## 2 Light Clock
### Light Synchronization of Clocks Means Using Light Clocks  
The theorem on the signal clock (light clock):  
**Theorem 1**. : _Assumption: The clocks in inertial systems are synchronized with the signal (light). Conclusion: Clocks measure time exactly as signal clocks (light clocks)._  
Proof of Theorem 1.: The synchronization of two clocks with light is shown in Figure 2.  
The two clocks are located in the inertial system \(U^{\prime}\). The distance between clocks is \(D^{\prime}=\)_constants_. When clock A indicates value \(t^{\prime}{}_{A1}\), a light impulse is sent from it to clock \(B\). If the one-way speed of light in this direction is \(c^{+}\), then when the light impulse reaches the clock \(B\), the following value must be set on it  
\[t^{\prime}_{B}=t^{\prime}_{A1}+D^{\prime}/c^{+} \tag{1}\]  
Synchronization of clocks must also operate on the opposite side. The light impulse is reflected immediately by clock \(B\) and returned to clock \(A\). If the one-way speed of light on  
Figure 1: The signal clock is based on the signal propagating in the distinguished reference system. the way back has a value of \(c^{-}\), then when the light impulse returns to clock \(A\), it indicates the value  
\[t^{\prime}_{A2}=t^{\prime}_{B}+D^{\prime}/c^{-} \tag{2}\]  
On this basis, we can see that the time elapse on the clock \(A\) is exactly the same as the total time flow of light back and forth, and it is  
\[t^{\prime}_{A2}-t^{\prime}_{A1}=D^{\prime}/c^{+}+D^{\prime}/c^{-} \tag{3}\]  
The time required for the light signal to travel \(A\)\(\rightarrow\)\(B\)\(\rightarrow\)\(A\) is used as a standard for the adjustment of clock \(A\). This means that the time required for the light to travel back and forth along \(D^{\prime}\) arm is exactly the same as the time elapse on clock \(A\). This means that clock \(A\) measures the time in the same way as a light clock. This proves the conclusion. \(\square\)  
Dependence (3) can be transformed into another form  
\[t^{\prime}_{A2}-t^{\prime}_{A1}=D^{\prime}\left(\frac{1}{c^{+}}+\frac{1}{c^{ -}}\right)=\frac{\frac{2D^{\prime}}{\frac{1}{c^{+}}+\frac{1}{c^{-}}}}{=\frac {2D^{\prime}}{c_{av}}=\frac{2D^{\prime}}{c}} \tag{4}\]  
The time lapse on clock \(A\) in one cycle depends on the arm length along which the light flows and the average speed of light \(c_{av}\) on the way back and forth. It is worth noting that the time lapse on clock \(A\) does not depend on the one-way speed of light \(c^{+}\) and \(c^{-}\) if \(c_{av}=c=\mathit{constants}\) (assumption IV). Synchronization of \(A\) and \(B\) clocks depends on the one-way speed of light \(c^{+}\), and therefore synchronization depends on what theory this process is based on (classical kinematics, Special Theory of Relativity, or any of the Special Theory of Ether). However, clock \(B\) does not affect the speed at which clock \(A\) measures time. Although in the synchronization process the light impulse was sent to clock \(B\), the speed at which clock \(A\) measures the time depends only on the total time it takes for the light impulse to go back and forth. This means that clock \(A\) measures the time exactly like a light clock. Since the requests received for clock \(A\) apply to every clock, all light synchronized clocks measure the time exactly the same as a light clock. Thanks to the claim about a signal clock, it is known that in all kinematics, the standard of time is a  
(etalon) of the same time unit. It is the same for an observer from the \(U^{\prime}\) system; the length of clock arm \(D^{\prime}{}_{x}\) always has the same value because the clock arm is the same as the standard length. For an observer with the universal system \(U\), the length of the clock arm may depend on the speed at which the clock moves relative to it. We will mark this length with the symbol \(D_{x}(v)\). If \(v=0\), then the length of the clock arm is the same for observers from \(U^{\prime}\) and \(U\) systems, and therefore \(D^{\prime}{}_{x}=D_{x}(0)\).