Cook's New Electrogravity Theory

The NET 10 - Mach-Cook Parallel

Note: the page has directed some visitors from the Mach-Cook Parallel introduction to here. For those of you just joining, welcome to the New Electrogravity Theory (the NET). We're in mid-discussion now, so please try not to interfere with the others who are way advanced by now and don't need distractions at this point from those just joining. Ahem...

Okay, that last page involved some heavy equations. And if you're like most people and not terribly a lover of math, you probably didn't grasp, nor care for, much of that last page. Fortunately we will start this page off extraordinarily easy, as easy as one plus one. However, to do so, we are cheating a bit, as we will leave the proof of one important finding of Mr. Cook's for a later page or a later date. The reason for this is because it involves tetration techniques and homeomorphic factors that are way, way beyond anything anyone is going to want to read here. In fact, Cook even needed to submit the equations to an expert on tetration in order to prove it, which this other kind gentleman effortlessly did.

Again, we will keep it as simple as possible here in order to maintain readership only. The tetration proof will be provided later and outside the NET. Just so one understands that the final equation on this page is not ad hoc in the least; it is proven mathematically.

Let's explore some torus geometry. Like a donut, a torus has an outer radius and an inner radius. The electron travels around the proton in such a formation. The NET has their values as this, where the Inner and Outer radii are simply separated by the width of the electron.

Where B_r is the Bohr radius of Hydrogen from (5) and e_r is the electron radius from (2).

At n = 1

O_r = -5.292053... x 10^-11 m

At n = 2

O_r = -2.116737... x 10^-10 m

At n = 3

O_r = -4.762623... x 10^-10 m

Where B_r is the Bohr radius of Hydrogen from (5) and e_r is the electron radius from (2).

At n = 1

I_r = -5.291490... x 10^-11 m

At n = 2

I_r = -2.116680... x 10^-10 m

At n = 3

I_r = -4.762566... x 10^-10 m

With the Inner and outer radii known, the surface area of Hydrogen can be calculated.

Where O_r is the outer radius of Hydrogen from (101) above, I_r is the inner radius from (102) above, pi is the Irrational number equal to 3.14159..., lambda_eo is the Electron Orbit Wavelength from (11), lambda_es is the Electron Spin Wavelength from (21), -Lambda_R is the Lorentz Factor from the proton's perspective and +Lambda_R is the factor from the electron's perspective both from (8).

At n = 1

S_aH = -5.886981... x 10^-24 m^2

At n = 2

S_aH = -2.354792... x 10^-23 m^2

At n = 3

S_aH = -5.298283... x 10^-23 m^2

Which is interesting (at least to me) that we have something as hard to get a handle on as the Lorentz Factor tied in with the basic geometry or a torus.

Interesting, but...

Now we will use the exact symbols used in aerodynamics, but in this case on the much, much smaller scale. This is the beginning of the Mach-Cook Parallel. Let's begin with the pressure exerted on the electron simply for being in the Hydrogen atom. This is analogous to that of the static air pressure on an airplane without being in motion.

Where q is the Electron Charge from (1) and S_aH is the Hydrogen Surface Area from (103 & 104) from above.

At n = 1

P_s = +2.721558... x 10^4 C m^-2

At n = 2

P_s = -6.803896... x 10^3 C m^-2

At n = 3

P_s = +3.023954... x 10^3 C m^-2

Here we can begin to see once again the positive to negative switching occuring, which we hadn't see since equation (65). This shows now that we are moving back toward more electrodynamics in order to join up with aerodynamics.

And just as the air pressure changes on an airplane in motion, so too does the charge pressure for the electron as it orbits.

Where rho_i is the Imaginary Charge Density (resistance) from (40-42), V_g is the Electron Group Velocity (orbit velocity), V_gi is its Imaginary counterpart from (6 & 7) and the Integers are negative in accordance with the NET rule for Integers.

At n = 1

q_c = -2.058918... x 10^23 C m^-2

At n = 2

q_c = +8.042650... x 10^20 C m^-2

At n = 3

q_c = -3.138117... x 10^19 C m^-2

It is here that Cook was able to link up standard aerodynamics with the electron's motion.

Where V_g is the Electron Group Velocity (orbit velocity), V_gi is its Imaginary counterpart from (6 & 7), the Integers are negative in accordance with the NET rule for Integers, c is the Velocity of Light, ci its Imaginary counterpart, -Lambda_R is the Lorentz Factor from the proton's perspective, +Lambda_R is the factor from the electron's perspective both from (8), n is the Quantum Number, Chi_R is the Real Cook Factor from (19), -alphai is the Imaginary Fine Structure Constant pertaining to the proton and +alphai pertaining to the electron from (9 & 96).

At n = 1

c_p = 0.999946... (dimensionless)

At n = 2

c_p = 0.999986... (dimensionless)

At n = 3

c_p = 0.999994... (dimensionless)

Which eventually converges on one, as the electron moves away from the proton. What is infinitely more complicated to solve for is the incompressible coefficient. Fortunately, by looking at the denominator of (111) above, we see a hint to the proof that will not be shown here, as mentioned at the beginning of this page.

Where c_p is the Pressure Coefficient from (108-111) above, Z is the Mach-Cook Number (represented as M in aerodynamics), n is the Quantum Number, -alphai is the Imaginary Fine Structure Constant pertaining to the proton, +alphai pertaining to the electron from (9 & 96), Chi_R is the Real Cook Factor from (19), Lambda_R is the Lorentz Factor from (8) and the Integers are negative except the one in the Sqruare Root in accordance with the rules of the NET.

At n = 1

c_po = 0.999920... (dimensionless)

At n = 2

c_po = 0.999933... (dimensionless)

At n = 3

c_po = 0.999914... (dimensionless)

What's interesting in the above values, even though they are almost equal to one, is that whenever the electron is in even-numbered orbitals, the Incompressible Coefficient jumps up slightly. Look at the values above again. Other than that, it converges infinitely to zero as the electron moves further and further from the proton.

Now, why is Z in there? And what is it?

We want to solve for it using (114). This is the Mach Number in Aerodynamics (you know the term, "Mach three," "Mach Five," etc.), but represented as an M in those cases. In this case, however, down at the atomic level, we will call this the Mach-Cook Number Z, which does not increase at exact Integers like M. Fortunately, Jeff Cook was able to discover exactly how it does increase as the electron jumps from one orbital to the next and has provided it for others to work with.

Here it is...

Where alphai is the Fine Structure Constant pertaining to the electron from (9 & 96), n is the Quantum Number, Re (Xc (n)) is the Real part of the X-Wave from (88 & 89) and Im (Xc (n)) is the Imaginary part from (90-93).

At n = 1

Zi = alphai (dimensionless)

At n = 2

Zi = 1.032001...i x 10^-2 (dimensionless)

At n = 3

Zi = 1.263938...i x 10^-2 (dimensionless)

I cannot begin to express how beautiful that is!

Why?

Because this suggests not only that an electron passes from orbital to orbital through the joints of X-Waves, but also that an airplane does the same when it travels > speed of sound and that we too would be able to seemlessly pass the so-called limit of c without having an adverse effect whatsoever.

It suggests that Einstein was mistaken in his interpretation of his math that just because the Lorentz Factor's values become Imaginary once a mass in motion approaches the speed of light, "the speed of light therefore must be a limiting velocity." This assessment seems to not be true at all considering the above equations.

To show that in greater detail, I will now demonstrate the Lorentz Factor at the speed of sound, which we can do based on the equations above, as well as for the speed of light with the same given moving mass.

Being that the standard Mach number: M = v / u, where v is the velocity of the moving mass and u is the speed of sound, referring to equation (110) above, and that the standard Pressure Coefficient: c_p = 1 - v^2 / u^2, one can divide c_p (for all velocities recorded of our moving mass as it approaches and surpasses u by minus one and then give its square root in order to solve for the Lorentz Factor in relation with the speed of sound instead of the speed of light. The dimensions will be the same, but the signs will need some adjusting in accordance with the New Electrogravuty Theory.

Now, if we record the values of the accelerating mass at each fifty meters per second faster in its travels, beginning with 100 meters per second, when the craft surpasses u the Lorentz Factor becomes Imaginary for all values thereafter. Here are the values of this example on the Complex Plane.

Surpassing u on the Complex Plane

The first value on the Real axis closest to zero is our first recorded value at 100 meters per second, and each to the right are the next four. Then, just after breaching u, our next value is 5.025189...i, way up above our graph. Then the values descend and converge on i.

Here are the values from our example if we work from the speed of sound = 343 m s^-1:

At...

v = 100 m s^-2, Lambda_R = .304785...

v = 150 m s^-2, Lambda_R = .486283...

v = 200 m s^-2, Lambda_R = .717731...

v = 250 m s^-2, Lambda_R = 1.064562...

v = 300 m s^-2, Lambda_R = 1.804186...

v = 350 m s^-2, Lambda_R = 5.025189...i

v = 400 m s^-2, Lambda_R = 1.943695...i

Now, if we change the signs to be in-line with the NET and then ignore the Imaginary values, this is what the graph looks like...

Graph of surpassing u without considering the Imaginary values

Why, it looks oddly like that linear X-Wave in the image of the logo at the top of this page!

Yup. That's why we're even discussing this.

Now let's do the same thing for this same mass passing c, breaching the speed of light. Now consider, it is this and only this (precisely) that Einstein saw in his equations that led him to conclude that nothing can travel faster than c. And that's a solid fact. Please again note that...this is the exact same equation he used and what you are about to see is exactly what he saw that led him to that conclusion. There is nothing else beyond this in his entire theory that suggested or hinted toward what you will see. Okay?

Let's record the values of the speed of the mass at each 8 x 10^7 m s^-1, beginning with the first record at 2 x 10^7 m s^-1, and use the Lorentz Factor exactly as Einstein did, which is Lambda_R = ( 1 - v^2 / c^2 )^-1.

Surpassing c on the Complex Plane

In the same, the first mark on the Real plane just to the right of zero, actually to the right of one, is our first recorded mark. Then as the mass approaches c, the values move to the right on the Real axis.

Once c is breached, in accordance with Einstein's Theory of Relativity, the values magically appear on the Imaginary axis far north, descend and then converge.

The absolute only thing different between this and the above example with the speed of sound is that when using the Lorentz Factor for the speed of sound, the values begin at zero and end at i. In the case with the speed of light, the values begin at 1 and end at 0. Mathematically, however, the exact same distance on the Complex plane is transversed.

Isn't that a significant difference though, that one begins and ends at different values on the plane?

Not at all, in terms of a limiting velocity! It means virtually nothing, as the Lorentz Factor is a dimensionless property and it's actual values have no real bearing on the structure of the mass in travel anyway, only its magnitude, which are identical. The fact that there is no physical bearing of Lorentz contraction on an actual traveling mass was proven way back when, long before Einstein's Relativity. And then in 1959 it was proven by two physicists, one of which is one of Cook's heroes (Roger Penrose), who both proved in the same year that the Lorentz Factor only has to do with viewing angle, and many of Einstein's conversations about his math could not exactly be so. Again, nothing wrong with Einstein's math, just some of his comments about it. We are studying one of those here. However, the fact that the values converge on a different constant does suggest one very important thing in terms of how an outside observer would see things.

An outside observer listening to a high speed jet pass the sound barrier perpendicularly (from the observer) will no longer hear the sound coming from from a straight line point; rather, the sound seems to follow from behind the jet. The sound remains just as loud though as it did before the transition. In fact, no matter how fast the jet travels faster than u, the sound will not diminish in the least; it will just follow farther and farther behind it. This is because the values converges on an Imaginary one. And everyone knows that by multiplying a factor of one by any dimension has no effect whatsoever.

This is not the case, however, when multiplying a factor of zero by any given dimension. In such case, the dimension tends to cancel altogether. Thus, in terms of the Lorentz Factor at play with the speed of light, an outside observer would begin to see the craft...well, fade out.

And how fast would it fade out?

It depends upon how fast the craft is accelerating. If the plane simply crosses c and then maintains a steady superluminal velocity thereafter, the craft might appear transluscent, a bit faster: transparent--faster even more, invisible. This is exactly what the math suggests by it converging on zero instead of i. Just remember, the Lorentz Factor has no physical bearing on the craft itself from its own point of view.

So again, if we change the signs in accordance with the NET and ignore the i, we can view these values linearly.

Graph of surpassing c without considering the Imaginary values

Again the linear X-wave from the logo at the top of this page?

That's right. Same very one. Why do you think Mr. Cook studies this, 'cause it's rewarding, 'cause chicks dig it? No. 'Cause he sees the connection. And that's the only reason. It's there.

Okay, so what this says is that we can test this experimentally, right? Instead of using a radar gun to measure Length Contraction, we can simply send sonar pulses at a high-speed jet at multiple angles and measure its contraction to verify this, right?

Yes and no. In 1959, Roger Penrose also proved that Length Contraction does not actually occur as Einstein's interpretation suggested. Insetad, due to the viewing angle, as a traveling mass approaches the observer, the mass appears elongated, as it passes, skewed and when it travels away it appears contracted. But yes, this would be a very straightforward and important experiment to test.

Here's the setup for the Experiment for Determining the Validity of the Mach-Cook Parallel...

1) Acquire a small jet (easy enough), capable of traveling almost up to the speed of sound (could be a bigger challenge).

2) Record the actual length of the jet before flight (of course).

3) Acquire 3 devices to send sonar pulses through air.

4) Set up 3 flybys, one at 1/2 u, the second at 2/3 u and the last up to (or slightly >) 90% u.

5) Angle the first (a) sonar device facing the oncoming direction, one (b) pointed straight up and the third (c) angled in the outgoing direction...the devices must be stationary of course.

6) During the flybys, using sonar on multiply takes at high frequency, record the length of the jet in flight.

EXPECTED RESULTS:

1/2 u: the jet should appear slightly longer than it should be from (a), slightly skewed from (b) and contracted from (c)

2/3 u: the jet should appear even more longer than it really is from (a), even more skewed from (b) and even more contracted from (c)

~90% u: the jet should appear at its maximum elongation of the 3 speeds from (a), maximum skewed from (b) and maximum contracted from (c)

What would all this prove?

Well, if it isn't obvious by now, if the expected results occur exactly as stated, it would 1) demonstrate that the Mach-Cook Parallel is proven exactly as Mr. Cook states, 2) Enstein is absolutely 100% incorrect in stating that nothing can travel faster than the speed of light and 3) Roger Penrose is correct about the Lorentz Factor and the viewing angle.

Those are some heavy implications hanging on a very replicable experiment...just waiting to be tried!

If it doesn'tt occur exactly as expected, then there are likely two other possibilities (maybe more, but two that are obvious). If the length is constant, but indeed contracted at one speed for (a), (b) and (c), then Roger Penrose is incorrect about length contraction, Einstein is correct about it, but still wrong about surpassing c and Cook is still right about the Mach-Cook Parallel and being able to surpass c.

The other obvious possibility is that the length would turn out to be exactly the same at all speeds, the same as its actual length. This would mean Cook is completely wrong about all this, Einstein is still absolutely 100% correct about not being able to surpass c, but probably still wrong about length contraction and Penrose is probably still completely correct and certainly the awesome physicist his reputation provides for him today.

But...which will it be?

In the meantime, until such an experiment takes place, we shall now continue with the NET, and the further implications that follow in this theory.

Click here to return to the Mach-Cook Parallel Intro

Or continue or go back with the NET...