Next Steps General Relativity

I'll cover the Stress-Energy Tensor next in General Relativity

Also, I will improve the suite of Pi-Shell drawing tools to make them interactive.  I think I may add one which will draw a diameter line.  Also, I may do one which looks like the Pythagorean Theorem.

The plan is to base them on HTML 5 which as a computer science person, I really think the syntax and user friendliness rocks!

Tool for Drawing Pi-Shells size change when they experience velocity

Here is a tool which draws Pi-Shells which are under the influence of velocity.  It uses HTML 5 which is built into the latest modern browsers.  Tested on Opera/Firefox/Chrome.

It shows the Observer 1.0 Area loss due to velocity
The size of the new Pi-Shell with the area loss.
It uses the Lorentz-Fitzgerald Transformation

http://www.pispacephysicstheory.com/html/PiShellDrawings.html
 
Example image


Note:

I will add the HTML to an Appendix document later.  Alternatively, just open the doc and view the source.

Einstein Field Equation Navier piece next

I'd like to do a post on the EFE components which match the Navier stokes piece (Pressure and Energy momentum) in the meanwhile. I'll extend it to cover temperature and viscosity etc;

HTML piece next

I'll work on the html piece next. This will take a some time. Hopefully not too much.

The GR Metric In Pi-Space Video Description

The Next Video and some HTML

I plan to do a video on the General Relativity Metric Tensor next

Additionally, I will look into a HTML 5 page which is interactive and will draw some Pi-Shells and allow the user to put in particular v/c velocities. HTML 5 is supported by most modern browsers now and has a Canvas feature where one can draw 2D Graphic primitives, similar to ones which look like the the Pi-Shells in my documentation. These should be more accurate than the diagrams in my doc. I just guessed the sizes of 0.6 and 0.8 for example.

Once I do this, I plan to do a high level overview of how to integrate the Stress-Tensor into Pi-Space. Part of cleanup for this is to get the "divide by C" piece consistent.

Maybe after this, I'll cover supporting the EM (Maxwell) Stress Tensor as well...

Proper Time in Pi-Space

Thoughts on upcoming videos

I'd like to possibly do videos on

GR Proper Time
GR Metric

next.

I am also mulling over the idea of an interactive web page which will draw Pi-Shells of varying sizes based on inputs like velocity etc;

Updates to the Advanced Formulas

I've added some gravity and force related topics into the Advanced Formulas section.

These are

Laplace
Gauss
Poisson
Gradient
Divergence

GR Proper Time
GR The Metric

This chapter is what I call the "go-to" chapter containing all the high level concepts with lots of worked examples.

I will fine tune the additions over time.

I'd like to add a couple more diagrams but this is for later.

Right now I am pretty tired and may switch back to my Podcast for a while.

I feel this is reasonable progress for the time being.

GR is very complicated and it take a lot of time to summarize the ideas effectively in Pi-Space.

Latest Updated to Fields and GR and what's next

PDF and HTML updated.

Next: Adding the Stress Tensor Components to GR Fields In Pi-Space.  This is tricky to solve in GR but in Pi-Space adding Stress-Enegy Tensor components is not too bad.  This will be based on my Navier-Stokes work where there is a velocity and energy form.

But first....

I will update the Advanced Formulas first with my latest findings.

Mainly Proper Time and Gravity pieces.

The Metric In Pi-Space

Metric write up coming soon

I've taken my time with the Metric piece as it covers quite a few ideas.

All things going well, I will do the write up in the next day or so.

Also, I will update the PDFs.

Importantly, I want to add some of this information to the Advanced Doc.

I will add Proper Time which is pretty important and the Metric.

I will also add Gauss and the Gradient.

Further Thoughts On The Metric

I'll try to have a reasonable description of the Metric early next week in terms of how to understand it in Pi-Space.  I'll cover the Schwarzchild Metric and give a quick intro into some of the more Advanced ones.

Where GR does diverge from Pi-Space is in the way that the path of least time in the field is computed.  I will provide a general algorithm based on my current work.  This is the more tricky part of this section but one I will personally enjoy.

Initial thoughts on the Metric Signature in GR

In GR we have two signatures in GR -+++ and +----.  Mostly from what I see GR uses -+++.  Pi-Space has a preference which is +----.  This is a product of the Geometry of Pi-Space.  I will explain why this is in the Metric piece I will write.  You can do it the other way around and it's no great shakes.  However I like consistency.  So I will clear up why from a Geometric perspective one should use one type for the Geometric understanding of a Pi-Shell.

Time updates

PDFs are updated

I've fixed up the Blog Post on Time and the Four Vector.

Next: The metric.

Once I do that I'll update the Advanced Formulas.

Reworking Time Plus The Four Vector

The plan is to show some worked calculations of Proper Time showing Einstein's GR way, SR way and then the new Pi-Space way in the reworked version of this piece.  Proper Time and the Metric are closely aligned so one should follow from the other.  I will also show an example of the Schwarzchild Proper Time also.  Moving forward, I'll attempt to show how the Metrics and Proper Time can be plugged into Pi-Space in conjunction with the Stress-Energy pieces (for later).  This is tricky and I will attempt to do it without too many redrafts but sometimes you gotta get it wrong to get it right...

Errata: Time Cleanup

I need to clean up the Proper Time Math.  It's not great.  It'll take a day or so.  Need to do this before I proceed.

Initial Thoughts On The Metric

I want to explain how the GR Metric is mapped to Pi-Space.  From what I see it's reasonably straight forward.  There are a few of them but I'll cover the Flat Space Time metric first.  Later I may look into the Schwarzchild and Kerr etc;  First though, the Metric.

The Four Vector And Time In Pi-Space