Advance Notification: I am moving the location of the Blog

I will move to blog.pispacephysicstheory.com

This blog has served me well but I'll move over to a fresh one which is wordpress based shortly.

I won't move the current contents.  They will stay where they are for as long as the hosting is here.

I want to try posts which are not just cut'n'paste images and I want to have proper categories for the posts and stuff like that.

Next Topics

Dirac Delta Function
QM States

Once I do these, I'll update the PDF

Dirac QM Ket Vector In Pi-Space

I'll do a write up at the weekend

I'll cover the last topic mentioned.

After that, I'll cover the Dirac Delta Function.

Next QM Topic

Ket Vectors

Dirac QM Notation In Pi-Space

Note: The Diameter is the “Probability Amplitude” and the Area is the “Probability”.  We get to the Probability by Squaring the Amplitudes aka Diameters.

Little Delay QM this week

Little delay this week.  Hoping to have the QM post early this week.

Dirac QM this weekend

I will do my first post on Dirac QM this weekend and set the scene for the geometric meaning of the existing notation developed by PAM Dirac.

I will build from there.  From what I see it's reasonably straightforward.

Simulating Gravity In Pi-Space On a Computer

The model for Gravity in Pi-Space is pretty straight-forward.  We have a Local Layer and we have a Non-Local layer.  The Non-Local layer contains field points which are smaller than the Planck length.  Therefore we need a software solution which models 3D space having Non Local Pi-Shells which are smaller than Local ones.  In a simulation, they do not need to be smaller than the Planck length but they do need to be smaller than the local Pi-Shells and they need to create a 3d Fabric.  The Local Pi-Shells then move towards the place where the Non Local Pi-Shells are the smallest.  They also change the size of the Local Pi-Shells.  Smaller Pi-Shells are designed to move faster.  They need to also store a vector component.   

For example, if we model any object in the simulation, we need to assign Pi-Shells to it.  For computational efficiency on a weak computer, we make the Local Pi-Shells reasonably large.  For a powerful computer we can make them smaller.  Therefore the object contains these Local Pi-Shells and they influence the direction it moves in and how it reacts to gravity.  In reality, the Atoms do this job and everything is mostly contained by them; so they are one and the same thing.  On a computer system where we have limited processing power, we need to be judicious what size local Pi-Shell we pick.  Therefore we may have an object containing a limited number of them but spanning and containing the object.

In terms of specifics, copying Earth gravity for example, all one needs to do is ensure that the Non Local Field Points  get smaller (lose area) in the direction of COG by 9.8/C^2 for every Meter we move in the direction of the centre of Gravity.

If we take an example of a cube of Field Point space we can make the Field points smaller as we move to the base of the object.  Therefore it we place an object inside this Field Point space, it will move down to the base of the object, accelerating as it moves down.

It does this by becoming slightly smaller.  The constant area change translates into an increased velocity and should match what happens in reality. 

We can also give the Local Pi-Shells their own clock tick which is proportional to the diameter size and then we have the equivalent of Proper Time.

Over The Weekend

Over the weekend I will write up a simple post on how to model Gravity as described in Pi-Space on a computer system.  This will be different than the Orbits piece as I will describe placing Objects inside Pi-Space so-to-speak.

///Note: I am working on cleanup on another project so this is just a small filler before I tackle QM Proper///

The idea is that using Pi-Space we can create some kind of a Physics engine it should be "relatively easy" to model some of the more complex things in our reality such as throwing things up in the air and making objects stick to a surface, or even having an apple drop from a tree onto an avatar's head... :-)

I will also cover the EM piece as well showing how that can be jointly modeled.

Once I reverse engineer physics, the next big topic as I see it is Computer Simulations.

3d Modeling Idea and other thoughts

In parallel, I'll try to see if I can find a tool to model some of these Pi-Shell ideas in a Virtual 3D environment which can be moved around.  I'll look at some of the tools out there.  This is more of a longer term idea.

NOTE: I'm happy with Mathematica for the formula examples where it makes sense.  So nothing will change there.  I'd like to take better advantage of the in-built browser support for formulas so I don't have to cut'n'paste images.

After clean-up Dirac

I will start explaining Dirac's notation shortly now that the clean-up is done.

To do this I want to produce a simple drawing of a Probability Pi-Shell and explain geometrically how this relates to <a*|b|a> which is one of the most well used notations.

There's also the Schrodinger and Heisenberg versions but first Dirac.

Cleanup / Improvement of the Documents

I've figured out how to insert a Table of Content in each sub document as part of a Master Document.

Moving forward, I will update each document to have its own Table of Contents.

To be honest it's something that always bugged me about the docs so for me doing this is a high priority.

The first one to have a TOC is the Advanced Quantum doc.  (Nerdy) Yah!!!

CURRENT DONE LIST

Advanced Quantum Theory
Introduction to the Theory
Quantum Theory
Temperature and Super Conductivity
Advanced Formulas
Orbits
Gravity
More on Gravity
Newton's Laws

***DONE***

Other pieces are the 'Skunk works' ***DONE***

Fix up Formulas to include all Formulas in index. ***DONE***

Thoughts on Modelling an Oscillating Probability Pi-Shell In Pi-Space

In QM we'll use the -kx formulation for an oscillating probability wave function.  In Pi-Space, we'll have an oscillating Probability Pi-Shell and we'll use the Pi-Space formula for this which was derived in the Advanced Quantum Doc.

versus

Updates to PDF and HTML

Added "Field Points and Probability Pi-Shells" to the "Fields and General Relativity" Doc.

I am still researching QM.  Will be a small while before I do a post.

Videos and Wave within Wave

I've a couple more videos to go through.

Also, I've been thinking about the math of the wave within wave and it's mostly the addition of wave functions.

So, I am visualizing a model something like

LocalWaveModel + NonLocalWaveModel = Wave within Wave (see Advanced Quantum)

This is an extension of the Dirac/Schrodinger approach where we can model Mass as an Inner Wave (Non Local Wave Function) in addition to the particle on the line so to speak. (Local Wave Function which is a Hamiltonian/Other acting on a Schrodinger Wave Function).

Mixtures of Cos/Sine give the exponent formulation.

I'll formalize this later but this will be the Pi-Space approach.

This should be very compatible with what is already there.

Changed my mind on the Cleanup

I will rename the chapter instead of reworking it, having read through it.

It will be "Quantum Theory Intro, Hydrodynamics and Navier Stokes."

***Done***

Clean up of Fluid Dynamics / Navier Stokes

At present, the Fluid Dynamics piece including Navier Stokes is inside the Quantum Theory doc which is not correct.  Before I add anything new to the Theory I want to clean this up and create a standalone doc for Fluid Dynamics / Navier Stokes.

I'll call it "Fluid Dynamics including Navier Stokes".

Next Piece - Scale and Field Point Changes

I'd like to try and explain why sub-atomic particles are influenced more by small fluctations in the Field Points compared with the Classic Pi-Shells next.

Once I do this, I will start the work on Dirac/QM.

I may watch a couple more videos on his work but so far it looks ok.

Field Points versus Probability Pi-Shells in Pi-Space

So far in GR, we have Field Points and in QM we have Probability Pi-Shells.

These are two representations of the same things.

The Probability Pi-Shell, like the Field points form the fabric of Space Time.  Therefore they are both smaller than the Planck Length.

In GR we model them getting smaller as one moves toward the center of gravity.

In GR in terms of measurement, we represent the Field Points altering the size of the Classic Pi-Shell which is typically modeled as an atom.

The Metric is the area size to the atom in terms of an area change relative to an observer.

Proper Time is the diameter change relative to an observer.

So GR mainly focuses on how relatively large “local” Pi-Shells move through the Field Points which form Space Time.

Next we deal with Probability Pi-Shells which deals with how the Field Points themselves change size.  This is different from GR where we measure the changes to the Classic Pi-Shells moving through Field Point Space Time.

Here we need to work out the changes to the sizes of the Field Points themselves.

As I’ve shown already, we cannot measure them using current technology so we use a predictive mechanism using probabilities.  As I’ve already shown, the higher the probability, the smaller the Field Point can become.

Just like in GR, any quantum particle moving through this Field Point Space Time, will follow the path of Least time which means it moves towards the Field Points which are the smallest.

The field points also oscillate which means that they change size due to their interaction with wave functions which are modeled in QM.

Note that in GR, one does not need to model the size change of the field points, all one must do is model the change to the area of the moving Pi-Shell or the change to its area as it moves within this field.  This therefore maps to the Potential.  This is outlined in the Classic Gravity sections.  Also, like QM, the Geodesic is the Path of Least Time for a Classic Pi-Shell so the two approaches are the same.

Cleanup and posts

I am looking into an improved tool for publishing my website so posts here will be a little slower while I try to learn joomla.  I am pretty happy with this blog for my posts so I plan to keep this where it is for now.  I am hoping to do a physics post this weekend all things going well.

Thoughts on Field Points and Probability Pi-Shells Next

In the current GR and QM doc, I describe "Field Points" and "Probability Pi-Shells". 

I've given this some thought, so I will make this my next post on Pi-Space which is to describe the difference between/similarities with both approaches.  Both terms deal with the same Pi-Shells in different ways.

The GR Field Points deal with their effect on a classical moving Pi-Shell or a Pi-Shell trapped inside a Gravity field (Proper Time and the Metric for example)

The Probability Pi-Shell deals with the statationary Field Points themselves and how they get larger/smaller and detail how they affect the motion of Quantum Particles.  I'll describe how the Probabilities are our mechanism to measure their changing sizes.

I'll flesh it out a little in the post.

Some Cleanup of the Pi-Space Site

I've fixed up some broken links

Also, I've improved the Formulas HTML file to include references to the most recent work, namely temperature and superconductivity plus fields and qm.

Improving The Advanced Formulas Section

I plan to add the "Evolution of Ideas" piece to the Advanced Formulas piece at the end of it, to show how the concepts are formed in Pi-Space.  The idea is to provide a verbal description of Pi-Space, complimenting the Math.

Thoughts On Infinities

In the next part of the theory, there is an issue to do with Renormalization and Infinities which has plagued QM and Pi-Space needs to offer some kind of a solution.

I did some work on a similar issue to do with the Einstein work earlier in the Advanced Formulas Section.  Bascially, using the Einstein approach, mass/inertia becomes infinite near C.

In the Pi-Space Physics Theory, we model the Pi-Shell getting smaller and don't get an infinity.  I explain the logic in the doc.

Please check out the Advanced Formula Section for Relativistic Kinetic Energy if you are unsure.  I will use a similar approach for renormalization, so it should be reasonably straight forward to address this issue (hopefully).

Right now I am just gathering together a list of QM topics and this is one.

Cleanup of the Advanced Quantum Document

I want to do a small amount of clean up of the Advanced Quantum Doc before I proceed.  When I wrote this, I had not developed the Probability Pi-Shell.  I want to add some references to it.

*** Ok it's done.  I've referenced the Fields And General Relativity With QED and Dirac".  The Probability piece that was there was a little bit woolly.  More concrete now. ***

Thoughts On Drawing/Visualizing A Quantum Mechanical System

One of the biggest problems with QM is an inability to visualize what is going on.  So far QED Arrow diagrams offer one approach.  However, what I will attempt to do is to use the Pi-Space Physics Theory to draw what QM is solving.  For example, the Complex Conjugate is key to QM.  In Pi-Space, I'll be able to draw the Probability Pi-Shell diagram for this, and so on.

The hope is that it makes QM more intuitive, if nothing else.

So far from my research, the QM piece fits reasonably well but I still have to complete it before I do any posts.

It's painstaking but reasonably straightforward.

Thoughts On Quantum Mechanics

I'm trawling through some lectures on Quantum Mechanics and building up a list of topics to reverse engineers into Pi-Space.  The basic approach is to show how Probability Pi-Shells are the same as the Field Points for General Relativity.  First, I need to reverse engineer QM into Probability Pi-Shells.  QM is a large topic from what I see and this will take some time but so far the mappings look reasonably straightforward.

Once I do this, I may also reverse engineer Kaluza Klein.  This will all form this chapter.

The Cosmological Constant in Pi-Space

Cosmological Constant while I am researching Quantum Mechanics

I'll do a write up on the Cosmological Constant while I am researching Quantum Mechanics.  This is part of the EFE (Einstein Field Equation). The approach I will take is to describe "Super Massive Local Waves".

Reverse engineering the probability QM vector

Update is that I will reverse engineer the probability amplitude vector into the Probability Pi-Shell.  The mapping is reasonably straightforward and will build on the QED piece.  Complex conjugation looks like The Square Rule on initial inspection.  More later.

Researching Quantum Mechanics Next

I'll be finding good research material for Quantum Mechanics next.  I'll be a while before I post on this topic as I have to understand it in the same way I needed to do for General Relativity.  The idea is to unify both approaches under the same approach of Field Points representing Probability and General Relativity Space Time.  I had the advantage with QED of having followed it a little before this.

Updates to the Advanced Formulas PDF/Doc

Added section on QED/Probability Pi-Shell

More on the Probability Pi-Shell

Retrofitting the Probabilities Into Advanced Formulas and Dirac

I'll improve the last section to show how to do probability addition and show how it's based on Pi-Shell addition using the Pythagorean Theorem.  I'll rework an existing diagram so it's not hand drawn.

Once I do that I'll work some more on the work of Dirac.

Paul Adrien Maurice Dirac (8 August 1902 – 20 October 1984)

Note: There are a couple of typos in the last post which I will fix in the later pdf, I rushed it a little.

Probability Pi-Shell versus Classic Pi-Shell

Thoughts on Dirac Notation

I'll look into reverse engineering Dirac's notation next.  Of all the pieces I've studied so far, this piece confounds me the most but it should be ok if I take my time with it.  Now that I've reverse engineered Feynman and GR, I am hoping it should not be too bad.  I'd like this all to be part of Space Time because it should all be unified.  This is my attempt at tying it all together.  I still have not forgotten about the cosmological constant.  I may drop this in before the Dirac Piece.

Next The Probability Pi-Shell

I want to define the Probability Pi-Shell next.  So far, I have drawn one but I would like to formally define it and explain how it works compared to the traditional "Local Wave" Pi-Shell.

Next Steps

That is as much as I want to cover with QED in terms of arrows etc;

After this I want to look into the Math for reflection and refraction.  The hand made diagrams offer the Pi-Space Theory approach.

For now, I will take a short break from this.

Latest updates to PDFs for QED

Mostly hand drawn stuff for Feynman QED work

Refraction
Arrow Addition
Lenses
Probability of Reflection within Glass

Refraction In Pi-Space

Lenses in Pi-Space

Thoughts on hand crafted notes

For now, the weather is sunny and I like to figure this stuff out in the garden.  Also the diagrams are complex and it's easier to draw in first draft.

Next topic is refraction, I think.

Note: This is all part of how Pi-Space treats Space Time.  QED is part of it.

Surface Reflections Explained In Pi-Space

When the Field points are getting smaller, the light passes through.

When the Field points are getting larger, the light reflects.

Reflections from a surface next

Next I will explain how reflections from a surface work.

In the Feynman book a certain percent reflect and the others pass through.

I will explain why this happens in Pi-Space.

Feynman Arrow Addition in Pi-Space

Feynman arrow addition in Pi-Space.  Basically, the path of least time is the path the particle takes which has a probability of existing over time t.  Draw an arrow representing each path and add them together.  The probability is proportional to the smallest diameters squared to get the overall area change.  The greater the arrow length, the smaller the Pi-Shells on the path is over time t.  Adding the arrows is Pi-Shell addition.  We square the arrow lengths.

Note: In the diagram below, the path with probability of 0.8 should have smaller Pi-Shells on this path A versus path B with probability of 0.4.  So the probability is related to the diameter shrinkage.  We square it to get the area which is Pi-Space addition.  See Introduction to Pi-Space.

Therefore arrow length is proportional to relative diameter loss.  The smaller Field point Pi-Shells are the path most travelled over time t and which increases their probability.