Universe Expansion Representation Inconsistency
I have just read the Wikipedia article on the
Metric expansion of space. In that article, the writer presents
the raisin bread analogy and says "The dough between raisins in
this model acts as the space between galaxies while the raisins
as "bound objects" are not subject to the expansion." I have
wondered for 30 years why scientists consider the locality of
mass as being bound -- exempt from expansion. In other words, the
ant on the balloon can measure the expansion of his two
dimensional space using a yardstick -- which is exempt from the
effects of the expansion of space. It would seem to me that the
yardstick would expand, the raison would expand, as well as the
ant. This results in our small observers not being able to detect
the expansion of space in any way. However as light progresses
toward us from a source nearly 12 billion years ago, it travels
through space that is expanding and is consequently red shifted.
Somehow the energy of each photon is spread out over a greater
"distance", its energy reduced, and wavelength increased. I can
nearly buy that explanation.
Now that is interesting. If true, I think it would imply that the
wavelength of emitted light should increase with time whether or not
the light moves always in the same direction. If so, a simple
experiment would test the hypothesis, but we probably do not have
the technology required to perform it well enough to prove anything.
We might imagine, for example, producing light with a very precisely
known wavelength (Mossbauer source?), capturing it in an etalon for as
long as can be achieved (bounce it off that mirror on the moon?), and
comparing its wavelength with that of freshly produced light. But
red-shift data tell us at what rate wavelengths must increase with
time, and this rate seems small enough that the experiment I am imagining
is pretty far beyond our current ability.
I do not have an answer yet, but am working on this one.
This is actually a question I have asked myself before and have not come
across anything insightful. Whenever I hear the ant on the ball or dots
on the balloon analogy, I always wonder if they mean to imply that the
dots and ants are getting bigger or not. Anyhow, it has never been clear
to me that this is the case. Not being a specialist in cosmology or
astrophysics, I do not have any ready knowledge of substance (i.e., my own
thoughts are pure speculation). I asked a few friends at lunch today
and it produced a very lively discussion. However, we also came to no
conclusion except that our own knowledge is a bit lacking (my friends
are also condensed matter physics people). So, I am going to ask a couple
of my friends at Fermilab what they think and go from there.
The little bit of question specific research that I am able to get
through seems to indicate that this may in fact be a question we do not
have a ripe and ready answer to. In fact people may be actively trying
to answer this question along with the host of others concerning the
expansion of the universe (is the universe open or closed? why the heck
is it that things far away appear to be moving away from us too fast?
some observations even have them accelerating away!)
Our lunch time speculation has left us wondering if it would even be
possible to observe this effect. The inflationary universe owes a great
deal to the observations started by Hubble. These all (to my knowledge)
are extra-galactic in nature. ie, we are measuring the red shift (or in
rare cases blue shift) of other galaxies. I would like to know if it is even
possible to measure the red or blue shift of stars in our own galaxy.
Well, we obviously can as the galaxy is spiraling. But what I mean is
can we detect an aberration from the measurements that could be
attributed to this? If so, how about planets?
It may take a few days for me to get back to you on all this. It is a
busy week, but none-the-less it is a great question and I will try my best
to get an accurate answer (even if it is just that the best people do not
know and it is beyond our ability to measure).
Materials Science Division
Argonne National Laboratory
This is a really great question.
The best answer is that it is reasonable to assume that this expansion
takes place, but is so small as to be neglected and unobservable.
First, let us settle one notion. If everything (and I mean everything)
were changing with time, such that the universe, the yard-stick, and the
relative force strengths (the coupling strength) were all changing in
the same way and proportionally, then there would be no way to measure
such a change. That is to say the universe appears unchanged
(symmetric). Anyhow, let us assume that is not what is going on.
Does the yard stick change size as the universe expands? It depends on
The only observable effect of the expansion are the recessional velocity
shifts of other galaxies (ok, indirectly you can argue that the cosmic
background radiation temperature is also part of it. But that is also
"extra-galactic" in origin too). So if your yardstick is that long,
then you would see the effects. Could such a single physical object that
large exist? Probably not. So how about a real yardstick? And raisins
and ants and so forth?
The best "reliable" thing people have come up with is to look at what
effects this expansion would have on planets in the solar system or on
other stars in our galaxy. A little math based on some reasonable
assumptions puts the acceleration due to this expansion at 10 ^ (-47)
m/sec^2. That is terribly small and can be compared against the
earth-sun acceleration of 10 ^ (-3) m/sec^2 (or the acceleration on
earth of objects 10 m/sec^2). Therefore, with such a small effect (a
separation of 44 orders of magnitude), we could never even hope to see a
change in the planetary relations in our solar system due to the
expansion of space(and time) itself. It may be possible (if we are
clever enough) to one day observe the effects of the expansion on
clusters of galaxies (or our own cluster), but it is still an effect that
is 7 orders of magnitude smaller than the gravitational accelerations.
So what if we waited long enough such that our yardstick would be
affected by such small changes. Would it then change in size? Probably
not. Even if the universe expands a tiny amount, the electrostatic
attractions would limit this growth and keep the yardstick the same
size. The attractive forces between neighboring atoms in an object
behave very much like springs and even if space were expanding between
the atoms, the tiny force pulling them apart would be completely
dominated by the restoring force of the electrostatic "spring".
So it is really too small for us to observe. It is reasonable to assume
that it is occurring, but for all intents and purposes it will be
impossible to detect except on the largest of all length scales.
I hope that helps. And give my regards to your inquisitive grandchild.
May they never stop asking questions!
The best sources I found on this are from Cooperstock et al, in the
Astrophysical Journal vol 503, pages 61-66, 1998, and J.L. Anderson,
Physical Review Letters, vol 75, pages 3602-04, 1995.
Michael S. Pierce
Materials Science Division
Argonne National Laboratory
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Update: June 2012