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Doppler Effect
We don't experience redshift naturally on Earth because light moves too fast, but a similar thing happens with sound that helps explain redshift. Austrian mathematician Christian Andreas Doppler noted that when an object is moving toward us, it has a higher pitch because we perceive the high-frequency sound waves, but as it moves away, we hear the low frequency, longer sound waves. Light moving away from us is stretched into the longest frequency waves of the red light area of the spectrum. In other words, visible light "shifts" into red.
Spectrum Analysis
Using specialized telescopes, scientists can record the light spectrum of distant objects in space and use those findings to detect redshift by comparing the data to reference spectra. They can look for atomic emission and absorption lines in the spectra and measure them to determine the redshift. They can use the same type of process to deduce the chemical composition of stars as well as the degree of redshift.
Cosmological Redshift
Traditionally, red-shifting objects present evidence of an expanding universe. If light from objects in space shifts toward into red, it indicates that relative to our position, such objects move away from us. If light from other galaxies redshifts in all directions, it suggests that space itself is expanding. In 1929, Edwin Hubble proposed this. He found that redshift got greater as the galaxies got farther away, which suggests a slowly expanding universe and evidence to support the Big Bang Theory.
Alternative Interpretations
There are other reasons besides an expanding universe that light from other galaxies might redshift. For example, when you see a red sky at sunset, it is because dust and particles are refracting the light so that more red light is visible. Some galaxies appear have debris and dust that cause red-shifting. Additionally, anomalies in data may indicate that other factors, such as galaxy cluster density or the effects of protogalaxies, might create redshift and not changes in distance.