In the theory of relativity, specifically in special relativity, there is a relationship between the wavelength of a photon and the perceived time interval between events. This relationship is described by the concept of time dilation.
According to special relativity, the speed of light in a vacuum is constant and the same for all observers, regardless of their relative motion. This means that the speed of light is invariant, and it plays a fundamental role in defining the structure of spacetime.
When an observer is moving relative to a light source, they will measure a different frequency (or equivalently, a different wavelength) of the light compared to an observer at rest with respect to the source. This phenomenon is known as the Doppler effect. However, the speed of light itself remains the same for all observers.
Time dilation, on the other hand, refers to the difference in the passage of time between two observers who are in relative motion or in different gravitational fields. It is not directly related to changes in the wavelength of light. Time dilation occurs due to the fundamental principles of relativity, which state that the laws of physics should be the same for all observers, regardless of their relative motion.
In practical terms, time dilation means that clocks carried by objects in relative motion or in different gravitational fields will run at different rates. The effect becomes more pronounced as the relative velocity or gravitational field strength increases.
To summarize, time dilation and changes in the wavelength of light (frequency shifts) are separate phenomena in the theory of relativity. Time dilation is a consequence of the theory, while changes in the wavelength of light are described by the Doppler effect but do not directly cause time dilation.