Differentiating between two photons of the same wavelength originating from close and far parts of the universe can be challenging. In general, photons of the same wavelength do not carry information about their specific origin unless they are somehow modulated or encoded during their journey.
However, there are a few indirect methods that scientists can use to determine the distance traveled by photons. Here are two commonly employed techniques:
Redshift: When light from distant objects in the universe, such as galaxies or quasars, travels a vast distance to reach us, the expansion of space causes the wavelength of the light to stretch. This stretching effect is known as redshift. By measuring the redshift of light, astronomers can estimate the distance to the source. If the photons from p1 and p2 have different redshift values, it could indicate that they originated from different distances.
Time of Arrival: The speed of light is finite, and it takes time for light to travel from one point to another. Therefore, if the photons from p1 and p2 were emitted simultaneously, the one arriving later would indicate a longer travel distance. By precisely measuring the time of arrival of photons, scientists can infer their relative distances.
It's important to note that determining the precise origin of individual photons is challenging, especially for photons with the same wavelength. Scientists often rely on statistical analyses and observations of large numbers of photons to make inferences about the distances of their sources in the universe.