Alice Law Version 7

(c+v)(c-v) Mathematics and Fields

Han Erim

May 7, 2012

Copyright © 2012 Han Erim, All Rights Reserved.

(c+v)(c-v) MATHEMATICS AND FIELDS

In the Mathematics of Relativity section, we saw that the mathematics of Electromagnetic Theory should actually be (c+v)(c-v). In this section, we will examine the reason behind this formulation.

When FIELDS are taken into account, the reason behind the formation of (c+v)(c-v) mathematics can be explained very easily. Fields are not a foreign concept to us. Physics was introduced to field theory in the 1700s. Field forces were used to explain the orbital movements of celestial bodies. This was followed by the use of fields in electric charges. We can even trace it further back—magnetism was already known in the 1600s. Today, the concept of fields is used to explain the four fundamental interactions we know: gravitational force, weak interaction, strong interaction, and electromagnetic interaction.

And that’s not all — today we use many devices that operate using fields, such as televisions, radios, and electric motors, in our daily lives. We can measure and observe the effects of fields and know certain principles about them, which we utilize in technology and industry. It is true that our knowledge of fields is limited, but we have always benefited from them, and we will continue to do so. The Relativity Theory of Alice Law also uses fields to explain the reason behind (c+v)(c-v) mathematics.

Figure 1

We know that all objects have their own field. At the very least, we can say that every object has a gravitational field. A field can be symbolized as shown in the figure. The object is at the center, and its field surrounds it like a sphere. Within the space around an object, its field is always present. If the object moves, it carries its field along with it. These two relationships are essential in understanding why the (c+v)(c-v) mathematics emerges.

I - There is always the object’s field in the space surrounding it

II - The object carries its field along as it moves.

The numbers shown in the figure symbolically represent how the object defines its own field.

Each part of an object is a separate object and has its own field.

An important aspect we must not overlook in (c+v)(c-v) mathematics is that an object is composed of many sub-objects. Any part of an object can be considered a separate object. Each sub-part has its own, unique field.

Think of yourself as an object. You have your own field. But you also have arms, legs, and fingers — and each of these limbs has a field of its own.

We can mentally reduce the sub-objects that make up an object down to the atomic scale, or perhaps even further. However, it is not necessary to go that far to understand the reason behind (c+v)(c-v) mathematics. The principle that “each part of an object is a separate object and has its own field” is more than sufficient.

Figure 2

Let’s consider, as in the figure, a ball as the object along with its field. We mount a ruler on the ball and point a light source toward it. We know that the speed of light approaching the ball will be "c" relative to the ball. Therefore, according to the ruler attached to the ball, the speed of light will also be "c".

Let’s transfer the result we obtained in the Mathematics of Relativity section to this context. The (c+v)(c−v) mathematics tells us this: If we move the ball, the speed of the light approaching the ball will still be "c" relative to the ball’s own reference frame—it remains unchanged.

As shown in the figure, when we move the ball, both the ruler and the ball’s field move with the ball. From this, we can draw the following conclusion: Since the speed of the light approaching the ball remains "c" relative to the ruler, it must also be "c" relative to the field. The direction and speed of the ball’s movement do not affect the light’s speed with respect to the field. The fact that the speed of light remains "c" relative to the field even when the ball is moving indicates that light travels inside the field of the ball. And only because of this can the ball always measure the speed of the incoming light as "c".

To summarize, the conclusion is as follows:

Light travels inside fields. Its speed relative to the field it is traveling in is always "c". The motion of the object owning the field does not affect the speed of the light traveling within and relative to that field. Therefore, in measurements made at the target where the light arrives, its speed is always found to be "c". As a result, electromagnetic interaction occurs via fields. Light utilizes fields. This conclusion is made possible by the (c+v)(c-v) mathematics.

Figure 3

Since light does not travel through empty space but within fields, its speed will not be "c" relative to all reference frames. This is what we observe here. According to the observer in the figure, the speed of light moving toward the ball will be "c" only if the ball is stationary. Otherwise, it will not be "c".

This figure already shows us how we could experimentally determine (c+v)(c-v) mathematics. If we measure the speed of the light approaching the ball from the ball’s reference frame, we will find "c". But if we measure it from the flashlight’s reference frame, we should find a value different from "c".

There are many examples of measurements made from the position of the ball. The most famous is the Michelson–Morley experiment. However, even today, we cannot give a clear example of a measurement made from the position of the flashlight. This is what I meant when I said that physicists have historically made a huge oversight. Had this measurement been made in the past—at the time it should have been made—they would have discovered the (c+v)(c-v) mathematics over 100 years ago. And if they had then investigated why, they very likely would have realized this connection with fields. Associating (c+v)(c-v) mathematics with fields is not a difficult task.

Now, let me tell you about a very important detail. Please listen to me carefully. Physics is a science that is built stone by stone. If a stone at the bottom is not placed properly, the one on top will wobble. Let’s talk about our example from the previous page and suppose that the speed of light going toward the moving ball was measured from the flashlight’s frame. And let’s say that the result of the measurement was a value different from "c".

If this measurement had been done before the construction of the Theory of Relativity, it would have naturally led to the (c+v)(c-v) mathematics. There would have been no obstacle in your way. But if the measurement was done after the Theory of Relativity was established, the result you obtained would not become clear in your mind, nor would it guide you correctly. Because you would inevitably be forced to relate the differing result to time dilation as predicted by Relativity.

That is to say, the sequence of developments in physics is extremely important. First, the speed of light must be measured from both the flashlight’s and the ball’s reference frames. If both measurements yield the speed of light as "c", then you have sufficient reason to construct the Theory of Relativity. Because the core logic of the Theory of Relativity is built on the thesis that the speed of light is constant in all frames of reference. But if you find differing results in the measurements, you would never think of building such a theory.

In the past, decisions were made before all the necessary measurements were completed, and the proper order in physics was disrupted. The foundations of Electromagnetic Theory were built not on facts but on assumptions. Accepting the incorrect assumption that light travels in a vacuum was the mistake. That mistake was then carried over into the Theory of Relativity. As a result, a very unfortunate situation has emerged in physics. Electromagnetic Theory remained incomplete, and the Theory of Relativity was built on an incorrect foundation. Today, the confusion seen in the interpretation of GPS results is a consequence of this. Even though the (c+v)(c-v) mathematics emerges in GPS data, physicists have failed to recognize it. Because their ability to think, reason, and draw conclusions has been deeply harmed by past mistakes. In physics, the foundations must be laid securely.