How do photons carry momentum when they don't have mass and always move at the speed of light?
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. (See page 99.) When they strike something, they exert a force upon it. Thus they also have associated with them a momentum.
What is the solution to Olbers' paradox?
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.
What are the recent observations involving gamma ray bursters? Any new conclusions?
The major controversy over gamma-ray bursters (aside from what they are) is whether they are of cosmological, i.e. extragalactic, origin, or whether they come from within the Galaxy. Obviously, this has a bearing on the identity of what is producing the bursts. The distribution of bursters seems to be quite isotropic, which suggests an extragalactic source, since the Galaxy is quite anisotropic, except possibly for its dark halo. However, some galactic sources can be remarkably isotropic, so this does not completely settle the question. Some recent observations have suggested that a burst may have been repeated over a fairly short timescale, which is an argument for a relatively nearby source. However, it has not been possible to localize the apparent repeater well enough to verify that it is indeed the same object and not two objects that happen to lie very close together on the sky. There have also been some studies suggesting evidence of cosmological time dilation in gamma ray bursts, implying that they are occurring at high redshifts.
The latest news is that there have now been reports of optical identifications of gamma ray burst sources. These sources were then studied with the HST and the Keck Telescope. At the moment there is still some uncertainty in the observations, but it is more and more evident that gamma ray bursts are associated with high redshift galaxies.
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.
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?
Certainly. It would require a large redshift, of course, but it can happen.
Yes, you must take into account the total mass-energy density. At the present time in the cosmos the energy contribution from the microwave background is the only significant energy component and it is small compared to the matter density. This wasn't true early on in the history of the universe, when it was the other way around. Mass energy doesn't seem to be conserved in the overall expansion of the universe. See discussion beginning page 339.
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.
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.
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.
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.
Higher precision measurements would 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. See, for example, the Microwave Anisotropy Probe home page.
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?
Everyone who is interested in cosmology has been waiting for these new results to be released. 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 (angular size versus redshift test, see figure 12.11 in the textbook). 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:
Copyright © 1998 John F. Hawley