Note: This post is an English adaptation of my original Chinese article (URL). Some parts have been modified for clarity, cultural relevance, or to better fit the English-speaking audience.
The Veritasium channel discussed the question of whether the speed of light is constant in one of its videos (here), where it highlighted the following fact: In essence, all direct measurements of the speed of light are measurements of its round-trip speed, because the one-way speed of light is not directly measurable.
The mathematical proof for this conclusion was provided by Hans Reichenbach. In essence, by positing that the moment light completes a one-way path is $t_2=t_1+\varepsilon (t_3-t_1)$, where $0 < \varepsilon < 1$, $t_1$ is the start time, $t_3$ is the time when the light completes its return journey, and $c$ is the constant for the round-trip speed of light, he demonstrated that:
$$ \left\{\begin{matrix} c_{\to} = & \dfrac{c}{2 \varepsilon } \\ c_{\gets} = & \dfrac{c}{2 (1-\varepsilon ) } \end{matrix}\right. $$
From this, it is evident that, fundamentally, no physical experiment can measure the one-way speed of light. However, for the sake of simplicity, Albert Einstein, in his theory of relativity, adopted $\varepsilon = \dfrac{1}{2}$ to obtain $c_{\to} = c_{\gets} = c$. This formulation possesses significant symmetry and simplicity, making its acceptance by the physics community a logical consequence.
A user in the comments section (of my original Chinese article) proposed a profound idea: “This is based on synchronizing clocks using light signals. If two clocks, synchronized at the same point, are then slowly moved to two different locations, could this method be used for measurement?“
This is an excellent thought! However, it is unfortunately still not feasible. This is because after two clocks are synchronized, if one is moved away at a slow, constant velocity ($v$) to a distance ($L$), the effects of time dilation must be considered. However, the Lorentz factor in the time dilation formula used in modern physics itself incorporates the one-way speed of light, $\textcolor{red}{c}$. This implies that the measurement formula in your proposed experiment is inherently dependent on the value of the one-way speed of light $\Big($the time difference between the two clocks in the calculation is $\Delta t_{delay} = \Delta t\,(1-\textcolor{red}{\gamma}) = \dfrac{L}{v}\,\left (1-\sqrt{1-\dfrac{v^2}{\textcolor{red}{c}^2}} \right )$$\Big)$, which leads to the problem of circular reasoning. If you were to adopt Reichenbach’s convention and derive your own formula for time dilation for use in your hypothetical experiment, it would still contain the value $\varepsilon$, which you must presuppose. Therefore, the circular argument cannot be circumvented.
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