Dimensions in the Reciprocal System

[jpkira]

so time - a label - can move - in another label space .... what does that mean?

[MWells]

so time - a label - can move - in another label space .... what does that mean?

The idea is that the labels of space and time exist as numerator and denominator of a fraction in the equation of "motion". In the Reciprocal System, motion is primary. All "things" such as matter and photons or "forces" and "fields" of electricity, magnetism, and gravity are composed of motion, not the other way around. So it'd be more correct to restate "time - a label - can change - with another label space". "Motion" in the Reciprocal System is merely a change of a relation of these labels. This is a purely mathematical (abstract) device. In order to apply this device to the empirically observed domain, the units of motion within its own reference system need to be translated to the desired conventional reference system.

Any conventional reference system one can choose, for example Euclidean space with clock time or "Minkowski space" as a 4D space-time manifold, will necessarily be only a partial expression - a shadow - of the underlying constituent motion.

[PJ_Finnegan]

@Bruce





I've tried to follow the discussion above, but being a newbie I seem to lack the basic premises, so bear with me.





My understanding so far is that we can start from two spaces: the "conventional" universe we perceive with our senses and instruments (what RS calls the "material sector" or "MS"), and a "true" universe ("TU") made of three directions of scalar motion, containing if you want the "hidden variables" of a Bohm-esque universe. There's also a third space, the "cosmic sector", but for the time being we can ignore it.





My questions are:





1) The 3 axis in the TU are not continuous (in the real numbers domain) but only contain discrete quantities, i.e. the possible s/t values for each of the 3 dimensions of motion. So along each "s/t" axis are only defined the points 1/n in the (0,1] interval (s/t=1/n) and the points "n" in the [1,infinite) interval (s/t=1/(t/s) and being the possible values of t/s=1/n, s/t=n). Is that assumption correct?





2) When the postulates of RS state that the universe is Euclidean, do they refer to the MS or the TU?


If they refer to the TU, it simply means that the 3 motion directions in the TU are orthogonal "axis" (i.e. their dot product is null)? It wouldn't make sense because the Euclidean space by definition is R^n and its metric (dot product) is defined over real numbers, not discrete quantities like we find along the 3 TU axis.


If they refer to the MS, do they mean that its 3 space dimensions are Euclidean, or that its 4 dimensions (3 space + 1 time) are? Because as you surely know, in the Relativity Theory, the MS is modelled as a 4-dimension Riemann manifold with non-Euclidean (Minkowski) metric, so definitely not Euclidean.





3) A point in the TU (identified by its coordinates in the 3D space defined by the 3 scalar motion directions) is univocally mapped, or "projected" if you want, to a "location" (a 4-coordinate point, 3 spatial + 1 temporal) in the MS? My understanding so far is that a point in the TU identifies a displacement from the unit speed of 1 along each of the 3 motion axis, defining not a location in the MS but a TYPE of particle (or force?) in it. (BTW how is it possible that a point in the TU identifies both a particle type and a force?)





4) The "natural progression" or "natural reference system" the RS talks about is in the TU or in the MS? If it was in the TU it would be a simple, static sphere of radius 1 (s/t=1 along each of the 3 motion axis), but you seem to treat it like an expanding sphere (at the speed of light) in the MS, on which the galaxies and thus all observable matter is located, so it seems to be in the MS. But if all the MS's matter is on this "natural reference system", how is it possible that gravity pulls the matter towards the center of this expanding sphere like the RS states? Besides, the experimental astronomical evidence claims that the observable universe expansion is accelerating, meaning that the "balloon" is currently inflating at a fraction of c.

[bperet]

1) The 3 axis in the TU are not continuous (in the real numbers domain) but only contain discrete quantities, i.e. the possible s/t values for each of the 3 dimensions of motion. So along each "s/t" axis are only defined the points 1/n in the (0,1] interval (s/t=1/n) and the points "n" in the [1,infinite) interval (s/t=1/(t/s) and being the possible values of t/s=1/n, s/t=n). Is that assumption correct?

If by TU you are referring to the scalar dimensions (three ratios that form the projective invariant of the system), then it does not have any axes because it has no inherent geometry. The magnitudes in the numerator and denominator of those ratios (dimensions) are the whole, counting numbers, 1..n, where "n" is always finite--there is no zero nor infinity.

Larson always fixes one aspect at unity and varies the other, so the ratios are always in the form of 1/n or n/1. Because there is no geometry, it does not matter which aspect (numerator or denominator) is named "space" or "time" at this point. All that matters is that an invariant, cross-ratio of 1:1::s:t is being defined that can be used to project into the material or cosmic coordinate systems.

2) When the postulates of RS state that the universe is Euclidean, do they refer to the MS or the TU?

Refer to the diagram I made in: RS2-102 Fundamental Postulates (last page). Since "Euclidean" is a type of geometry, and the TU has no geometry, it therefore refers to the consequences drawn from the second postulate to define the MS and CS. Coordinate relationships are Euclidean (Larson included this because of all the non-Euclidean theories that were coming out when he was publishing his books.)

3) A point in the TU (identified by its coordinates in the 3D space defined by the 3 scalar motion directions) is univocally mapped, or "projected" if you want, to a "location" (a 4-coordinate point, 3 spatial + 1 temporal) in the MS? My understanding so far is that a point in the TU identifies a displacement from the unit speed of 1 along each of the 3 motion axis, defining not a location in the MS but a TYPE of particle (or force?) in it. (BTW how is it possible that a point in the TU identifies both a particle type and a force?)

I'm confused by your use of "point." To get a location, you need a projective plane to establish a coordinate system (or in a 3D+T system, a "projective volume"). The TU has no such assumption. All it has is magnitude. Only a single, scalar dimension (ratio) can be projected into a coordinate system as a structure (photon, particle or atom). The structure then has the property of "location" in the coordinate system. The 2nd and 3rd scalar dimensions then modify the behavior of the projected dimension, adding behavioral properties.

Regarding "force"... see the topic: Force and Force Fields. (Old topic, but still applicable.)

4) The "natural progression" or "natural reference system" the RS talks about is in the TU or in the MS?

The progression is just a scalar expansion at unit speed (the speed of light). It defines the datum of measure (1/1) that forms the "end of the tape measure" to which we measure displacements. It is not a thing unto itself--just a property of the Universe to want to fly apart at the speed of light.

Astronomers had to invent "dark energy" to account for this natural property of scalar motion. But there is no actually energy there (a non-unit displacement of t/s)... that's why they will never find it.

If it was in the TU it would be a simple, static sphere of radius 1 (s/t=1 along each of the 3 motion axis), but you seem to treat it like an expanding sphere (at the speed of light) in the MS, on which the galaxies and thus all observable matter is located, so it seems to be in the MS. But if all the MS's matter is on this "natural reference system", how is it possible that gravity pulls the matter towards the center of this expanding sphere like the RS states? Besides, the experimental astronomical evidence claims that the observable universe expansion is accelerating, meaning that the "balloon" is currently inflating at a fraction of c.

Not exactly... to understand how the progression behaves in a coordinate system, take a grid of points separated by unit distance (units don't matter, inches, cm, etc, just as long at they are 1 unit apart). Now "progress" the system by doubling the distances between the points. Now if you've stretched your ruler along with the graph paper, doubling the length of the ruler as well, you will find that all the points are still one unit apart, because the mechanism with which you were measuring that distances also "progressed."

Gravity does the opposite, it is a net, inward motion at the speed of light, so it wants to half the distance for each step of the progression. That gives the appearance of all the points pulling together.

Now there are two "levels" to gravity that Larson does not make clear. In his system, the first level of gravitation (inward motion) is the direction reversal, that neutralizes the outward progression. In other words, the progression doubles the distance, and the reversal halves it... 2/1 x 1/2 = 1/1 -- no change. Then he takes that "line" formed by the direction revesal and does a "inward scalar rotation" on it, to get that 2nd unit of gravity, so you end up with 2/1 (progression) x 1/2 (reversal) x 1/2 (inward rotation) = 1/2 -- everything wants to move towards everything else.

Combine these outwards and inwards motions and you get the appearance of "force"--though no two objects are actually pushing or pulling on each other, any more than two cars on the Interstate, heading towards each other, are being pulled together by the individual masses of the cars. It is just inherent velocity--in the scalar sense of inward/outward, rather than along a vector.

Besides, the experimental astronomical evidence claims that the observable universe expansion is accelerating, meaning that the "balloon" is currently inflating at a fraction of c.

Considering that their telescopes cannot see further than 357 light years, probably true... see topic: Visibility of Stars and Galaxies (Problem).

[PJ_Finnegan]

(sorry but I don't know how to quote other posts, so I'll put them in bold+italic)

I'm confused by your use of "point." To get a location, you need a projective plane to establish a coordinate system (or in a 3D+T system, a "projective volume"). The TU has no such assumption. All it has is magnitude.

I was trying to model the TU as a vector space, containing discrete points having the 3 dimensions of motion (w₁, w₂, w₃) as their coordinates, in order to conceptually map one TU discrete point/vector to another point in the MS "continuum" (which is probably also discrete because of the Planck's space and time quantizations).

But if the RS claims that one motion dimension is enough to have a corresponding point in MS, there must exist formulas projecting a scalar into four scalars, as follows:

x = f₁(w₁)

y = f₂(w₁)

z = f₃(w₁)

t = f₄(w₁)

and a fifth formula giving the particle type, depending an all 3 motion coordinates:

p = f₅(w₁, w₂, w₃)

or just the latter two:

p = f₅(w₂, w₃)

where (x,y,z,t) are the MS coordinates and p would ideally be a natural number giving the particle type, i.e. 0=photon, 1=electron, and so on. These "hardwired" formula would be pretty crucial to the theory.



Does the RS provide them and if so, what are they?



Coordinate relationships are Euclidean (Larson included this because of all the non-Euclidean theories that were coming out when he was publishing his books.)



This may be true for the 3 spatial coordinates, but not for the space and time coordinates considered together. The problem with the 3D space + independent 1D time model is that it pre-dates the Relativity Theory (even the special one) and brings us back to the Galileian/Newtonian universe where time is independent from space. Einstein's SRT (even Lorentz transformations alone) showed that this is not the case, but time and space are strictly entwined, the space/time coordinates transformation between two inertial coordinate reference systems being t₂= f(x₁,y₁,z₁,t_1,v), where v is the relative speed between the two origins. If you model the MS as a 4D coordinate system as the RT does, the metric tensor is not a diagonal unit matrix, so the space is not Euclidean. Maybe Larson only referred to the 3D coordinates, but I don't see the practical utility to revert to the Newtonian/Galileian model.

Not exactly... to understand how the progression behaves in a coordinate system, take a grid of points separated by unit distance (units don't matter, inches, cm, etc, just as long at they are 1 unit apart).

What is confusing is that Larson does an example of the galaxies being on this "natural progression". They lag behing instead, due to gravity. The natural progression should then be the "outer limit" of the MS, an unreachable sphere which started to expand a light speed since the begininng of the Universe?

Considering that their telescopes cannot see further than 357 light years, probably true

I thought that the farthest object seen by Hubble was billions of light years away... at least according to this article.

[PJ_Finnegan]

So given the lack of response I must assume there are no such formulas. I would be surprised of the contrary: I don't think it's matematically possible to find formulas projecting a discrete domain into a rational codomain.

Too bad, I wanted to believe that Larson was really onto something. Maybe he had some valid intuition but I don't think his theory is usable for practical purposes as of now.

[Horace]

Points don't exist in "TU" as you call it it, they are created later in the development as multiple motions are related to each other.

Wait for the the migration to phpBB software, like I am. You'll get your answers then.

[PJ_Finnegan]

I reckon the TU is made of 3 discrete directions of motions. Every direction can assume the values {1/N, N}, whose cardinality is 2N (non-zero natural numbers), i.e. 2N "points". This would be the domain of 4 mysterious functions projecting the 1st direction to a point in the 4D continuum, that is a codomain in R^4 (signed reals).

I don't think it's mathematically feasible to project 2N to R. And if it was, I'd be curious to know what these functions are.

[Horace]

I reckon the TU is made of 3 discrete directions of motions. Every direction can assume the values {1/N, N}, whose cardinality is 2N (non-zero natural numbers), i.e. 2N "points". This would be the domain of 4 mysterious functions projecting the 1st direction to a point in the 4D continuum, that is a codomain in R^4 (signed reals).

Before you get to mapping 3 dimensions of scalar motion, it would be prudent to do a 1D case first.
Are you ready to project a 1D direction into a point in R²? Do you think that projecting a direction to a point even can be done or makes sense?

[dbundy]

This is an interesting discussion, but to reach the correct solution, we
have to start from the correct premise. The set of all possible motion
ratios, defined as s/t or the inverse, t/s, like the set of rational
numbers, has only three properties: Dimension, "Direction" and Magnitude.

In a three-dimensional universe, only four dimensions are possible: 0,
1, 2 and 3. There are only two "directions" possible, greater-than one
and lesser-than one. Consequently, all magnitudes that are members of
the set extend from (1/1)³ to (1/inf)³ and (inf/1)³.

That's the starting point. If we don't start there, nothing else matters.

Larson's first assumption was that the motion s/t = t/s = (1/1)³, as a
uniform expansion, or progression, could only deviate at some "point" in
time or at some "point" in space, if a reversal of "direction" in the
progression of one aspect or another of the uniform motion occurred.

Such a reversal in one aspect or another of the uniform progression,
creates a space or a time displacement in the uniform motion at that
"point." Depending upon which aspect is constantly reversing, the
resulting displacement equates to a discrete motion, which is either
lesser than unit progression, or greater than unit progression, at that
"point."

The second assumption he made was that such a constant reversal in the
time or the space aspect of the universal progression at some "point"
occurred only in one dimension of the motion, separating the resulting
entity from the progression in the remaining dimensions. Larson
identified this entity with the observed photon, something that several
of his followers could not reconcile with the known behavior of photons.

Nehru suggested the bi-rotation model of the photon, which Peret and
Gopi have further developed, by taking a closer look at the properties
of geometry, eliminating the need for reversals in the progression at a
given "point." My approach is to keep Larson's assumption of reversals
and follow the properties of numbers, assuming that a reversal in a
three-dimensional progression, would be three-dimensional, not
one-dimensional.

In this case, the time displaced entity, s/t = (1/2)³, progresses
(increases) only in time, while the inverse of this entity, s/t =
(2/1)³, progresses (increases) only in space, since, in each case, the
reversing aspect neither increases or decreases, like a soldier marching
in place, while the reciprocal aspect continues to increase (progress)
normally.

However, the reciprocal, or orthogonal progression of these respective
entities introduces the possibility that they could collide and thus
combine. We label such a combined entity as an S|T unit, progressing
both in space and time, as does the observed photon.

Now, whether or not the above development defines functions to project
rationals into a R⁴ codomain or not, I cannot say, but I can say that no one has ever
confronted me with an argument of logical fallacy, regarding it.

Let me just add the observation that, given the above development, these
S|T units can be logically combined to form more complex entities in the
what Larson called the stationary coordinate system. In fact, in the
case of a combination of three S|T units, combinations of these discrete
units of scalar motion form entities corresponding to those of the
legacy system of physical theory's first family of particles in the
standard model of particle physics. Further combinations lead to the
elements of the periodic table.

With the formation of these physical entities, the points of a
stationary reference system are realized: The distance between two such
entities, forms a line; the area bound by three, not on a line,
forms a plane; and the volume contained within four, or more, not on a
line or a plane, forms a ball. The science of Euclidean geometry
follows from there.

What Larson accomplished was simply phenominal, and he did it by
redefining the nature of space and time, just as modern physicists are
recognizing the need for it. Now, thanks to Larson, we can understand
space, the distance between the positions of objects within the
stationary coordinate system, as nothing less than the history of the
motion of those objects, which can only be measured by reproducing the
motion that separated them; that is to say, neither space without time,
nor time without space, can be measured.