave)

-1/3 Quark (We model -1/3 as 0.333 of the Cos wave)

If we add +2/3, +2/3 and -1/3 we get +1 which is the Charge Type wave, we get the original

Charge Type +1 wave I defined earlier (A positron in this case, as opposed to Electron

charge). (We add two 0.666 Sin waves and one 0.333 Cos wave)

Next, these Quarks in turn carry QCD “color” which is another wave within this wave. I’ll

cover this next but at this stage one could almost begin to predict what I can write if one

understands this simple design pattern.

So if we draw a Proton which is charge, charge type and 3 quarks, this is what it looks like as

a simple formula with a visual representation.

1.19 Modeling Quark QCD Color In Pi-Space

QCD Color has three forms Red, Green and Blue. The way these are modeled in Pi-Space is

that they are waves which are contained within the Quark waves (-1/3 or +2/3).

There are three cases.

We will arbitrarily model them in the following way.

Red: Quark carrying a Cosine wave

Green: Quark carrying a Sine wave

Blue: Quark carrying neither Cosine nor Sine waves.

These are the three states.

Let’s extend the last example.

So if we draw a Proton which carries a charge wave, a charge type wave which is made from

3 quarks, this is what it looks like as a simple formula with a visual representation.

Note: We do not precisely model the number of carried waves at each level. We keep it

simple 10, 20, 30… Also we assume that the contained Color wave is the same size as the

Quark wave.

Further down , each quark can carry three possible colors.

For this discussion, we consider the Quark -1/3 and show how it can carry color.

Red Quark -1/3 (Cosine wave)

Plot[Sin[𝑥]+Sin[10𝑥]+0.3333Cos[20𝑥]+0.3333Cos[30𝑥],{𝑥,0,20}]

Green Quark -1/3 (Sine wave)

Plot[Sin[𝑥]+Sin[10𝑥]+0.3333Cos[20𝑥]+0.3333Sin[30𝑥],{𝑥,0,20}]

Blue Quark -1/3 (No wave carried)

Plot[Sin[𝑥]+Sin[10𝑥]+0.3333Cos[20𝑥],{𝑥,0,20}]

1.20 QCD Quark Confinement In Pi-Space

There is presently no analytic proof for why QCD Quark Confinement exists. Let’s try to

explain how this works in the Pi-Space analytically using the Wave within Wave model and

show why it makes sense according to this Theory.

Let’s take a look at one of the Quarks that was defined earlier.



If one looks at this diagram, one can see that the Quark carrying color is confined inside

individual larger parent waves. Therefore one cannot simply “take out” a quark with Color.

It is an intrinsic part of the part charge type wave which is an intrinsic part of the charge

wave. Put another way, the waves are embedded inside one another. Also if one wants to

move a Quark from one wave to another, this will produce the Quark , AntiQuark pattern

which means that they must move outside the confines of their parent wave.

One cannot “see” a Quark because it is Non Local. However, it is there on the Non Local

plane. The QCD color also holds the waves together and I will discuss force later but not

now. Therefore the scatter plots should reveal the Non Local waves within the “local”

scattering. I will discuss asymptotic freedom next for a quark according to the theory and

show how this works according to this design pattern.

1.21 QCD Quark Asymptotic Freedom Pi-Space

Let’s describe Asymptotic Freedom. It has been discovered experimentally that the Color

force is a multiple of distance. Traditionally, force is divided by distance and falls away as

one moves objects apart but not in this case. How can we describe this?

Let’s consider the following formula.

rkr

kV 2

1

Where

K1 = strength of Coulomb attraction of the Quarks

K2 = strength of the Color force attraction about 1 GeV/fm

In Pi-Space, the potential is about a Pi-Shell or wave getting larger. KE is about a Pi-Shell or

wave getting smaller.

Force is therefore an area change (gain/loss) or wave change (wavelength longer/shorter)

In Pi-Space, we have the concept of our reality like a “wave onion”. We have two pairs of

waves on each layer which are out of synch with each other. Mathematically, we can

represent these two waves by the Exponent using imaginary numbers which is how Quantum

Mechanics handles a single layer of the “wave onion” so to speak.

xixe ix sincos

Each wave can in turn carry other pair of waves so the waves are inside waves. We can

assign arbitrary wave layer numbers to them using the N(x) notation. Each wave affects the

other. The size of an N(1) wave be affected by the N(2) child waves.

Let’s show how our reality breaks down using this idea and focus just on the EM wave.

Later, I will show how Gravity fits into this overall design pattern. Note: It resides in the

N(0) and N(1) layer and is out of phase with EM.

Typically there are three states. Parent wave carrying Cosine, Sine and Neutral (carrying

neither Cosines nor Sine)




N(3) = Non Non Non Local Wave (2/3 Quark Charge Type, 1/3 Quark)

N(4) = Non Non Non Non Local Wave (QCD Color Red, Green, Blue)

All N(x) states affect the size of the N(0) wave state which is where we define our

experimental reality with Force and Momentum. Therefore a change in the N(3) state can

affect N(0). The same is also true of the N(4) state.

Recall in Pi-Space that waves moves towards a location where their waves become smaller.

This is the Principle of Least action described in Pi-Space.

Let’s add the wave location to the formula described earlier.

Let’s consider the following formula.

rkNr

kNV 2

1 )4()3(

N(3) represents the Quark-Quark interaction and the changes in the wave sizes. They are

bound to the Charge Type Wave which they form.

N(4) represents the Color type waves inside the Quark wave. Their wave length is

dramatically smaller and these waves reside inside N(3). If one stretches N(3) wave, what we

typically think of as 3 Quarks, then the N(4) waves resist this by k2 times the distance.

The way this is described is 3 balls held together by springs which resist being pulled apart.

In Pi-Space, the way we model this is 3 N(3) waves forming the charge type wave N(2). The

3 N(3) waves (the three balls so speak) carry N(4) charge type waves (red,blue,green) which

we can model as “springs”/waves. They resist as N(3) Quarks are pulled apart because they

want to be smaller. This is the principle of least action.

These N(4) waves typically do not form particles. Recall in Pi-Space that to form a particle

from a wave all one has to do is have two waves collide orthogonally. This is why we square

diameters using the Square Rule. The squaring of these waves form the Quark particles from

the Quark waves. Once we have these, then we can model the force in terms of area change

of Quark particles and divide by r.

Recall, here is how we model QCD Color



N(1) = Sin(x) = Charge

N(2) = Sin(10x) = Charge Type

N(3) = 0.3333Cos(20x) = Quark -1/3

N(4) = 0.3333Sin(30x)= QCD Green

Note: 10,20,30 are arbitrary and do not reflect actual charge/quark/color settings.

1.22 Modeling Gravity and EM in Pi-Space

Now all the major pieces are in place to model Gravity and EM. Both are wave based. The

Electric component of EM is carried on the same wave as the Gravity wave which carries the

Mass wave. Both EM and Gravity are out of Phase with one another.

For the purposes of this discussion, we make Gravity (Sine) and EM (Electric Cosine) but

this is arbitrary.

The Gravity component is derived from the Mass wave. Let’s break down the layers.

N(0) = Sin(x) = Gravity wave

N(1) = Sin (10x) = Mass waves

Note: The Gravity wave is the product of the N(1) mass wave.

The Electric wave

N(0) = Cos(x) = Electric wave

N(1) = Cos(10x) = Charge waves

From earlier treatment, we can dive further in the Electric component to Quarks and QCD

color but for now, we just focus on EM and Gravity at N(0) and N(1).

This design pattern explains why both EM and Gravity cause force. As the N(1) waves

change, either can alter the field or the particle, causing movement. Later, I’ll explain the

respective strengths of the forces.

It also explains why both can use the same type for formula for Coulomb’s Charge and

Newtonian Force. We just replace Mass with Charge and have a different Force Constant.

So, let’s draw this.

Note how both EM and Gravity are almost identical, thus similar force formulas Fg and Fc.

Gravity is the product of Mass and Electric force is the product of Charge. In the case of EM

+ Gravity both are carried by the same particle. In the case of a non-charged particle, just the

Gravity (Mass wave) is carried.

Note: I have not covered Magnetic Field as this is the Non Local field interaction piece. In

earlier work, I also showed that Turbulence is similar to the Magnetic Field in that it is also a

Non Local field interaction piece.

We can map the Non Local field interaction piece in Pi-Space in the following way.

Field interaction is the Boson idea in the Standard Model.

Field interaction is also the Brane idea in String Theory.

Bringing both diagrams together

1.23 Modeling Strong and Weak Force in Pi-Space

Some forces are strong and others are weak. Forces emanate from different N(x) layers and

therefore exhibit different properties on the local plane.

In terms of a particle, Force deals with the area change of said Particle relative to an observer

particle. See earlier work on Pi-Space. Also force change can also manifest itself as a

wavelength becoming shorter for example.

We have Gravity, EM, Weak Force and the Strong Force. So far I have covered Gravity, EM

and the Strong Force.

Electric Force and Gravity Force both emanate from the N(1) layer but with different parent

N(0) waves.

Electric Force is stronger because there are more charge “waves” on the N(1) layer.

The ratio of charge waves N(1) to electric waves N(0) is defined by the Fine Constant which

works out at 1/137. I will do a separate post on this.

Therefore one can conclude that the ratio is smaller for N(1) mass Waves to N(1) Gravity

waves.

There is also the ratio of the difference in the Coulombs Electric Constant and the

Gravitational Constant G. This is a comparison of two N(1) waves (mass and charge) sharing

two different parent N(0) waves (Gravity wave, Electric wave)

N(1) waves affect the N(0) wave directly and their span.

In the case of the Strong Force, we are dealing with Force waves which reside in the Color

N(4) layer. These waves exist inside the N(3) Quark waves and have a much shorter

wavelength than the N(1) waves. Therefore their force is much stronger. However, because

they exist inside the Quarks N(3) their range is limited by the size of these parent waves. So

although they have stronger force, their range is limited.

The closer a Non Local wave is to the Local Wave N(0), the more widespread the force is in

the local space.

The more waves that are carried the greater the force.

The lower the wave is in terms of layers relative to the Local wave, the greater the force is

due to the smaller Ultra relativistic wavelength but the force range is more limited.

1.24 Modeling A Neutron In Pi-Space

A Neutron has no charge

We can define a simple notation called N(x)




Therefore N(2) is not present.

1.25 Modeling the Neutrino in Pi-Space

Let’s extend the Local N(0) notation to point to either the parent Electric or Gravity wave

which are out of phase.

So

Ne(0) = Local Electric Wave

Ng(0) = Local Gravity Wave

The fact that the Standard Model states that a Neutrino has no mass but it's found that it has

some which oscillates, indicates (according to Pi-Space Theory) that the Neutrino wave(s)

is/are actually on the Ng(2) layer. Note Ng(1) is the Mass wave. So the oscillations at the

Ng(2) layer cause the Mass to "appear" when they are in phase.

Therefore


Ng(1) = Mass wave

Ng(2) = Oscillating Neutrino wave

Also

Ne(2) is where the Quarks live. There are 3 of them and there are 3 Neutrino flavors.

Although Ne(2) and Ng(2) are out of phase they do cross one another’s path.

Drawing the Neutrino therefore, we get

We notionally model a small amount of mass as 11x versus 10x. Therefore, a Neutrino has

very little mass on the Ng(0) wave

Plot[Cos[𝑥]+Cos[10𝑥]+Cos[11𝑥],{𝑥,0,20}]

Note that this mass also lives alongside the Neutral charge which is modeled as a Sine wave

Let’s see how we can demonstrate how we can get oscillations when we combine the Ng(x)

and the Ne(x) wave.

Plot[{Cos[𝑥]+Cos[10𝑥]+Cos[11𝑥],Sin[𝑥]+Sin[10𝑥]},{𝑥,0,20}]

1.26 Modeling the W+,W- and Z Bozons in Pi-Space

Bozons mediate force. In the case of the Weak force, we have W+,W- and Z Bozons.

These have mass which is carried on Ng(x). Let’s focus on the Ne(x) versions of them.

W+

For Positive Charge (we use Ne(2) Sine wave). Note the three terms in the formula below

indicating Ne(0), Ne(1) and Ne(2).

W-

For Negative Charge (we use Ne(2) Cosine wave)

Z

Neutral charge which is modeled as a Sine wave

1.27 Modeling the Photon

The Photon is a gauge Bozon. This is pretty straightforward to model. We define just the

Ne(x) Electric wave for now. The Nm(x) Magnetic wave is the same just orthogonal. It’s

Ne(0).

1.28 Modeling an Electron and Positron In Pi-Space

An Electron -1 charge

Ne(0) = Sine = Electric Sine wave (photon)

Ne(1) = Sine = Charge

Ne(2) = Cosine = -1 Charge

For Positron Charge +1 (we use Ne(1) Cosine wave). Note the three terms in the formula

below indicating Ne(0), Ne(1) and Ne(2).


Ne(1) = Cosine = Anti Charge (Positron)

Ne(2) = Sine = +1 Charge

A Positron is an antiparticle. If it comes in contact with an electron they will annihilate.

Therefore Ne(0) stays the same. So the charge is an “anticharge”. By this I mean Ne(1) is a

Cosine as opposed to a Sine. Inside this is a positive charge type wave which is a Sine wave.

So if these two collide they will cancel and produce gamma ray photons.

1.29 Mass Gap In Pi-Space

The question is "How can a wave moving at the speed of light have rest mass?"

The answer in Pi-Space Theory is that Ng(0) is the Gravity wave which is local, traveling

max speed of light.

Inside this is Ng(1) where we have the "Rest Mass" waves. These are carried by Ng(0).

I've already described this in previous posts.

Mass is carried according to the Pi-Space Theory. It's the "Pack Mule" design pattern.

1.30 QCD Anti-Blue in Pi-Space

For Positron Charge +1 (we use Ne(1) Cosine wave). Note the three terms in the formula

below indicating Ne(0), Ne(1) and Ne(2).



Ne(2) = Sine = +1 Charge

We can extend this to become a QCD Anti-Blue. The Charge Type wave is made up of three

Quarks and the Quarks contain QCD Blue.

Previously we defined

Blue Quark -1/3 (No wave carried)

Plot[Sin[𝑥]+Sin[10𝑥]+0.3333Cos[20𝑥],{𝑥,0,20}]

So from this we can derive



Ne(2) = 0.3333 Sin = Anti Quark

Ne(4) = Empty (which means QCD Blue in our case – this is arbitrary)

Note: QCD anti-blue is the simplest example because Ne(4) is empty. For red and green we

have waves for Ne(4). This means that the odds of a particle canceling with an anti-particle

are higher if Ne(4) is not occupied. Therefore, QCD waves do not automatically cancel with

anti-particles because both wave patterns are equal and opposite which is more difficult to

achieve when Ne(4) is occupied for example. In the case of a Positron and an Electron the

odds of annihilation are higher because the depth of the waves are less.

1.31 Modeling the Higgs Boson in Pi-Space

Let’s extend the Local N(0) notation to point to either the parent Electric or Gravity wave

which are out of phase.

So

Ne(0) = Local Electric Wave


Ng(1) is the Mass wave.


Ng(1) = Mass wave


Therefore the Higgs Boson is the Ng(1) wave which is either absorbed or emitted. “Free

Space” contains these oscillating waves.

A Light Wave is part of Ne(0) and does not contain any Ng(x) waves, therefore it can travel

at the Speed of Light C.

Also, if a particle contains Ng(1) waves (aka Mass) they move slower. This is how to explain

the Higgs Boson in Pi-Space.

Zero Charge/Mass (0 mass/charge waves)

Note: We use Sine as the Ng(x) carrier wave (this is arbitrary)

1. Increasing Mass/Charge (10 mass/charge waves)

2. Greater Mass/Charge (50 mass/charge waves)

1.32 Beta Decay Feynman Diagram in Pi-Space

We can covert the Feynman diagram for Beta Decay into a Pi-Space wave diagram.

[1] Neutron

Ne(0) = Local Wave (Electrical)

Ne(1) = Non Local Wave (Charge Quantity)

Ne(2) = Non Non Local Wave (Charge Type, Positive, Negative)

2/3 -1/3 -1/3 waves cancel out (udd) at N(2)

Therefore N(2) is not present.

[2] Proton

So if we draw a Proton which is charge, charge type and 3 quarks (udu), this is what it looks

like as a simple formula with a visual representation.

Ne(0) = Local Wave (Electrical)

Ne(1) = Non Local Wave (Charge Quantity)

Ne(2) = Non Non Local Wave (Charge Type, Positive, Negative)

Ne(2) is present

[3] W Minus Bozon

A Bozon is emitted which is a W minus to take into account balance the wave change.

W-

For Negative Charge (we use Ne(2) Cosine wave)

[4] Electron Anti Neutrino

Note: So far we have just deal with the Electric Charge wave piece. There is also a mass

discrepancy, so we need an Electron Neutrino to ensure that Mass is conserved as well. We

also model mass as a wave. This is where the Electron Anti Neutrino comes in.


Ng(1) = Mass wave


We notionally model a small amount of mass as 11x versus 10x. Therefore, a Neutrino has

very little mass on the Ng(0) wave

Plot[Cos[𝑥]+Cos[10𝑥]+Cos[11𝑥],{𝑥,0,20}]

Note: I never did an electron anti-neutrino but an anti-neutrino has Ng(2) wave which is a

Sine as opposed to Cosine. Therefore, the mass is conserved.

[4] Electron

The final piece of Beta Decay is the emission of the Electron. This is created by the W-

Boson.

An Electron -1 charge


Ne(1) = Sine = Charge

Ne(2) = Cosine = -1 Charge

Conclusion

We can see that the Feynman diagrams are an excellent way to drill down into a Pi-Space

wave diagram. What the Pi-Space diagrams offer is a way to understand that underlying

wave algebra and symmetries at the deepest level of our reality.

Exercise

Take any other Feynman diagram[s] and reverse engineer them in the same way using the Pi-

Space notation.

1.33 Simple Proof Faster Than Speed of Light In Pi-Space

This is just a simple proof for Non Local waves which can operate faster than the Speed of

Light

Consider the Universe expanding based on Ng(2) waves

This is where the "Dark Matter" is and where the Higgs Field is

The Ng(2) field is Non Local and completes faster than the Local Wave which has max speed

C

The Ng(2) mass waves are responsible for the expansion of the Universe

It has been observed that the Universe is expanding faster than the Speed of Light

Therefore Non Local waves can travel faster than Speed of Light.

Note: In Pi-Space, "space" is composed of Ng(2) waves not some "other thing" capable of >

C. It's _all_ waves in case one tries to play with the meaning of "space".

1.34 Modeling Matter and Anti Matter Using The Pi-Space Notation

We model mass on Ng(1) as a Sine wave

1. Mass (10 mass waves)

Anti-Matter is Ng(1) and is a Cosine wave. If both collide they cancel each other out.

Energy is released as Bosons.

1.35 Modeling an Anti Neutrino Using The Pi-Space Notation

Anti-Matter is Ng(1) and is a modeled as a Cosine wave (similar to anti-matter).

The Anti-Neutrino is inside this Ng(2). We model a small amount of neutrino mass.

Plot[Sin[𝑥]+Cos[10𝑥]+Cos[11𝑥],{𝑥,0,20}]

Versus a “normal neutrino”. If both collide they cancel.

Plot[Sin[𝑥]+Sin[10𝑥]+Sin[11𝑥],{𝑥,0,20}]

1.36 Modeling all the forces EM, Strong Force, Weak Force, G plus the Strong Dark Matter Force in Pi-Space

In Pi-Space, the four well known forces are EM, Strong Force, Weak Force and Gravity.

However, Pi-Space also models the Strong Dark Matter force which is where dark matter lies

and is responsible for the >C expansion of the Universe.

The building block of this design pattern is Ne(x) for the electric wave and Ng(x) for the

Gravity waves.

Ne(0) and Ng(0) are out of phase with one another. Therefore they can both be modeled

using the Newtonian Fg and Coulomb Fc force notation except with different constants.

EM, Strong Force and Weak Force are modeled in Ne(x)

Ne(0) is the Electric Wave. The Magnetic wave is paired with this orthogonally.

Ne(1) is the charge quantity wave.

Ne(2) is the charge type wave made of Quarks.

Ne(3) is where the QCD wave is and this is where the Strong Force is. The waves are smaller

but stronger.

Beta Decay which demonstrates the weak force is how the wave types change and “decay”.

The exchange Bozons are also waves but are emitted or absorbed by Ne(x).

These are the major forces on the Electric wave side.

On the Mass side modeled as Ng(x), we start with the Gravity wave.

Ng(0) is where the Gravity waves are and it is modeled by the inner mass waves.

Ng(1) are the mass waves themselves

Ng(2) are the inner mass waves which form Neutrinos.

Ne(3) and beyond is where the dark matter is. Similar to Ne(3) these dark matter waves have

very strong force but it is localized to a small area.

Therefore, we think of dark matter in Pi-Space as small localized mass waves which are non

local. They complete before Ng(0) and therefore appear to complete faster than the speed of

light. This is why our Universe appears to be expanding faster than the speed of light. The

Ng(3) dark matter waves are expanding our “points of” space with great strength and speed

but are localized to a single point similar to Ne(3).

There are many more Ng(3) waves than Ng(0)/Ng(1) waves thus accounting for all the

“hidden mass” in our Universe.

Ng(3) and beyond is termed the “Strong Dark Matter Force” in Pi-Space, similar to the

Strong Force on the Electric Wave.

1 advanced quantum theory in pi-space · pdf file1 advanced quantum theory in pi-space in this...

Documents