Let’s consider a very distant galaxy, suppose it has no peculiar velocity, and let’s assume space expansion; If I understand correctly there would be a redshift due to the value of space expansion at the time when photons were emitted from this galaxy, then there would be a redshift due to space expansion (and its possible variations) all along the travel in space and time of these photons toward our present point of observation. How do these two redshift values compare? Is the first one negligible compared to the second one?


Here is what redshifts we are talking about:

The light from most objects in the Universe is redshifted as seen from the Earth. Only a few objects, mainly local objects like planets and some nearby stars, are blueshifted. This is because our Universe is expanding. The redshift of an object can be measured by examining the absorption or emission lines in its spectrum. These sets of lines are unique for each atomic element and always have the same spacing. When an object in space moves toward or away from us, the absorption or emission lines will be found at different wavelengths than where they would be if the object was not moving (relative to us).


The unshifted is what the particlular atomic spectrum looks in our laboratories here on earth. The red shifted tell us that the light comes from original atoms that are receeding from us, and the blue shifted tell us that the atoms are approaching us, with the corresponding velocity

Continuing from the link:

The cosmological redshift is a redshift caused by the expansion of space. As a result of the Big Bang (the tremendous explosion which marked the beginning of our Universe), the Universe is expanding and most of the galaxies within it are moving away from each other. Astronomers have discovered that all distant galaxies are moving away from us and that the farther away they are, the faster they are moving. This recession of galaxies away from us causes the light from these galaxies to be redshifted. As a result of this, at very large redshifts, much of the ultraviolet and visible light from distant sources is shifted into the infrared part of the spectrum. This means that infrared studies can give us much information about the ultraviolet and visible spectra of very young, distant galaxies.

With this in mind, the spectra from receding galaxies have all the information about the expansion of space too. It is the velocities of the original source that are recorded in the spectra, whether due to orbital motions or space expansion, at the source the velocities are added and that is what comes recorded in the shift of the spectra. The photons themselves follow the general relativity geodesics. The expansion of the space they travel through is taken care in the geodesic.

The shift is the doppler shift:

The Doppler effect (or the Doppler shift) is the change in frequency or wavelength of a wave in relation to observer who is moving relative to the wave source

It is an effect of coordinate transformations needed between observer and source.

  • $\begingroup$ thank you for this detailed answer. I'm actually wondering how the influence of general relativity geodesics on traveling photons compare with the influence of the velocity of the original source on the shift. $\endgroup$ – O.Lambert Sep 16 '18 at 10:41
  • $\begingroup$ the geodesics are part ofthe coordinate system on which zero mass particles travel, The shift is the difference in inertial frames. It exists classically too. Suppose you are in a train an throw a ball backwards in the direction of the tracks . At rest the ball will leave your hand with velocity v, and the velocity and kinetic energy will be the same for an observer on the ground next to the tracks. When the train is in motion , you will still throw it with the velocity v, and the same kinetic energy with respect to the train, $\endgroup$ – anna v Sep 16 '18 at 11:07
  • $\begingroup$ In fact, what I fail to understand is : speed of light is fixed and absolute at 3x10^8 m/s, and timespace expansion is not an actual growth of distance, but something like a dilatation of metrics. So photons traveling through an expanding spacetime would still travel at a speed of 3x10^8 m/s but the unit would be a sort of expanded meters / expanded seconds. Am I right ? Because from my modest understanding, there would then be no shift resulting from spacetime expansion during photons journey ; if speed does not change, wavelength does not neither, right ? $\endgroup$ – O.Lambert Sep 16 '18 at 11:07
  • $\begingroup$ but the ball will fall on the tracks with smaller velocity and smaller energy because of the addition with a negative sign of the train's velocity , $\endgroup$ – anna v Sep 16 '18 at 11:07
  • $\begingroup$ Then we would conclude that red/blueshift is only due to original source velocity (local + space expansion), and so, since we know that the farther away galaxies are, the faster they are moving away and away from eachother ; it would imply that the farther away we look back in time, the bigger space expansion was ; implying decelerated expansion. Which is obviously the exact opposite of what we now know from recent surveys of Supernovae Ia. Where am I wrong ? $\endgroup$ – O.Lambert Sep 16 '18 at 11:08

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