Alice Law Version 7
The Alice Equation
May 7, 2012
Copyright © 2012 Han Erim, All Rights Reserved.
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.
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
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.
The Alice Equation
Establish: December 2001
Copyright © 2000-2012. Han Erim. All Rights Reserved.