## 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.
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### Time Region Speeds

This was the original conversation between Nehru and myself concerning time region speeds, photons, coordinate systems and other factors that lead to the incorporation of counterspace and projective geometry into the RS re-evaluation.
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time_region_speeds.doc
Time region speeds
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bperet
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### Time Region Speeds 2/3/2003

Hi Nehru,

I'm not sure what you mean when you ask me to list atoms in natural units (the notation of subatoms), rather than terms of EDU. D, He and Li aren't subatomic... the only relationship I know would be to use the 2n^2 relationship. The alpha particle, in Larson's old notation, would be 1 1/2 - 1 1/2 - 0.

As to your ideas on primary motion...

It seems logical that since you can have linear motion without rotational motion, that you could also have rotational motion without linear motion; the SRB in (4). But it would appear that this SRB, though having spin, would not have any angular momentum, since the "r" in mvr = 0. As such, would it not just be an indiscernible "location marker" in the reference system?

I would agree that there can be no linear motion in the time region. I was thinking of this also, because speed in the TR is measured as 1/t^2, which is 2-dimensional, and linear motion requires only one dimension.

I am still having a difficult time with your "1-dimensional" or Nuclear Zone concept, as it differs from the 3-dimensional TR, though I do follow where you are going with the 4-dimensional time region concept.

It also occurs to me that the "minimum" motion would be that of the progression of the natural reference system, which would be linear in time-space and space-time, and rotary in the time region and space region. This would support the idea that rotation is primary in the TR, but is equivalent to uniform motion. And, just as rotation can be added to linear motion in the time-space region, linear motion can be added to rotation in the time region.

Now the photon model described in #6 I would agree with. It makes a lot of sense. And the derivations in #7 seem to be logical (though the "neutron" should be the "muon neutrino" with the structure described).

The only thing I would question is the SRB. From the structure you propose, it would seem that the progression appears as a outward, scalar motion (rotationally distributed linear motion) in time-space, and as pure rotational motion in the time region--with spin, but no angular momentum. And that "spin", being unbounded, would be analogous to the infinite linear motion in time-space.

Bruce
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### Time Region Speeds 2/4/2003

As a followup to my last reply, it also occurs to me that since "linear" motion in the time-space region is a bi-vector, the unbounded rotational motion in the time region would be a bi-rotation, so would it be possible to have a "single" rotational base?
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k_nehru
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### Time Region Speeds - 2; 2/5/2003

Dear Bruce

Thanks for the reply. I think we need to clarify the relation between the 'intrinsic angular momentum' (the Spin), the angular frequency (denoted by the small-case letter 'omega'), and energy. I will do that in a later communication. I will also try to clarify what I meant by the Atomic Zone and the Nuclear Zone of the Time Region.

Nehru
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time_region_speeds-2.doc
Time region speeds 2
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### Time Region Speeds - 3; 2/7/2003

Dear Bruce

Nehru
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time_region_speeds-3.doc
Time region speeds 3
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### Time Region Speeds - 3; 2/8/2003

Dear Nehru,

The word document has questions and comments. I added "Sheet 2" to the Excel spreadsheet to include some more possible identifications, based on a computer model I am putting together.

Bruce
Attachments
Time Region Questions.doc
Tentative Identifications of Particles.xls
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### Another question; 2/10/2003

In Corollary #10 (multiple dimensions) in your Non-Locality article, you state that it requires 3n dimensions to represent "n" particles between two T-frames.

Now that we know the time region is 4-dimensional, does this still hold true, or should it be "4n dimensions?"

Bruce
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k_nehru
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### Time Region Speeds - 4; 2/11/2003

Dear Bruce

Nehru
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time_region_speeds-4.doc
Time region speeds 4
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### Model of 1d rotation; 2/13/2003

Hello Nehru,

You stated that: "R[NAT] is the Natural Unit of Rotation (2pi radians or 4pi steradians)."

I tried to model the 1-dimensional rotation and the results were not as expected. See attached animated GIF. I used the same control logic as linear motion, but found that it required 2 units to complete 2pi radians of rotation, making the Natural Unit of Rotation "pi radians" or "2pi steradians".

In essence, this amounts to an outward (0-pi) followed by an inward (pi-2pi) motion. This might go well with the pattern of rotation you describe or the time region in "Time Region Speeds #4" -- consider that the rotation reverses every half cycle (making a full circle), and the total area swept by the arc is the displacement.

It does repeat the pattern you describe: 1 (0-1pi), -1 (pi-2pi), 2 (2pi-3pi), -2 (3pi-4pi), 3 (4pi-5pi), -3 (5pi-6pi), 4 (6pi-7pi), -4 (7pi-8pi) and the total area swept using a half circle matches the displacement, 1, 2, 3, 4, ... 8. The displacement can also be found from the ending position of the rotation, in multiples of pi.

Let me clarify that the animated GIF shows both halves of the bi-rotation, so it APPEARS to complete a full circle within 1 unit. This appearance may be deceiving us into thinking that the Natural Unit of Rotation is 2pi radians / 4pi steradians.

If you email program does not support animated GIF files, you will just see an dumbell-shaped shadow on the X axis. Just save the attachment to a file, and open it with Internet Explorer, and IE will animate it.

(I had to use a radius of 1 unit; a radius of zero did not display anything).

Bruce
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r1.gif (41.02 KiB) Viewed 16860 times
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### Time Region Speeds - 4; 2/13/2003

I like your new notational system, based on speeds. When I was programming Larson's system on the computer, I did the same thing without realizing it, running the displacements from 1-8 and always using a positive "c" value, so the last element was 8-31, rather than 5-4-(1). It was the only way to get the model to work. At least now I understand why it works!

Use of the colon is good. Definitely need to distinguish it from Larson's notation. I think you may have already noticed that I prefer the minus sign over the underscore. It is easier to deal with.

You wrote: "'a1', 'a2' and 'c' we can call them 'R1', 'R2' and 'R3'"

Might I suggest calling them R1:R2:r3, using the lower case "r" to indicate that it is a single rotation, and not a double one? Otherwise, the inference will be to consider all three as double-rotations.

Very interesting development with the c-electrons and c-positrons... to my knowledge, physicists have not yet identified a true "anti-electron", assuming it is the positron. This might explain why. And then there are the considerations of the bi-rotating electron pairs -- which brings up another question:

Electron as 1:0:-1 ... also: -1:0:1 ? Would not such a combination be likely in a birotating pair, since it preserves parity?

Which also brings another question to mind: how is +/- rotation determined? Rotational direction requires an outside reference point to be established. Recall that Larry Denslow brought that up during his talk in the common room at the 1996 ISUS retreat? My clarification comment being (from multiple viewpoints), "you can never agree on which way it is turning, but you can always agree on how fast."

You wrote: "The next point that needs clarification is about the 'double' nature of the Atomic RB as against the RB of the Sub-atoms. Do we have to take that the rotations 'R1' and 'R2' pertain to two SCALAR DIMENSIONS and 'R3' to the THIRD? I look forward to your ideas."

I guess my question in response to scalar dimensions would be, "does it matter?" From what I understand of Larson's work, the other "two" scalar dimensions had no other purpose but to account for scalar modifications to existing motions, particularly in the intermediate and ultra-high speed ranges. If all three are used to represent rotation in the time region, does not that limit their expression to modify motion in or beyond the atomic zone?

Assuming that you did have a correspondence of scalar dimensions to the rotational systems, the "r3" would raise some issues, because it is not a full expression of that third, scalar dimension. If the first two scalar dimensions can be represented by double-rotation, then the third should also be--constrained only by the dimensions available. And without "space" available in the time region, the only place it could be represented would be a modification to an existing motion, perhaps the linear motion in the nuclear zone?

There is one more possiblity that I can think of, but I'll address it separately, after I run a simulation on it, to see if it is viable.

Bruce
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