Time dilation is a fascinating concept from Einstein’s theory of relativity, which states that time can pass at different rates depending on the relative velocity of observers. This phenomenon can be measured using precise instruments, such as atomic clocks, in a variety of experimental settings. Below are three practical examples that illustrate how time dilation can be measured in moving clocks.
In this experiment, we can observe the effects of time dilation using a high-speed train. The context involves a scenario where an observer stands on a platform while a train, equipped with an atomic clock, travels at a significant fraction of the speed of light.
An atomic clock on the train measures time as it moves. The observer on the platform also has a synchronized atomic clock. As the train speeds past, both clocks are compared. Due to the effects of time dilation, the clock on the train will show less elapsed time than the clock on the platform when the train comes to a stop. This discrepancy can be calculated using the formula for time dilation:
[ t’ = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}} ]
Where:
In this case, if the train travels at 0.8c, the time dilation effect would be significant enough to measure.
GPS satellites orbiting the Earth experience time dilation due to their high speeds and the weaker gravitational field compared to clocks on the surface. This experiment shows how time dilation must be accounted for in GPS technology.
Each GPS satellite carries atomic clocks that are synchronized with clocks on Earth. However, as the satellites move quickly in their orbits at about 14,000 km/h (approximately 0.004c), their clocks run slower than those on the ground due to time dilation.
The combined effects of special relativity (due to speed) and general relativity (due to gravitational differences) must be calculated to ensure accurate positioning data. The time difference is approximately 38 microseconds per day, which is corrected for in GPS calculations.
In particle physics, high-energy particles moving close to the speed of light provide an excellent context for measuring time dilation. At CERN, scientists accelerate particles, such as protons, to nearly the speed of light in the Large Hadron Collider (LHC).
When these particles are accelerated, their lifetimes appear longer to observers at rest compared to what is measured in stationary reference frames. For instance, muons (particles created in cosmic ray interactions) have a lifetime of about 2.2 microseconds when at rest. However, when moving at relativistic speeds, they can travel much farther before decaying, demonstrating time dilation.
In this experiment, physicists measure the distance muons travel before they decay to quantify the time dilation effect.