In the context of the light clock experiment, the observed time dilation is not solely a result of the Doppler effect. While the Doppler effect does play a role in relativistic effects, such as the shift in frequency of light waves due to relative motion, it is not the sole explanation for time dilation.
The time dilation observed in the light clock experiment is a consequence of both the Doppler effect and the fundamental principles of relativity, including the constancy of the speed of light and the relativity of simultaneity. Let's consider the thought experiment:
In the light clock experiment, a stationary observer observes a moving observer carrying a light clock. The moving observer's clock consists of two mirrors placed a fixed distance apart, with light bouncing back and forth between them. From the perspective of the stationary observer, the moving observer's clock appears to tick slower compared to their own clock.
This observed time dilation is not merely a result of the Doppler effect. The Doppler effect would indeed cause a frequency shift in the light waves emitted by the moving observer, resulting in a change in perceived color or frequency. However, time dilation goes beyond this frequency shift.
The observed time dilation in the light clock experiment arises from the combined effects of the relative motion between the observers and the principles of relativity. The constancy of the speed of light leads to the observed time dilation as the moving observer's velocity changes the round-trip path length of light within their clock. This change in path length affects the apparent ticking rate of the clock, resulting in time appearing to run slower for the moving observer from the stationary observer's perspective.
Connecting a counter to the light clock can indeed provide a direct measurement of the time dilation experienced by the moving observer. By counting the number of ticks or cycles of the light clock, one can quantitatively compare the passage of time between the moving and stationary frames of reference. The counter allows for a more precise measurement of the time dilation effect.
To summarize, while the Doppler effect is involved in relativistic effects, the observed time dilation in the light clock experiment is a consequence of both the Doppler effect and the fundamental principles of relativity, including the constancy of the speed of light and the relativity of simultaneity. Connecting a counter to the light clock allows for a direct measurement and quantification of the time dilation experienced by the moving observer.