In 2001 Goldhaber
and the Supernova Cosmology Project
published results of a time dilation analysis of 60 supernovae. A plot
of their width factor w versus the redshift z is shown
If the redshift were due to a tired light effect, the width of a supernova
light curve would be independent of the redshift, as shown by the red
If the redshift is due to an expanding Universe, the width factor should
be w = (1+z) as shown by the blue line.
The best fit to the data is the black line, and it is clearly consistent with
the blue line and rules out the tired light model.
My best fit line is
w = 0.985*(1+z)(1.045 +/- 0.089)
using a least sum of absolute errors robust estimator to find the fit
and the half-sample bootstrap to estimate the errors. This data excludes
the tired light model by more than 11 standard deviations.
Blondin et al. (2008)
also studied distant supernovae, but used spectra to judge the age of
the supernovae. They found an aging rate that varied like
1/(1+z)(0.97 +/- 0.10),
compatible with the expected
1/(1+z) for expanding Universes, but 9.7 standard deviations
away from the constant aging rate expected in the tired light model.
The tired light model can not produce a blackbody spectrum for the
Cosmic Microwave Background without some incredible coincidences.
The expanding balloon analogy for cosmological models can be used to
show this. The figure below shows the analogy at
two different times.
Note that the galaxies (yellow blobs) do not grow, but the distance
between galaxies grows, and that the photons move and shift from blue to
red as the Universe expands, and the photon density goes down.
But in the tired light model, illustrated below, the density does not go
Thus in the tired light model the energy of the CMB photons will go down
but the density will not go down to match the density of a cooler blackbody.
The local Universe is transparent and has a wide range of temperatures,
so it does not produce a blackbody, which requires an isothermal
absorbing situation. So the CMB must have come from a far away part
of the Universe, and its photons will thus lose energy by the tired light
effect. The plot below shows what happens if the CMB comes from
z = 0.1.
Assume that the CMB starts out as a T = (1+z)*To = 2.998 K
blackbody, which is the blue curve.
Because the photons only lose energy but do not decrease their
density, the resulting red curve is not a blackbody at To = 2.725,
but is instead (1+z)3 = 1.331 times a blackbody.
The FIRAS data limit this prefactor
to 1.00001+/-0.00005, which requires that the CMB come from redshifts
less than 0.00005, or distances less than 0.25 Mpc. This is less than the
distance to the Andromeda Galaxy M31, and we know the Universe is
transparent well beyond this distance.
In fact, since millimeter wave emission is observed to come from galaxies
at redshifts of 4.7 or higher, the tired light model fails this test
by 100,000 standard deviations.
the CMB cannot be redshifted starlight.
Some diehards refuse to face these facts, and continue to push
tired light models of the CMB,
but these models do not agree with the observations.
The tired light model fails the Tolman surface brightness test.
This is essentially the same effect as the CMB prefactor test,
but applied to the surface brightness of galaxies instead of to the
emissivities of blackbodies.
Lubin & Sandage (2001)
show that tired light fails this test by 10 standard deviations.