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.

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