Static Universe

In article , Phillip
Helbig---undress to reply writes:

Perhaps it is a question of definition, but the fact that the trajectory
followed by a photon is the same as that of a massive particle (in the
limit of small mass, so that its own gravitational field can be
neglected) shows that they interact much as ordinary matter does.

Of course, also in the limit of speed = speed of light. One can thus
calculate the bending of light in Newtonian gravity.

But wait: GR gives an effect which is a factor of 2 larger. So, in this
sense, light interacts twice as strongly with gravity than one might
otherwise expect.

In any case, there is no argument over the observations of gravitational
bending of light, nor over their interpretation, nor whether they
conform to the predictions of GR.

If one takes the GR view that there is no "force" of gravity, then
obviously there is no "force" acting on light and hence no interaction.
But this applies to massive objects as well.

One can quibble about definitions, but is there any real sense in which
"photons do not interact gravitationally" (but, presumably the exception
proving the rule here, other stuff does)?

On Wed, 13 Apr 11, Phillip Helbig wrote:
GR gives an effect which is a factor of 2 larger. So, in this
sense, light interacts twice as strongly with gravity than one might
otherwise expect.

This is just because GR substitutes space-time in place of Newtonian
space.

If one takes the GR view that there is no "force" of gravity, then
obviously there is no "force" acting on light and hence no interaction.
But this applies to massive objects as well.

Except that the massive object subtends its own gravitational field,
of course.

One can quibble about definitions, but is there any real sense in which
"photons do not interact gravitationally" (but, presumably the exception
proving the rule here, other stuff does)?

This is a topic I posted on quite a bit on sci.physics back in the
1990's. Discussions on the nature of the travelling photon usually
carry hidden assumptions, such as motion being continuous, even though
experiments like Wheeler's delayed-choice specifically disestablish
that. QED also models the photon's position as statistical even in
the direction of propagation. The point is that we can't model the
photon as inhabiting its flight path at any point at all. If it isn't
there, it won't interact or gravitate.

Think about what it means to travel at the speed of C. Neither
distance nor time are present -- so spacetime is absent. The speed of
C is simply a boundary condition of physical law, and photons use that
to get around. I suppose that radiation is much like conduction to
the photon, which just steps from emission to registration with
nothing in between. Of course, it may travel 10^7 light years in the
meantime, but that's our spacetimey problem which we solve with
Schroedinger equations and whatnot.

A key point of relativity is that whatever happens, happens in every
reference frame. In the case of the photon, it has no time to exist
or interact in its own flight path, therefore we won't see any such
interaction happen. The photon does not interact because it can't, in
its own frame.

The "real sense" that you ask about, Phil, the falsifiable sense, is
that momentum is not exchanged. Photons have momentum, of course, so
a sufficient mass which "bends" light paths should get a momentum
impulse from each photon. But it doesn't and this will never be
measured. Let me know when a laboratory measures otherwise (ha ha).

Sorry if this was wordy, but physicists often seem locked into an idea
that GR is some kind of theory of the nature of light. It isn't.

Eric Flesch

On Apr 11, 9:45 am, Eric Gisse wrote:
On Apr 10, 11:33 am, Thomas Smid wrote:

Contrary to the belief of many people on USENET, apparently including
yourself, you can't just snap your fingers and have well established
phenomena suddenly decide to do things it has never done before.

Sure, photon-photon scattering has been observed. But the intensities
required for that little move were a fair bit higher than the
emptiness that is space.

You still don't seem to be getting my argument: it is only the long
distance (or time if you want) that makes the effect observable at
all. In the lab it would be way too small to be detected even with the
highest electric fields possible.

Plus photons are actual particles.

Photons are not particles but electromagnetic waves. The particle
model can for instance not explain the photoionization process (the
necessary energy could not be transferred if this is considered to be
an elastic particle collision, and there would be no way to explain
the fact that photoelectrons are emitted primarily in the direction of
the electric field vector of the light wave; the wave model can
explain all this; see my page http://www.physicsmyths.org.uk/photons.htm
for more).
Plus,

Making stuff up won't fly.

There is a difference between making things up (i.e. claiming things
that are factually untrue) and suggesting a new theory (or expanding
an existing theory) to interpret certain facts. Without the latter
scientific progress would be impossible.
\
1) There is no way that photoelectrons of around 10 eV could lose
sufficient energy such as to end up with a kinetic temperature of
around 10^-2 eV (100K) (as assumed in these papers).

Except electrons aren't the ones doing the work here. Read the paper.

Only electron collisions could populate the upper levels. The energy
transfer in an elastic collision of two masses m and M is of the order
m/M which makes it impossible for anything but electrons to transfer
10s of eV if the kinetic temperature is only of the order of 100K.


2.) It is assumed in these papers that the fine-structure levels are
populated according to a Boltzmann distribution. This would require
that elastic collision time scales are shorter than the life time of
the levels.

No such requirement exists. Do you have a short proof or a reference
that justifies this?

Well, take any book that derives the Maxwell or Boltzmann
distribution. It should be self-evident from this. Or read my web page
http://www.plasmaphysics.org.uk/maxwell.htm .


Taking the values assumed here, the elastic collision time
scale with neutrals would be about 10^10 sec. I am not familiar with

I'm rather curious to know how you pulled 10^10 sec for a
characteristic collision time out of the air.

velocity of H molecules at 100K : v^P^5 cm/sec
density of H : n^P cm^-3
collision cross section Q^P^-16 cm^2

i.e the collision time
whereas the lifetime of the C I J^P transition (see Ge et al.) 1.3*10^7 sec

that is, LTE (and thus a Boltzmann distribution) does not apply here.



The (z,T) diagram compares observations of the CMB at DIFFERENT
redshifts. Go ahead - draw a straight line of T Doesn't fit anything except (Srianand et al.), and most certainly not
the paper you just cited. You might note the much smaller error bars -
things have come a good way in 11 years.

But I did draw a straight line of T?nd it fits all
data points (see http://www.plasmaphysics.org.uk/imgs/srianand.gif ,
and the 1 or 2 more recent measurements would also be covered by
this). The only justification for the (1+z) line is here the COBE
measurement, and this point was obtained by a completely different
method. Claiming that these data confirm the (1+z) increase of the CMB
temperature is simply without any basis (I wouldn't even have passed a
practical undergraduate unit with this kind of 'data analysis'). What
could be so difficult for one observing group to measure lets say 4 or
5 objects with different redshift and sufficient accuracy by an
*identical* method and with the same instrument and then plot the data
points against z? One would not even have to bother about the absolute
value of T obtained, as this is very likely to suffer from systematic
errors anyway (considering all the obscure assumptions and estimates
that go into the data analysis in the mentioned papers). As it stands,
with each group basically producing one data point in different ways,
the result is scientifically worthless.

Thomas

On Apr 8, 6:28 am, Thomas Smid wrote:
On Apr 7, 9:06 am, Thomas Smid wrote:

On Apr 5, 7:03 am, Eric Gisse wrote:
..

Ok. How does it explain the Tolman surface brightness test (direct
test of expansion vs other possibilities)

As mentioned already, if the redshift not only increases the
wavelength of the electromagnetic waves but also reduces their
amplitude inversely proportionally (as suggested on pagehttp://www.physicsmyths.org.uk/redshift.htm), then this leads already
to a decrease of the intensity proportional to z^-2 . If you
furthermore take my theory for the photoelectric effect (http://www.plasmaphysics.org.uk/photoionization.htm) then there adds
another factor z^-2 due to the fact that the photoionization
efficiency is proportional to the square of the field strength (Eq.
(8)), i.e. overall it is proportional to z^-4. So no expanding
universe is needed to explain the observed surface brightnesses.

Actually, I noticed that my argument was not quite correct, as I did
not take into account that the ionization time (Eq.(8) on that page)
also contains the frequency nu which obviously will be inversely
proportional to the redshift. Thus the intensity (which according to
my theory is the inverse of the ionization time) would only go like
z^-3 (or rather (z+1)^-3). Even though this is actually more
consistent with observations than a (z+1)^-4 decrease (seehttp://en.wikipedia.org/wiki/Tolman_surface_brightness_test) my
equation also additionally contains the coherence time tau_c, and I
can't find a stringent argument at the moment how this would be
affected by the redshift. Bear with me until I have thought this issue
through.again.

I noticed that I made an error here in the first place, because my
equation for the ionization efficiency of an electromagnetic wave (~
t_c*E^2/f ) is effectively a measure of the photon flux, whereas the
observed surface brightness of galaxies is usually formulated in terms
of the energy flux. In terms of photons, the observed surface
brightness is actually ~1/(z+1)^2 (energy flux 1/(z+1)^3).

Now the coherence time t_c should actually be independent of the
redshift if one assumes that the 'stretching' of the wave train does
not affect the location of its center (as suggested in the
illustration on my page http://www.physicsmyths.org.uk/redshift.htm ),
because then the number of phase jumps that the wave field has within
some unit distance is the same for the original and the redshifted
version.

Since the frequency f would obviously be ~1/(z+1), this means that the
ionization efficiency equation would require E^2*(z+1) ~ 1/(z+1)^2 or
E ~ 1/(z+1)^1.5 . Since according to the argument given under the
above link, the stretching of random wavetrains would tend to increase
the field strength by a factor (z+1)^0.5 (due to the increasing
overlap), this means that the field strength of the individual wave
train must decrease with 1/(z+1)^2 (not like 1/(z+1) as suggested on
the page). I don't know a stringent argument at the moment how to
justify this particular dependence, but on the other hand I don't know
an argument either that would rule it out.

Thomas

On Apr 15, 4:17 pm, Thomas Smid wrote:
On Apr 11, 9:45 am, Eric Gisse wrote:

I am not sure what happened in my previous post. Google seems to have
made some code changes that mess up equations.. I repeat my answers
with spaces around the equal signs. Maybe it displays correctly:

Taking the values assumed here, the elastic collision time
scale with neutrals would be about 10^10 sec. I am not familiar with

I'm rather curious to know how you pulled 10^10 sec for a
characteristic collision time out of the air.


velocity of H molecules at 100K : v = 10^5 cm/sec
density of H : n = 10 cm^-3
collision cross section Q = 10^-16 cm^2

i.e the collision time = 1/(v*n*Q) = 10^10 sec

whereas the lifetime of the CI J = 1-0 transition (see Ge et al.) =
1.3*10^7 sec

that is, LTE (and thus a Boltzmann distribution) does not apply here.

The (z,T) diagram compares observations of the CMB at DIFFERENT
redshifts. Go ahead - draw a straight line of T = 8K. Doesn't fit anything except (Srianand et al.), and most certainly not
the paper you just cited. You might note the much smaller error bars -
things have come a good way in 11 years.

But I did draw a straight line of T = 8K through it and it fits all
data points (see http://www.plasmaphysics.org.uk/imgs/srianand.gif ,
and the 1 or 2 more recent measurements would also be covered by
this). The only justification for the (1+z) line is here the COBE
measurement, and this point was obtained by a completely different
method. Claiming that these data confirm the (1+z) increase of the CMB
temperature is simply without any basis (I wouldn't even have passed a
practical undergraduate unit with this kind of 'data analysis'). What
could be so difficult for one observing group to measure lets say 4 or
5 objects with different redshift and sufficient accuracy by an
*identical* method and with the same instrument and then plot the data
points against z? One would not even have to bother about the absolute
value of T obtained, as this is very likely to suffer from systematic
errors anyway (considering all the obscure assumptions and estimates
that go into the data analysis in the mentioned papers). As it stands,
with each group basically producing one data point in different ways,
the result is scientifically worthless.

Thomas


[[Mod. note -- It's irrelevant that different methods were used to
obtained different data points -- what matters is that a cosmological
model must fit *all* the correct data points to be viable.

If you look at figure 4 of
Noterdaeme et al,
"The evolution of the Cosmic Microwave Background Temperatu
Measurements of T_CMB at high redshift from carbon monoxide
excitation"
http://arxiv.org/abs/1012.3164
it's clear that the hot-big-bang prediction fits the data beautifully,
and that no horizontal line (T independent of z) comes even close to
fitting the data. (In fact, both of these last two statements would
remain true even if you ignored the z=0 data point in that figure.)
-- jt]]

On Apr 15, 9:17 am, Thomas Smid wrote:
On Apr 11, 9:45 am, Eric Gisse wrote:

On Apr 10, 11:33 am, Thomas Smid wrote:
Contrary to the belief of many people on USENET, apparently including
yourself, you can't just snap your fingers and have well established
phenomena suddenly decide to do things it has never done before.

Sure, photon-photon scattering has been observed. But the intensities
required for that little move were a fair bit higher than the
emptiness that is space.

You still don't seem to be getting my argument: it is only the long
distance (or time if you want) that makes the effect observable at
all. In the lab it would be way too small to be detected even with the
highest electric fields possible.

Except there is no supporting theory for this. Just your personal
desire for that particular outcome.

You have nothing quantitative. Just the result you want.


Plus photons are actual particles.

Photons are not particles but electromagnetic waves. The particle
model can for instance not explain the photoionization process (the
necessary energy could not be transferred if this is considered to be
an elastic particle collision, and there would be no way to explain
the fact that photoelectrons are emitted primarily in the direction of
the electric field vector of the light wave; the wave model can
explain all this; see my pagehttp://www.physicsmyths.org.uk/photons.htm
for more).

I am not in the mood to give a remedial course in electromagnetic
theory and modern physics today.

But I assure you that you need one both.


Plus,
Making stuff up won't fly.

There is a difference between making things up (i.e. claiming things
that are factually untrue) and suggesting a new theory (or expanding
an existing theory) to interpret certain facts. Without the latter
scientific progress would be impossible.

Except you don't have a theory. You have the result you want (electric
field causes redshift!) without ANY justification. You know it does
not fit with the observed behavior of electromagnetic waves, but here
you are.

\

1) There is no way that photoelectrons of around 10 eV could lose
sufficient energy such as to end up with a kinetic temperature of
around 10^-2 eV (100K) (as assumed in these papers).

Except electrons aren't the ones doing the work here. Read the paper.

Only electron collisions could populate the upper levels. The energy
transfer in an elastic collision of two masses m and M is of the order
m/M which makes it impossible for anything but electrons to transfer
10s of eV if the kinetic temperature is only of the order of 100K.

So by your own reasoning the energy of excitation could come from the
CMBR.

Excellent. Saves me from having to work through your argument in
detail.


2.) It is assumed in these papers that the fine-structure levels are
populated according to a Boltzmann distribution. This would require
that elastic collision time scales are shorter than the life time of
the levels.

No such requirement exists. Do you have a short proof or a reference
that justifies this?

Well, take any book that derives the Maxwell or Boltzmann
distribution. It should be self-evident from this. Or read my web pagehttp://www.plasmaphysics.org.uk/maxwell.htm.

You seem to have forgotten that the distribution says nothing about
energy levels or other such things. In fact, the assumption is that
there are no long range interactions between the atoms.

Which is a fair assumption here because - again - the carbon gas is
neutral.




Taking the values assumed here, the elastic collision time
scale with neutrals would be about 10^10 sec. I am not familiar with

I'm rather curious to know how you pulled 10^10 sec for a
characteristic collision time out of the air.

velocity of H molecules at 100K : v^P^5 cm/sec
density of H : n^P cm^-3
collision cross section Q^P^-16 cm^2

i.e the collision time
whereas the lifetime of the C I J^P transition (see Ge et al.) 1.3*10^7 sec

that is, LTE (and thus a Boltzmann distribution) does not apply here.

What does this have to do with ANYTHING? The Carbon isn't being
ionized, it is merely getting its' outermost electron pushed up a
little bit out of its' ground state. The distribution is still going
to be Maxwellian as long as it isn't a plasma.


The (z,T) diagram compares observations of the CMB at DIFFERENT
redshifts. Go ahead - draw a straight line of T Doesn't fit anything except (Srianand et al.), and most certainly not
the paper you just cited. You might note the much smaller error bars -
things have come a good way in 11 years.

But I did draw a straight line of T?nd it fits all
data points (seehttp://www.plasmaphysics.org.uk/imgs/srianand.gif,
and the 1 or 2 more recent measurements would also be covered by
this).

Uh, so let me get this straight. You are arguing that there is an 8
degree heat source EVERYWHERE IN THE UNIVERSE....except locally? I
could draw a sine wave through that data too. But like your fit, it is
physically NONSENSE.


The only justification for the (1+z) line is here the COBE
measurement, and this point was obtained by a completely different
method.

Yeah, it is impossible for two different ways of measuring something
to agree.

Glad you caught that.

Claiming that these data confirm the (1+z) increase of the CMB
temperature is simply without any basis (I wouldn't even have passed a
practical undergraduate unit with this kind of 'data analysis'). What
could be so difficult for one observing group to measure lets say 4 or
5 objects with different redshift and sufficient accuracy by an
*identical* method and with the same instrument and then plot the data
points against z?

For fu....you didn't even try to do a literature search.

http://arxiv.org/pdf/1012.3164

You are wrong. Give up.

One would not even have to bother about the absolute
value of T obtained, as this is very likely to suffer from systematic
errors anyway (considering all the obscure assumptions and estimates
that go into the data analysis in the mentioned papers). As it stands,
with each group basically producing one data point in different ways,
the result is scientifically worthless.

Thomas

This is what separates cranks from scientists. You have been given
multiple independent results, and you reject all of them because they
disprove your claims. You cannot find actual fault in the analysis,
yet you still blather forth about systematics and how the data is
worthless.

Find a new hobby. I am done with you here.

[[Mod. note -- It's irrelevant that different methods were used to
obtained different data points -- what matters is that a cosmological
model must fit *all* the correct data points to be viable.

If you look at figure 4 of
Noterdaeme et al,
"The evolution of the Cosmic Microwave Background Temperatu
Measurements of T_CMB at high redshift from carbon monoxide
excitation"
http://arxiv.org/abs/1012.3164
it's clear that the hot-big-bang prediction fits the data beautifully,
and that no horizontal line (T independent of z) comes even close to
fitting the data. (In fact, both of these last two statements would
remain true even if you ignored the z=0 data point in that figure.)

Sure, all observations should comply with the suggested model, but the
point is that, as it is, the *only* significant z-dependence of the
CMB temperature seems to be be associated with the different methods/
groups that obtained the data. In the reference you gave, one can for
instance still fit the red data with a constant temperature (only one
or two error bars miss the line by a small amount). All pair-
combinations of the red error bars overlap, so the difference between
their mean values is statistically insignificant (apart from the
second and last points and even here this is not statistically
significant considering the fact that these are just standard error
bars (see http://www.graphpad.com/articles/errorbars.htm )). And the
blue data points do not look any more convincing on their own in this
respect.

But anyway, as I said earlier, the analysis in these papers is based
on the assumption that the level densities are given by a Boltzmann
distribution, which would only be justified if the levels are both
populated and depopulated by collisions. However, as the natural decay
times of the levels are much smaller than the collision times (the
latter being about 10^10 sec), this conditions is far from being
fulfilled. The assumption of a Boltzmann distribution introduces
therefore a systematic error here which renders the data invalid in
the first place.

Thomas

[[Mod. note -- Your statement that a Boltzmann distribution "would
only be justified if the levels are both populated and depopulated
by collisions" is exactly backwards -- a Boltzmann distribution is
justified (only) if the levels are in radiative equilibrium with
the CMBR photons, i.e., if collisional excitation does *not* occur,
i.e., if the mean-time-to-collision is *long*.

Noterdaeme et al mention the requirement to correct for collisional
excitation in some other measurements in their section 2.1.
-- jt]]

On Apr 17, 3:54 pm, Thomas Smid wrote:
[[Mod. note -- It's irrelevant that different methods were used to
obtained different data points -- what matters is that a cosmological
model must fit *all* the correct data points to be viable.

If you look at figure 4 of
Noterdaeme et al,
"The evolution of the Cosmic Microwave Background Temperatu
Measurements of T_CMB at high redshift from carbon monoxide
excitation"
http://arxiv.org/abs/1012.3164
it's clear that the hot-big-bang prediction fits the data beautifully,
and that no horizontal line (T independent of z) comes even close to
fitting the data. (In fact, both of these last two statements would
remain true even if you ignored the z=0 data point in that figure.)

Sure, all observations should comply with the suggested model, but the
point is that, as it is, the *only* significant z-dependence of the
CMB temperature seems to be be associated with the different methods/
groups that obtained the data.

Observe how deftly the goal post has moved. Earlier the claim was that
this couldn't POSSIBLY be accurate because it was just one Earthbound
datapoint and a few neutral carbon datapoints.

Now the claim is that suddenly it is a problem when three methods +
local agree. Which is somehow a problem, rather than further
independent confirmation.

In the reference you gave, one can for

I gave the reference.

The funny thing is that you had done literally no literature searches
by yourself previous to that. Which makes your changing of arguments
rather remarkable in speed.

instance still fit the red data with a constant temperature (only one
or two error bars miss the line by a small amount). All pair-

Yeah only one or two data points out of 4, which are 4 out of about 20
points. Only 25 to 50% of the data needs to be dumped for your
nonphysical theory to fit some of the data from a particular method.
Note the lack of discussion of the CO [green] data points. Horizontal
lines certainly don't fit green by itself, and certainly does not fit
red+green. Or any other combination of red/green/blue.

combinations of the red error bars overlap, so the difference between
their mean values is statistically insignificant (apart from the
second and last points and even here this is not statistically
significant considering the fact that these are just standard error
bars (seehttp://www.graphpad.com/articles/errorbars.htm)).

I suspect you need the introduction to error analysis more than anyone
else here.

You are using 'statistical significance' to argue that the data means
nothing, a few data points at a time. You seem to be rather afraid of
discussing the whole graph.

And the
blue data points do not look any more convincing on their own in this
respect.

But they aren't on their own, are they? They are on the same graph as
8 other data points from other methods, which considered together
rather than one-at-a-time paints a rather clear picture. Your model is
wrong.


But anyway, as I said earlier, the analysis in these papers is based
on the assumption that the level densities are given by a Boltzmann
distribution, which would only be justified if the levels are both
populated and depopulated by collisions.

UHHH, NO. The exact opposite is required, otherwise the observations
correspond to the mean temperature of the gas rather than the CMBR.

[[Mod. note -- When I originally posted this article a few hours ago,
I mistakenly chopped off the last line. I'm sorry for the fumble-fingers.
Here is the full text of the article. -- jt]]

On Apr 17, 3:54 pm, Thomas Smid wrote:
[[Mod. note -- It's irrelevant that different methods were used to
obtained different data points -- what matters is that a cosmological
model must fit *all* the correct data points to be viable.

If you look at figure 4 of
Noterdaeme et al,
"The evolution of the Cosmic Microwave Background Temperatu
Measurements of T_CMB at high redshift from carbon monoxide
excitation"
http://arxiv.org/abs/1012.3164
it's clear that the hot-big-bang prediction fits the data beautifully,
and that no horizontal line (T independent of z) comes even close to
fitting the data. (In fact, both of these last two statements would
remain true even if you ignored the z=0 data point in that figure.)

Sure, all observations should comply with the suggested model, but the
point is that, as it is, the *only* significant z-dependence of the
CMB temperature seems to be be associated with the different methods/
groups that obtained the data.

Observe how deftly the goal post has moved. Earlier the claim was that
this couldn't POSSIBLY be accurate because it was just one Earthbound
datapoint and a few neutral carbon datapoints.

Now the claim is that suddenly it is a problem when three methods +
local agree. Which is somehow a problem, rather than further
independent confirmation.

In the reference you gave, one can for

I gave the reference.

The funny thing is that you had done literally no literature searches
by yourself previous to that. Which makes your changing of arguments
rather remarkable in speed.

instance still fit the red data with a constant temperature (only one
or two error bars miss the line by a small amount). All pair-

Yeah only one or two data points out of 4, which are 4 out of about 20
points. Only 25 to 50% of the data needs to be dumped for your
nonphysical theory to fit some of the data from a particular method.
Note the lack of discussion of the CO [green] data points. Horizontal
lines certainly don't fit green by itself, and certainly does not fit
red+green. Or any other combination of red/green/blue.

combinations of the red error bars overlap, so the difference between
their mean values is statistically insignificant (apart from the
second and last points and even here this is not statistically
significant considering the fact that these are just standard error
bars (seehttp://www.graphpad.com/articles/errorbars.htm)).

I suspect you need the introduction to error analysis more than anyone
else here.

You are using 'statistical significance' to argue that the data means
nothing, a few data points at a time. You seem to be rather afraid of
discussing the whole graph.

And the
blue data points do not look any more convincing on their own in this
respect.

But they aren't on their own, are they? They are on the same graph as
8 other data points from other methods, which considered together
rather than one-at-a-time paints a rather clear picture. Your model is
wrong.


But anyway, as I said earlier, the analysis in these papers is based
on the assumption that the level densities are given by a Boltzmann
distribution, which would only be justified if the levels are both
populated and depopulated by collisions.

UHHH, NO. The exact opposite is required, otherwise the observations
correspond to the mean temperature of the gas rather than the CMBR.

[...mod note covers rest...]

On Apr 17, 10:54*pm, Thomas Smid wrote:

But anyway, as I said earlier, the analysis in these papers is based
on the assumption that the level densities are given by a Boltzmann
distribution, which would only be justified if the levels are both
populated and depopulated by collisions. However, as the natural decay
times of the levels are much smaller than the collision times (the
latter being about 10^10 sec), this conditions is far from being
fulfilled. The assumption of a Boltzmann distribution introduces
therefore a systematic error here which renders the data invalid in
the first place.

Thomas

[[Mod. note -- Your statement that a Boltzmann distribution "would
only be justified if the levels are both populated and depopulated
by collisions" is exactly backwards -- a Boltzmann distribution is
justified (only) if the levels are in radiative equilibrium with
the CMBR photons, i.e., if collisional excitation does *not* occur,
i.e., if the mean-time-to-collision is *long*.

No, simply a radiative equilibrium doesn't result in a Boltzmann
distribution. Required for this is a thermodynamic equilibrium, and
this a condition which is established locally. With the CMBR
originating from billions of (light)years away, it would be therefore
be a contradiction in terms to assume it is in thermodynamic
equilibrium with a local volume of matter.

Anyway, as far as I am concerned, electromagnetic radiation should not
be able at all to directly populate an upper atomic level, as discrete
transitions resonantly *scatter* radiation but do not absorb it (and
resonance scattering is a coherent (one-step) process and therefore
not associated with changing the level populations). The level can
only be populated be recombination (and subsequent cascading), or
electron impact excitation. With regard to the latter, one can
estimate here the excitation rate from the density, velocity and
collision cross section: the electron density in the referenced
papers is taken as about 10^-2 cm^-3; the electron velocity is about
10^7 cm/sec (according to an electron temperature of 100K); the
Coulomb collision cross section is roughly Q=e^4/(E*dE) (in cgs units,
where e is the elementary charge, E the collision energy and dE the
energy transfer). In this case we have to assume E to correspond to
about 10 eV = 1.6*10-11 erg (the kinetic energy of the atomic
electrons) and dE=3.2*10-15 erg (energy transfer corresponding to a
temperature of 20K), so Q=10^-12 cm^2. With this, the collisional
excitation frequency becomes nu_coll = 10^-2 *10^7 *10^-12 = 10^-7
sec^-1. And this is already an order of magnitude larger than the
excitation frequency due to the CMBR mentioned for instance in Ge at
al. (Eq.(5)). So even if the CMBR could populate the upper level, and
even if this would result in a Boltzmann distribution, it would be
insignificant compared to the electron impact excitation.

Thomas