Part I - Re-examining Coordinate Systems

This forum is dedicated to the student just starting out with the concepts of the Reciprocal System, or RS2. Questions and clarifications for the RS/RS2 concepts go here; please place new ideas and commentary in the appropriate RS2 fora.
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Part I - Re-examining Coordinate Systems

Whenever we talk of the expanding space, we do not have difficulty mentally imagining it. We naturally envisage a continuous increase of Cartesian distance in 3-space (that is, volume), starting from the zero or the 'origin.' Furthermore, we do not have difficulty imagining an un-ending, infinite, expansion.

Now Larson's crucial discovery that space, time, and motion are quantized demands a re-examination of our common sense (Cartesian) view of the expansion of space. Since there would be a MINIMUM quantity of space, Snat, we are not justified in envisioning the expansion of space as commencing from the Cartesian origin/zero---it rather commences from Snat. In other words, the effective origin (of the expansion) is a spherical SURFACE of radius Snat---not the Cartesian zero POINT.

The next question is what happens when we cross this sphere of radius Snat and go inside! The effective (physical) origin of the 'expansion' is UNIFORMLY DISTRIBUTED on the entire inside of this spherical surface. Let us call this the "distributed origin." There is still expansion but this expansion appears as a radial contraction to us (the Cartesian observers).

There are two important consequences of this fact, namely, that the 'origin' of motion in the inside region is not zero but uniformly distributed over the inside surface of the sphere of radius Snat.

Firstly, all radial directions, from any point on the 'spherical origin' toward the center of the Cartesian frame are totally equivalent. They become scalar from the point of view of the Cartesian observer.

Secondly, the 'expansion'---that is, the contraction in the Cartesian reference frame---continues infinitely like it does in the outside region. The contraction, commencing from the distributed origin, progresses for ever inward toward the Cartesian origin, which is the INFINITY of the inside region, never eaching it. Some researchers called this the counter-space infinity, CSI.

Nehru, Bruce
Every dogma has its day...

Mr. Kent
Posts: 3
Joined: Sun Apr 19, 2020 8:57 am

Re: Part I - Re-examining Coordinate Systems

bperet wrote:
Tue Aug 03, 2004 2:23 pm
In other words, the effective origin (of the expansion) is a spherical SURFACE of radius Snat---not the Cartesian zero POINT.

The next question is what happens when we cross this sphere of radius Snat and go inside! The effective (physical) origin of the 'expansion' is UNIFORMLY DISTRIBUTED on the entire inside of this spherical surface. Let us call this the "distributed origin." There is still expansion but this expansion appears as a radial contraction to us (the Cartesian observers).
A question of clarification - I understand the difference between using Cartesian zero point as origin and correcting it with the conceptualization of a spherical surface of radius Snat, but I'm a bit unclear on how the inside of that spherical surface (the 'distributed origin') appears as contraction to the Cartesian observer as the exterior expands. Can anyone help clarify this for me? As this conceptual sphere expands outwardly, does the interior have to contract in order to maintain the 'thickness' of the sphere as uniform? Does the 'thickness' of the sphere represent a unit speed boundary? Or am I mixing up concepts?

Mr. Kent
Posts: 3
Joined: Sun Apr 19, 2020 8:57 am

Re: Part I - Re-examining Coordinate Systems

bperet wrote:
Tue Aug 03, 2004 2:23 pm
The next question is what happens when we cross this sphere of radius Snat and go inside! The effective (physical) origin of the 'expansion' is UNIFORMLY DISTRIBUTED on the entire inside of this spherical surface. Let us call this the "distributed origin." There is still expansion but this expansion appears as a radial contraction to us (the Cartesian observers).
I'm a bit confused as to why the inside of the sphere (the 'distributed origin') appears as a contraction; would it not stay the same size? Or must it appear as contraction as the exterior expands in order to keep the 'thickness' of the sphere uniform?

I did attempt to post this question a few days ago, but the board would not allow me to. So, apologies if my question is not as thorough as it otherwise might have been. I am aware of Bruce's passing (RIP) and am asking at large as I know he cannot answer.

user737
Posts: 188
Joined: Wed Oct 24, 2018 7:39 pm

Re: Part I - Re-examining Coordinate Systems

Mr. Kent wrote:
Wed Apr 22, 2020 1:39 pm
bperet wrote:
Tue Aug 03, 2004 2:23 pm
The next question is what happens when we cross this sphere of radius Snat and go inside! The effective (physical) origin of the 'expansion' is UNIFORMLY DISTRIBUTED on the entire inside of this spherical surface. Let us call this the "distributed origin." There is still expansion but this expansion appears as a radial contraction to us (the Cartesian observers).
Mr. Kent wrote:
Wed Apr 22, 2020 1:39 pm
I'm a bit confused as to why the inside of the sphere (the 'distributed origin') appears as a contraction; would it not stay the same size? Or must it appear as contraction as the exterior expands in order to keep the 'thickness' of the sphere uniform?
The plane at infinity (space) and point at infinity (counterspace) exchange aspects of expression when moving across the unit speed boundary.

These are not structures but motions (speed regions) and so there is no material thickness.

What was a point at the origin becomes a plane -- the inside surface of a sphere -- becomes the origin (2D) and that motion is distributed over an area in 3D coordinate space:

Continuous outward motion (towards a center point at infinity) appears as a contraction as motion is distributed over increasingly greater temporal volume which must then normalized (scaled) to equivalent space for observation in extension space. This begets the concept of density when projected into 3D coordinate space with resulting normalization to clock time. The farther outwards in counterspace (inwards in space), the greater the density.
Mr. Kent wrote:
Wed Apr 22, 2020 1:39 pm
I did attempt to post this question a few days ago, but the board would not allow me to. So, apologies if my question is not as thorough as it otherwise might have been. I am aware of Bruce's passing (RIP) and am asking at large as I know he cannot answer.
There was a lapse in authorizing new-user registration. Welcome.
Infinite Rider on the Big Dogma

user737
Posts: 188
Joined: Wed Oct 24, 2018 7:39 pm

Re: Part I - Re-examining Coordinate Systems

Mr. Kent wrote:
Mon Apr 20, 2020 8:15 am
bperet wrote:
Tue Aug 03, 2004 2:23 pm
In other words, the effective origin (of the expansion) is a spherical SURFACE of radius Snat---not the Cartesian zero POINT.

The next question is what happens when we cross this sphere of radius Snat and go inside! The effective (physical) origin of the 'expansion' is UNIFORMLY DISTRIBUTED on the entire inside of this spherical surface. Let us call this the "distributed origin." There is still expansion but this expansion appears as a radial contraction to us (the Cartesian observers).
A question of clarification - I understand the difference between using Cartesian zero point as origin and correcting it with the conceptualization of a spherical surface of radius Snat, but I'm a bit unclear on how the inside of that spherical surface (the 'distributed origin') appears as contraction to the Cartesian observer as the exterior expands. Can anyone help clarify this for me? As this conceptual sphere expands outwardly, does the interior have to contract in order to maintain the 'thickness' of the sphere as uniform? Does the 'thickness' of the sphere represent a unit speed boundary? Or am I mixing up concepts?
We are speaking of a sphere where s = 1 and all motion is in time (1/t2). The spatial aspect is constant with motion in time only (energy).

The boundary can be considered as though speed-contours on a topographical map where s/t=1.

There is no "thickness" as these are motions (speeds or inverse speeds) not material structures. The boundary (for an individual motion, not necessarily an aggregate) is discrete. A line has zero "thickness" much as a "point" has no dimension.

You're thinking of the motion as spatial -- outward in space. Now go outward in time -- inward in space.

Please don't get frustrated -- you can do it. It takes time and effort. Keep reading and if you haven't already Larson's publications are a necessary primer IMHO.
Infinite Rider on the Big Dogma

Mr. Kent
Posts: 3
Joined: Sun Apr 19, 2020 8:57 am

Re: Part I - Re-examining Coordinate Systems

user737 wrote:
Sat May 09, 2020 10:45 am

Please don't get frustrated -- you can do it. It takes time and effort. Keep reading and if you haven't already Larson's publications are a necessary primer IMHO.
Thank you for the encouragement. I'm drawn to RS(2) and will continue in my attempts until I 'get it'. It's not easy, but everyone I've come across on the AQ forum has been exceedingly kind and helpful. Rare in today's world unfortunately. So, thanks again.

And I do have copies of Larson's books; which one do you recommend that I start with?

user737
Posts: 188
Joined: Wed Oct 24, 2018 7:39 pm