Meeting a Terrific Challenge

Discussion of Larson Research Center work.

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dbundy
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Re: Meeting a Terrific Challenge

Post by dbundy » Fri Mar 31, 2017 11:00 am

At the end of the previous comment above, I asked how we would go about writing a function to expand the zero point of the unit circle on the complex plane, in all directions over time, to π, the area of the unit circle, and back to zero. I'm sure someone much smarter than I am has already done this, but, if so, I don't know about it. It seems straightforward enough, but I may be showing my naivete.

Recall that the reason we want to do this is that we want to translate the vector motion of the LST, as used in the model of the atom, to the scalar motion of the LRC's RST-based model of the atom, which has no vector motion, but consists of strictly scalar motion.

We want to use the "complex exponential," eπi = -1, because it consists of the sum of the cosine and i times the sine, of the angle θ. This is very useful for reconstructing a sine or cosine wave over time, but it's also applicable to the scalar motion expansion/contraction of the RSt's S|T unit, since the sine and cosine of angle θ are orthogonal and thus reciprocal magnitudes, as are the S and T oscillations of the S|T unit.

However, the ratio between the angles of the right triangle, upon which the sine and cosine are based, produce four changes of sign (polarity) as the angle θ grows from 0 to 90, 90 to 180, 180 to 270 and 270 to 360 degrees, each of which are associated with the four quadrantal rotations (4 x π/2). What we want are two changes of sign (a change equivalent to a rotation from 0 to 180, and from 180 to 360), as the sphere expands and contracts, over π, in each "direction."

This requires us to view the complex exponential, eiωt, from a new perspective. Instead of viewing it as the 2π rotation cycle in the positive direction, and its negative form, e-iωt, as the 2π rotation cycle in the negative direction, where their sum is divided by 2, i.e. ((eiωt) + (e-iωt))/2, to extract cos(ωt), we should view the same thing as a 2 x π = 2π expansion/contraction cycle, over two, 2π rotations.

Of course, there is an important distinction that remains to be made between scalar motion and vector motion: Scalar motion expands/contracts in all the "directions" of a given dimension simultaneously, while vector motion changes location in one "direction" at a time.

In one dimension of scalar motion, an oscillating length for example, there are two "directions" involved (positive and negative). Therefore, the scalar expansion/contraction of the 1D diameter takes place in these two opposite "directions," relative to the point of origin. So, one cycle of 1D oscillation involves expansion/contraction along four lengths of "radii," if you will: one in each of two opposite "directions," when expanding outward, and one in each of two opposite "directions," when contracting inward.

In two dimensions of scalar motion, as in the area of the circle, however, there are four "directions" (two positive and two negative). Therefore, the scalar expansion/contraction of the area takes place in these four opposing "directions" (quadrants) relative to the point of origin. The motion takes place in all of them simultaneously. So, one full cycle, involves motion over eight "radii," if you will: over four when expanding outward and back over the same four when contracting inward.

The corresponding 1D vector motion, on the other hand, always moves a point along the length of the radius, one "direction" at a time: For example, it extends outward one positive unit, retracts inward one positive unit, extends outward one negative unit and retracts inward one negative unit, every cycle. Moreover, vector motion in more than one dimension at a time is impossible, even though separate motions in more than one dimension, may be combined, as they are in the case of the sine and cosine of e, which is actually the rotation of a complex number of magnitude one.

Vector motion along the x axis, composed of 1/2(e) and 1/2(e-iθ), when the angle θ changes over time, as ωt, is shown here, as the vector sum of two opposite vector rotations. This vector sum transits the unit radius, four times per cycle, in and out, in two opposite "directions."

I wish I could produce a similar video for the corresponding motion of the changing scalar area, but I'll have to settle for a crude animated gif to show the comparison. First, I have to explain, though, that the reason the correspondence between the 1D vector motion of rotation and the 2D scalar motion of oscillation exists is that the unit of 2π radians of the unit circle is actually a dimensionless number, which can be derived from both a 1D length and a 2D area.

The dimension of the arc length of the 2π radians along the circumference, which is used to define the radian, is, of course, the same as the dimension of the 1D radius, while the dimensions of the area sector determined by the 1D arcs are obviously the same as the area of the circle. Thus, at the unit magnitude of r, the disparity in dimensions makes no difference, and the magnitude of the rotation is simply twice that of the expansion/contraction; that is, the rotation cycle is 2π versus the 1π expansion cycle.

2πr/r = 2π and πr2/r2 = π.

Consequently, given that the complex exponential, eπi, is equal to π radians, it is also equal to the number of area units of the expanded circle, but these units have different dimensions. In terms of rotating around the circle, the complex exponential is only half way around it, at π radians. To complete one revolution of the circle, it must rotate another π radians, thus taking two π, 1D radians of rotation, to "paint" one π, 2D radians of area, if you will.

I know that it is so much more precise and scientific to explain all this in terms of the functions of calculus, which people are used to seeing, but, for me, that approach is tantamount to taking the long way around. The simple truth we need to grasp is that the ratio of the circle's area to its circumference is 1:2. Thus, the rotation around the unit circle's circumference is a distance twice the magnitude of the area of the corresponding sector that the unit radius sweeps, and, since we know that the complex exponential, in its ωt form, rotates the angle θ of the unit radius, we can think of the vector rotation, as driving the scalar oscillation (or even vice versa), as shown in the animated gif below:

Image

In the graphic above, I didn't follow the usual convention used, when plotting the sine/cosine of angle θ, by starting at 90 degrees and increasing counter-clockwise, but instead I started at 0 degrees, proceeding clockwise around the circle, and, as the graphic shows, as the angle increases, the magnitude of the 1D arc of the black circle's circumference that is transited to that point is equal to the entire circumference of the red expanding circle, during the first, 2π, rotation cycle. During the second, 2π, rotation cycle, the red circle contracts back to zero, completing one full scalar cycle.

However, since there are two, reciprocal oscillations that constitute the S|T unit, one space oscillation and one time oscillation, the associated, inverse rotation of the view of the rotation shown in the graphic above, occurs on the other side of the circle, which if we turned it around, would be rotating in the counter-clockwise "direction."

The result would be two, inverse, scalar oscillations. One is fully expanded at the beginning of the two rotation cycles, while the other is fully contracted at the beginning:

Image

The two, 2π rotation cycles associated with these two scalar expansions are not shown in this graphic, but if we were to show them side by side, one would be rotating around the unit circle in the clockwise "direction" while the other would be rotating in the counter-clockwise "direction."

The bottom line is to show that there is a correspondence between the vector motion of the LST's complex exponential, eiωt, with its inverse, e-iωt, and the two, inverse scalar oscillations of the S|T unit.

Of course, the oscillations of the S|T unit are three dimensional volume oscillations, but they can be characterized by any of their dimensional components. In this case, the 2D scalar motion is isomorphic to the LST's 2D vector motion known as a "quantity of motion," or more commonly, momentum, even though no mass or vector velocity is involved.

This is important for our theoretical development, since in our model of the atom, the space-like (negative) oscillation of the electron combines with the time-like (positive) oscillation of the proton, and there is no separation between the two, such as the all important Bohr radius in the LST model, which gives rise either to an orbiting point charge in the Bohr model, or a set of circulating electric currents in Mills' modification of the Bohr model.

With this much understood, we need to show that the 2D scalar motion of our model can be seen as the equivalent to the angular momentum of Mills' model, which will hopefully enable us to construct a scalar motion model of the atom as successful as his is.

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bperet
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Re: Meeting a Terrific Challenge

Post by bperet » Sun Apr 02, 2017 10:41 am

dbundy wrote:
Fri Mar 31, 2017 11:00 am
I'm sure someone much smarter than I am has already done this, but, if so, I don't know about it. It seems straightforward enough, but I may be showing my naivete.
Yes, the person is Prof. KVK Nehru and it is called "birotation."
Every dogma has its day...

dbundy
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Re: Meeting a Terrific Challenge

Post by dbundy » Mon Apr 03, 2017 10:10 am

There's no doubt Nehru is much smarter than I am, but I don't think his bi-rotation is a scalar motion. A scalar change, by definition, is a change in size, and rotation of a fixed size necessarily has to be a vector motion, it seems to me.

It's hard to get away from vector motion, though. Nehru wrote, "While it is clear that a SHM underlies the photon from the phenomena of interference and diffraction, the genesis of SHM, given only uniform speed (as in scalar motion), is not possible except through rotation." I disagree, of course, because, as I have already stated, rotation of a fixed radius cannot be a scalar motion, by definition.

As I have shown in previous posts, both space and time displacement from the uniform scalar motion dubbed the progression is possible without rotation. Indeed, Larson believed that the only possibility for deviation from uniform speed was the idea of "direction" reversal. His conclusion was challenged from the outset by many who believed that the introduction of the idea was not justified given no mechanism could be cited as the cause of the reversal, but he insisted that no mechanism is required, just the fact that it is something that is conceivable was enough. "What can exist, does exist," was his answer.

The trouble is, as Nehru's point of view demonstrates, the words that Larson used to describe his conclusions were easily misconstrued. Nehru wrote that Larson's "direction" reversals are incompatible with simple harmonic motion (SHM). "The speed has to be a square wave," he writes (see here.)

Larson couldn't rebut this argument, but insisted that the reversals had to be SHM. The position that the LRC research has taken is that Larson was both right and wrong: He was right about the "direction" reversals, but he was wrong about the dimensions of those reversals. They are not 1D reversals, but 3D reversals. SHM does result from a 3D oscillation, because, the motion of expansion in all directions, from a point, is exponential.

Therefore, at the end of one unit of expansion, when the "direction" reversal takes place, the change is not abrupt as in a square wave. In fact, it follows the smooth "direction" change of rotation, as shown in my previous post. At least that is the conclusion upon which the LRC research has been based.

If it's incorrect, time will tell.

dbundy
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Re: Meeting a Terrific Challenge

Post by dbundy » Fri Apr 21, 2017 8:28 am

When Randell Mills modified the Bohr atomic model, by modifying the traditional model of the electron, changing it from an orbiting point charge to a sphere of circulating charge currents, creating a shell of electric charge surrounding the proton, the vector motion equation of the new model did not change from that of the old model.

According to the webpage of Jeff Driscoll, what did change was the value of two terms in the equation of motion: The value of the electric charge, e, and the value of the radius r, as shown below:

Image

The value of +e changed to +e/n, where n is the number of the Bohr orbit, because, in Mills' model, a photon is resonating within the shell, changing the effective charge felt between the proton and the rings of circulating charge currents on the shell's surface.

The value of r is changed from Bohr's square of the orbital radius times the electron de Broglie wavelength, a0, to just the orbital radius times a0, because, unlike the orbit, the shell expands to a radius that precisely accommodates one electron de Broglie wavelength. In the Bohr model, the orbit accommodates the number of de Broglie wavelengths that will fit the circumference of the orbit, at a given radius r.

This is a crucial point, and the point where A. Rathke asserts that Mills goes astray, because the wavelength of his solution to the classical wave equation of motion cannot correspond to the classical circumference of Bohr's electron orbit. In other words, the wavelength of Mills' solution to the classical wave equation does not allow a "quantisation condition," where λ = 2πr, instead of Bohr's quantisation condition, where nλ = 2πr, according to Rathke.

I cannot follow the arguments either way, but the experimental evidence that I have seen seems to clearly vindicate the work of Mills.

If Mills is correct, then combining the de Broglie formula, where the wavelength is equal to h/mv, with the equation Mills derived from the classical wave equation, where the wavelength is equal to h/2πr, we get 2πr = h/mv, instead of 2πr = nh/mv, and this makes all the difference!

At n = 1, where the radius of the Bohr orbit is equal to one wavelength, a0, the wavelength outputs of the two equations are the same, but when n is greater than, or less than, one, the wavelength outputs of the two models are different, unless they are calculated in terms of kinetic and potential energy exchanges, according to angular momentum equal to h/2π, or h bar.

In this case, using the angular momentum, instead of the number of electron wavelengths, in the classical equation, the total energy is always the same in both models, for all values of n ≥ 1, because, the calculation of the total energy of the orbiting electron and the orbitsphere, from the sum of the kinetic and potential energy calculations of both, are equal, as shown by Driscoll.

Moreover, given the two changes (in +e and r), the n2 term in Bohr's model makes magnitudes of n < 1 impossible, so only in Mills' model is it theoretically possible to produce hydrinos, or hydrogen atoms at lower than the unit ground state.

As they say, however, "out of small things, proceedeth that which is great!" The discovery of hydrino energy, resulting from this new theory of the atom, could potentially turn the industrial world upside down. But this is not all: Mills' theory destroys the LST's theory of quantum mechanics, because it explains the dual nature of matter, which QM has struggled with for almost a century, in terms of a transformation of the electron from a sphere of charge, surrounding the proton, to a propagating planar wave, at ionization.

So, instead of matter being regarded as composed of particles that are also waves, with all the paradox associated with that assertion, the new theory regards it as composed of particles that become waves, and waves that become particles, removing the paradox.

Yet, what is iconoclastic for the LST's QM theory is great news for the ongoing development of the RST-based theory, because in our system all physical phenomena, including matter, are either motions, combinations of motions, or relations between them.

For the LST community, Mills' theory represents a quantum advancement (even though they don't recognize it yet). Nevertheless, it is still one that is based on vector motion, while the RST community knows the trouble in theoretical physics, to which that approach must inevitably lead.

In our attempt to develop an RST-based theory at the LRC, the scalar motions that constitute all the fermions and bosons of the physical universe, including the electrons and protons and photons, etc, with which we are dealing here, are considered as oscillating space and time volumes, as we have been showing. Hence, we have to somehow equate the angular momentum of the Bohr model's orbiting point masses and the angular momentum of the Mills' model of circulating charge currents, both of which are a concept construed from the 1D tangential velocity of mass, to a concept of a 2D radial change of space and time, or the motion of 2D oscillations, the 1D aspects of which are net space oscillations (negative "charges") or net time oscillations (positive "charges").

In the previous post, we were able to relate the mathematics of the 1D vector motion of oscillation to the 2D scalar motion of oscillation, which ought to enable us to relate the physics of the angular momentum of vector rotations (mvr) to the physics of the "momentum" of scalar oscillations (2πr is the derivative of πr2), even though there is no oscillating mass in the scalar model.

The implication is that the measurable properties of these scalar motion combinations stem from their intrinsic multi-dimensional character. In other words, the "mass" of these combinations of scalar oscillations is simply the magnitude of resistance to their net 3D scalar motion (s3/t3), while their "momentum" is the magnitude of resistance to their net 2D scalar motion (s2/t2), and their "charge" is merely the magnitude of resistance to their net 1D scalar motion (s1/t1).

In terms of the hydrogen atom, the proton plus the electron, the number of space and time oscillations, the Ss and Ts of the constituent S|T units, if you will, is given by the equation:

H = P + (-e) = (10/20 + 10/13 + 26/13) + (6/12 + 6/3 + 6/3) = 46|46 + 18|18 = 64|64

Adding the middle terms of the proton and electron, gives us the net of their opposite "charges" in H, where n = 1:

(10/13) + (6/3) = 16/16 = 1/1, or net zero "charge" (0 time/space displacement).

In the vector model, this net zero "charge" is represented as a balance of forces, between the outward force of the angular momentum, L, of the electron and the inward force of attraction between the opposite charges. As the energy of the orbiting electron increments one level, the magnitude of the orbital radius increases by the square, to maintain the balance, while the spherical radius increases by one, to maintain it.

Since the Bohr radius at n = 1, is a0, our task is to find the equivalent "mass," "angular momentum," and "charge" in our scalar model at that radius, assuming that the radius of the scalar oscillations, n, increases by one, as in Mills' model, not by the square, as in Bohr's model.

Of course, it appears that the two concepts are disparate and not directly comparable, because the radius of the oscillation is constantly changing, from 0 to n, in the scalar model, unlike in the vector model, where the radius is constant for a given n level.

However, since there are two, reciprocal, oscillations in the S|T units, which are inversely proportional, the combined motion of the outward radial velocity, vO, and the inward radial velocity, vI, is entirely analogous to the simple harmonic motion (SHM) of a swinging pendulum, or oscillating mass on a spring, in which the total energy of the motion remains constant, through a continual exchange of its kinetic and potential energy.

In the case of an oscillating mass on a spring, the mass is subject to the linear elastic restoring force given by Hooke's Law. The motion is sinusoidal in time and demonstrates a single resonant frequency, as shown in the HyperPhysics graphic below:

Image

In the S|T oscillation, the net magnitude of the radii and thus the net magnitude of the 2D area (2D space/2D time) between them remains constant over the time (space) oscillation. That is to say, as the radius of the space oscillation increases from 0 to a0, the radius of the time oscillation decreases from a0 to 0, and vice-versa, so that, in effect, the SHM of the scalar motion oscillation, vs, is analogous to the SHM of the oscillating mass on a spring.

If, say, 2 joules of work start the oscillation of the mass, then those two joules of total energy will continue to be transformed from kinetic to potential energy and vice versa, over time, to maintain the total of 2 joules between them, if friction, etc, are not involved. This is the basis of all LST physics. It is the basis of the wave equation, upon which Mills builds his theory of the orbitsphere:

Image

"where ρ(t, x) is the time dependent charge density function of the electron in time and space, and v is the velocity of the charge-density wave."

What is crucial for the RST community to understand, however, is that the fundamental postulate of the system, that all properties of matter are only manifestations of scalar motion, changes everything. Mass and all its derivatives in the energy group have no role in the science of the scalar motion of the material system. They are only useful, as Newton and others of the LST discovered, in the world of vector motion, where the relations of interacting particles, in different inertial reference systems, must be taken into account, according to the rules of that science.

In the theoretical world of the RST, the rules and laws of vector motion only apply when observations of physical phenomena require a knowledge of them to confirm theoretical conclusions, but RST science is not bound by them per se. This is what makes the challenge of building the science so terrific. How do we dispense with the concepts of mass and momentum and energy, as developed so successfully in LST theories, and replace them with concepts of 3D, 2D and 1D scalar motion in RST theories?

We will explore one possible approach next time.

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