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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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