Re: Expanding Universe

["John S. Denker" <jsd@MONMOUTH.COM>]

In response to questions from Tim O'Donnell and others, at 08:28 PM 3/21/01
-0800, Roger Freedman wrote:

> There are actually three types of wavelength shift:
>
> * Cosmological redshifts
...
> * Doppler shifts
...
> * Gravitational redshifts


The distinction between the gravitational redshift and the other two
categories is clear.  The distinction between the other two categories is
rather subtle.  This distinction has been repeatedly asserted in recent
postings, but it has not been explained.  In particular, the following is a
mere assertion, *not* an explanation:

At 08:28 PM 3/21/01 -0800, Roger Freedman wrote:
>
> There are actually three types of wavelength shift:
>
> * Cosmological redshifts, due to the expansion of the universe (the
> "Hubble flow"). As an example, a cluster of galaxies at a distance of
> 50 megaparsecs (160 million light-years) has a recessional velocity
> of about 3500 km/s, corresponding to a redshift z = (wavelength
> shift)/(rest wavelength) = 0.012.
>
> * Doppler shifts due to motion within the universe. As an example,
> the galaxies that make up a cluster move within the cluster at speeds
> of a few hundred km/s. These motions can be in any direction, so by
> themselves they could produce either a blueshift or a redshift. As an
> example, the galaxy M31 in Andromeda (part of the same cluster as the
> Milky Way, and a mere 750 kiloparsecs away) is approaching us at 300
> km/s. For our example cluster of galaxies at 50 megaparsecs, the
> superposition of the motion of galaxies within the cluster on the
> cosmological expansion gives a range of recessional velocities from
> about 3200 to 3800 km/s. Doppler shifts of galaxies within clusters
> are less important for more distant clusters, which have larger
> cosmological redshifts.

By way of analogy, suppose I observe a flock of geese 160 meters away.
  * The flock as a whole has a recessional velocity of 3.500 m/s,
corresponding to a certain redshift in the noise that they make.
  * There will also be motions "within" the flock.  These motions could be
in any direction, so by themselves they could produce either a blueshift or
a redshift.

In this analogy, the point is that the shift due to the overall motion of
the flock can be attributed to a Doppler shift, in just the same way as the
shift due to the individual motions.

This analogy applies to galaxies within 160 million lightyears, or even a
few billion lightyears.  The evidence from these galaxies does not prove
(or even illustrate) the assertion that their observed shifts are
non-Doppler in origin.  This evidence, by itself, is not sufficient to
refute the following hypothesis:
   Hypothetically, spacetime _per se_ is not expanding.  It is a
   passive, Newtonian universe.  This universe just happens to be
   filled with galaxies which are running away from each other,
   due to a remarkable initial condition.

===========================================

So, the questions remain:
 -- What does it *mean* to have a non-Doppler non-gravitational redshift?
 -- Under what conditions might we observe a non-Doppler non-gravitational
redshift?

To answer these questions, we need to come up an observed redshift that
  * cannot be explained by gravitation, and also
  * cannot be explained by the motion of the emitter _at_the_time_
    the signal was emitted.

The first part is easy, since gravitational redshifts are usually quite small.

As for the second part, the best evidence is the microwave background
radiation.  We start the argument by observing that this radiation must
have had a temperature of many thousands of Kelvin when it was emitted, and
is observed at 3 Kelvin now.  This means it has a redshift Z > 1000.  This
stands in marked contrast to the galaxy data, which has Z = 0.012 in the
example given above.

The next step is to consider whether Z > 1000 could be explained by a
Doppler shift.  In principle, it could be.  The relativistic Doppler-shift
formula can certainly produce arbitrarily-large redshifts.

In order to proceed, we need to know more than the raw observations;  we
need to have a physical model of how these cosmic background photons were
emitted.  So let us assume the photons were emitted by a cloud of ions and
newly-formed atoms, in or near thermal equilibrium at a temperature of
thousands of Kelvin.  That means that the emitters had thermal velocities,
on the order of kilometers per second, not the ultra-relativistic
velocities necessary to explain Z > 1000.  We must also argue that after
emission, the atoms cooled and became transparent to the background
radiation, to an excellent approximation.

Remember, the Doppler formula depends on the velocity (relative to the
receiver) of the emitter, _at_the_time_ of emission.  The subsequent fate
of the emitter is irrelevant.

So if we apply the Doppler formula to the aforementioned cosmic background
radiation, we would expect it to still be in the form of X-rays and visible
light.  This is contrary to the observation that it is in the form of
microwaves.  So we must search for a non-Doppler explanation.

In fact there is a non-Doppler explanation:  We argue that at the time of
emission, the radiation was everywhere in space.  It is still everywhere in
space.  The interesting thing is, the space has expanded.  As the space
expanded, the gas of photons adiabatically cooled.

At this point we have a basically-correct picture of what it means to have
a non-Doppler non-gravitational redshift.

Even at this stage, though, it is possible to have many
misconceptions.  For instance, adiabatic cooling in an expanding universe
is arguably different from the adiabatic cooling that we observe by
expanding a cylinder full of photons.  In the cylinder, you could correctly
attribute the cooling to repeated Doppler shifts, as the photons bounce off
of the moving piston.  The cooling of the background radiation, however,
cannot be attributed to the motion of any piston, or the bouncing of any
photon;  instead we are assuming that the photons have been in free flight
ever since they were emitted.

So we begin to suspect that the non-Doppler explanation is very deep and
subtle.  It cuts right to the core of what we mean by "free flight".

To see what is going on, consider a standing wave in the background
radiation.  (Such a standing wave can be formed by the superposition of
leftward and rightward running waves.)  Draw the worldlines of the nodes of
this standing wave.  In a non-expanding universe, the nodes just sit
stationary.  The worldlines are parallel straight lines.  Now take the
paper on which the worldlines are written, and stretch the top part
sideways, leaving the bottom part unstretched.  The worldlines spread
out.  They are no longer parallel.

In an expanding universe, the equations of motion are changed.  If point A
and point B are at initially at rest, they will remain at rest to first
order, but over longer periods of time they will *not* remain at
rest.  This applies to Newton's laws, and to Maxwell's equations, and
everything else.  That is, it applies to free particles at point A and
point B, and it also applies to the nodes of the electromagnetic standing
wave at point A and point B.  The whole notion of (d/dt) and (d/dx) are
changed.

Note that the stretching is not the whole story if the particles are not
free. Bound particles and bound groups of particles can use their binding
force to overcome the spreading tendency.  This is important, because if
*everything* expanded, there would be no un-expanded rulers with which to
measure the expansion.  (You can't learn anything by measuring an expanded
universe with expanded rulers.)

=================

To sum up:

 -- The Hubble data from nearby clusters of galaxies is *not* sufficient
to prove (or even illustrate) the notion of a non-Doppler non-gravitational
redshift.

 ++ We say that the cosmic background radiation has a non-Doppler
redshift, because it acquired the redshift *after* it was emitted.

We must consider the observation of the background radiation one of the
most important observations of the 20th century.

  http://www.nobel.se/physics/laureates/1978/penzias-autobio.html
  http://www.nobel.se/physics/laureates/1978/wilson-autobio.html