Previously we showed how you can use geometry and simple enough expression to obtain a formula for relativistic doplerovkoe offset. Here we consider special cases and experiments that accompany such math. It should be noted that in all further formulas of this work, we take the speed of propagation of the waves from the transmitter is equal to the speed of light, because we believe that waves carry photons: \[v_2 = c, \quad \beta_2 = 1 \qquad (2.1)\]

Fig.2. The scheme of experiments to obtain the effects of red and blue shifting in the longitudinal motion, while blue shift during lateral movement.

This effect is observed if the object emits waves towards a stationary receiver, moving away from him (Fig. 2a). In the receiver there is a decrease in frequency or increase in wavelength, and the spectrum — shift of lines toward the red end. This phenomenon is called red shift. Based on the formula (1.10) of the previous paragraph we have to take the angle \(\theta\) is equal to zero. Then the Doppler shift of frequency will look like this: \[{f \over f'} = \gamma_1 (1 - \beta_1) = \sqrt{1 - \beta_1 \over 1 + \beta_1} \qquad (2.2)\] where: \(\gamma_1 = 1 / \sqrt{1 - \beta_1^2}\) and \(\beta_1 = v_1 / c\). The most expressive effect of the red shift can be observed in the spectrum moving away from the Earth stars and galaxies [1].

This effect is the reverse of the previous one [2]. Here the transmitter is approaching radially towards the receiver (Fig. 2b), while the observed increase in the frequency or decreasing wavelength, and the spectrum — shift of lines toward the blue end. Based on the formula (1.10) of the previous paragraph we have to take the angle \(\theta\) equals \(\pi\). Then the Doppler shift of frequency will look like this: \[{f \over f'} = \gamma_1 (1 + \beta_1) = \sqrt{1 + \beta_1 \over 1 - \beta_1} \qquad (2.3)\] Experimental verification of the relativistic longitudinal Doppler effect with the surveillance while the red and blue offset were held AVCOM and Stilwell in 1938 [3].

In this case, the transmitter is placed on the rotor and rotates emitting waves. The receiver is placed on the stator and is stationary (Fig. 2c). Because in this case, the global vectors \(\mathbf{LL}\) and \(\mathbf{L}\) are perpendicular to each other, the angle \(\theta\) equals \(\pi/2\), hence \(\cos(\theta)=0\), and the formula (1.10) and the Doppler shift becomes the following form: \[{f \over f'} = \gamma_1 = {1 \over \sqrt{1 - \beta_1^2}} \qquad (2.4)\] As we can see, there is an increase in the frequency and spectrum of — line shifts to the blue end. Interestingly, for the theory of relativity, the experience was completely unexpected, and it was explained with great difficulty. For example, the same formula in the special theory of relativity predicts a red shift, i.e. a completely opposite result. Meanwhile, the experiment Campy to the theory of relativity, was to be direct evidence of time dilation and of the correctness of the constructions of Lorentz. Using a single space blue shift in the transverse movement is explained easily and clearly.

It is possible to explain this effect and a lot easier. After all, in the coordinate system of the moving transmitter time slows down, and hence reduce the gaps between the waves that captures the listener and described by the formula (2.4). And if you look at this phenomenon is even bigger, the increase in frequency can mean increasing the corresponding Planck energy: \(E=hf\) [4], which is what happens from the point of view of the theory of a single space.