How do we know that the light from a distant, moving source has shifted from one part of the spectrum to another?
We know that the light has shifted, as we can compare a source's light spectrum to other sources we know about on Earth.
Each element has a unique spectral 'fingerprint', which is a series of bands that appear in the light spectrum at very well defined positions. The positions of these bands relate to the way in which the electrons are arranged around an element. Quantum mechanics dictates that the electrons can only have certain energy levels, and when an atom gets hot, transitions between these levels start to occur. When an electron falls from a higher energy level to a lower energy level, a photon is given off. The fact that the possible energy levels of these electrons are limited in any given atom, means that the energies of the photons given off are also limited to specific values. Therefore, narrow bands are seen in the spectrum of, say, a distant star, at wavelengths corresponding to these specific energies.
The arrangement and positioning of these bands has been measured in a laboratory by heating an element (e.g. hydrogen or helium, which are very common in stars) and looking at the spectrum it produces. When compared to the spectrum of a distant star, it is relatively easy to see how far this 'fingerprint' has moved. This can not only tell us how fast the star is moving away from or towards us, but also what it is made of.
Christopher Martin, MSci, Physics Postgraduate, University of Nottingham, GB
Observation of nearby stars and computer models of stellar evolution have given us reliable values for the emission spectra of certain types of celestial bodies. Thus if we detect light coming from a distant body which has a spectrum similar in pattern to a known type, but shifted to either the red or blue, we can be fairly certain we are seeing a known object type either receding or approaching.
This is not to say that your question does not touch on an assumption made by the astronomers making these measurements (and we know what can sometimes happen when we assume!): that this is not some unknown object type that just HAPPENS to have the same spectrum pattern, only shifted up or down. Fair enough, this is an (albeit highly likely) assumption astronomers make. But without assumptions, almost no logical extrapolation and induction would be possible, and science could not do much of anything.
Rob Landolfi, Science Teacher
'There is no inductive method which could lead to the fundamental concepts of physics. Failure to understand this fact constituted the basic philosophical error of so many investigators of the nineteenth century.'