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Question:
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.



Replies:
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.

Tim Mooney


Howdy,

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).

best wishes,

Michael Pierce
Materials Science Division
Argonne National Laboratory


Hello,

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 yardstick!

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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