Thoughts On The Four Vector

I've been trying to figure out the most important GR dependency to explain in Pi-Space.  I had thought I would do the Stress Energy Tensor but I need to explain the most basic part of this.  Therefore the next one is the Four Vector which is foundational in GR.  I will show how it's mapped to a Pi-Shell.

Errata - Correction to the Last Post

Hi,

I've correctected the last post

Mass Field And Particle Mass Interaction In Pi-Space

becomes

Gravity Field And Particle Mass Interaction In Pi-Space

Basically, I've defined the Gravity Field points which are greater than the Planck Length.  The Mass field does exist but it's one layer down too deep.

I am very sorry for any confusion but it's first draft and this can happen on occasion. 

PDF have been fixed as well.

Happy Easter.

 

Other components next

I'd like to explain how pressure, temperature, viscosity, shear etc; factor into altering the size of the Gravity Field points.

Once this is done, I'll explain Distance,  Time / Space Time.

Gravity Field And Particle Mass Interaction In Pi-Space

Initial Draft of Fields And General Relativity

I've added the PDF and HTML first draft.

The Next Idea - Interaction

I will explain how the field interacts the particle.  This is a foundational relationship.  Bascially, the Field interacts with the Particle and the Particle interacts with the Field.

Once I do this, I will create the "Fields and General Relativity" PDF.

Wave and Particle Duality In Pi-Space Field

 Note: The amendment to these diagrams which I will explain is the changing diameters of these Pi-Shells (both large and small) and how this ultimately map to the Einstein concept of Curvature.

What's next?

This is first draft so I will fix up a little as I go along...

An important principle is coming next.

Wave and Particle Duality.

I want to cover how each point in a field can contain (or be represented by) both a Wave and a Particle/Pi-Shell no matter what Layer we are on.

Defining A Field Notation In Pi-Space

Document Updates....

Errata: Wave FDe(y) should be Field FDe(y)

Thoughts On Pi-Space Field Definition

In order to provide a sensible view of Space and Time in Field format I will need to offer my own version of a Field.  The question that arises is how far is this from established ideas?  The basic idea is to re-use the Pi-Shell idea for the field definition layers.  Therefore an electric field is a FDe(0) field and vacuum energy in space is FDg(1).  In terms of size the FDg(1) is at the mass layer of Ng(1) and so these Pi-Shells are smaller than the Planck length.  Basically this idea is not a million miles away from the Quantum Field Theory idea of balls on strings..  The balls are Pi-Shells which have variable diameters which maps later to the  Einstein idea of curvature.  More detail on this coming soon.

Fields and General Relativity Approach

I think I have a reasonable handle on General Relativity now in terms of the Four Vector approach and the Minkowsky Pseudo Riemann space using curved tensors.  Now then...

The idea is not to reverse engineer every aspect of General Relativity right the way down to the Christoffel Symbols sub-calculations and the Einstein summation notation.  Dare I say it, that's "just detail" but I will explain what a Four Vector is and Proper time etc; but I won't be deriving the Schwarzchild Metric (my brain hurts just thinking about this in GR), however I will offer a Pi-Space equivalent to Proper Time and the Four Vector for example and all the rest like modeling a black hole etc;....

What I will reverse engineer are the important concepts and map them to Pi-Space ones.  However, this must be done gradually.  I have built up a biggish list but each are "bite sized chunks".

So I will start with the Four-Vector and how Einstein built from this a version of Curved Space which is the accepted version of how Gravity works and show how to get the same answer from a Pi-Shell moving in a field of acceleration etc;

I will then propose a wave based model which will theoretically offer the same "feature set" so-to-speak and will be based on a Wave based field format inhabited by Pi-Shells of varying sizes.

Additionally, why would one use Pi-Space at all?

Well from what I see, on initial inspection, one should be able to model from the "very big to the very small" using the Pi-Space approach.  Mostly, as I understand it, GR is good at the "big stuff"/cosmology and it works quite well but is more challenging on the small stuff.

Also Pi-Space will be pretty easy to use.  There will be no non linear partial differential equations nightmare...  I base this statement on the work I did on Navier Stokes where I had an energy and velocity formulation.

There will be an approach to least time as well in competition with the Geodesic approach.

All things going well, I will start on this at the weekend (unless I get confused about General Relativity again ;-) ).

Completed GR Videos And Next Steps

I've watched all 12 GR videos.  I have a better idea on GR now although doing actual calculations is still pretty vague but I have the concepts.  Therefore right now, I will look into Proper Time and the Four Vector.  These are one of the building blocks of GR so I'll proably start reverse engineering this first.

Jules Henri Poincaré  France 29 April 1854 – 17 July 1912

Formulated the Four Vector

Hermann Minkowski Poland (June 22, 1864 – January 12, 1909)  Space Time Diagrams based on Four Vector

Thoughts On A Geometric Interpretation of General Relativity

It's always good to add value to an existing idea, so I will try and add a Geometric Interpretation of GR.  There's a lot in it.  Mostly I am still trawling through it and one of the pieces which I think is worth helping understand is the Four Vector in GR.  In this case, Time is seen as an extra spacial dimension.  I will endeavor to explain this in Pi-Space.  Mostly, this is already there in another form in the Introduction to the Theory but I'd like to put on a GR "hat" so to speak and map some of the foundational ideas.

Also, I'd like to wish every one a happy St. Patrick's Day.

Note: I am still working my way through the Stanford Lectures which have been very helpful.

Thoughts on the new Field Notation

So far I have the Nx(y) notation. So Ne(0) is the Electric Waves.

I am thinking I will have a field notation called FDx(y)

Therefore

FDx(x) = Field x with Layer y

FDe(0) = Local Electric Field

FDg(0) = Local Gravity Field

How is a three dimensional field created?  Current thinking is two Exponent^i*Pi colliding at right angles.

Thoughts On Where Does The Field Come From

I've been trawling through GR and although it descibes what Gravity is in terms of Curvature, it doesn't answer the question as to where does the originating Gravity field come from Mathematically.  Basically, for Pi-Space I'll look into relating the Gravity field to a "wave/energy field" generated by some kind of Exponent formulation creating three dimensions.  I am still mulling over this at the moment and it's pretty tricky but I'd like to take this approach.

GR To Pi-Space Mapping Thoughts

Current thinking is that I will show how to map the Geodesic and the Curvature idea of GR to one where a particle moves towards the place where the smallest wavelength is in the "Pi-Space Field".  So the idea will be to map from Generalized Curvature to Fields of Waves of different wavelengths (wavelengths shorten as one moves closer to a planet's mass = space curving).  Basically, I'll try and show that they are essentially the same idea.

Thoughts On Breaking Down The Einstein Field Equations

Presently, I am breaking down the Einstein Field Equations.  Riemann geometry is very interesting but a notational minefield so my plan is to map it back to the underlying concept from which the Math began.  I will map the EFE components to their geometric components.  Also, I will cover the Energy and Diameter components in terms of mapping.

Thoughts On Cleanup

I may add Gauss' Law and the Derivative to the Advanced Formulas section shortly.  Later, this will be part of the start to the General Relativity treatment.

GR Dependencies

Ok so making some head way with this.  Like the Navier Stokes I need to figure out the dependencies as Einstein's GR is built upon the work of those who came before him.  For now, I will call them out.  I may need to study the work of these scientists shortly.

Georg Friedrich Bernhard Riemann (September 17, 1826 – July 20, 1866)

Manifolds / Geometry

Gregorio Ricci-Curbastro 12 January 1853 – 6 August 1925

Ricci Flow

Tullio Levi-Civita 29 March 1873 – 29 December 1941

Tensors

Elwin Bruno Christoffel (November 10, 1829 in Montjoie, now called Monschau – March 15, 1900 in Strasbourg)

Christoffel  Symbol

GR Update

I'm currently looking into covariant and contravariant vectors.  I've also watched a few GR Stanford Lectures.  It's slow going.  No real idea how long this will take but I am making progress...

Small Cleanup of Introduction

I've added some text on Temperature and Super Conductivity.

Plus, I've added some detail on the forthcoming section.

Initial Thoughts on General Relativity

I tried to crack this nut once before and the Math notation defeated me.  Therefore, I had to take two steps backwards in order to take one GR step forward.  Now I have the Wave within Wave model, Temperature and Super Conductivity and the work I did on the Quantum Level.

The basic approach is to study the topic at a high level and work down.

I have already done Gravity and Black Holes using the SR Einstein approach which is reasonably intuitive.

In this coming chapter, I intend to merge the Wave within Wave approach with the Classical formulas.

Also, I will formalize the "field" and attempt to map this to the Einstein GR Fields.

I also have a very "raw" theory for the origin of the Cosmological Constant.  Note: It's a "new" idea N(-1) which is an extension of the current Wave model.  Basically, the "Super Local" waves.  These are the waves which carry the "Local" N(0) waves and ties into the Dark Energy idea.  Right now, this idea is very raw but it's the direction I am pointing in at present.