29. RELATIONSHIP OF (C+V) (C-V) MATHEMATICS WITH
GRAVITATIONAL FORCE AND CHARGE FORCES
(c+v) (c-v) mathematics gives important clues on the existence of a
mechanism in nature. This mechanism is called FIELD mechanism. Let’s
have a look at these two equations.
“Gosh…
where do these come from? What is it got to do with it? One is the Law
of Universal Gravitation and the other is Coulomb’s Law that describes
the force between static electrical charges. What do we have these here
when our topic is (c+v) (c-v) mathematics?” Please don’t say these
because these two equations have a close relationship with (c+v) (c-v)
mathematics.
The Law of Universal Gravitation:
Two objects apply forces directly proportional with the multiplication
of their masses and inversely proportional to the square of the
distance between them.
Coulomb’s Law:
Two objects that have electrical charges apply forces directly
proportional with the multiplication of their charges and inversely
proportional to the square of the distance between them.
Both laws include some vital information that guide us and that we may
use to explain the reason of (c+v) (c-v) mathematics. Let’s have a look
at that information now.
The first piece of information is the following: Valid for both the
equations, there is no limit to the distance between two objects or two
electrical charges. The distance difference, whether it is one
centimeter, one meter, thousands of kilometers, a few light years or
millions of light years, does not lead to a change in these
equations.
The second piece of information is that features of objects are not
important. There is no limitation such as only and only objects
included in this class apply forces to each other. It is enough for the
Law of Universal Gravitation to have objects that have masses and for
Coulomb’s Law to have objects that have electrical charges.
The third piece of information is that these forces are applied to all
objects that are in the universe simultaneously instead of specific
objects. I mean, there is no limit such as while an object is applying
forces to another object, it cannot apply forces to another object.
While Earth applies forces to the Moon, it also applies forces to the
Sun, Jupiter, Pluto, and the Andromeda Galaxy or to a celestial body
that we can see with Hubble Telescope millions of light years away. It
was a bit general example, so be more specific. The Law of Universal
Gravitation says that an atom, since it carries mass, apply forces to
all the other atoms no matter where they are in the universe. Coulomb’s
Law says that an electron, since it carries a charge, apply forces to
all the other electrons and protons no matter where they are in the
universe. Here, the fact that an electron that applies forces is inside
a neutral atom has no importance (Neutral Atom: The negatively charged
electrons and the positively charged protons that form an atom are
matched with one another and, for this reason, the electrical charge of
an atom is theoretically zero.). It is, in fact, a situation that is so
interesting and that forces our imagination as much as possible. You
switch on the light in your room at home, electrons start running in a
wire towards the lamp and all the other electrons on the other side of
the universe are informed about this. How many electrons are running
and what their speeds are… they know it all (or they will, let’s say)!
I’d like to tell you a weirder thing. And there is also a possibility
that the delivery of relocation information to other objects takes
place in zero time. I didn’t say this to start an argument; I’m just
trying to tell what the equations mean. If we are careful, we can see
that both equations are independent of the speeds of objects. At the
moment an object changes its place, the distances it has between the
other objects will change and, for this reason, the force will change,
as well. We can interpret this situation as “The change in the force
takes place in zero time”. Therefore, if these equations always have
absolute accuracy, there is also a result meaning that relocation
information of an object is delivered to all other objects in zero
time. If it is not delivered in zero time, it means that there is a
flaw, a neglected part, in the writing of the equations. And, in this
case, the equations that indicates the force between two objects that
are motionless relative to each other accurately but that fall short
for the forces between objects that are in motion. This is not
something that may not happen. If you remember a very special example
similar to this, we saw it in the equation c = f0.λ0
that was used for the electromagnetic wave speed equation and the
correct equation had to be c = f0.λ1.
The fourth information is that these forces stop at nothing and can go
through matter. Let’s me explain it with a simple example. When Earth
goes between the moon and the sun, does the force that the sun applies
to the moon change? Does Earth prevent the force of the Sun to reach
the Moon? If something that happened, the orbit of the Moon would
change and we would detect and notice it. The situation is like this
for the gravitational force at least; I think it might be a bit
different for charge forces because we can get isolated areas that
electrical charges cannot go through.
Now I’d like to show you that gravitational force stops
at nothing. For this, I’d like to explain what "m1.m2"
multiplication in the equation of the Law of Universal Gravitation 
means with an example.
We have 5 shots (metal balls) each weighing one
kilogram. By attaching three of them together we get mass m1
and the other two together we get mass m2. The gravitational
force between these two masses is F=G. (3x2)/d2. And m1.m2
= 3x2 = 6. Firstly, what is the meaning of the number 6 that we got by
multiplying the masses? I’m going to try to explain this. Then we will
focus on the distance “d” between two masses.
We
multiplied the amounts of masses to find the gravitational force [1],
but now let’s do it in a more sensitive way: calculate gravitational
force of each shot that forms the m1 mass with each shot in m2
mass [2] and add up the results that we get and find the gravitational
force in this way [3].
[1]
m1 is made up of (A,B,C) elements and m2
is made up of (D,E) elements. Using this information and the average
distance for the distance, an equation like the following is obtained.
[2]
As seen below, we get the same result with the force that we calculated by using the elements for the m1.m2 multiplication of masses. The masses of the elements in this example were 1 unit.
[3]
In reality, how many elements the masses m1
and m2
are made up of or what the mass values of the elements are do not
matter for the result. I prepared the table below to show this. In the
table below, it is assumed that m1 mass is 19 units and m2
mass is 9 units. The elements that make up of m1 and m2
are given random mass values. “m1.m2”
multiplication gives us 19x9=171. As seen in the table, the addition of
the multiplication of the elements with each other is also equal to 171
(the sum of the numbers in the yellow section).
|
m1 mass = 19 Units, 9 Elements |
||||||||
|---|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | G | H | I |
| 1,3 | 4,5 | 1,56 | 1,96 | 1,9 | 2,62 | 1,24 | 2,36 | 1,56 |
|
m2 mass = 9 Units, 6 Elements |
||||||||
| J | K | L | M | N | O | |||
| 1,1 | 0,8 | 1,8 | 1,4 | 0,5 | 3,4 | |||
|
m1 . m2 = 9 × 19 = 171 |
||||||||
| J | K | L | M | N | O | |||
| A | 1,43 | 1,04 | 2,34 | 1,82 | 0,65 | 4,42 | ||
| B | 4,95 | 3,6 | 8,1 | 6,3 | 2,25 | 15,3 | ||
| C | 1,716 | 1,248 | 2,808 | 2,184 | 0,78 | 5,304 | ||
| D | 2,156 | 1,568 | 3,528 | 2,744 | 0,98 | 6,664 | ||
| E | 2,09 | 1,52 | 3,42 | 2,66 | 0,95 | 6,46 | ||
| F | 2,882 | 2,096 | 4,716 | 3,668 | 1,31 | 8,908 | ||
| G | 1,364 | 0,992 | 2,232 | 1,736 | 0,62 | 4,216 | ||
| H | 2,596 | 1,888 | 4,248 | 3,304 | 1,18 | 8,024 | ||
| I | 1,716 | 1,248 | 2,808 | 2,184 | 0,78 | 5,304 | ||
| SUM OF NUMBERS IN THE YELLOW AREA = 171 | ||||||||
As
can be understood from the table, the important thing for the
gravitational force and the Electrical Charge Force is the sum of the
forces that elements of an object apply to the elements of the other
object. The resulting force is made up of this sum. The functioning
mechanism of nature is this way. Matter is made up of atoms. Therefore,
elements that constitute mass are atoms (We can go into a deeper level;
we can also say that matter is made up of sub-atomic particles that
constitute atoms, but let’s stick to the atomic scale.). If we assume
that Earth is made up of around 1.33*1050 atoms and the Moon
is made up of roughly 1.33*1048
atoms and if we think that each atom on Earth applies gravitational
force to each atom on the Moon, we can see how crazy things nature
does. Besides, it is estimated that the universe is made of 1081
atoms. From this, we can conclude that each and every atom applies
forces to 1081 atoms at the same time.
Now, we should focus on the topic of the distance between. While
showing the force between elements, I used the average distance above
[4]. It is clear that the force calculated by using the distances
between elements will give the real result [5].
[4]
[5]
In the gravitational force equation, the distances between the objects’
centers of masses are the reference points [6].
[6]
In the calculation done with the elements, on the other hand, the
accuracy of the equation will increase as the distances will be taken
into consideration in a very sensitive manner. But, when the distances
are taken into account for both calculations, is there a difference
between the results obtained? If yes, how much is this difference?
I wrote a special computer program to find the answer to this question.
In the program, I did the necessary calculations by using 9000 points
as elements for each mass. The mass of an element was taken as 1 unit.
You can see the result in the table below.
| m1 | 9000 | Unit | |
| m2 | 9000 | Unit | |
|
İşlem sayısı |
81000000 | ||
|
Note: The universal gravitational constant (G) is a fixed factor and has not been included in the calculations.
|
|||
|
Calculated Gravitational Forces |
||
|
d Distance between two mass centers |
FN Universal Gravitational Force
Force calculated using the general formula
|
FE
Force calculated using distances between elements of two masses
|
| 300 | 900 | 981,3608966 |
| 500 | 324 | 333,4265753 |
| 1000 | 81 | 81,56725952 |
| 10000 | 0,81 | 0,81005952 |
| 100.000 | 0,0081 | 0,00810001 |
| 1.000.000 | 0,000081 | 0,0000810000 |
|
10.000.000 |
0,0000081 | 0,0000008100000 |
|
100.000.000 |
0,00000081 | 0,0000000081 |
FN : Universal Gravitational Force.
The force that is calculated with the regular formula
FE : The force that is calculated with the help of
distances between elements of two masses
As can be seen in the table, long distances for FN and FE
forces give the same results in both calculations. In reality, there
can never be FN = FE.
However, as we can see, as the distances get longer, the difference
between forces decreases and it turns into an unimportant situation
like at how many digits after the comma the equation becomes
insignificant.
As the distances between masses get shorter, the opposite is the case.
We see that the difference between FN and FE
forces increase and that FE
force gradually get higher values. Naturally, the existence of this
situation should change our perspective of gravitational force. For
instance, while studying movements of planets in orbits that are close
to stars, it is important to think how accurate is to calculate by
using FN force. FE is at work during stellar
collisions, as well. In these types of analyses, it is necessary to
take FE force into consideration instead of FN
force. FE is the force that affects us while we go and
measure our weights on a scale.
The model I did is 2-dimensional: 900 points that I used for the masses
and 90002
= 81.000.000 number of processes is enough to give us an average idea.
I believe it is a real necessity to reach a lot more sensitive
information with more points and with 3-dimensional models.
What I told you above are the conclusions that I reached from the
equation .
Of course, the universal gravitational force equation includes other
information as well. For example, “Why is the force inversely
proportional to the square of distance?” I cannot answer this
question. “What is the Universal Gravitational Constant indicated by
G?”
I cannot answer this one, either. I had worked on the G constant for a
while before. I can’t say I reached any significant information.
However, if we think that the descriptions of second, mass and meter
are created artificially, we can reach some conclusions.
There are three important details in what we covered here in terms of
our topic.
• Effects of these forces reach infinite distances.
• Total force is formed from elements.
• These forces stop at nothing and they can pass through matter.
I wanted to show you these. Now, let’s go back to our topic.