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Red shift and blue shift refers to light becoming more reddish or more blueish.

A useful analogy is the Doppler effect with sound. The sounds of an approaching police car has a higher pitch than normal, whilst if it is receding the pitch would be lower. Objects that make noise and are moving towards you make a higher pitched sounds, and objects that are moving away from you make a lower pitched noise.

The same things happens with light; objects moving towards you appear more blueish (and are referred to as having been blue shifted) and objects moving away appear more reddish.

We are not aware of this in normal life because the speed of light is huge, and only objects moving away or towards you with a non-negligible fraction of this speed will have any significant blue or red shift.

It is important to note that there is a difference here with the red shift usually used by cosmologists. They often specify the distance to a far away galaxy by its red shift. This can be done because of Hubble's Law which says that the more distant a galaxy is the faster it recedes from us (and therefore the more red shifted it is). Hubble's Law thus provides a way to relate red shift to distance.

The important difference is the cause of the red shift. Whilst it is true that a distant galaxy may move away from us, it is just as likely to move towards us (and thus appear blue shifted). However, the main cause of the cosmological red shift is the expansion of the Universe! As light travels towards us space itself is stretched out by the expansion of the Universe and the wavelength of light is stretched because of this. The wavelength of light thus increases, which also causes red shift (since red has a higher wavelength than blue light for example). The longer light traveled (i.e. the further the galaxy is away) the more this happens, thus the more red shifted and we recover Hubble's Law.

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