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How can I explain to my 17 year old pupils that the observed redshift of distant galaxies cannot be interpreted as a doppler effect and inescapably leads to the conclusion that space itself is expanding?

I understand that this redshift is well explained in general relativity (GR) by assuming that space itself is expanding. As a consequence, distant galaxies recede from us and the wavelength of the light is "streched". Expansion, redshift and the Hubble law are explained coherently in GR, as well as many other phenomena (e.g. the cosmic microwave background), and the GR predictions about redshift agree with observations.

I understand that the redshift of distant galaxies cannot be explained as a doppler effect of their motion through space. Why exactly is a pupil's doppler interpretation wrong?

My first answer: "Blueshifted galaxies (e.g. Andromeda) are only seen in our local neighborhood, not far away. All distant galaxies show a redshift. At larger distances (as measured e.g. with Cepheïds) the redshift is larger. For a doppler interpretation of the redshift distant galaxies we must necessarily assume that we are in a special place, to the discomfort of Copernicus. In this view, space cannot be homogeneous and isotropic." Is this answer correct?

My second answer: "A doppler effect only occurs at the moment the light is emitted, whereas the cosmological redshift in GR grows while the light is traveling to us." My problem with this answer (if it is correct): what observational evidence do we have for a gradual (GR) increase of the redshift, disproving the possibility of an "instantaneous doppler shift at the moment of emission"?

My third answer: "For galaxies at $z>1$ you can only have $v<c$ if you use the doppler formula from special relativity (SR): $v=\frac{(z+1)^2-1}{(z+1)^2+1}\cdot c$". My problem with this answer: what's wrong with using the doppler formula from SR as long as someone views the universe as static, in a steady state? With just the right amount of dark energy to balance the gravitational contraction, if you wish?

My fourth answer: "Recent observations of distant SN Ia show a duration-redshift relation that can only be explained with time dilation [see Davis and Lineweaver, 2004, "Expanding Confusion etc."]" My problem with this answer: does time dilation prove we have expanding space, in disagreement with a doppler effect?

My fifth answer would involve the magnitude-redshift relation for distant SN Ia [Davis and Lineweaver], but that's too complicated for my pupils.

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    $\begingroup$ There are always different levels of explanation. While technically not correctly characterized as a doppler redshift, I would not say that explaining it to 17 year olds that way without involving general relativity is exceptionally poor teaching. Even the "special place" Copernican interpretation is not required, unless you want to hold on to a "rigid space" model. I would say that at this level letting go of a rigid space is a good idea and using language like "expanding space makes it look like the galaxies are retreating ever faster and it causes a doppler effect-like redshift" is OK. $\endgroup$ – CuriousOne Jan 9 '16 at 22:03
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In Stephen Weinberg's well-known book "The First Three Minutes," he talks solely about Doppler shifts. A good review and analysis of the "expanding space" vs. Doppler shift question was provided by Bunn and Hogg, "The kinematic origin of the cosmological red shift," Am. J. Phys. 77 (8), 2009, pp. 688-694. They make convincing arguments that the red shift is best understood as a series of Doppler shifts in overlapping space-time regions small enough so that Minkowski (flat) space-time geometry is an excellent approximation. Regardless, they say in the Conclusion: "There is no “fact of the matter” about the interpretation of the cosmological redshift: what one concludes depends on one’s coordinate system or method of calculation." Their argument for the Doppler shift says it is more "natural" because it is consistent with a number of well-established facts about the general relativistic theory of gravity.

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  • $\begingroup$ While I don't work in this area, I think that the reason many authors discourage people from thinking about cosmological redshifts as "Doppler" is that thinking in terms of "motion away from us" makes several basic errors attractive (think "we're in the middle" and "the universe is expanding into pre-existing space"). Bunn's treatment is sensible but arises from a sophisticated understanding of what "velocity" is involved. $\endgroup$ – dmckee Jan 10 '16 at 2:59
  • $\begingroup$ Yes I also think that cosmological redshift is stressed under this name to emphasise space expansion. However it is not observationally different from a Doppler shift. $\endgroup$ – Alchimista Nov 18 '17 at 10:36
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There are two parts to understanding this:

  1. Space is expanding - we know this to be true because as distance increases, so does recessional velocity (Hubble's law). So the more space in-between, the faster it recedes. Therefore the space itself is responsible for the recessions, and thus must be expanding. There is simply so much evidence for Hubble's law, that the probability that every galaxy (except very close galaxies) just happens to be receding from us is minuscule.

  2. Why the light is stretching - there are two equivalent ways to think about this.

    • In the sources rest frame: the light source emits light at the rest wavelength and as the light propagates through space it's physical properties (wavelength) expand with space. N.B. amplitude doesn't increase because it's not physical.
    • In the observers rest frame: the source is moving away from us, so when it emits the light is immediately Doppler shifted red-wards, and then proceeds through space at this wavelength.

Note both ways of thinking in 2 fall under the definition of cosmological redshift, despite from the observers frame it looks a lot like a Doppler shift. I think the distinction is that any Doppler shift due to the expansion of space, should be considered cosmological redshift.

Hope this helps.

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