Reciprocal System Research Society

Larson uses "displacements" as a notational system for particles and atoms. His displacements are very simple, they are just the speed deviation from Unity, with the positive value being a temporal deviation, and the negative (enclosed in parenthesis) being a spatial deviation.

Thus, the electron with a speed of 1/1-1/1-2/1 has a displacement (and notation) of 0-0-(1) (spatial), whereas the positron with a speed of 1/1-1/1-1/2 has a displacement of 0-0-1 (temporal).

The system naturally lacks some proper representation, as Nehru mentioned in another article on notation, as there was no way to represent something like 3/2, which has BOTH a spatial displacement of (2) and temporal displacement of 1 at the same time.

Back when I realized that the "Octave", and the unit speed/natural datum of the Universe was just a displacement of "1", it has made me re-think the displacement concept as there was no difference between a "unit displacement" and a "unit speed."

In my latest RS2 research, I tried a different definition of "displacement" from Larson's concept of a deviation from "1"... the "displacement" being the shear between spatial and temporal speeds. Basically, to get the displacement, just use the equation, "d = t - s", where "t" and "s" are the speeds involved in an s/t relationship.

Thus, the electron: 1/1-1/1-2/1 still has Larson's displacement of 0-0-(1) being 1-1=0, 1-1=0, 1-2=-1.

BUT, an electron with speeds of 1/1-1/1-55/54 ALSO has a displacement of 0-0-(1) since 54-55 = -1; the big difference being that an electron can now have an intrinsic speed (55 space/54 time) or energy to it, while still looking and acting exactly like a single, rotating unit of space.

This structure works well with high-energy experiments, where conditions are usually far from the normal environment. I also suspect it might be the basis of Larson's "vibration 2" mentioned in Basic Properties of Matter, but I have yet to investigate this.

Again, still testing the idea. Basically, anything with a displacement of "1" in one dimension, is a positron/electron. A speed displacement of "2" in one dimension is then a photon (the two bi-rotating components).

When you consider that a photon is the carrier of charge for an electron, there are now two independent variables to consider in the energy of a charged electron--the speed of the electron, and the speed of the photon creating the charge. This goes a long way in explaining a lot of RF (Radio Frequency) applications that Larson's model was not able to address--like the excessive RF noise produced by static electricity.

Does this different idea of "displacement", giving energy to particles while still retaining their effective displacements, seem to fit other areas of the RS?

Comments appreciated!

The new displacement model, where the displacement is computed by the difference between the temporal and spatial speed aspects (t - s = d) has worked out well, so far, and is not actually all that different from Larson's original model.

Larson considers displacement to be a "displacement from unity", hence "no displacement" is "unit speed". But in the previously cited example, a speed of 1/1-1/1-55/54 cannot be represented in Larson's notation in his conventional sense, because there is both temporal and spatial displacement... in the RS2 displacement model, it is 0-0-(1), the electron.

It further occurs to me that Unity, "1", the speed of light, doesn't have to be ONE. Unit speed can also be represented as 54/54 (or any speed with the same value in both aspects), and for all practical purposes, looks and acts just like "1". That's why the new displacement model works... it is STILL a "displacement from unity", but in this case, "unity" is 54/54, not 1/1, and thus 55/54 - 54/54 = 1/0 = (1).

So the displacement of any motion is the displacement from the "effective" unity, the largest unit ratio that can be removed from the speed. Therefore, d = t-s works.

While discussing some things with Prof. Nehru yesterday, we came across the following point:

In Larson's RS, the deviations from unity occur due to some thing called 'direction reversals'.The explanation given is "in a speed of 1/n, space undergoes reversals whereas time progresses uniformly".

So now,how do we derive the concept of a reversal from the fundamental postulates?In RS2, we have the derivation based on assumptions placed on Projective geometry. Do any of these assumptions provide for the kind of polarity which Larson uses in his 'direction reversals'?

For example, unity [1] becomes a dichotomy [1/2*2/1].Since this is a separation, there may be no need for a reversal of direction,but the motion may merely be separated... If we take a 3 unit progression (3/3 = 1) by associating 2 units of time progression with one unit of space progression and vice versa,we can obtain 1/2*2/1.However, I am not sure what I mean when I say 'separation',I am still thinking on it.

From this, the idea of even speeds being an average of odd speeds will disappear, as will the complications of reversals happening both in space and in time simultaneously.It could throw more light on the displacement from unity in different ways: 1/2,3/4,n/n+1.

Bruce wrote:

Does this different idea of "displacement", giving energy to particles while still retaining their effective displacements, seem to fit other areas of the RS?

Prof. Nehru was also mentioning an idea that the energy and its inverse may create the displacements. I did not follow it completely, he may explain the idea further.

Cheers,

Gopi

Gopi wrote:

While discussing some things with Prof. Nehru yesterday, we came across the following point:

Good to hear Nehru is back on the job. I've missed his contributions.

Gopi wrote:

In Larson's RS, the deviations from unity occur due to some thing called 'direction reversals'. The explanation given is "in a speed of 1/n, space undergoes reversals whereas time progresses uniformly".

So now,how do we derive the concept of a reversal from the fundamental postulates?In RS2, we have the derivation based on assumptions placed on Projective geometry. Do any of these assumptions provide for the kind of polarity which Larson uses in his 'direction reversals'?

The cause in RS2 is different, but the results are the same. Remember that "space", from our perspective in the material sector, is rectangular, whereas "time" is polar (aka, "counterspace").

All we have to work with in RS2 is an increase in speed, in either the temporal or spatial aspect of the ratio. In the case of 1/n cited, the increase is in time (n). Unlike Larson, where time is considered linear, the "n" here is a counterspatial "turn", which manifests as rotation from the material POV.

When thinking of rotation, do not think of "zero to 2 pi", think of it as "zero to pi" then "pi to zero". I think the nature of the "direction reversal" then becomes apparent. Each unit of displacement of the temporal, polar speed manifests first as 0-pi (outward), then pi-0 (inward) -- AS VIEWED IN SPACE.

Remember that it is ALL outward POLAR motion in time, since a counterspace "turn" is unbounded. But the projection of the turn into space ("polar" being 2-dimensional) appears as a 2-dimensional shear, which we call "rotation".

Thus, for example, the 1/3 motion which Larson describes as IOI/OOO is exactly the same in RS2... the outward progression is omitted in the 1/3 notation, so the first "O" being pi-2pi in time, or "in" in space, the second being 2pi-3pi, or "out" in space, the third being from 3pi to 4pi, or "in" in space.

See also Nehru's paper on the Law of Conservation of Direction.

Gopi wrote:

For example, unity [1] becomes a dichotomy [1/2*2/1]. Since this is a separation, there may be no need for a reversal of direction,but the motion may merely be separated...

The dichotomy here is probably one of symmetry; I refer to it as the "Law of Conservation of Motion". The reversals of direction would be in each aspect, which would cause the combination to move apart to different absolute locations in the natural reference system (one moving in time, the other moving in space).

Though depending upon the nature of the linkage, they may still be linked, kind of like photons in the EPR paradox, which could be an interesting analysis unto itself.

Gopi wrote:

If we take a 3 unit progression (3/3 = 1) by associating 2 units of time progression with one unit of space progression and vice versa,we can obtain 1/2*2/1. However, I am not sure what I mean when I say 'separation',I am still thinking on it.

I actually understand where you are heading with this. Also been on my mind since I started the "linkage" topic.

Another consideration in RS2, since it is based on an invariant cross-ratio, is that unit ratio has no aspects, since it is NOT a cross-ratio! (in the homogeneous matrix, the matrix would be all zeros). Therefore, speeds such as 3/3 cannot exist since the points defining the ratios become coincident. For something to manifest, it must have a non-unity cross-ratio.

I know I'm probably losing you, because I only have a light grasp on this at the moment, but at the projective (scalar) stratum, we would see 1/3 as "1" over "3" -- a magnitude of 1 linked to a magnitude of 3.

Once you are in an Affine projection, then you have the zero and infinity reference points to use to define a ratio as "inward" or "outward", because you now have the concept of "direction."

So Larson's "direction reversals" are the Affine perspective of projective cross-ratios (scalar speeds).

Gopi wrote:

From this, the idea of even speeds being an average of odd speeds will disappear, as will the complications of reversals happening both in space and in time simultaneously.It could throw more light on the displacement from unity in different ways: 1/2,3/4,n/n+1.

Another of the problems with Larson's model is that he starts with the photon, which has that nasty "wavelength" of TWO units, and thus can only have odd values. Not a problem in RS2, because we start with the positron, and even value. Since the photon is a bi-rotation, it always moves as 2*cos(a) (see the topic on photons and the Euler relations concerning the rotations) so any speed combination is possible.

When trying to represent material and cosmic motions in the same transform, I noticed that the "displacement" has two, different representations, based on the type of measure used. Larson recognized both, but without the consideration of a polar / imaginary region (T-frame), he didn't notice the difference.

There are two types of "measure":

Step Measure: the normal walking measure, where each step is the same length; a characteristic of rectilinear realms.

Growth Measure: the rotational measure, where each step is the same angle. When this is projected onto a line, it appears that each step is getting bigger (moving away), or smaller (moving towards). It is easy enough to see... take a flashlight and point it straight at the ground. It produces a circular beam on the grown. Now angle it away, and the circle becomes an oval; the sharper the angle, the more deformed the oval until it becomes a parabola (no longer closed).

I have been using the form S + iT for material motion, and T + iS for cosmic motion. Since we measure "space", we also see two different types of measure... for material particles, step measure--locations on an X-Y-Z grid. But for a cosmic particle, space is polar--growth measure. Growth measure is measured by the Turn, which has an infinite angle and cannot be directly represented in space.

So, if we apply the rectilinear rules of our perception to a rotational space, the tendency is to interpret each interval--a "growth measure" displacement--as being step measure. But when we do this, a problem arises: the first angular step then becomes 1/2 of a circle -- PI radians. That is set as our standard of measure. The next interval, 1/3, by the rules of step measure, would also have to be PI radians, bringing us back to the starting point. From the spatial observers perspective, "2" (or 1/2) then becomes the maximum displacement in one dimension, since you've returned to where you started.

When we move to the 3rd interval, we continue to add another PI angle to the measure, and end up back at PI. It appears that the motion is transversing the same path... but yet, it does not act the same... 3PI acts differently than 1PI, even though it plots to the exact same point.

To get around this, physics introduced a new concept: spin. The 3rd growth interval, measured as a step, has a spin of 3/2. The "spin" is just the indirect, angular growth measure, since we cannot measure it directly, as it is a polar (imaginary) region.

Some conclusions:

• The unit of step measure, a linear displacement, is 1.
• The unit of growth measure, a rotational displacement, observed as step measure, is PI.
• Material particles will move in straight lines.
• Cosmic particles will move in arcs.
• Aggregates of material and cosmic motions should move in a helical path.
• Cosmic motions have "spin" in space (making "valence" electrons cosmic positrons).
• Material motions have "spin" in time (could be measured as moving backward in clock time).

bperet wrote:

To get around this, physics introduced a new concept: spin. The 3rd growth interval, measured as a step, has a spin of 3/2

Earlier in the Time-region speeds forums there was talk of a "rotational depth". So you are suggesting that the spin and growth measure are the same as this "depth", I think?

Gopi wrote:

bperet wrote:

To get around this, physics introduced a new concept: spin. The 3rd growth interval, measured as a step, has a spin of 3/2

Earlier in the Time-region speeds forums there was talk of a "rotational depth". So you are suggesting that the spin and growth measure are the same as this "depth", I think?

We went through a lot of different ideas to get a representation. I was looking at the spins for quantum energy levels, and found there are a lot of higher half-integer spins, well beyond 1/2, 1 and 3/2. I also suspect that there is some confusion between spin as a 1D rotation (2pi) and spin as a solid rotation (4pi), compounded upon the "rotational depth", how many times we would appear to cross the 0-degree boundary. Curiously enough, I have not yet run across a concept like "spin 10"... it was always an odd ratio, like 5/2, so I have to wonder if the depth of an integer spin is even detectable.

Every 2 steps of growth measure (pi radians) would be a single increment to rotational depth, since we are counting the number of angular zero crossings.