|MadSci Network: Astronomy|
Dear Edward, This is a very interesting question that deals with an important property of light. We need to be careful, though, to keep in mind exactly what causes the time dilation or redshift. Rather than gravitational time dilation, let me first start with special relativistic time dilation. It will give us an important example of what happens when we return to our beginning frame of reference. Special relativistic time dilation occurs when one person (we usually say a frame of reference) tries to measure the rate of time passing for another person (a different frame of reference) when the second person is moving relative to the first person. The first person will measure the second personís time as advancing more slowly than the first personís, but the second person will also measure the first personís time as moving more slowly, too! The explanation for this seemingly impossible scenario is because of the way the measurements must be made. Both individuals see the other person as moving and they themselves as remaining at rest. They must perform similar measurements on the other person and so they arrive at similar conclusions. Part of your question, though, is whether time dilation is additive. The answer is in some sense yes, some sense no. Letís say that Person A sees Person B as moving along the x-axis (really, any direction would do) and Person B sees Person C moving along the x- axis, too, in the same direction as Person A sees Person B moving. Person B will measure Person Cís time as dilated, and Person A will see Person Cís time as dilated more than Person B will. The relative velocity between Persons A and C will not be the sum of the velocities between Persons A and B and Persons B and C, however! For example, letís say that Person A measures Person B as moving at 100,000km/s and Person B measures Person C as moving at 100,000km/s. Person A will not measure Person C as moving at 200,000km/s, but rather at 180,000km/s! This is because Person B measures different times and distances for Person C than Person A does. The important point is that since velocities are not additive, the time dilations are not strictly additive. The dilation can get larger if each successive person is moving in the same direction, but there is also another important point here. If Person C measures another person, say Person D as moving to the left at 180,000km/s, then Person D would have no time dilation relative to Person A. In other words, the time dilation is ďreversedĒ when you get back to the original frame. Basically, Person D would be at rest relative to Person A and so they would measure the same times. Now what does all of this have to do with the redshift of light? Well, you are correct that light will redshift as it leaves a star, but if we consider what will happen if light is gravitationally bent around a star something else happens, too. As the light approaches the star, it is blue shifted, then the red shift as it moves away from the star returns the light back to its original wavelength, although it is now traveling in a different direction. What about light traveling though a uniform mass distribution? Well, the only way that light will be gravitationally redshifted is if it is moving through a non-zero gravitational field, as you mentioned, like light climbing up out of the gravitational field of a quasar. A universe with a uniform mass distribution (dark matter for example) would not have any preferred direction and so would have a zero gravitational field. Light traveling through such a mass distribution would not be redshifted, and so, a uniform distribution of dark matter would not explain the redshift of light from distant sources. Well, I hope I have answered your question, Edward. If you would like some more information, please let us know. Sincerely, Jim Guinn
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