Redshift Mechanisms and Supernova Lightcurves

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]]

(Thomas Smid) wrote in message
...
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:
[...]

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]]

The problem with this idea is that the motivation for a tired light model
is to preserve a static Universe. In a static Universe the light travel
time between the supernova and the observer has to be constant, and thus
the observed duration of the lightcurve has to be the same as the emitted
duration of the lightcurve. To say otherwise is to throw out the baby
with the bathwater.

However, it is true that if you halve all frequencies you double all
durations including the lightcurve duration. This is exactly what the
standard Doppler or expansion model for the redshift does. But you
really need an expanding Universe then to accommodate the greater
light travel time seen at the end of the lightcurve.

--Edward L. (Ned) Wright, UCLA Professor of Physics and Astronomy
See http:www.astro.ucla.edu/~wright/cosmolog.htm

(Ned Wright) wrote in message ...
The problem with this idea is that the motivation for a tired light model
is to preserve a static Universe. In a static Universe the light travel
time between the supernova and the observer has to be constant, and thus
the observed duration of the lightcurve has to be the same as the emitted
duration of the lightcurve. To say otherwise is to throw out the baby
with the bathwater.

However, it is true that if you halve all frequencies you double all
durations including the lightcurve duration. This is exactly what the
standard Doppler or expansion model for the redshift does. But you
really need an expanding Universe then to accommodate the greater
light travel time seen at the end of the lightcurve.

--Edward L. (Ned) Wright, UCLA Professor of Physics and Astronomy
See http:www.astro.ucla.edu/~wright/cosmolog.htm

Your argument would be correct for light propagating through a perfect
vacuum, but not if you have a kind of dispersive medium. In this case,
the lightcurve would correspond to the group velocity of the wave but
not the phase velocity, and, as you have realized yourself on your
page http://www.astro.ucla.edu/~wright/an...ispersion.html in a
different context, you can then not strictly apply the 'propagation
time' argument anymore.
I don't want to push the comparison with dispersion too far though at
this stage, yet it should be clear that a 'stretching' of the
wavetrains of light between the charged particles in the intergalactic
plasma (as suggested on my webpage
http://www.plasmaphysics.org.uk/research/#A11) should redshift the
frequency as well as broaden the lightcurve, even in a static universe
(as indicated in my opening post above).


[[Mod. note -- It seems to me that a plasma effect would be (strongly)
frequency-dependent. Astronomical redshifts are independent of frequency,
so I don't see how a plasma effect could produce them. -- jt]]

(Thomas Smid) wrote in message ...
(Ned Wright) wrote in message ...
The problem with this idea is that the motivation for a tired light model
is to preserve a static Universe. In a static Universe the light travel
time between the supernova and the observer has to be constant, and thus
the observed duration of the lightcurve has to be the same as the emitted
duration of the lightcurve. To say otherwise is to throw out the baby
with the bathwater.

However, it is true that if you halve all frequencies you double all
durations including the lightcurve duration. This is exactly what the
standard Doppler or expansion model for the redshift does. But you
really need an expanding Universe then to accommodate the greater
light travel time seen at the end of the lightcurve.

--Edward L. (Ned) Wright, UCLA Professor of Physics and Astronomy
See http:www.astro.ucla.edu/~wright/cosmolog.htm

Your argument would be correct for light propagating through a perfect
vacuum, but not if you have a kind of dispersive medium. In this case,
the lightcurve would correspond to the group velocity of the wave but
not the phase velocity, and, as you have realized yourself on your
page http://www.astro.ucla.edu/~wright/an...ispersion.html in a
different context, you can then not strictly apply the 'propagation
time' argument anymore.
I don't want to push the comparison with dispersion too far though at
this stage, yet it should be clear that a 'stretching' of the
wavetrains of light between the charged particles in the intergalactic
plasma (as suggested on my webpage
http://www.plasmaphysics.org.uk/research/#A11) should redshift the
frequency as well as broaden the lightcurve, even in a static universe
(as indicated in my opening post above).


[[Mod. note -- It seems to me that a plasma effect would be (strongly)
frequency-dependent. Astronomical redshifts are independent of frequency,
so I don't see how a plasma effect could produce them. -- jt]]

Dispersion causes a differential delay between different frequencies.
That does not cause a redshift, so dispersion is not a redshift
mechanism. Nor is dispersion observed in supernova light curves.

So if the supernova emits red and blue light simultaneously:
RBRBRBRBRB
them after traveling in a medium which disperses like a plasma one
would see:
B B B B B R R R R R
Thus the red lightcurve is not stretched by dispersion, and the blue
lightcurve is not stretched by dispersion. So dispersion does not
cause a redshift, but a redshift is observed. Dispersion does create
a difference in arrival times between red and blue light, but this is
not observed. Dispersion does not cause a stretch in the lightcurve
at any wavelength, but a stretch is seen in all observed wavelengths.
So dispersion appears to be a red herring. This fishy proposal should
be no surprise to any reader of Mr. Smid's web page.

--Edward L. (Ned) Wright, UCLA Professor of Physics and Astronomy
See http:www.astro.ucla.edu/~wright/cosmolog.htm

[[Mod. note -- It seems to me that a plasma effect would be (strongly)
frequency-dependent. Astronomical redshifts are independent of frequency,
so I don't see how a plasma effect could produce them. -- jt]]

As indicated in my opening post, one should note take the comparison
of the redshift with a dispersion effect too literally. I mentioned
this merely in order to show that a suitable mechanism could deform
the wave packets such as to lead to the redshift and still conform to
the constancy of the speed of light.
The usual dispersion theory can in fact not be applied in case of the
intergalactic plasma because not only is the average distance of the
charges much larger than the wavelength of light but even much larger
than the coherence length of the wavetrains (the coherence length of
light emitted from the collisional plasma in the photosphere of stars
is around 10^-2 cm whereas the intergalactic charges should have a
typical distance of 100 cm or more). For most of the time there isn't
therefore even a single charge within a 'photon' length. However, the
latter is then still in the electric field of the charges which could
lead to the redshift (it may actually be the field gradient which
causes this).
Again, this is would be a new phenomenon which can not be derived from
the usual dispersion theory as it is outside its scope. Even without a
quantitative theory for this, it could be tested observationally
however as for sufficiently long wavelengths and/or coherence lengthts
of the light, the redshift effect should be reduced and eventually
disappear altogether (in my opinion the Cosmic Microwave Background
radiation might be an indicator of such a threshold). One might also
be able to demonstrate the effect in the lab by observing the
propagation of light in a suitable static electric field.

(Ned Wright) wrote in message ...
Dispersion causes a differential delay between different frequencies.
That does not cause a redshift, so dispersion is not a redshift
mechanism. Nor is dispersion observed in supernova light curves.

So if the supernova emits red and blue light simultaneously:
RBRBRBRBRB
them after traveling in a medium which disperses like a plasma one
would see:
B B B B B R R R R R
Thus the red lightcurve is not stretched by dispersion, and the blue
lightcurve is not stretched by dispersion. So dispersion does not
cause a redshift, but a redshift is observed. Dispersion does create
a difference in arrival times between red and blue light, but this is
not observed. Dispersion does not cause a stretch in the lightcurve
at any wavelength, but a stretch is seen in all observed wavelengths.
So dispersion appears to be a red herring. This fishy proposal should
be no surprise to any reader of Mr. Smid's web page.

--Edward L. (Ned) Wright, UCLA Professor of Physics and Astronomy
See http:www.astro.ucla.edu/~wright/cosmolog.htm

I posted this already a a reply to the moderators note:

As indicated in my opening post, one should note take the comparison
of the redshift with a dispersion effect too literally. I mentioned
this merely in order to show that a suitable mechanism could deform
the wave packets such as to lead to the redshift and still conform to
the constancy of the speed of light.
The usual dispersion theory can in fact not be applied in case of the
intergalactic plasma because not only is the average distance of the
charges much larger than the wavelength of light but even much larger
than the coherence length of the wavetrains (the coherence length of
light emitted from the collisional plasma in the photosphere of stars
is around 10^-2 cm whereas the intergalactic charges should have a
typical distance of 100 cm or more). For most of the time there isn't
therefore even a single charge within a 'photon' length. However, the
latter is then still in the electric field of the charges which could
lead to the redshift (it may actually be the field gradient which
causes this).
Again, this is would be a new phenomenon which can not be derived from
the usual dispersion theory as it is outside its scope. Even without a
quantitative theory for this, it could be tested observationally
however as for sufficiently long wavelengths and/or coherence lengthts
of the light, the redshift effect should be reduced and eventually
disappear altogether (in my opinion the Cosmic Microwave Background
radiation might be an indicator of such a threshold). One might also
be able to demonstrate the effect in the lab by observing the
propagation of light in a suitable static electric field.

[[Mod. note -- html url reformatted to plain-ASCII, since usenet
doesn't do html. -- jt]]

Additionally to the mathematical argument in my opening post and my
subsequent arguments, I have also produced a schematic diagram
( http://www.plasmaphysics.org.uk/imgs/lightcurve.jpg )
which illustrates that a suitable stretching of the
wavetrains of light can not only lead to the redshift but also to a
corresponding change in the slope of the lightcurve and still maintain
the distance between the center of the wave packets i.e. the constancy
of the speed of light (which should be associated with the group
velocity of the wave packets) (apologies for the poor quality of the
image, but I hope the diagram makes sense nevertheless).


[[Mod. note -- I don't think anyone denies that if *all* times are
stretched by some factor (1+z), you get precisely the usual redshift,
including the observations that (eg) 1-week supernova light-curve
widths are stretched to 3 weeks at z=2, etc etc. That's the easy part.

The hards part are
(a) Figuring out -- in detail -- *how* anything other than a
cosmological expansion can stretch *all* times by the same factor.
As previously noted, plasma effects (dispersion, time delay, etc)
are highly frequency-dependent, and so don't seem like a good
explanation.
(b) Figuring out how to accomodate the dialated time scales in a
non-standard cosmology. As Ned Wright noted, the changes in
supernova time scales are (strongly) inconsistent with any sort
of static cosmology.
-- jt]]

[[Mod. note -- I don't think anyone denies that if *all* times are
stretched by some factor (1+z), you get precisely the usual redshift,
including the observations that (eg) 1-week supernova light-curve
widths are stretched to 3 weeks at z=2, etc etc. That's the easy part.

The hards part are
(a) Figuring out -- in detail -- *how* anything other than a
cosmological expansion can stretch *all* times by the same factor.
As previously noted, plasma effects (dispersion, time delay, etc)
are highly frequency-dependent, and so don't seem like a good
explanation.
(b) Figuring out how to accomodate the dialated time scales in a
non-standard cosmology. As Ned Wright noted, the changes in
supernova time scales are (strongly) inconsistent with any sort
of static cosmology.
-- jt]]

You are consequently implying that the 'accomodation' problem would
prevent any redshift altogether unless the distance between source and
observer increases. This argument would only hold in case of a
continuous sinusoidal wave where it is obvious that the same number of
cycles will occupy a larger distance if the wavelength increases.
However,if you are dealing with uncorrelated wavetrains that are short
compared to the total distance, the redshifted wavepackets are spread
over the same total length as the original ones, apart from the small
distance corresponding to the expansion of the individual wavetrain.
The latter is is observationally irrelevant however, as it is (like
the sinusoidal wave) associated with the phase velocity but not the
group velocity of the wavetrains (see
http://www.plasmaphysics.org.uk/imgs/redshift.gif for an
illustration).

It is also worth noting that a delay of the lightcurve of one week
corresponds only to about a fraction 10^-11 of the total travel time
(1 billion years). This is less than the accuracy with which the speed
of light is known. It is therefore well possible that corresponding
variations of the speed of light additionally compensate for the
'accomodation' problem.

(Thomas Smid) wrote in message ...


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)

Perhaps of some interest would be to read some of the following works
by Ruth A. Daly et al: http://www.bk.psu.edu/faculty/daly/

Cheers,

Ned

(Ned Flanders) wrote in message ...
(Thomas Smid) wrote in message ...


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)

Perhaps of some interest would be to read some of the following works
by Ruth A. Daly et al: http://www.bk.psu.edu/faculty/daly/

Cheers,

Ned

I had a look at Ruth Daly's works but couldn't really find anything
that would directly apply here. As mentioned, of interest would be in
particular data of objects where the redshift factor has been measured
independently in the optical and radio region of the spectrum. I found
some data published in the book 'Radio Recombination Lines (Ed. P.A.
Shaver)', but the corresponding radio lines have a wavelength of the
order of 1 cm which is probably still about 2 orders of magnitude
smaller than the average distance between charged particles in the
intergalactic plasma, i.e. the redshift factor would not be affected
yet by the inhomogeneities of the small scale electric field.
If anybody knows redshift factors determined for even greater
wavelengths, I would appreciate any information in this respect.