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.

 

 

Addition of Arrows explained in Pi-Space next

I've figured out a reasonably clear way to explain this and the math with some simple diagrams.  All things going well I will write it up over the weekend.

I will delve a little deeper into the detail of the probability and the angle of the arrows and how they are added and why it works according to Pi-Space.

Further Refinements

I'll look into the Feynman arrow addition mechanism and explain how that works in Pi-Space.  From an initial inspection, it looks like my pi-shell addition using law of the cosines.  However, in this case, we're dealing with "probability pi-shells".  Need some time to check out this further.  No fixed date for when but hopefully not too long...  Check out my work on Orbits for how I handled law of cosines and pi-shell addition previously in "local" space.

PDFs Updated

Additions

Mapping-
Probability Amplitudes
Feynman Arrow Notation

Errata On Probabilties In Pi-Space

In the last few posts, I have stated that the highest probability is the smallest Field Point.  I will change this to "large combined arrow is the high probability that it has the smallest Field Point".  The sizes change dynamically with time t.  This is a small but important change.  Probabilities are STILL there.

This fix will be in the PDF.

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Arrows and Field Points....

Small break and some next steps

I've made a simple foray into probabilities so I will return to my other project for a little while.  When I return to the physics I will update the PDF and show some more Feynman examples, mostly at a high level.

QED in Pi-Space

Errata: Not a reflective surface but water, diagram is above not below.
Errata: __Proability__ that the Field Points are the smallest.

Next steps

I want to look at the work of Feynman next in terms of his arrow diagrams and his stop watch concept.  This will lead on explaining the Feynman path integral idea.  I will explain why the path integrals work from a Pi-Space perspective.

Calculating Probabilities In Pi-Space

Note: We map the wave amplitude to the diameter change of the Field Point.

Adding a Detector to Wave And Particle Experiment in Pi-Space

Once a detector is added to an experiment positioned over the slits, one finds that the particle only goes through this slit.  Why is this?  The answer in Pi-Space is that the Field Point space time particles are the smallest at this point.  The reason why they are the smallest at this place is because the detector needs to “observer” the area.  To do this, it needs to fire particles over this location.  The act of firing the particles over this location causes the field points to be the smallest at this point.  Therefore the non-observing particle chose to go through the slot which is being observed.

Next piece on Wave and Particle

Next, we have the case where we add a detector and the experiment behaves differently.  I will explain this shortly, in the next few days.  It is reasonably straight forward.

After that I'll explain the Schrodinger math of addition and squaring and the reason why it works.

Wave And Particle in Pi-Space