and c = (the square root of -1)
By Conrad J Countess

Work in Progress - Last edited (12/9/08)

E=mc² tells us that energy and matter are equal, related through mathematical conversion factor, (c²). This geometrical interpretation gives the equation physical form, and illustrates how energy equals and turns to matter by acquiring a circular and/or spherical configuration. 

These findings coincides with Compton's, and de Broglie's, (E=hf=mc² ) which indicate a smooth transition from EM waves to matter particles, (photons to electrons) along the same EM spectrum when momentum is high enough.

 

http://www.karlsen-particle.com/page/24213/

These also coincide with Bohr's idea that the wavelength of electron is equal to the circumference of a circle whose energy is equal to mc² and that it has angular momentum of an integer multiple of h/2pi or H-bar This indicates wavelength  = (r or radius x 2pi) = (h x 2pi) = (c x 2pi).

 

http://www.colorado.edu/physics/2000/quantumzone/debroglie.html

This indicates wavelength  = (r or radius x 2pi) and (r) may be an experimentally verifiable measurement.

What I will do here is to give a geometrical demonstration of how a wave turns into a particle by acquiring circular and or spherical motion, thereby also demonstrating how E=hf (the equation for EM waves) = E=mc²(the equation for matter) or (E=hf=mc²), at the level of electron/positron,

and Bohr's idea of how the wavelength of electron = circumference of circle as I show how a wave turns into a circle and sphere.

Also I will show how a backward spinning ,standing spherical wave, making two rotations in order to complete one wave cycle, logically and geometrically emerges from this .

This is the current description of an electron which is said to get its -1 charge from its backward spin. This and another geometrical description of (), arrived at independently by another source which I reference, and which coincides almost exactly with my description of c², prompts me to state that c =. To state it more accurately, [(c) is the natural unites square root of the natural unite (-1)].

 Based on the analogy that (a line of 1 inch in the horizontal direction), times (a line of 1 inch in the 90 degree angular or vertical direction) equals (a square inch), I theorized that (the speed of light in the linear direction) times (the speed of light in the 90 degree angular direction) equals c². As it turns out  a geometrical analysis of this revealed that this would lead to a 90 degree arc which if constant would create a circle from a 2D wave, furthermore which if the amplitude is constant would be folded in two to create a sphere , or a sphere from a 3D or circular polarized wave, of the exact same measure. One configuration of the sphere directly matched the description of an electron, (a backward spinning standing spherical wave, making 2 rotations in order to complete one wave cycle), and the other configuration matches description of positron. And thus c² might be considered c circled or c sphered and we will look at both circle and sphere and c = as stated above.

The way all this evidence came so smoothly together cannot be just coincidence as the more coincidences involved, the more probable that it is correct, and is just one more mathematical support for this idea, a statistical one. In other words, the more coincidences there are - the more likely it is not just a coincidence but actually fact.  

 

Geometrical illustration of c²

In this context, c² means c in the linear direction, for instance horizontal, times c in the 90 degree angular or vertical direction .

This is analogous to a horizontal line times a vertical line of equal measure = a square. Illustrated below

Two equal forces such as a centrifugal and centripetal force, at a 90 degree angles to each other, exerted upon a planet, or satellite, or  an object attached to a string will create orbital or circular motion. Sometimes circular motion is referred to as (v²) as in (a=v²/r) formula for acceleration of circular motion and thus a=c²/r or a=c²/c, would apply here to energy in circular motion.

The above graphic illustrates energy traveling at c along a 90 degree arc which if constant creates a circle. The arc is drawn between two equal lines of force at 90 degree angles to each other represented by the same 2 lines which can also create a square like the very first graphic. These two forces represent what is called the centrifugal and centripetal force balance that creates circular motion.

Is there any experimental evidence that electromagnetic waves carry momentum which can cause circular motion if 2 forces are at 90 degree angle to each other?

Yes see this:

“Light is an electromagnetic wave that can carry angular momentum by way of circular polarization. Transverse waves such as light, can have polarization in two directions, "left-right", "up-down" or any combination thereof. As an analogy, you can shake the end of a slinky up and down, left to right, or at some arbitrary angle. Linear polarization occurs when these two components occur in phase, e.g. you shake the end of your slinky back and forth along the same path. When the two components are of equal amplitude but 90 degrees out of phase, however, circular polarization is created. This is what happens when you shake the end of your slinky in a circular motion.” From website: http://www.physlink.com/Education/AskExperts/ae694.cfm,

We might extend the above logic base on experimental evidence to include that two similar components in the up/down and back/forth or x and y planes of equal amplitude and 90 degrees out of phase, may cause circular motion, along the x and y plane just as I have suggested. And that when this occurs in all three dimensions or x-y -z planes, that this might cause a 3D standing spherical wave. Perhaps experiments along the same lines as that mentioned on above web site will bear this out.

 

 

 

	Ground State Dark Energy moving at c represented by one dimensional line moving to the right along the x axis This represents expansive centrifugal force moving away from a center at the speed of light as space between origin and destiny of photon expands. Exerts centrifugal force related to energy of c or E=h*1. Represents Ground State Dark energy, Cosmological Constant and energy of h or Planck's constant before frequency is factored in. According to Newton, when something moves at a constant rate in a straight line, it is like not moving at all. And so c=h from this perspective, can be considered the (rest frame of the universe), from which all waves and rest mass particles emerge once energy is added to this.
	The Beginning of Gravity All added energy to this basic centrifugal force of c = h goes into frequency as waves that extend at a right angle or along the y axis in this case as contractive centripetal force, which increase in energy and mass as frequency increases, in quantum increments of E=hf/c2 or E=m/c2, as divisions of c2. Exerts combination of centrifugal and centripetal force related to energy of hf or a division of c2, in direction of motion, depending on frequency. Gravity is said to be equivalent to acceleration, which is any motion that deviates from a straight line at constant speed. Waves as well as gravity emerge from this deviation, which is acceleration.
	What is length of last photon before rest mass? When energy moves in the x direction the same distance at the same time as it does in the y direction it is moving at c2 represented by the wave inside the red square and moves from the bottom left corner of the square to the top right corner. The wave to the left represents a wave at c2 that does not attain rest mass because it continues to move at c along the x axis and should not be permitted. Last photon wavelength must be a wavelength longer than this 2 square long wave. It should be 4 squares long, which as we will see is 4 spherical electron diameters long, which is also equal to 4 times the amplitudes of the wave.
	2D Approximation of Rest Mass If energy swings up from the bottom left corner of the red square at the velocity of c2 its momentum should carry it over the top enabling it to make a backward circular motion and attain rest mass if the backward motion counter balances the forward motion of c and also gives the energy a more equal distribution around a center of rotation. The energy influenced by two equal forces such as a centrifugal and centripetal at 90 degrees to each other follow a 90 degree arc which if constant creates a circle  This represents what I think is analogous to energy moving at c2.  I think that at this point h/2pi and c2 share some form of intimate relationship because they are both energy in circular rotation. Notice how large circle of energy is compared to square. If amplitude is kept constant confined by square, it would take 2 rotations to complete 1 wave cycle. Sense amplitude is twice as high it is like 2 waves stacked on each other   Is there any experimental proof that an electromagnetic wave has momentum? Yes, see this. http://www.physlink.com/Education/AskExperts/ae694.cfm,
	Formation of a Standing Spherical Wave If the large circle is confined to the square, or we begin with 3d circular polarized wave, we could get a backward spinning, standing spherical wave, that makes 2 rotations in order to complete 1 wave cycle just as indicated above. This fits the description of an electron which is said to make 2 rotations in order to complete 1 wave cycle and get its -1 charge from its backward spin being counter to its trajectory. One could also get a forward spinning wave with positive charge or (positron), in some cases. This along with the description of (the square root of -1,) in book entitled, “The Story of The Square Root of -1”, which states that the geometrical description of the (square root of -1) is (1 unite vector at a 90 degree angle to the primary vector, creating a 90 degree counterclockwise rotation which matches my description of c2 prompts me to conclude that c = (square root of -1)
Notice that the length of the square, (which is also the length that light travels in the linear direction and /or the 90 degree angular direction in order to create the 90 degree arc), is equal to the radius of the circle. Sense (circumference of a circle) = (radius x 2pi) This geometrical illustration coincidences with Bohr's idea that wavelength of electron = circumference of circle with angular momentum of integer multiple of (h / 2pi). (circumference or wavelength = r x 2pi) = (c x 2pi) = (h x 2pi) which is the inverse of Bohr's (h / 2pi)	Imagine that the large circular waves to the left  is confined to the square because the amplitude is kept constant. It will be folded in two and forced to make two rotations in order to complete one wave cycle. The combined diameters of the two smaller circles equals that of the larger. The combined circumference or wavelength of the smaller circles, equals that of the larger. This is because circumference  = (diameter x pi) = (r x 2pi). The wavelength making two rotations might equal(1/2d +1/2d  x pi), while larger circle = (1d x pi).
One can also see from this view that the 90 degree arc, which if constant creates a circle, can be formed from two lines at 90 degree angle to each other, just as the square can. This demonstrated geometrically how the (speed of light squared) can be interpreted as (the speed of light circled)	If we consider this circle with a cross in it to represent the 2 circles above facing us edge on, one spinning left to right in the horizontal (x and z) plane and the other spinning up and down in the vertical (y and z) plane, while simultaneously rotating backwards along the x, y plane, this could represent a standing spherical wave that spins backwards counter to its trajectory, giving it a -1 charge, and making 2 rotations in order to complete one wave cycle (spin 1/2). This is the current geometrical description of an electron.

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An excerpt from:

An Imaginary Tale: The Story of the Square Root of -1
by Paul J. Nahin

page 53 paragraph  2: 
“square root of -1 is directed line segment of length 1 pointing straight up along the vertical  axis
or at long last, [i = = 1 ∠ 90 degree angle]
This is so important a statement that it is the only mathematical expression in the entire book that I have enclosed”
page 54 paragraph 2:
“multiplying be square root of -1 is geometrically, simply a rotation by 90 degrees in the counterclockwise sense
Because of this property square root of -1 is often said to be rotator operator, in addition to being an imaginary number.”

page 104 paragraph 2:
“In a revealing article criticizing Einstein's and Minkowski's c , a national bureau of Standards physicist admitted that

Square root of -1 has a legitimate application in pure mathematic, where it forms a part of various ingenious devices for handling otherwise intractable situations”

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From: http://mathworld.wolfram.com/MinkowskiSpace.html:

Minkowski space is a four-dimensional space possessing a Minkowski metric

Alternatively (but less desirably), it can be considered to have a Euclidean metric but with imaginary time coordinate , where is the speed of light, by convention is normally used, and i is the imaginary number . Minkowski space unifies Euclidean three-space plus time (the "fourth dimension") in Einstein's theory of special relativity.

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From: http://web.archive.org/web/20030410200416/www.virtualchaos.org/science/apndx.html:

MINKOWSKI'S FOUR - DIMENSIONAL SPACE
("WORLD") [Supplementary to Section XVII]

We can characterize the Lorentz Transformation still more simply if we introduce the imaginary sqr(-1) times ct in place of t as time-variable. If, in accordance with this, we insert

• x 1 = x

• x 2 = y

• x 3 = z

• x 4 = imaginary sqr(-1) times ct

• 
  

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From: http://web.archive.org/web/20030224085925/www.virtualchaos.org/science/sqrt(-1).html:

The Square Root of Negative One
Virtual Chaos

"With the opening simplification, we can now treat the time dimension in the same way as we treat the space one. The expression ct is the amount of space that light can travel[c] in a period of time[t]. This means that an amount of time can be given as a spatial length, as long as we multiply it by the square root of negative one.

Understanding the significance of this imaginary number would link space, time, matter, energy, gravity, and inertia, all to a single unit of conversion."

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If c² or (c in linear direction, x c pointing straight up in 90 degree angular direction), creates 90 degree counter clockwise rotation or arc, and if this is also what creates a backward spinning, standing spherical wave, such as electron of -1 charge, than (c = ), and Einstein's and Minkowski's, (ct x ),( )and (c )=  energy in circular and /or spherical rotation with rest mass and also = (E=mc2)

From this we see c² to be the (single unite of conversion), (mathematical conversion factor), or more accurately, (geometrical conversion frequency), between all the above space, time, matter, energy, gravity, and inertia, including charge, as it seems to be the natural cut off frequency, eliminating need for renormalization, and running coupling constants problem, and also unifying "Special Relativity" and , "General Relativity" as "Lorentz contraction", turns to space-time curvature on Quantum level and unifying "Quantum Theory", as EM waves turn matter particles, demonstrating that the EM spectrum is also the energy/matter spectrum. Both waves and particles have same cut of frequency of c², which eliminates both infinite frequency for EM waves and matter waves.This is also a quantum gravity theory. This is because waves are said to cease to exist when the wave is shorter than the atomic or molecular graininess of the medium that it is traveling through. This may indicate that space-time is grainy at this level. And sense we know that the EM wave really doesn't cease to exist but only changes form, other waves that we once thought to cease to exist like sound waves in air or water may not either, but merely began to rotate at the speed of sound squared, thereby escaping detection, and this should happen at the level of the air or water molecular length scale, depending on the propagation medium, air or water. 

If waves cease to exist at level when shorter than medium of propagation than all waves when squared to create circular motion may be a measure of this level and vise verse.

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From: http://en.wikipedia.org/wiki/Mass-energy_equivalence

Under section:

mass velocity relationship

"E=mc2, which is a sum of the rest energy m0c2 and the kinetic energy. This total energy is mathematically more elegant, and fits better with the momentum in relativity. But to come to this conclusion, Einstein needed to think carefully about collisions. This expression for the energy implied that matter at rest has a huge amount of energy, and it is not clear whether this energy is physically real, or just a mathematical artifact with no physical meaning.

under section:

Low-speed Expansion   By considering the emission of energy in different frames, Einstein could show that the rest energy has a real physical meaning."

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Einstein needed proof that c2 had real physical significance and was not just a mathematical conversion factor. He got that proof.

This geometrical description goes a step further to suggesting that c2 is an actual conversion frequency/wavelength at high end of EM spectrum where energy turns to matter by acquiring a circular and or spherical configuration and therefor provides more information than just the equation alone.

Conrad J Countess

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Latest evidence on geometrical structure of electron from site: http://www.youtube.com/watch?v=ofp-OHIq6Wo&feature=related

entitled: Scientists in Sweden film moving electron for the first time.

It resembles a elongated standing spherical wave, rotating about two axis, fitting description which I have geometrically demonstrated, as opposed to a point particle or probability wave.

If my geometrical description is correct, the diameter of the electron should be equal to full amplitude (positive and  negative), of last photon before rest mass in (gamma ray range). And also equal to 1/4 its wavelength, as I have also geometrically demonstrated.

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References:

http://www.encyclopedia.com/topic/centripetal_force_and_centrifugal_force.aspx

http://www.mathpages.com/home/kmath633/kmath633.htm

http://math.ucr.edu/home/baez/physics/General/Centrifugal/centri.html

http://webpages.ursinus.edu/lriley/courses/p111/labs/node5.html

http://www.davis-inc.com/physics/

http://www.britannica.com/EBchecked/topic/130389/Compton-wavelength

http://www.virtualchaos.org/science/sqrt(-1).htm.

 

(C squared) = (C circled) and (c = square root of -1)

What are the implications of this discovery?

By Conrad Countess

When I first introduced this idea to different physics groups including this one, (sci-physics), I got mostly negative response. Most did not permit me to post, saying that it ran counter to the accepted ideas in physics. I was not upset though, as in fact I was glad that I had discovered something new that no one else had ever thought of before, as far as I could tell from their outraged reactions. Thankfully this group let me post, and for that I am grateful. And won't it be nice when the truth of the idea is finally acknowledged, and not only will I get credit, but so will this group for taking a chance on mavericks like some of us.

I've learned so much since I've been posting on this site. Some of the members have scolded me as though I was a child, because as a self taught student of physics, I did not know some of the first year physics definitions and terms taught in the formal setting, like velocity means "speed and direction", not just speed, as it does in the ordinary world; or acceleration means "any deviation from a straight line of constant motion", which include turning, speeding up, or slowing down, instead of just speeding up as it does for the average driver, although I did take a Physics 101 course in college years ago.

I learned a lot from them and I hope that they learned a lot from me also. For instance, all great discoveries don't come out of the universities, or by following established lines of thought..

Case in point: The idea that "frequency is infinite", stops some physicist from looking for a high energy cut off frequency, which I found at c^2. The "infinite frequency", idea came out of "the black box experiment", which assumed that vibrating electrons, that cannot even vibrate at the speed of light, can produce infinite vibrational frequency. This led to an idea called "the ultra-violet catastrophe". See these:

http://en.wikipedia.org/wiki/Ultraviolet_catastrophe

:http://www.colorado.edu/physics/2000/waves_particles/wavpart4.html

Besides being counter to the idea of the quantum, which sets a limit to size, and should include frequency/ wavelength, it also leads to the idea of infinite energy, within the infinitely small space. This is probably where some of the "Black Whole", and "Big Bang", ideas come from. The idea of infinite frequency, also appears in quantum physics concerning matter particles, which include electrons. It seems very contradictory for quantum-theory, which  presupposes a smallest energy limit, not to presuppose a smallest energy wave and frequency cut-off also. Not doing so has led to a problem called (renormalization and running coupling constants), that some say plagues quantum physics.  But if the speed of light is a limiting factor it should affect frequency speed also. As it turns out it does, and frequency converges to (c^2) which is rest mass,  not diverge to (v^2) interpreted as infinity in black box experiment. And so we have a natural high frequency cut off where energy turns to rest mass namely the (electron/positron) and naturally leads to coupling constants, (charge), (mass), (length), and so on, that are stable and don't run.

The possible elimination of the renormalization problem, that is said to plague quantum physics, may be one of the greatest uses of this discovery.

http://en.wikipedia.org/wiki/Renormalization

http://www.pha.jhu.edu/~blechman/papers/renormalization/

http://math.ucr.edu/home/baez/renormalization.html

Although I admitted that the speed of light is a limiting factor it is not the highest speed. That is another obstacle. The speed of light in vacuum may be the highest in linear direction but not when frequency is factored in. Higher frequency has higher kinetic energy and this energy comes from higher speed manifested in "higher cycles per time unite". According to vector addition the total speed of the wave should include not only the linear speed of c, but the angular speed as well, which raises the speed of higher frequency above that of lower, and gives it its higher kinetic energy.

When frequency is taken into account, the speed of light varies according to frequency and c^2 is revealed to be a frequency at high end of EM spectrum where energy turns to matter because it takes on a circular and /or spherical configuration. It is a true demonstration of E=hf=mc^2, as the point on the EM spectrum where electrons and or positrons are created. I was talking to a friend and fellow poet "Juanita Jackson", and she mistakenly called the (EM spectrum), the (energy/matter spectrum). I corrected her and politely stated that it means (electro-magnetic spectrum). But than I corrected myself and stated that she was also correct in calling it the (energy/matter spectrum) as the revelation that c^2 is a frequency where energy turns to matter along the same spectrum reveals that the EM spectrum is also the (energy/matter spectrum). Thank you Juanita, and I will be using that allot more from now on..

Another idea that may have stopped physicist from finding this. The idea that vectors are added not multiplied. This is true in some cases but when you have a centripetal and centrifugal force at 90 degree angle creating circular motion, that velocity is said to be squared (multiplied), not added. This may indicate a quantum change in the mathematics that govern vectors of motion that are unequal, to vectors of motion that are equal and at right angle to each other, providing a balance of centrifugal and centripetal forces to create circular and or spherical motion, thereby allowing the quantum change of energy to rest mass, and wave to a particle.

"Dimensional analysis", can also be an obstacle. I've been told that my idea violated dimensional analysis by several people. Dimensional analysis states that, and this is directly copied from http://en.wikipedia.org/wiki/Dimensional_analysis

Introduction
pp 1 "The dimensions of a physical quantity are associated with combinations of mass, length, time, electric charge, and temperature, represented by symbols M, L, T, Q, and Θ (respectively) each raised to rational powers. As examples, the dimension of the physical quantity speed is "distance/time" (L/T or LT ⁻¹), and the dimension of the physical quantity force is "mass×acceleration" or "mass×(distance/time)/time" (ML/T ² or MLT ⁻²). In principle, other dimensions of physical quantity could be defined as "fundamental" (such as momentum or energy or electric current) in lieu of some of those shown above."

pp 2 "Two different units of the same physical quantity have conversion factors between them. For example: 1 in = 2.54 cm; then (2.54 cm/in) is called a conversion factor (between two representations expressed in different units of a common quantity) and is itself dimensionless and equal to one. There are no conversion factors between dimensional symbols."

pp 6 "only quantities of the same dimension can be added or subtracted. For example, the mass of a rat and the mass of a flea may be added, but the mass of a flea and the length of a rat cannot be meaningfully added. Physical quantities having different dimensions cannot be compared to one another either. For example, "3 m > 1 g" is not a meaningful expression."

pp 7 "Only like-dimensioned quantities may be added, subtracted, compared, or equated. When unlike dimensioned quantities appear opposite of the "+" or "−" or "=" sign, that physical equation is not plausible, which might prompt one to correct errors before proceeding to use it.

Sure we know about fleas and rats but dimensional analysis is transcended by E=mc², which is equating two previously unrelated qualities (energy and matter). These were just as different as mass and length in the old days and would have been a violation of dimensional analysis before E=mc². As a matter of fact, mass, length, charge, time, and energy, are not supposed to be equatable and conversion factor is said to be dimensionless and non existent between dimensional symbols, of which we know (E) and (m), in E=mc² are, as well as knowing that this conversion factor c², is dimensional (has real physical significance), as Einstein proved. But now this geometrical interpretation reveals c² to be conversion unit between not only, energy and matter, but time, length ,charge, inertial mass=gravitational mass, just as stated in above reference about the significance of square root of -1.

And we might even throw in the mass of a rat and length of a flea if we get good enough at it.

One more thing that is an obstacle, the idea that photons are massless, and that the idea of relative mass should be abandoned. Photons do have mass that is demonstrated by the photo electric effect. The higher the frequency and shorter the wavelength - the higher the mass, energy, and momentum.

  From:

http://en.wikipedia.org/wiki/De_Broglie_hypothesis  

"The de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle and that the frequency is directly proportional to the particle's kinetic energy"

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Rest mass is relative mass in a more equal distribution around a center of rotation. It is energy along the same EM (electro / magnetic), spectrum which can also be called the (energy / matter) spectrum, where energy turns to matter because the angular momentum equals and balances the linear momentum, trapping the energy in a closed loop of rotation.

It is also well known that a photon will increase in frequency as it enters a gravitational field by E or M =hf/c²

In theory and perhaps in practice, if a photon enters strong enough gravity field, it should increase in frequency at E=hf/c², eventually reaching E=hf = mc² 

The equation E=hf=mc^2 promoted by De Broglie and others, is also saying to those who can read it, that (mc^2) is a frequency/wavelength, which is also demonstrated by the wave nature of the electron.

 

 

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To be continued

Conrad Countess

 

cjcountess@yahoo.com

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More Simple Graphics That May Help to Visualize This Concept

Last edited (12/9/08)

From c to c² Energy to Rest Mass
Along the EM spectrum: AKA the (energy/matter spectrum)

By Conrad J.Countess

Ground state dark energy, before frequency is factored in, results in expansive centrifugal force as energy moves in straight line of motion and expands the distance between its origin and destiny at the speed of c. This is the energy of expanding space or cosmological constant that as we will see balances the centripetal gravitational force. Although space as a whole expands spherically, the aspect of it which allows for the formation of waves and particles move as lines of force from the center of the source, weather that center is of the universe or a star, and these, (what some call strings), form the basis of waves and particles.

 

 

Any added energy to it causes waves to churn up because no speed can be added to the centrifugal speed limit of c so extra energy goes into centripetal speed of cycles per second, or other appropriate time unite, of frequency as extra energy is bounces off of the speed of light barrier and is displaced into the angular direction. Energy is squeezed against the light barrier like a compressed spring.  The more energy, the tighter the spring, and the more cycles per time unite.

When the speed reaches c in right angle frequency direction this is c² and motion of centrifugal and centripetal forces are balanced. Energy is deflected backward because of speed limit of c in frequency direction also. This results in rest mass or the ability to come to rest in a neutral gravitational field because of helicopter like hover effect that spinning objects posses when energy is equally distributed around a center of rotation. This taken together with the fact that light bends toward gravity and increases in frequency as it gets closer to gravity source indicates that this is also a quantum gravity theory. Like loop quantum gravity and string theory gravitational mass as rest mass, is result of energy traveling in a loop.

Therefore the speed limit of light itself gives rise to waves with mass and centripetal force of gravity and shapes them into rest mass particles at high enough energies namely c², because of the speed limit of light in the linear centrifugal and right angle frequency directions.

 

  Some scientists like to use the analogy of a calm body of water for the background energy field as in the “Higgs field theory”, in which waves are churned up by disturbances which gives rise to forces and particles which is very similar to this.

 

 

Energy Created by Vibrating Massive Particles such as Electrons, Wavelength and Vibrational Frequency is Limited by The Speed of Light. 

 

And of course electrons may be formed from high energy photons entering a strong gravitational field as the gravity field raises their frequency above the rest mass threshold.

See this for demonstration: http://www.colorado.edu/physics/2000/waves_particles/wavpart4.html

 

A-------B----------C m/c^2---m=c^2---mc^2

Electron or positron is only free particle at which E=hf=mc^2 (A) or left side of line represents low end of (EM) spectrum as (E=hf/c^2) or energy divided by c^2.and includes whole range of EM waves below c^2 from Cosmic microwave background energy and below to gamma rays (B) represents intersection of line and circle and only point on EM spectrum where (Rest Mass and EM) are equivalent at exactly (c^2).  Although E=m/c^2 and E=mc^2 might arguably represent an electron or single rest mass particle also sense 1/1 = 1x1 =1, an equation representing exactly (c^2) not divided by or multiplied by, would be Taylor made for a single rest mass particle such as an (electron or positron). I chose to represent this by (E=hf=c^2 and/or E=m=c^2 E=hf@c^2 and/or E=m@c^2 ). (C) represents (E=mc^2) as mass times c^2 and can also represent compound matter form single rest mass particles to the whole universe of mass. Only at the intersection of the line and the circle do (EM) and (Rest Mass) equate at c^2 exactly at which point one could use E=hf=mc^2. The electron and positron represent this point on EM spectrum. Above and below that they diverge from this equality just as the straight line diverges from the circle. As an analogy, if the line atop the circle represented a straight line of travel of, "10,000" mi from intersecting point to either end of line, this could show how one could end up in outer space following this straight line instead of in China (my true destination), if I followed the curvature of earth 10,000 mi to other side of globe.

 

Conrad Countess

 

 

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