Chapter 6 

THE “LORENTZ TRANSFORMATION”

6.1 The essence that light propagation is independent from its source.

      Under the stimulus of a light source, the produced preliminary WG pulses enter the “WG ether”. According to wave theory, the “WG” pulse current induces the perturbation in the “WG ether” and reacts on the source, resulting in an intermittent pulse emitted from the source. Such wave-particle interference or more correctly the standing wave propagating form is indeed the equalization of the light energy, and the essential mechanism of wave-particle duality.

    Obviously, under the above-mentioned mechanism, the propagating speed of the electromagnetic wave only depends on the character of “WG ether”, and is independent of the motion of the light source.

 6.2 The “Lorendz transformation” and its two premises in WG theory

Therefore in two inertial coordinates k and k’, the coordinate transformation to describe the same event must satisfy the following conditions:

    (1) The inertial coordinates k and k’ drag the “WG ether” in their individual coordinates completely or strongly. Refer to chapter 4 and the relevant contents about the “Effective dragging (to WG ether) indirectly”

   (2) The sensor and sending of an event between the coordinates k and k’ must be by light ray and light sensor.

    Using the above the two conditions we can prove that the rules of motion of the “WG” in optical state is a Lorentz invariant, ie. They are invariant under Lorentz group SO (3,l) operation. Consider two observers in k and k’. Assume that they bring a clock and a flash lamp with them. Let the observer in k emit two light signals in time interval T on k’s clock. It means that two pulses that produce two perturbations in “WG ether” will disturb the WG substance in the lamp. We assert that at least on k’s clock the time interval of receiving two such signals must be proportion to T, denoted as aT, with a representing the character of motion k’ in respect to k. If k and k’ are inertial observers, a must be a constant independent of time. Since we have assumed they are equivalent to each other, the application of the transformation in two inertial coordinates is exchangeable, and a must be the same. Furthermore we can assume their clocks have been calibrated to zero when they meet. At that time k emits a signal to k’, and k’ will receive it immediately. After an interval T, k emits a signal to k’ again and k’ sends back a signal when he has received the signal. The time interval for observer k’ receiving two signals is aT, and for observer k is a² T (Fig. 1)

       The time for the second signal emitted from k to k’ and coming back from k’ to k is (a² – l )T. Therefore a single journey is (a² – l )T / 2. On the other hand, when observer k’ receives the second signal the time on k’s clock is (a² + l) T / 2. At this moment the coordinate of k’ determined by k’s clock is (a² + l) T / 2, and the spatial coordinate is (a² – l )T / 2. Therefore the velocity of k’ with respect to k is

    After simple algebra we get

 In the following I would like to derive the Lorentz transformation. Assume that (x, t) are coordinates of observer k, being used to denote an event P. The observer k sends a light signal through “WG ether” to event P at time t-x, and has it back at time t+x.

Similarly k’ observer using coordinate (x’, t’) to denote the same event P sends a signal to P at (t’-x’) and has it back at (t’+ x’) (Fig. 2). Again we assume their clocks have been calibrated. Using the above argument we have

          t’ – x’ = a ( t – x )

         t + x  = a ( t’ + x’ )                                 (6.3)

     From (6.3) we get 

      Using (6.1) and (6.2) we have

This is exactly the Lorentz transformation formula. From it we have also

       t’² – x’² = t² – x²                                      (6.6)

      The equation (6.6) exhibits the essence of the invariant in the WG optical state propagating in the “WG ether “ reserving invariant of space-time under Lorentz transformation. In fact the above argument is valid for pure spatial rotation

                                                                                (6.7)

t² – (x² + y² + z²) is invariant. Equation (6.5) represents a velocity transformation in x direction.

                           (6.8)

 Replacing v by tanh?₁ , (6.8) can be written as

                               (6.9)

      Similarly the other two Lorentz transformations are

                                                                             (6.10)

 The definition of the infinitesimal generator is