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Chapter 14 Questions |
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How do photons carry momentum when they don't have mass and always move at the speed of light? |
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Mass is necessary for momentum only in Newtonian physics. Even in Newtonian mechanics, anything that can produce a force has a momentum, since the Second Law may be written in the form F=dp/dt, where p is the momentum. Newtonian (linear) momentum and kinetic energy are closely related, with momentum equal to mv and kinetic energy given by mv2/2. In special relativity, the connection between momentum and energy is even more intimate. The relativistic generalization of the Newtonian three-dimensional momentum (recall that momentum is a vector quantity) introduces energy as the fourth (timelike) dimension. Photons carry energy equal to Planck's constant times their frequency. When they strike something, they exert a force upon it. A force is equal to a change of momentum with respect to time. Thus they also have associated with them a momentum. |
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What is the solution to Olbers' paradox? |
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Basically, the assumptions as to the nature of the universe that go into stating the premise of Olbers' paradox are incorrect. Briefly, the solution is that the stars do not live forever. Thus along many lines of sight we reach stars that have died; and in a universe of finite age we eventually come along any line of sight to a time before any stars formed. The expansion of the universe also plays a role by preventing the cosmological background radiation from being in the visible band, but this is tangential to the classical Olbers' paradox, which asks why the night sky is not as bright as the surface of an average star. An interesting thing to think about, however, is that if you look at the sky in any direction you are looking back in time to when the universe was as bright as the surface of a star. But cosmological redshift has rendered this light invisible to our eyes. |
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How does the expanding universe make a photon lose energy? |
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By redshifting. A photon traveling through a spacetime described by the Robertson-Walker metric is redshifted to lower energy. Where has the lost energy gone? Perhaps since the metric represents a real change in spacetime with time, it is not surprising that energy isn't conserved, since energy conservation is a consequence of symmetry with respect to translations in time. |
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If it is possible for visible light to be redshifted OUT of the visible range, is it possible for X-ray or gamma rays to be redshifted into the visible range? |
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Certainly. It requires a large redshift, of course, but it can happen. |
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How is it possible for the microwave background radiation to be everywhere if it was emitted from a point in the Big Bang? If the universe were expanding, wouldn't it be redshifted? |
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The radiation comes from hot plasma that was located throughout space in the big bang. Keep in mind that the big bang was not a point explosion. Since the radiation filled all space from the beginning, it is still everywhere. It has redshifted by about a factor of 1000 since it streamed free of the matter. The high redshift explains why it is in the microwave region of the spectrum today. |
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If we were around when a closed universe began to recollapse would we notice a cosmological blueshift? Would the energy that was lost due to redshift be regained in the approach to the big crunch? |
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If the universe turned around and started to recollapse you would notice nearby galaxies beginning to have blueshifts. The blueshift effect would, over time, extend to ever more distant galaxies. The photons in the CBR would regain lost energy and the universe would reheat as the collapse proceeded. |
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Is there a telescope in production that would be placed in space with many reflectors that would collect more light than the Hubble? |
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Yes, the Next Generation Space Telescope. It is presently in the planning stage where design concepts are being developed. See the web page on the NGST. |
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Could there ever be a practical "earthly" use of the cosmic background radiation? (Other than to determine the origin of the universe?) |
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What, determining the origin of the universe isn't good enough for you? You can use it to make a hissing sound in your microwave receiver. That's not terribly useful, however. If you want to run a heat engine using the cosmic background you would need something colder, but obtaining a colder temperature on Earth would certainly require more energy than you could extract from your heat engine, by the second law of thermodynamics. |
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What is the significance of studying the CBR to higher precision with another COBE-type mission? |
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Higher precision measurements permit a better determination of the size and amplitude of the fluctuations in the background radiation, and these could be related to the structures (e.g., galaxy clusters, superclusters) we see in the universe today. These observations have led to the current concordance model of the cosmos. See the WMAP home page. |
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I heard and read about the WMAP results saying they've determined the age and geometry of the universe. Can we actually say (with certainty) now that the universe is 13.7 Gyr old and that it's flat? |
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Everyone who is interested in cosmology had been waiting for the results from the WMAP experiment. They represent a careful, precise measurement of the tiny temperature fluctuations on the cosmic background radiation. Ever since the COBE experiment showed that these fluctuations exist, theorists have been calculating what the statistical properties of these fluctuations might be: how many fluctuations of a specific angular size and how big the typical temperature variation would be. These properties depend on the geometry of the universe and its content. One example is the computation of the size of the biggest fluctuation. This can be computed from models of the early universe. Then, how big that appears on the sky provides a way to measure the geometry of the universe. That is what shows that the universe is flat. What is particularly interesting is that the numbers derived for the basic parameters of the universe are in good agreement with the numbers calculated by independent means. So, although there is always more work to do with this stuff, the uncertainties in the numbers have been greatly reduced. Cosmologists used to have to be content with uncertainties of a factor of two. For reference the results are:
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Copyright © 2005 John F. Hawley |