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The Question
(Submitted August 20, 2009)
Friedmann identified that Einstein's field theories allow for an
expanding universe. I am puzzled by the fact that in a universe
expanding under the laws of Einstein's field theories, everything is
expanding, not only the distances between the objects of the universe.
Thus a yardstick or a metre stick expands along with the rest of the
universe.
On these grounds, I must conclude that the metric distances in a metric
space are conserved irrespective of any expansion occurring within the
frame of Einstein's field theories. How is it possible that the wavelength
of the background microwave radiation is construed to having increased
on a metric scale when that scale should have expanded along with the
expansion of the wavelength, leaving the wavelength the same as it was in
the young universe?
The Answer
This is a good question. You have to keep in mind that Einstein'
theory is 4 dimensional, not 3. In the Friedmann solution, the space
parts (3 dimensions) are expanding (or contracting) uniformly;
however, the time component is not. If the time component were also
expanding at the same rate, then one could not observe the universe to
be expanding.
A good way to see this is through the example of the CMB which you
have brought up. As the CMB travels through space, the wavelength is
stretched by the expansion; however, the time has not. If the time
component also stretched, we would observe the CMB to have smaller
intervals between oscillations. In fact, this factor would exactly
cancel out the stretching of the space, and we would observe it at its
original optical wavelengths.
Dave Chuss
for Ask an Astrophysicist
PS. Note also that physical yardsticks do not actually expand with the
expanding universe. See our
answer on that question.
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