The velocity of Light

The first knowledge relative to Lorentz Transformation (LT) is the velocity of light. A velocity has a speed and a direction.

Scientists already proved that the speed of light is independent to the speed of the source of light. For sources with low speed, you may refer to Sagnac effect (1913 by George Sagnac) and for sources with high speed you may refer to the experiment reported on 8/20/1964 by T. Alvager, F. Farley, J. Kjellman and I. Wallin.

1-1. How about the velocity?

Let me start this knowledge from a simple setup. Let a train moves at a constant speed v along a straight segment of railroad. I will need your help to point a flashlight to outside of the train from an open window and let the flashlight perpendicular to the plane containing the frame of that window.

Then I want you to turn the flashlight on and off once in the night time so that there should be a ray of light rushes out into the dark space. Now, I need you to imagine the speed of the ray and the direction of it.

About the speed, scientists already assure us that the speed of photons will not be influenced by the speed of the flashlight so that it will not be (c^2+v^2)^(1/2). The speed of photons is a constant c, in vacuum.

I hope you understand this ugly way to display the wrong speed of (c^2+v^2)^(1/2). The symbol of "^" is to represent the function of exponents, c^2 is for the square of c and (c^2+v^2)^(1/2) is for the positive square root of (c^2+v^2).

How about the direction of the ray? Let me ask you to turn the flashlight on and off when you see the center line of a road perpendicular to the railroad. In that situation I will say the direction of that ray is away from the train and along the center line of that road. Do you think so?

I hope you do. Then, as the middle train on the diagram of next page, I will assume that I already put a huge mirror face to the train at the center line of the road about 100 meter away to reflect the ray back to the train.

Now, please imagine this situation and decide if the returning ray will hit the center point of the front circular, square or rectangular surface of your flashlight.

If your answer is will not, which is what I believe, then your idea is showed on the bottom train of the diagram on next page. If your answer is yes then I will talk about it later.

1-2. A Natural Selection

If you select that the return ray will not hit the center point of the face of your flashlight then the velocity of light is independent to the velocity of the source of light. I call it the natural selection of the velocity of light and mark that kind of ray by a Cn vector.

A Cn vector will go by its own direction. No matter how fast the source of light moves or how fast the source of light spins, a Cn vector will represent the speed c and the direction like the ray is emitted from a stationary source in the universe.

When technology is good enough to record nanosecond and nanometer accurately, scientists could use the setup in 1-1 to design an experiment. I hope that Cn vectors will be verified.

Under the definition of Cn vectors, the figure 39-6 on page 1200 of "University Physics" tenth edition by Young & Freedman published in year 2000 (Book 1) will need some modifications.

Under the definition of Cn vectors, the figure\38-5 on page 963 of "Fundamentals of Physics extended" fifth edition by Halliday, Resnick and Walker published in year 1997 (Book 2) will also need some modifications and the proved result after the modification will be "time acceleration", not "time dilation" any more.

1-3. The Mainstream Selection

Yes, logically speaking, a ray may adjust its direction according to the velocity of the source of light while maintaining its speed c. Why? Because scientists don't know a ray thoroughly yet.

I mark that kind of rays by Cm vectors. This kind of vector is a confusing vector. It will partially follow the operational rules of vectors. The Cm vectors will follow the operational rule for directions but not the operational rule for scales.

Yes, regarding following the operational rules of vectors, a Cn vector is worse than a Cm vector because a Cn vector will ignore both of the scale and direction of the velocity vector of the source of light.

The mainstream selection in physics is that the return ray in the section 1-1 will hit the center point of the face of your flashlight. That means Cm vectors is the choice of most scientists of physics in representing a ray of light wave.

Remember that, neither Cn vectors nor Cm vectors are mathematical vectors. Both of them violet the operational rules of mathematical vectors. They are for physics only.

I believe that someday scientists should be able to put this train experiment into test. When that day comes you or your children may see the result of the competition between model of Cn vectors and model of Cm vectors.

1-4. The Cm vectors

Since photons is an important object of physics let me talk more about the character of Cm vectors.

Mathematically, when scientists decide the direction of a ray emitting from a moving source at constant velocity V, it will be like the combined vector, the Cc vector, in the following diagram.

The length of Cc is |Cc| = (c^2+v^2)^(1/2), where |V| = v. The length of Cn vectors and Cm vectors are |Cn|=|Cm|= c.

As you can tell, when |V| > 0, we always have |Cm| < |Cc| but the direction of Cm is always the same as it of Cc.

The idea of mainstream professors of physics makes photons behave in between of independent (the spped) and dependent (the direction) to the velocity of the source of light.

The photons in a ray will follow the direction of vector Cc, which is the direction of combined vector from vectors of Cc and V. That is the dependent portion, the direction of photons depend on the velocity of the source of light.

But photons in a ray will not always accept the speed portion of the vector Cc. When |V| = 0, we do have |Cc| = |Cm| = c but when |V| > 0, |Cc| > |Cm| = c.

I hope you have a clear picture of how the velocity of the source of light influence the behavior of photons it emits. We don't know which model of Cn and Cm is matching the nature, the fact, but currently most professors of physics believe that Cm vectors is the right model.

The model of Cn vectors let the velocity of light totally independent of the velocity of the source of light.

Michelson Morley experiment

Scientists use the model of Cm to explain the famous Michelson Morley experiment (MMX, 1887) so that the null result of MMX causes scientists to rely on Lorentz Transformation (LT) for a logical explanation of MMX.

However, following the model of Cn vectors, you will understand that when the reflecting ray returns back to the beam splitter, either in the figure 37-16 on page 1154 of (Book 1) or figure 36-45 on page 927 of (Book 2), it will not reach the center point of the splitter as the model of Cm vectors expected.

When the apparatus turns as designed procedure of MMX, the model of Cn vectors shows the reflecting ray and the...