# Finding the cosmological redshift of a galaxy in the expanding Universe

Firstly, I understand what the Doppler effect is when it comes to sound or light waves.

From everything that I've read, we are told that the universe is constantly expanding since the all the radiation we observed is red-shifted. Assuming we are observing a distant galaxy/start that is moving away from us, the EMR waves incident on us from that galaxy is red shifted. My question is:

how do we know that the light is red shifted? When you measure its wavelength you are given just ONE value Λ, right? How does one know what its original wavelength was to begin with? Its only after we know both the values (the actual wavelength when it was emitted and the wavelength that we measure hear on earth) that we can claim that the galaxy/star is moving away.

I always assumed that one would observe both the wavelength of the photons and the energy and there is some sort of disparity there that tells us the light is red-shifted. But that does not make sense since one usually determines the wavelength based on the energy of the photon......I am confused here. Any answer will be appreciated. Thanks.

-
The energy of a photon is uniquely determined by its wavelength, by $E=hc/\lambda$, so you couldn't try to use some disparity between a photon's energy and its wavelength to discover anything. –  David Richerby Aug 12 at 9:27

Every star or galaxy contains some elements, and each element emits a particular frequency. Here are the lines of the Sun (https://en.wikipedia.org/wiki/Fraunhofer_lines)

In particular, Hydrogen is present almost everywhere and Hydrogen lines are visible in most galaxy spectra. The Hydrogen-alpha line is particularly strong in many galaxies.

This electromagnetic radiation is at the precise frequency of 1420.40575177 MHz, which is equivalent to the vacuum wavelength of 21.1 0611405413 cm in free space.

They simply compare the standard value of the H-line ( or of any other element) with the one coming from the star/galaxy, and get the value of z (the redshift).

A value of 211 cm would give a redshift (211/21.1): z = 10

Update

But that does not make sense since one usually determines the wavelength based on the energy of the photon

Such high frequencies cannot be detected. Usually it is the other way round, but you are right: there is only one wavelength that corresponds to a frequency, and that never changes

I have a followup question. Does one measure the energy of the photon incident and then calculate what its "observed" wavelength is?

Spectrography measures directly, as I said, the wavelength of the radiation, (https://en.wikipedia.org/wiki/Spectrography)

if it is 211 cm., you know right away the cosmological redshift (z) = 10

-
Hey, I have a followup question. Does one measure the energy of the photon incident and then calculate what its "observed" wavelength is? –  user57074 Aug 12 at 7:08
@user57074 You should ask that as a new question and not in a comment. But in short, the photon has the energy of the "observed" wavelength - when you change the inertial frame, energy is no longer "conserved" the way you'd expect it to be –  Tobias Kienzler Aug 12 at 9:22