I understand that the universe is generally agreed to be expanding based on observations. What I have read is that space itself is expanding. My question is why does this expansion of space affect the spectra of light itself?

It has been observed countless time since Hubble that light from distant galaxies arrive to us with spectra shifted to longer wavelengths (red-shifted). If a wavelength of light is defined with a metric of spatial distance, then what is the significance of spatial distance itself increasing? Would not the expansion of space where our instruments of observing light also matter?

To add to my confusion on red-shifts, here is the Planck-Einstein relation:

$\lambda = \frac{hc}{E_{photon}}$

Wavelength is a function of $c$, but would this constant (distance over time metric) be affected if space dilates? The same rationale goes for time, but I have heard that time at a fixed location would not be affected by the expansion of space, but I am uncertain how time for moving objects are affected.

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    $\begingroup$ I think this has a lot to do with the "substantivalist" versus "relationist" views of spacetime, which are exhaustively discussed by Sklar in his book titled "Space. Time, and Spacetime". Tracing the issue of whether space can be conceived as resembling a substance back to verbal wrangling between Newton and Liebnitz, it antedates the theory of inflation, but is quite relativistic and was written several decades after Hubble's 1929 discovery. The math in it is less challenging than a lot seen on PSE. $\endgroup$ – Edouard Aug 14 at 3:45
  • $\begingroup$ The third paragraph doesn't seem to have any logical connection to the first two. $\endgroup$ – Ben Crowell Aug 14 at 13:04
  • $\begingroup$ Indeed. Edited. $\endgroup$ – imagineerThat Aug 14 at 18:49

Here is simple explanation:

  • Suppose a light source and a observer are in an expanding space.
  • Now think of two subsequent crests of wave emitted by the lightsource.
  • The second crest is emitted slightly later than the first one, hence the space has expanded slightly in the meantime.
  • Consequently, the second crest has to travel further to reach the observer, taking more time.*
  • Hence, the time between the arrivals of the crests at the observer is longer than the time between their emission at the source.
  • This is the same thing as saying that frequency of the wave is lower, or (since the speed of light is the same) that the wavelength is longer.

*(And since it is taking longer, space expands more while its travelling increasing its travel time a bit more.)

  • $\begingroup$ Just to make sure I understand, is this expanding space we are referring to the metric expansion of space? $\endgroup$ – imagineerThat Aug 14 at 19:23
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    $\begingroup$ @imagineerThat the observer and light source are not in expanding space. Locally their space/metric is static. It is the metric for the space in between them that is expanding. $\endgroup$ – Sextus Empiricus Aug 14 at 21:18

here is a layman's explanation:

There is a toy called a Slinky which is a loosely-wound coil spring made of either plastic or flat wire- if you haven't seen one, search on it to get the idea of how it looks.

We imagine the Slinky resting horizontally on a smooth floor, with its ends pulled apart to some convenient distance so adjacent coils of the spring are spread out and not touching. If you were to lie down on the floor next to it and view it from the side, the wire coils would trace out a sine wave curve.

Now we pull the ends of the Slinky farther apart, as if the space in which it is embedded were "expanding". We notice that the spacing between adjacent coils of the wire has increased, and in our sideways view of the coils, the sinusoid shape of the spring has "shifted" to correspond to a lower frequency.

This is analogous to the situation in an expanding space in which high-frequency sine waves are embedded: as space stretches out, so do the sine waves, and their frequency shifts down.

  • $\begingroup$ Great analogy. But does that differ from normal doppler red shift? Do things expand at all if the very metric is expanding? In the case for metric expansion, doesn't my yard stick also expand? $\endgroup$ – imagineerThat Aug 14 at 6:23
  • $\begingroup$ the yardstick does expand, but the effects of the expansion of the universe are manifest only on distance scales of order ~distance between galaxy clusters. $\endgroup$ – niels nielsen Aug 14 at 6:31
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    $\begingroup$ No the yardstick does not expand, because it is bound together other (mostly electromagnetic) forces. It is the properties of these forces (i.e. the material properties of the yardstick) that determine the size of the yardstick. $\endgroup$ – mmeent Aug 14 at 6:39
  • $\begingroup$ Yard sticks appear to expand as well, as in the ladder paradox although that's a different story. $\endgroup$ – Sextus Empiricus Aug 14 at 7:01
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    $\begingroup$ No, a local stationary yardstick will not expand in an expanding universe. (An accelerated expansion will apply a slight tension to the yardstick, hence a yardstick in an accelerating universe is slightly larger than without acceleration, but it will not grow (unless the acceleration grows)). $\endgroup$ – mmeent Aug 14 at 7:08

The layman explanation of the expanding universe is a balloon.

But now you have to imagine that observers behave like points on the balloon that do not grow like the waves on the balloon do.

scientist with telescope in an expanding balloon universe

More technically, it should be noted that not only doesn't the experimenter that is measuring the red shift remain unaffected by expansion of the universe but also the metric remains the same (ie the metric/space doesn't expand).

The Robertson Walker metric $d s^2 = dt^2 - a(t)^2 \left[ \frac{dr^2}{1-k r^2}+r^2d\Omega^2\right]$ is a solution for an idealized homogeneous isotropic universe, but the universe is coarse instead, and that (expanding) metric should be more like interpreted as the average of the metric. This averaging is done on very large time scales, for instance: even for clusters of galaxies we do not observe that they have expanded in time.

So the reason for the redshift is not the metric expanding (because it doesn't expand) but much more the relative speed of the observer as lurscher indicates in his answer. And an intuitive idea of the redshift/doppler effect is as mmeent explains in his answer: the increasing time delay between two separate moments or peaks of a wave.

  • $\begingroup$ Sorry I am a little confused, @mmeent clearly assumes the expansion of space in their answer, no? $\endgroup$ – imagineerThat Aug 14 at 19:20
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    $\begingroup$ @imagineerThat when I am saying "the metric does not expand" then I am referring to a differential expansion of space (in some places it expands in others it does not). The matter fills the universe like filaments with large voids in between them. The expansion is like a loaf of bread or a Swiss cheese. It is the voids in between the regions of high matter density that expand. $\endgroup$ – Sextus Empiricus Aug 14 at 19:57
  • $\begingroup$ Thanks. Just more for me to look into :) $\endgroup$ – imagineerThat Aug 14 at 20:39
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    $\begingroup$ @imagineerThat Some helpfull starting points can be 1. Albert Einstein and Ernst G. Straus 1945 The Influence of the Expansion of Space on the Gravitation Fields Surrounding the Individual Stars The idea is to have the static Schwarzschild metric patched to a non-static (expanding) Robertson Walker metric, and the conclusion is that within a certain region around non-homogeneous matter the expansion has no effect. 2 more thorough descriptions of these types of universe and space-time are called Inhomogeneous Cosmology $\endgroup$ – Sextus Empiricus Aug 14 at 21:13

The red-shift does not come from direct intervention from metric expansion itself, but from regular Doppler shift, albeit due to the separating velocity between source and detector, which depends itself on the distance between source and detector through Hubble's law

Just for completeness, I'll mention that the original hypothesis that red-shift came from metric expansion itself was historically called the tired light hypothesis, but they are nowadays considered widely disproved by observations

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    $\begingroup$ Ok, we're not living in the de Sitter space. What speed determines your Doppler shift? Tired light is a separate explanation from the metric expansion $\endgroup$ – OON Aug 14 at 5:29
  • $\begingroup$ There exists red shift the metric expansion as well though right? I'm curious about that in particular. $\endgroup$ – imagineerThat Aug 14 at 6:26
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    $\begingroup$ Tired light was something else, not (the hypothesis explaining how light would red shift, loose energy, in a static universe)? In an expanding universe the red shift is not only due to speed of objects but als expansion of space. $\endgroup$ – Sextus Empiricus Aug 14 at 6:56
  • $\begingroup$ @OON the recessional velocity of course. Which according to Hubble's law is $H D$, with $D$ the proper distance between source and detector $\endgroup$ – lurscher Aug 14 at 16:00
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    $\begingroup$ @lurscher This is wrong unless you talk about very small redshift. The cosmological redshift is determined by the ratio between scales of the universe at the time of emission and the time of receiving. This depends on the full cosmological history, not just on the recessional velocity at any time. Your answer is simply wrong. $\endgroup$ – OON Aug 14 at 16:59

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