Contents

One - MATHEMATICAL ILLUSION

  Wherefrom do all the worlds come? They come from space.
                All beings arise from space, and into space they return;
space is indeed their beginning,
                                                and space is their final end.
The Upanishads  

Physicists today often call the medium of electromagnetism "space."
What did the author of this ancient quote mean by the word translated as "space"?

Light is something we see by means of our eyes. The energy of photons moves through a lens to be focused upon a cell which contains a chemical which recognizes a particular frequency by decomposing in such a way as to trigger nerve impulses which ultimately go to a part of the brain which recognizes it as color. Enough of these impulses cause the brain to recognize a pattern that is a three-dimensional picture.

The light itself is a creation of movement, the movement of electrons. The electrons are also a creation of movement, the movement of the nether. And movement is an illusion of space and time.

The appearance of what we see, the way something feels, the apparent solidity of the matter of this world, are all illusions of space and time. We can comprehend the world in which we live, in terms of our lives and all they represent, only because we have special senses to transform the space/time movements of an invisible substance into our own illusions.

Our particular rate of perception allows us to comprehend lightning-fast movement as something other than what it really is. Our own intangibility allows us to experience the intangible. We are locked into a reality that is nothing like what it seems. This is the illusion of our universe, our gift from evolution, nature, the Creator, or all of the foregoing, so that we might enjoy our stories as contructs of linear experiences through time.

This illusion is reality because it is as real as anything we know and because we know of no other reality. Yet we know that our reality of the illusion is not the reality of other creatures, other beings, who exist in this same universe. Less extreme examples of these creatures are the hummingbirds, the shrews, and other small beings who move through the dimension of time at a different rate from our own, and who experience reality with senses attuned to different frequencies.

But in addition to the natural inclination we have to transform movement into matter and the invisible into the visible, we manage to create illusion for our own convenience, to see order wherever we look. We create our own mental illusions. Some of these illusions are mathematical, convenient for mathematical reasons. And to see what is really going on, it is necessary to look again at our mathematical certainties, some of which have grown in stature through the years to become the grandparents of other generations of mathematical illusion. And what we will examine now is rooted in physics.

The equations for kinetic energy and momentum must be understood in ultimate detail for us to understand how the nether equations truly work. In representing these equations, I may occasionally spell out terms that would normally be given with a superscript, such as "ss" in place of "s²".
 

The Reality Behind Potential Energy         Back

Kinetic energy is the energy that is produced upon impact when an object collides with something. For example, we can use a 10 pound weight falling for one second. The formula for kinetic energy is

E_k = (1/2)mv²

in which "m" is mass and "v" is the velocity upon impact with the ground.

Potential energy is the energy that would be produced if the object were to fall and strike the ground. The formula for potential energy is

E_p = mad

in which "a" is acceleration and "d" is the distance the object will fall before striking the ground.

Kinetic energy and potential energy are equal. The only difference is that one has happened and the other has not. So they differ only in the dimension of time (before and after). We must use different means to calculate each. Kinetic energy is calculated with velocity and potential energy is calculated with distance.

E_k = E_p

Have you ever wondered why kinetic energy, "E_k", equals "(1/2)mv²"?   Why is the "1/2" necessary?   Why did velocity twin itself? What is kinetic energy?   Actually, "E_k" and "E_p" (potential energy) can be compared.

Pounds of weight are not actually mass. They are units of force and force equals mass multiplied by acceleration. If "F" is force, "m" is mass, and "a" is acceleration,

F = ma

Gravity is an acceleration so

F = mg

Pounds divided by the value of gravity is slugs, a unit of mass. So 10 pounds divided by about 32 feet per second squared is the amount mass in slugs.

slugs = pounds / gravity

If a ten pound weight is dropped from a height of 16 feet, it will fall at the rate of about 32 feet per second per second. A ten pound weight will have a mass in slugs of 10/g and "g" is 32 feet per second per second. The velocity of the weight upon impact will be 32 feet per second and it will have been falling for one second. Its kinetic energy will be:

(1/2)(F/g)(v)(v) which is in this case

(1/2) [(10 pounds)/(32 ft/sec/sec)] (32 ft/sec)(32 ft/sec)

which comes to 160 foot-pounds of energy. The potential energy of the weight prior to its fall was 16 feet multiplied by 10 pounds of force, which is also 160 foot pounds of energy.

So E_p is equal to E_k in this case as it should be. We can show this equality and use it to analyze energy a bit farther as follows:

E_p = Potential Energy         E_k = Kinetic Energy
v_i = impact Velocity          v_o = starting Velocity
v_a = average Velocity
m = mass     g = gravity     H = height     F = force     d = distance
a = acceleration     t = time

E_p = HF     This is the common equation for potential energy, using "H" as "d"
E_k = (1/2)(m)(v_i)(v_i)     This is the common equation for kinetic energy
E_p = E_k     This is the case with objects which fall.
HF = (1/2)(m)(v_i)(v_i)     By substitution.
F = ma = mg     g = a     H = t(v_a)     HF = t(v_a)mg

        [t(v_a)][mg] = (1/2)(m)(v_i)(v_i)     By substitution.
                                              v_a = (v_o + v_i) / 2
                                              v_o = 0     Started with no velocity.
                                              v_a = (0 + v_i) / 2 = v_i / 2
    [t(v_i/2)][mg] = (1/2)m(v_i)(v_i)
          gt = v_i         Divided both sides by m (v_i / 2).

We arrive at v_i by using "gt", so we have an equality and E_p = E_k.

           E_k = (1/2)(m)(v_i)(v_i)
          E_p = (mv_i)(v_i/2)       Momentum = m v_i    v_i/2 = v_a
 

The Reality Behind Kinetic Energy         Back

From the foregoing, we see that E_k is really momentum times average velocity. But this is an illusion caused by an altered state of the true equation which prevents us from finding the truth. E_k is easy to understand when we analyze what follows.

        E_k = (mv_i)(v_i/2)    
        E_k = (mv_i)(gt/2)     Because gt = v_i,   (substitution).
        E_k = (mv_i)(at/2)     Because g = a,   (substitution).
        E_k = (ma)(tv_i/2)       (Rearrangement).
        E_k = Fd                 F = ma     (By substitution)
                                    t (v_i/2) = d         (Dimensional analysis)

Here we see that E_k is actually the acceleration of mass over a distance. The distance is expressed by velocity multiplied by time. v_i/2 is the same as v_a when the initial velocity is zero.

Ordinarily, we see momentum expressed using the impact velocity. This is appropriate when we are working with the impact of an object such as a rock that is thrown at a speed of 30 miles per hour. The rock is stopped abruptly and its energy upon impact is (1/2)(m)(v_i)(v_i) while its momentum is mv_i. But what has really happened?

The rock was on its way somewhere and something got in the way. If the something had not interfered with the rock, the rock would have continued merrily on its way. Since nether velocity is relative, the rock might as well have been at rest when the interfering object hit it. When the object "hit the rock", there was the deceleration (acceleration in scientific terms) of the rock (mass) over a very short distance (depth of the dent in what hit the rock). The deceleration was very rapid and it caused the rock to be accelerated in the opposite direction relatively speaking. The rock was "accelerated" from zero to 30 miles per hour very quickly and its average velocity during the acceleration was 15 miles per hour. Its final change in momentum was mv_i.
 

The Mass/Energy Equivalency Equation         Back

The mass/energy equivalency equation, E = mc², is a simplified version of the electron vortex E_k that applies to other vortices and vortex combinations such as the positron and the proton. This equation is:

E_k = (1/2) (M/t) (2 ^1/2 c) ².

"Mass" is nether Mass, and "M/t" is "m" because "m" is actually a Mass flow.

This equation simplified is E = mc ², and is supposed to be the "rest mass" of a subatomic particle. The term "rest" is misleading because this is the E_k of nether Mass moving into a vortex.   Kinetic energy is the only form of valid energy and it is based upon acceleration rather than velocity. Acceleration is change, and change is acceleration.   Velocity is just another form of inertia.   Inertia is merely the tendency of something (or even an abstract idea) to continue as it is unless something bothers it. And why should anything or idea do anything different unless something bothers it?

So here is another version of a mathematical illusion - something that works mathematically and yet disguises the true nature of the phenomenon.
 

Planck's Constant

This is probably the best place to first mention the reality of Planck's constant. It is neither momentum [which in terms of dimensional analysis is "m(d/t)"] nor energy [which in terms of dimensional analysis is "m(d/t)(d/t)"]. Instead it is something in between, "md(d/t)" which is why it is a bit confusing. It only becomes energy when "(1/t)" is part of it. Then it becomes

m(d/t)(d/t).

Planck's constant probably should have been considered the total quantity of "h/t" because it is the energy in one cycle of a frequency or a frequency of "1/t". Now we have this hybrid that is neither momentum nor energy and only becomes energy when it is multiplied by a frequency of one. It is no wonder that people tend to call it momentum part of the time and energy another part of the time.

h(1/t) = h/t       which we might call "H".

If "n" is the number of cycles in a photon, then the energy of the photon would be "Hn". Now to find the energy in a photon we must use "hf" which is "h(n/t)". Of course, the particle physicists (who pretend that the photon is a particle instead of a series of waves) can better confuse everyone by using a hybrid Planck's constant.  

Conclusion         Back

There are five things that I hope the reader remembers from this chapter.

(1) Potential energy is an illusion because velocity is relative. The only time E_p is expressed is when its velocity is altered. This alteration causes the apparent E_p to be calculated according the amount that the velocity is altered. One alteration in velocity may be different from another. This means that potential energy will vary according to the magnitude of the change in velocity. Therefore, potential energy is merely a relative term and does not exist except as a form of inertia.

(2) Kinetic energy is the inertia expressed when energy is applied to something to accelerate that something. This energy is not any form of (1/2)mv² because (1/2)mv² is merely a mathematical shortcut. It is handy to use when the velocity is known, and replaces acceleration and distance in the equation. The true energy is the product of mass, acceleration, and distance. It is the acceleration of the mass of the object affected over a certain distance.

E_k = mad     where "m" is mass, "a" is acceleration, and "d" is distance.

(3) Kinetic Energy can be thought of mathematically as the product of momentum and average velocity.

(4) E = mc² is actually the simplified version of
E_k = (1/2) (M/t) (2 ^1/2 c) ².

(5) Something is not necessarily true just because math shows it to be. One must look carefully at the math and see if it has a visual base - a model that makes sense upon which the math can be based. And one must look behind the math that seems to be true and see if it is a simplified version of a more complex mathematical truth.

 

The world is seldom what it seems.
To man, who dimly sees,
realities appear as dreams,
and dreams realities.
Thomas Moore
 

Contents - Next