Time Region Speeds

Discussion concerning the first major re-evaluation of Dewey B. Larson's Reciprocal System of theory, updated to include counterspace (Etheric spaces), projective geometry, and the non-local aspects of time/space.
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Re: The Imaginary Operator(s); 3/13/2003

Post by bperet »

Nehru,

Thanks for taking the time to write that. It was immense help. Until now, I never understood why you used three different operators that all had the same value.

>

I'm not sure what I mean by it, either. Since it was in a quasi-dream state, it would have been interpreted by my consciousness, based on my internal understanding of "i". That understanding is just a scalar value equal to the square root of -1. I learned it from Electrical Engineering, where things were X-Y only. We used "j", instead of "i", because "i" was the symbol for current, and "j" was not used in electrical symbols. (Back then, the computers we used only had upper case, so you couldn't distinguish "i" from "I" and had to use a different letter to represent the sqrt(-1)).

Therefore, my internal understanding says that "i" and "j" are just two names for the same thing (my initial learning of the concept), so "j" got dropped as being redundant. Based on that understanding, and your description of the complex numbers, I updated my "Ancients.doc" to reflect your convention, and added some more info from another page of notes that I found.

See attached.

Thanks,

Bruce
Attachments
Ancients.doc
(58 KiB) Downloaded 558 times
Every dogma has its day...
User avatar
k_nehru
Posts: 63
Joined: Mon Sep 27, 2004 12:25 am
Location: India

Genesis of "mass"; 3/16/2003

Post by k_nehru »

Dear Bruce

I am beginning to suspect whether the property called 'mass' exists inside the Time Region, or it appears only in the Time-Space Region? I have been endeavoring to show that rotational motion is primary in the Time Region, like linear motion is in the Time-Space Region. A principal characteristic of the "spin", or the intrinsic angular momentum, is the resistance to change the direction of the spin axis, called the 'moment of inertia'. This rotational property is analogous to inertia, or mass, which is the resistance to the change of direction of the linear speed. If the basic motion constituting the atom is a two-dimensional rotation (existing in the Time Region), its primary manifestation (in the Time Region) should be ROTATIONAL INERTIA---a resistance to change the 'angle' (direction) of the axis of rotation in space (or equivalent space, as the case may be). Since on crossing the Time Region and emerging into the Time-Space Region the primacy shifts from rotational to linear, the rotational inertia manifests as mass. Further there would be no preferred direction in the Time-Space Region, even though within the Time Region axial direction of the "spin" has existence and relevance. This explains the observed SPIN DEPENDENCE of the so-called nuclear (strong) force: that the force between two nucleons of parallel spin is stronger than the force between two nucleons of antiparallel spin.

Nehru
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Re: Genesis of 'mass'; 3/16/2003

Post by bperet »

Hi Nehru,

I have been deriving a computer model from my "Ancients" experience, and it has been turning up some things that might be relevant to our goals. First, I have some questions for you:

1) Motion in the time region is rotationally distributed in the time-space region, correct?

2) Is there any reason why that rotationally-distributed motion cannot be polyhedral, rather than spherical? Since we are dealing with discrete units, to me it would seem plausible that the rotational distribution would be discrete (faceted), rather than continuous.

3) What constitutes a "dimension" in the time region? Is it the iX, jY, kZ axes, the axis of rotation (as in your tetrahedral diagram), or something else? (I am wondering if the 4th power expression in the time region has to do with dimension, or just the number of primary rotations involved)?

I found some info on the internet on how to transform quaternions into homogeneous coordinates, so now I have a better understanding of them. I constructed a quaternion model of the TR rotations using HC, based on your information, starting with a basic double-rotation. Using pi as Rnat, the equivalent-space projection of the double-rotation showed up as a 4-faceted sphere -- a tetrahedron (4 discrete units, with the vertices at the circumradius). The 2 double-rotations transform to an octahedron (8 facets). The tetrahedron did not preserve parity, and wanted to either bond or dissolve, whereas the octahedron DID preserve parity, and was harmonically stable. ("Parity" is the concept of meshed gears -- adjacent, opposite rotations are stable, whereas adjacent, similar rotations are unstable and repel).

This leads me to believe that your idea of two double-rotations being the rotational base is correct (separation is pi radians, +/- i , which solves my hypersphere problems).

Increasing the rotations transformed into the Platonic solids, becoming increasingly "smooth" and sphere-like as the number of facets increased, moving from the octahedron, to the dodecahedron, to the icosahedron, to a 28-faceted solid that I don't know the name of. I couldn't help but notice that this follows the pattern of scalar reversals you have referred to as "folds". Opposing faces of the solids are the same rotational axis, so the number of "rotations" expressed are the facets/2: octahedron: 4 (2 per double-rotation, so we could say 2, 2 rather than 4), dodecahedron, 12/2=6, icosahedron, 20/2=10, 28-facet, 28/2=14... the same pattern of "folds", 2, 2, 6, 10, 14, 18, 22... corresponding to the shell structure, but including a crystalline geometry for the atom.

I am going to use "turn" to refer to the unbounded measurement of rotation in the TR, to distinguish it from bounded "angle" in the TSR.

Here is where I am questioning "dimension". Per our conversations, the two double-rotations (the octahedral projection) forms the sub-atomic particles, so we see them as 4-rotations, being 4-dimensional. But, once you reach helium, the rotational projection appears to change to the dodecahedron, which has 6 rotational axes plus the original 4 rotational axes (being a turn, rather than an angle). (I think you were trying to express this in your 'tetrahedron' model (TR #8) that was 6 dimensional, that I was unable to follow).

I can't help but notice that there is a 1:1 correspondence between the number of facets on these polyhedral projections, and the number of electrons allowed per Bohr "shell". Though the facets, themselves, being merely a projection of turn into time-space would only account for atomic number -- not the energy level interactions. The thought also occurs that since each of these facets represents an internal rotation -- a temporal displacement, that each facet could, in fact, "capture" an uncharged electron, thus giving the APPEARANCE in time-space of an electron "cloud" arranged in shells about a nucleus. (The electron, of course, would be captured inside unit boundary, but it would be projected into the polyhedral face when viewed outside the TR.)

I know you've suggested that electron capture may account for these energy level interactions, and from what I've found, that appears correct. I have some more detailed info on this, but I want to work up some figures and tables, to try to make it clearer.

Quote:
I am beginning to suspect whether the property called 'mass' exists inside the Time Region, or it appears only in the Time-Space Region? I have been endeavoring to show that rotational motion is primary in the Time Region, like linear motion is in the Time-Space Region.
You may be on to something here. To me, 'mass' and 'gravity' appear backwards, given their space-time units. We see "speeds", s/t, as particulate (local), and "energy", t/s, as waves (non-local). But then you have mass, a local, particulate phenomenon, as t^3/s^3, with the dimensions of energy, and gravity as non-local, with dimensions of speed, s^3/t^3. This may indicate that we are on the other side of the unit boundary for the mass/gravity concepts, than for other phenomena. As such, "mass" would be a time-space measurement, rather than a time region measurement.

Quote:
A principal characteristic of the "spin", or the intrinsic angular momentum, is the resistance to change the direction of the spin axis, called the 'moment of inertia'. This rotational property is analogous to inertia, or mass, which is the resistance to the change of direction of the linear speed.
Let me see if I follow you... momentum in the TSR is t^2/s^2. In the TR, s=1/t, so momentum in the TR would be t^2/(1/t)^2 = t^4?

Quote:
If the basic motion constituting the atom is a two-dimensional rotation (existing in the Time Region), its primary manifestation (in the Time Region) should be ROTATIONAL INERTIA---a resistance to change the 'angle' (direction) of the axis of rotation in space (or equivalent space, as the case may be).
I follow you up to the last line. Wouldn't it resist "change of angle" (called "shift" in Projective Geometry) in TIME, rather than space/eq space? Is inertia preserved across frame-inversion? If so, would that mean that a temporal "direction" is being translated to a vectorial direction in time-space?

Quote:
Since on crossing the Time Region and emerging into the Time-Space Region the primacy shifts from rotational to linear, the rotational inertia manifests as mass.
I think I understand... since it resists any change of rotational direction in time, it will also resist any change of linear direction in space (it matters not which direction).

Quote:
Further there would be no preferred direction in the Time-Space Region, even though within the Time Region axial direction of the "spin" has existence and relevance. This explains the observed SPIN DEPENDENCE of the so-called nuclear (strong) force: that the force between two nucleons of parallel spin is stronger than the force between two nucleons of antiparallel spin.
I just read about this in Nick Thomas's book on Counterspace. They refer to the concept as "shift" between two points (0 shift = parallel points -- strong force, if pi/2 shift, then orthogonal points -- weak force). It is apparently related by a cosine function. Is this the case with spin dependence?

I'll get you a follow-up shortly on the shells and energy levels I derived from the polyhedral double-rotation model. It is amazing how much it looks like the Bohr atom (equiv space view of time region rotation).

Bruce
Every dogma has its day...
User avatar
k_nehru
Posts: 63
Joined: Mon Sep 27, 2004 12:25 am
Location: India

Particle in a Box ::: Rotational Coord System; 3/18/2003

Post by k_nehru »

Dear Bruce

Please read the Attached two files.

Nehru
Attachments
Particle in a Box.doc
(24.5 KiB) Downloaded 547 times
Rotational vs Linear Cood Syss.doc
(21.5 KiB) Downloaded 538 times
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Re: Rotational Coord System; 3/18/2003

Post by bperet »

Dear Nehru,

I hope you can follow this... I'm not the best at explaining things at times!

See attached.

Bruce
Attachments
Rotational vs Linear Cood Sys BP.doc
(62 KiB) Downloaded 577 times
Every dogma has its day...
User avatar
k_nehru
Posts: 63
Joined: Mon Sep 27, 2004 12:25 am
Location: India

Platonic Solids :: Quantum Numbers; 3/19/2003

Post by k_nehru »

Dear Bruce

Please see the Attached file.

Nehru
Attachments
Platonic Solids_Quntum Nos.doc
(23 KiB) Downloaded 567 times
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Re: Platonic Solids :: Quantum Numbers; 3/19/2003

Post by bperet »

Hello Nehru,

“1/2h” should be “1/2ħ” (please see Eq. , ‘Particle in the Box’). In “!1/2h (Trot)” above what does ‘!’ stand for? What is “Trot”?

T(rot) = the total rotational kinetic energy that you mentioned in the paragraph above. It looks like I missed putting the "subscript" on "rot".

The "!" is actually a +/- sign, from the "Math B" font. Apparently you do not have the "Math" fonts on your system, so it went back to your default font, and displayed as an exclamation point. I suspect that there may be other symbols that are not displaying correctly.

I normally use the "Symbol" font for Greek letters and basic symbols, and "Math B" and "Math C" for the mathematical operators. I noticed you are using the extended unicode characters in the "Times New Roman" font, which I have not been using because they do not display properly on non-Microsoft products (the same problem; other browsers and word processors do not recognize the extended characters, and display as "junk" characters).

I will use the "Times New Roman" characters from now on, in our communications, so you can see what I am writing correctly. I have emailed Dan McCann to see if there is a solution to this, that we can use on the web sites.

Bruce
Every dogma has its day...
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Re: Platonic Solids :: Quantum Numbers; 3/19/2003

Post by bperet »

Attached are a couple images:

DoubleRot.jpg is the rotation transformation that produced the tetrahedron, which made me wonder about the rotational distribution being polyhedral. It is produced by two planar (double) rotations. This result was harmonically unstable, and violated parity.

Geometry.jpg is the transformation updated with four planar (double) rotations, or as Larson would describe, the double-rotational base, forming the octahedron (the intersection of two, anti-parallel tetrahedrons--one inverse of the other, out of phase by 30 degrees). This is analogous to two rotating photons, each tetrahedron representing one photon rotating system. This system is harmonically stable, with correct parity.

I'm reworking the more complex shapes. They are very hard to see, because of the "layering" effect created by the unbounded rotation. I'll send them when I get something reasonably viewable.

Bruce
Attachments
geometry.jpg
geometry.jpg (15.09 KiB) Viewed 13761 times
doublerot.jpg
doublerot.jpg (13.97 KiB) Viewed 13761 times
Every dogma has its day...
User avatar
k_nehru
Posts: 63
Joined: Mon Sep 27, 2004 12:25 am
Location: India

Particle in a Box - 2; 3/20/2003

Post by k_nehru »

Dear Bruce

Please see the Attached file.

Nehru
Attachments
Particle in a Box_2.doc
(20 KiB) Downloaded 529 times
User avatar
k_nehru
Posts: 63
Joined: Mon Sep 27, 2004 12:25 am
Location: India

Particle in a Box - 3; 3/21/2003

Post by k_nehru »

Dear Bruce

Please see the Attached file.

Nehru
Attachments
Particle in a Box_3.doc
(25 KiB) Downloaded 591 times
Post Reply