Alice Law Version 7

 

The Alice Equation

 

Han Erim

May 7, 2012

Copyright © 2012 Han Erim, All Rights Reserved.

 

 

THE ALICE EQUATION

What is the meaning of the value “v” in (c+v)(c-v) mathematics?

The movements of frames towards each other are taken in hand on the axis X for convenience in the animations that you have seen in the sections of the program. Therefore, there occurs a situation as if value v in (c+v)(c-v) mathematics showed the speed difference between the frames. (I have even said that in some parts of the program.) However, this is not accurately correct in reality.

The value v in (c+v)(c-v) mathematics shows the deviation rate from the speed of light. The value v does not show the speed difference between frames.

The movements of frames according to each other can be in any direction or any speed. Here we will see how to calculate the value v in this kind of situations. The mathematical equation used in the calculation method is highly important for both the Electromagnetic Theory and the Relativity Theory. As the equation was very important, I wanted to give a name to it and I named it THE ALICE EQUATION. 

Figür 1, Worksheet

On this page, we see the animate graphic that we will benefit from while calculating the value v in (c+v)(c-v) mathematics. A flashlight sends a short light beam to the observer. 

The points O, O', P, P' in the graphic are movable. These points enable us to set the movement direction and speed of the frames. We can set the graphic for any situation by changing the positions of these points and make analysis of (c+v)(c-v) mathematics. 

The graphic works according to the following principle: 
The light setting out from the frame A reaches the frame B.
In the process until the arrival time;
The frame A covers OO' distance
The frame B covers PP' distance. 
We can see all stages of the incident occurring by moving the slide.

In case you change the positions of O,O',P,P' points, the graphic automatically adapts itself to the new situation. 

BLUE ARROWS are distances which frames cover.

YELLOW ARROW describes the magnitude of the value v in (c+v)(c-v) mathematics. The purpose of this graphics is to see how it occurs. 

In the following pages, I will show you a few details that are important in my opinion related to the graphic.
Figür 2, POSITION OF GHOST

The animation has been set to the arrival moment of the light here. If you have changed it, please take the slider to the rightmost. 

By using a ruler that symbolizes the field of the observer, we can easily find out where the observer will see the ghost. The observer sees the ghost on the point where the signal gets into the field (G point) according to the reference system of the observer.

We can also identify the Ghost’s position through the resultant vector belonging to the OP and PP' straight lines.

THE SPEED OF THE LIGHT IS INDEPENDENT OF THE SOURCE IT IS EMITTED FROM.

Change the size and the direction of the blue arrow belonging to the flashlight by dragging the O' point, which is the arrival point of the flashlight, with your mouse. You will see that in which direction and at what speed the flashlight goes do not have any effect on the Ghost’s position at all. 

The electromagnetic waves move independently from the direction and speed of the source that they are emitted from. This topic is covered in detail in the section “EXPERIMENT” in the program.
Figür 3, THE PATH THAT THE LIGHT FOLLOWS

The path that the light follows is different for both the reference systems.

The light goes towards the Q point according to the reference system of the frame A. 

The light comes from the G point according to the reference system of the frame B. Do not forget that the light travels inside the field of the frame B.
Figür 4, THE ALICE EQUATION AND THE CALCULATION OF THE VALUE V

Leave the movable bar at the left most, namely at the beginning position.

If the frames did not move, the light would cover the OP distance in a time like t (OP = c . t)

We draw a circle whose center is O' and whose radius is equal to the OP distance. We connect the O'P' points with a straight line and meet this line with the circle by extending it (S point). The O'S distance will be equal to the OP distance (OP=O'S).

Now, let’s bring the slide to the right, to the end.

We know that the GP' distance is equal to the OP distance. Accordingly, the light will cover the GP' distance at the same t time. (GP'= OP = c . t) Therefore, in the measurements done from where the frame B is located (the arrival target of the light), the speed of the light is always found out to be “c”. 

Moreover, the situation is different for the frame A. The light covers the O'P' distance at the same t time. We see that the O'P' distance is smaller than the OP distance. (OP = O'S and OP>O'P'). As the light cover the O'P' distance at the same t time according to the frame A;
The speed of the light going towards the frame B according to the frame A is c'= O'P'/t. (We are talking about the graphic here. c>c'). 
We can write (c' = c-v) instead of the speed c'. Therefore the value v becomes the amount of change in the speed of the light. From this point of view, we can write the following to equations:
O'P' = c'. t = (c-v).t
P'S= v.t

The P'S distance that is shown with the yellow arrow gives the value v that we are looking for.
P'S= v . t 

Now we can write the Alice Equation.




We obtained the result (c-v) in the denominator at the right side for the graphic here. When we set the graphic for different movement directions, we can also obtain a result (c+v) for the denominator of the equation at the right side.

 





If the direction of the yellow arrow is inwards the circle the value v gets (-) value
If the direction of the yellow arrow is outwards the circle the value v gets (+) value

The button “Math” on the page presents this equation in sum.




Lastly, let’s see the relationship of the movement speeds of the frames with the distance OP.

If we assume that the speeds of the frames are V1 and V2;
The distances that the frames cover during the t time:

OO' = V1.t 
PP'= V2.t 

Since OP = c.t, the equations below are obtained for V1, V2 speed values; 


 

The Alice Equation

The Alice Equation that we see here plays a basic role for Time Dilation, Length Deformation, Simultaneity and the Doppler Effect that constitutes the main topics of relativity. All relativity effects occur in proportion to the magnitude of the value v whose formation we can see here. 

The graphic that we use also shows how the electromagnetic interaction occurs between frames that are in motion according to each other. Therefore, the Alice Equation is a valid and determinative equation for the Relativity Theory and the Electromagnetic Theory.

The value v shows the deviation amount from the speed of light. 

 

 

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