I came across Ned Wright's webpage
http://www.astro.ucla.edu/~wright/tiredlit.htm which states that
alternative explanations for the redshift of galaxies would not be
consistent with the z-dependence of supernova lightcurves. However,
this assertion is not further substantiated and as far as I can see
any wavelength independent redshift mechanism should indeed result in
the change of the supernova lightcurves:

Consider a sinusoidal lightwave modulated by a lightcurve L(t), i.e.
E(f,t)=E0*sin(f*t)*L(t) .
By expanding L(t) into a Fourier Integral i.e.
L(t)= Int[dF*cos(F*t)*a(F)]
and drawing the sine function under the integral one gets
E(f,t)=E0* Int[dF*sin(f*t)*cos(F*t)*a(F)].
Using the addition theorems for trigonometric functions, this is
equivalent to (apart from a constant factor)
E(f,t)=E0* Int[dF*(sin((f+F)*t) + sin((f-F)*t)*a(F)].
Applying now a redshift factor (1+z) changes the frequencies to
(f+F)/(1+z) and (f-F)/(1+z), i.e. the signal becomes
E(f,t,z)=E0* Int[dF*(sin((f+F)/(1+z)*t) + sin((f-F)/(1+z)*t)*a(F)]
,
and by reversing the addition theorem and taking the sine- function
out of the integral again
E(f,t,z)=E0* Int[dF*sin(f/(1+z)*t)*cos(F/(1+z)*t)*a(F)] =
= E0*sin(f/(1+z)*t)* Int[dF*cos(F/(1+z)*t)*a(F)] =
= E0*sin(f/(1+z)*t)*L(t/(1+z)).
This means that not only is the wave frequency redshifted but also the
light curve broadened.


For anyone intererested, I have myself suggested that the redshift of
galaxies is in fact caused by the small scale electric field due to
the intergalactic plasma (a kind of counter-part to the Faraday
-rotation in a magnetic field) (for more details see
http://www.plasmaphysics.org.uk/research/#A11).


[[Mod. note -- I think the key point in this derivation is that the
redshift factor (1+z) is applied to *all* frequencies. This is
equivalent to rescaling *all* times by (1+z), and thus reproduces
the standard result. (Which implies that, for example, a light curve
which in the rest frame of the emitter has a (say) full width at half
maximum of 1 week, is observed to have a full width at half maximum
of 3 weeks when redshifted at z=2.)

As Ned Wright's web page points out, simply attenuating the energies
of all photons by a (1+z) factor (as classical "tired light" models
predict) would shift wavelengths, but wouldn't give this additional
time dilation (and would thus be inconsistent with the observations
of this time dilation quoted in Ned Wright's web page).

-- jt]]