Could the Speed of Light Be Variable?

“Is the speed of light constant?” can refer to different questions: the locally measured speed in vacuum, the coordinate speed in a chosen chart, propagation in a material, or a proposed departure from relativity. The issue of synchronizing distant clocks belongs to the measurement question; it is not, by itself, evidence that light physically changes speed.

This note revises my original Chinese answer.

Round-trip measurements and synchronization

Suppose light leaves a stationary clock at $A$ at time $t_1$ , reflects at a stationary point $B$ a distance $L$ away, and returns at $t_3$ . The round-trip speed uses one clock:

c=\frac{2L}{t_3-t_1}.

Assigning an outward travel time requires a time reading at $B$ and a rule for synchronizing that clock with $A$ . Einstein synchronization assigns the reflection time

t_2=\frac{t_1+t_3}{2}.

More generally, the assignment $t_2=t_1+\varepsilon(t_3-t_1)$ , with $0<\varepsilon<1$ , produces coordinate speeds

c_{\to}=\frac{c}{2\varepsilon},\qquad c_{\leftarrow}=\frac{c}{2(1-\varepsilon)}.

The round-trip speed stays unchanged. Changing this convention changes the time coordinates and the expressions of physical laws consistently; it does not create a measurable change in the same experiment. Einstein's synchronization construction is given at the beginning of his 1905 paper.

The precise conclusion is that a one-way time between separated clocks presupposes a synchronization procedure and its physical interpretation. The formulas above are not a proof that every conceivable experiment concerning light propagation is uninformative.

What if we transport a clock slowly?

A reader of the original answer suggested synchronizing two clocks together and then slowly moving one to $B$ . Within special relativity, this is a valid way to approach Einstein synchronization.

For an ideal clock transported at constant speed $v$ over distance $L$ in the laboratory frame, ignoring the acceleration stages in this simplified calculation, the travel time is $L/v$ . The transported clock's lag is

\Delta\tau=\frac{L}{v}\left(1-\frac1\gamma\right) =\frac{L}{v}\left(1-\sqrt{1-\frac{v^2}{c^2}}\right),

where $\gamma=(1-v^2/c^2)^{-1/2}$ . As $v\to0$ ,

\Delta\tau\sim\frac{Lv}{2c^2}\longrightarrow0.

Clock transport therefore works under the stated clock dynamics. It does not select a synchronization-independent coordinate convention: interpreting the transported readings uses those dynamics. Calling the procedure simply impossible or circular would be too strong.

Convention versus physical variation

In special relativity, ideal local measurements of vacuum light speed give $c$ . A coordinate speed can differ in nonstandard coordinates, and light in a material can have a different propagation speed. Neither observation alone contradicts the vacuum statement.

A physical variable-speed proposal must specify an observable difference from relativity—for example, a change in clock comparisons or propagation relative to other measured quantities. Merely choosing unequal outward and return coordinate speeds does not supply such a difference.