Motion in the Time Region

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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bperet
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Motion in the Time Region

Post by bperet »

In the recent lecture I gave on RS2 (video was made and I'll make available), I was describing how motion inside the time region different from motion outside it.

Outside, we have something called "step measure", where it is like walking in steps, each step is the same distance as the last, and the number of steps you take is the total distance you have traveled. The sequence goes like this:

1, 2, 3, 4, 5... where '5' is the total number of steps you have taken, and also the total distance traveled.

Inside unit space (the spatial aspect of motion is fixed at unity), we are walking in time, not in space. Our material existence gives us physical senses that only allow us to directly measure SPACE, not time. To address this measure, Larson introduced the concept of "equivalent space", which is how much of a spatial change we perceive when moving in time, as long as the spatial aspect of motion is fixed at 1.0.

Picture equivalent space as a sphere with a radius=1.0. The most we can move in space is ONE step, from 1 to the center, zero, and we can't go any further. But, we CAN take a temporal walk... but this results in each step getting smaller than the last. Since we are starting with ONE, a first step, the second step is 1/2, the third, 1/3, the fourth 1/4. Unlike the step motion outside, the total number of steps taken is NOT the same as the total distance traveled. On our 4th step (1/4) we aren't standing 0.25 away from where we started, but 1/2+1/6+1/12 = 0.75, 3/4ths of the distance.

One should also notice that each step is a fraction of the REMAINING DISTANCE, not the total distance. So each step is smaller than the last:

step=1 (zero reference)

step=2, (1-0)/2 = 1/2

step=3 (1-1/2)/3 = 1/6

step=4 (1-1/2-1/6)/4 = 1/12

step=5 (1-1/2-1/6-1/12)/5 = 1/20

step=6 1/30

step=7 1/42

step=8 1/56, ...

It takes an infinite number of steps (in time) to actually reach the center of equivalent space.

Gopi pointed out in an email that each step can also be viewed as a running interval (in time), where you simply multiple the current step by the last:

1/1*1/2 = 1/2

1/2*1/3 = 1/6

1/3*1/4 = 1/12

1/4*1/5 = 1/20

...

Gopi wrote:
I think what the progression is, if I understood you correctly, is that in space, the intervals go as 1, 1/2, 1/2*1/3 = 1/6, 1/3*1/4 = 1/12, 1/4*1/5 = 1/20 etc. Now look at the denominators (time), you have 2, 6, 12, 20, 30 etc. Take the sum of the 2 steps: 2, 2+6, 6+12, 20+12, and you get the Bohr radii formula. (2,8,18,32...) This is basically 2(n2).
Let's take a closer look at that. In rectilinear space, the shortest distance between any to points is a straight line--just one way to get there. In the polar space of the time region, the shortest distance between any to points is a unit arc, which can be either clockwise or counter-clockwise, so you have TWO "shortest distance" paths to follow in a polar space, which results in pairing of motion, twice the unit distance, such as wavelengths (-180 to +180) or concepts like bi-rotation. Therefore, when we look at a "temporal walk", we will see the steps paired up. The simplest combination is the pairing of adjacencies, which gives us our net temporal displacements:

t=1 (0) + t=2 (1/2) = 2

t=2 (1/2) + t=3 (1/6) = 8

t=3 (1/6) + t=4 (1/12) = 18

t=4 (1/12) + t=5 (1/20) = 32

Or, to put an equation to it:

t(t-1) + t(t+1) = n2 - n + n2 + n = 2n2

Larson uses this sequence to compute the electric displacements in his Periodic Table. Each sequence would apply to ONE double-rotating system, and since the atom is composed of TWO double-rotating systems, we will see the periodicity doubling-up, 2,2, 8,8, 18,18, 32,32.

Gopi wrote:
Now take its contributions in space (Invert back), and you get 1/(2n2) and hence your Balmer stuff.
Which is quite an interesting observation. The electron, being a rotating unit of space, CAN be captured in the equivalent space of the atom, since the relation of space to space is not motion. Spectral lines, such as the Balmer series, are determined by the emission of photons captured by electrons. (In RS2, electrons CAN capture and emit photons; captured photons imposing a rotational vibration upon the electron, creating electric charge).

So what we end up observing is an atomic nucleus, composed of 1D and 2D temporal rotation, with a cloud of charged electrons distributed around it; their positions dependent upon the numerous speed ranges in equivalent space created by the atomic rotations.

It also infers that the "orbital electrons", though responsible for spectral lines, have nothing to do with chemical interactions!

Gopi wrote:
Another thought hit me when I was pondering this. I think in "Nature of Scalar Rotation" Nehru had identified the "folds" structure of the time region. I just tried this with the series of "steps" instead of the intervals.

First step is UNITY, equivalent of no step : 1.

Next step is 'inward', -1/2.

Next step is 1/3 of this step, but outward: 1/6.

And the next: -1/24. And so on.

We get the series: 1 - 1/2 + 1/6 - 1/24 + 1/120.... inf. = e(-1)

This is the basis of exponentially decreasing functions!! All we need is identifying the value of the scaling factor for these steps and we get different rates for the exponential function: e(-x).
If you fill out the sequence of folds based on the temporal intervals, you get:

+0

-0

+2

-6

+12

-20

+30

-42

Now take a delta on the positive and negative sides:

2 - 0 = 2 (+)

6 - 0 = 6 (-)

12 - 2 = 10 (+)

20 - 6 = 14 (-)

...

Which gives us the L subshell sequence of quantum numbers, 2s, 6p, 10d, 14f..., but with some conceptual rationale behind it. We are observing speed zones again, which appear to be the byproduct of a polyhedral projection of motion into space. If you think about it, since everything in the RS is quantized, the projection of motion will not be spherical, but polyhedral -- faces, edges and vertices. Look at the terms in the time intervals as geometric faces:

2: Plane

6: Cube

12: Dodecahedron

20: Icosahedron

If this is cross-referenced with Dr. Moon's article on the polyhedral structure of protons, I'll bet we have a solution to the atomic quantum levels and a bit of a different view of the atom.
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Complex Turns

Post by Gopi »

First, a couple of minor corrections...

bperet wrote:
t(t-1) + t(t+1) = n2 - n + n2plus n = 2n2

If this is cross-referenced with Dr. Moon's article on the polyhedral structure of protons, I'll bet we have a solution to the atomic quantum levels and a bit of a different view of the atom.
Now, with respect to the time region, TURN is primary, and TRANSLATION is secondary. Also, the projection of this motion onto the euclidean space has to meet certain criteria, for example the polar relationship outlined already:

bperet wrote:
In the polar space of the time region, the shortest distance between any to points is a unit arc, which can be either clockwise or counter-clockwise, so you have TWO "shortest distance" paths to follow in a polar space.
What this means that when we try to project motion in ONE dimension of Euclidean Space, onto polar-Euclidean space, we have a two-fold degeneracy. We can go from 1 to -1 on the real line in either of the two ways, as shown in the attached diagram (Complex number). Physically, there are hence two roots for converting a 1 to a -1 or a -1 to a 1: i and -i! Hence the introduction of the complex number is the logical consequence of having to take a polar-Euclidean into a Euclidean 1D within unit space. Since we are always Euclidean, we perceive all motion of time region in terms of complex numbers.

We have already seen that the exponential has a relation to the "folds" of the time region. But this exponential is a one dimensional relationship. If we take a two dimensional motion, the folds are to be distributed among TWO dimensions of polar-Euclidean space. Taking the same diagram as the reference, the first fold is along the real line, the second along the complex line (the 'perpendicular' axis of the Time Region) and so on, we have:

1 + i/2 - 1/6 - i/24 + 1/120.... = 1 + i/2 + i2/6 + i3/24 + i4/120 ... = ei

This is a MAGNETIC rotation, hence a polar-2D rotation. Also, from the diagram, we can see that it is just the Turn, so we have the relation:

Turn = eix

Shift = eix1 - eix2

Translation = x

Spatial Displacement = x1 - x2

This gives us the necessary information to determine the birotation as a cos(x)/sin(x) (both are basically the same, only separated by a Turn) function as derived by Nehru and Bruce. Turn clockwise plus Turn anticlockwise gives a birotation, and two 2D turns give a 1D shift.

Another interesting property is that in the 2D turn, if we replace 'i' by 'i2', we get back the one-dimensional exponential!! So the combination of TWO 2D rotations gives rise to a 1D rotation, which we observe as the exponential.

2D Rotation: eix

1D Rotation: e-x

Nuclear region has one-dimension of time, so this could be the reason for observing the radioactive decay as a one dimensional rotation. The math can make things a bit hazy here, so please post your comments as to the physics of it.

Gopi
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bperet
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Motion in the Time Region

Post by bperet »

Looking at Gopi's diagrams, something just occurred to me, though it has been staring at me in the face for years...

To the outside observer, the time region appears 4-dimensional. Nehru documented this quite well in his papers on quantum mechanics. We also know that quaternions make for a good, mathematical representation of rotation in the time region. When I've been plotting quaternion rotations, I used the typical, 3-axis system to represent rotations about x,y,z, just as most computers do--roll, pitch and yaw. When Gopi derived rotation using the natural exponent, which included a real component, it just hit me that I've been ignoring the real axis portion of the quaternion (H) in my thinking.

H = | 1 iX jY kZ |

Which is actually:

H = | w iX/w jY/w kZ/w |

And 'w' is a scale factor (a scalar number). Put in RS terms of space and time:

H = | s/1 t/s t/s t/s |

Look at the first component, the "real" scale factor, s/1... when normalized, s=1 (For a Euclidean projection the scale must be absolute and fixed at unity). In speed, a real function, s=1 is the UNIT SPACE BOUNDARY, which means that the first component of the quaternion is EQUIVALENT SPACE. The other three "imaginary" terms are in units of energy--a distributed, scalar motion.

I realized some time ago that the concepts of "clock time" and "clock space" are just perceptual scale factors (scalars), and actually aren't associated with the space and time aspects of motion. Since we can only directly observe 'space', our consciousness must normalize any temporal displacements to fit in a "unity time", where time is all scaled to unity, for our Euclidean view of the Universe.

We see this in homogeneous coordinates, used in computer virtual reality models:

C = | X Y Z 1 | or | X/w Y/w Z/w w/1 |

In space-time terms:

C = | s/t s/t s/t t/1 |

Which is three dimensions of 'speed' (coordinate space with clock time). For us to perceive "reality" on a computer model, t=1. This last factor is CLOCK TIME, which happens to APPEAR as a 4th dimension to space. Since t=1, the denominators are ignored, giving the result of:

C = | X Y Z t |

Since t=1, our common experience is simply:

X,Y,Z -- coordinate space (since we ignore unit values).

For our consciousness to operate in the material sector, time must be a linear progression in "step measure"; every second must have the same duration as every other--the "arrow of time". In reality that is not the case, since atoms are composed of a wide variety of temporal displacements--and virtually none are unity. There appears to be a mechanism that is part of our mind that creates this illusion of constant time that we call "reality", scaling and adjusting the input from our senses so we have a clean and consistent view.

Now the SAME situation occurs regarding both the cosmic sector and the time region. I'll skip the cosmic sector for the moment, since the "illusion" there translates to metaphysical components of our experience, "ESP", siddhis, etc.

In order for us to view the atomic regions, which are non-unity motions in time (time is not constant at unity), an "inverse illusion" must be created with similar conditions--we can only observe the spatial (aka "REAL") half of a complex relationship, and clock time must be brought to the same scale as outside observation--unity.

Unlike the outside region, where distance can be scaled to account for temporal displacement, we are stuck with space=1 inside the time region. This is where the concept of "equivalent space" comes in... the "spatial equivalent of time", created by our minds so it has something to scale to adjust for the temporal displacements inside the unit of space.

But it cannot become larger than unity, so we get the appearance of fractional space, quantities less than unity, which we can now observe and measure. What we end up observing is the "real" component of the complex rotations in equivalent space, scaled by "clock space" to fit into "equivalent space".

We will never be able to observe what is "inside" an atom, because all we can observe is that "shadow" cast upon the screen of equivalent space, which is a NET motion, not the actual motion. Even if they did find a way to shoot a photon or electron into the time region and get it to return to make an image on the screen, all they would ever see is a sphere, because the coordinate time information will be lost upon exiting the time region--time HAS NO DIRECTION in space.

Gopi wrote:
Nuclear region has one-dimension of time, so this could be the reason for observing the radioactive decay as a one dimensional rotation. The math can make things a bit hazy here, so please post your comments as to the physics of it.
It is probably more appropriate to say, "Nuclear region has one dimension of MOTION", composed of the real component of the quaternion motion, observed through equivalent space (s), scaled by clock time (t). But since we are dealing with temporal displacements, the speed is always less than unity, since s=1 and t>=1, and hence "equivalent" to the observer.

When you conceptualize the time region and atomic functions, you have to think in FOUR dimensions, one "real" and three "imaginary". It really helps. The way I do it is to think of the 4 axes as the diagonals of a cube--sort of a "diagon alley" to normal thinking. (The 3-axis, "spatial" system, would extend through the centers of the faces.)

This 1-real 3-imaginary structure seems to map directly to Nehru's concepts of the Nuclear Zone (1-dimensional, the 'real' component) and the Atomic Zone (3-dimensional, the "imaginary" component).
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davelook
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Motion in the Time Region

Post by davelook »

Are the 3 dimensions of time the cause of the probabilistic nature of QM?
Gopi
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Motion in the Time Region

Post by Gopi »

davelook wrote:
Are the 3 dimensions of time the cause of the probabilistic nature of QM?
Yes... more accurately, the projection of a directional motion in time onto space would give a probabilistic distribution outside. And since we need the three coordinate dimensions to define "direction in time", you could say it follows from the 3D nature of time.

Goes back to the same concept: Direction in time has no relation to direction in space, implying probability.
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Motion in the Time Region

Post by Phillip »

Thoughts to ponder:

Random probability.

Are we just saying that we do not know the mechanistic control factors?

I am looking hard at the statement:

"Direction in time has no relation to direction in space, implying

probability."

I am thinking there is a linkage that we have not defined yet. We say

the direction of gravity and the progression reverse at the unit

boundary. Somehow photons continuos motions on one side "become" linear

vibrations on the other side. Somehow electric and magnetic motions

inside become fields outside.

Isn't probabilistic just saying there are too many uncontrolled or

unknown variables to predict with precision. So what are the

uncontrolled and unknown?

There is a relationship between time and space. We call it motion.

And the Reciprocal System is all about studying the various forms of

motion.

So I ask, is there another form of motion which we have not yet defined

that will allow us to understand the relationship between direction in

time and direction in space?

I think that maybe we have missed it because to get from the cosmic

sector with three directions of time to the material sector with three

directions of space we need three conversions as we move into and out of

the two intermediate speed ranges which separate them. There may be

three relationships instead of one, thus it appears random.

We have focused a lot on being able to make magnitudes work out, but we

have allowed the directions to be random (or defined by rules). Are we

missing something?

Isn't the Time Region just a special case of the Cosmic Sector where s=1?

And isn't the unit boundary maybe three boundaries lumped together? Maybe

if we separate out the three transitions we will see why gravity and the

progression reverse at the unit boundary, photons are linear vibrations

and maybe why we gravitate and expand in the progression?

It has always bothered me that in a universe that seems so continuos and

smooth, there would be a major discontinuity at the unit boundary. And I

want to understand how the center point of a unit of space is a plane at

infinity in the cosmic sector. Is that not a directional conversion

problem?
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Motion in the Time Region

Post by bperet »

I just made a very interesting discovery that has, so far, proved to be the ultimate answer to life, the Universe and everything... at least concerning the Reciprocal System.

I was playing around with quaternions, with their real scalar and three imaginary ones, trying to see if it made a valid description of the atom. I was working upon Larson's assumption that only ONE of the three, scalar dimensions could be represented in a coordinate reference system (ie, dimension A is fully represented, B and C just modify the magnitudes of A). I couldn't see how you could get that out of a quaternion, though, since it only has a single magnitude which would be randomly directed in space.

While fooling around with some Argand diagrams (complex plane) and the Riemann sphere (where you add the point at zero [center] and the point at infinity [counterspace infinity] to the complex plane, making a topographic sphere), the thought occurred to me that... what IF, rather than ONE scalar dimension having full representation, only the REAL AXIS of each of the THREE complex rotations was what was actually being represented?

We know in RS2 the "ratio" is the underlying motion... low and behold, if you treat a complex number in a complex plane as a ratio of real to imaginary--a slope--we have a MOTION... but it is a motion of a different sort, with one aspect real and the other imaginary: s / it

We already know that the "real" component is 'space' and the "imaginary" is time, but look what it does...

real = space = yang = rectangular

----------------------------------------

imaginary = time = yin = polar

Translation in space, rotation in time, AS A SCALAR MOTION.

This means that the three, scalar dimension can be represented as:

Xs + iXt

Ys + jYt

Zs + kZt

Where the three, real numbers are coordinate space, and the three, imaginary numbers are coordinate time. The three complex numbers, themselves, are the three, independent SCALAR motions.

I've tried running a few computer simulations with this premise, and so far, "batting 1000"... IT WORKS! The way you handle it on the computer is:

s / it

Curious thing... when t gets to 4, i4, you're back at R=1 and no angle... ever notice that the maximum magnetic rotation is 4? So far, using the Euler relations, I've been able to compute the complex wave of the electron and the wave function of the photon (as described in birotation, using the complex plane as a Riemann surface).

I decided to check out Wiki on the cross-ratio again, and found they substantially updated the article since I last read it. Curiously enough... they are now defining the cross-ratio in the COMPLEX PLANE. And they state TWO conditions that make a cross-ratio real... collinear points (points on the same line, rectilinear geometry) OR concyclic points--the 4 points falling on a circle (points on the same circle, polar geometry). Here again, that same yang/yin representation, now done at the level of the cross-ratio.

So far, EVERY simulation I have run from stuff I've done in the past, WORKS WITH THIS CONCEPT. And some unexpected things are showing up... by using "complex scalar motion", each rotation in time DOES have some representation in space--the real axis. The temporal speeds then control the spatial orientation, which gives the explanation of why atoms arrange themselves in particular ways within a molecule--the whole field of crystallography, in addition to chemical bonding.

This is VERY promising start for the virtual Universe of Motion!
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davelook
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Motion in the Time Region

Post by davelook »

bperet wrote:

s / itCurious thing... when t gets to 4, i4, you're back at R=1 and no angle... ever notice that the maximum magnetic rotation is 4? So far, using the Euler relations, I've been able to compute the complex wave of the electron and the wave function of the photon (as described in birotation, using the complex plane as a Riemann surface).

I decided to check out Wiki on the cross-ratio again, and found they substantially updated the article since I last read it. Curiously enough... they are now defining the cross-ratio in the COMPLEX PLANE. And they state TWO conditions that make a cross-ratio real... collinear points (points on the same line, rectilinear geometry) OR concyclic points--the 4 points falling on a circle (points on the same circle, polar geometry).
Not sure if this is relevant, but did you read those fascinating papers "The Euler Identity – a Radial Mathematical Interpretation 1 & 2"? I was getting ready to post on the amazing property of the "roots of unity"... the roots of unity are just the complex unit circle divided into e((2pi)/x)i equal parts!

So the 2 square roots of unity are 1, -1. or e((2pi)/2)i

The 3 cube roots are 1, (-.5+.866i), (-.5-.866i) or e((2pi)/3)i

the 4 fourth roots are 1, -1, i, -i or e((2pi)/4)i

the fifth roots form a pentagon in the unit circle, or e((2pi)/5)i

....every 1/x power of 1 has a complex form as a x-agon in the unit circle!
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Motion in the Time Region

Post by davelook »

bperet wrote:

Where the three, real numbers are coordinate space, and the three, imaginary numbers are coordinate time. The three complex numbers, themselves, are the three, independent SCALAR motions.
So, would these 3 numbers be the A,B,C magnitudes of the elements, i.e. Helium 2,1,0 Carbon 6,6,1 (or-1), etc?
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Motion in the Time Region

Post by bperet »

davelook wrote:
bperet wrote:

Where the three, real numbers are coordinate space, and the three, imaginary numbers are coordinate time. The three complex numbers, themselves, are the three, independent SCALAR motions.
So, would these 3 numbers be the A,B,C magnitudes of the elements, i.e. Helium 2,1,0 Carbon 6,6,1 (or-1), etc?
Atoms are two, double-rotating systems, which would require 6 dimensions (two sets of A-B-C). Each complex motion would be one of the letters. Carbon would be 2-1-4. There is no need for the alternate representation, 2-2-(4), since that is just counting down from the top of the staircase, rather than counting up from the bottom.

I have been running some simulations of the photon this morning. Some interesting things have shown up.

First, it looks like I need to pay better attention to my own work... a complex number treated as a ratio can represent EITHER material or cosmic, not both. (s + it) gives you rectangular space and polar time, perfect for the material structures. But the cosmic is the other way around... polar space and rectangular time. So, what apparently is need is the CROSS-RATIO:

(s + ti) : (t + si)

Where the real aspect is rectangular, and the imaginary is polar. If you want a material particle, set the second to the identity (1+0i); if you want a cosmic particle, set the first to the identity (1+0i) and eliminate the material rotation. It also allows for a structure composed of BOTH material and cosmic rotations concurrently... life unit?

Comments on the birotating photon:
  1. The REAL components of the two rotating systems MUST BE EQUAL. When they are equal, dimensional reduction occurs and the result is ALL REAL:

    eix + e-ix = cos x + i sin x + cos x - i sin x = 2 cos x

    If the real components are not equal, you don't get the dimensional reduction (+sin -sin) and motion occurs in the imaginary half resulting in a complex wave.
  2. The amplitude of the wave = 2eR. When R=0, amplitude=2.
  3. The real component CAN BE NEGATIVE! Negative values decrease amplitude. As R-> -infinity, amplitude -> 0.
  4. The real component can be fractional. The smaller the fraction, the amplitude approaches 2.
  5. The polarity of the imaginary component is the direction of rotation (phase shift).
  6. The imaginary value is the number of cycles of the wave. 0+2i gives 2 cycles.
  7. The number of cycles must be the same for both rotations, or dimensional reduction does not occur. Therefore real and imaginary components must each have the same magnitude.
  8. The frequency of a photon DOES NOT APPEAR AS SPEED, because in order to have speed, there must be a relation of SPACE to TIME, and the "time" component, the imaginary part, is dimensionally reduced to ZERO, so you end up with a relation of space to nothing.
  9. For imaginary numbers, -i = 1/i. Birotation can then be expressed in two forms:

    1) eix + e-ix

    2) eix + e1/ix

    Which is interesting, because we now have a reciprocal relationship for the complex exponent, with no negative. From this, one can conclude that:

    CW rotation = 1 / (CCW rotation)

    In other words, clockwise and counter-clockwise orientations are reciprocally related in a polar system, and that CCW is "outward" (away from unity on the Argand diagram, with increasing exponents of i) and CW is "inward" (towards unity with decreasing exponents).
Some more discoveries to follow...[/]
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