The average particle energy needed to observe unification

Problem 1CQ Explain why it only appears that we are at the center of expansion of the universe and why an observer in another galaxy would see the same relative motion of all but the closest galaxies away from her.

Problem 31PE A section of superconducting wire carries a current of 100 A and requires 1.00 L of liquid nitrogen per hour to keep it below its critical temperature. For it to be economically advantageous to use a superconducting wire, the cost of cooling the wire must be less than the cost of energy lost to heat in the wire. Assume that the cost of liquid nitrogen is $0.30 per liter, and that electric energy costs $0.10 per kW·h. What is the resistance of a normal wire that costs as much in wasted electric energy as the cost of liquid nitrogen for the superconductor?

Problem 2PE Find the approximate mass of the dark and luminous matter in the Milky Way galaxy. Assume the luminous matter is due to approximately 1011 stars of average mass 1.5 times that of our Sun, and take the dark matter to be 10 times as massive as the luminous matter.

Problem 3CQ If the universe is infinite, does it have a center? Discuss.

Problem 1PE Find the approximate mass of the luminous matter in the Milky Way galaxy, given it has approximately 1011 stars of average mass 1.5 times that of our Sun.

Problem 2CQ If there is no observable edge to the universe, can we determine where its center of expansion is? Explain.

Problem 3PE (a) Estimate the mass of the luminous matter in the known universe, given there are 1011 galaxies, each containing 1011 stars of average mass 1.5 times that of our Sun. (b) How many protons (the most abundant nuclide) are there in this mass? (c) Estimate the total number of particles in the observable universe by multiplying the answer to (b) by two, since there is an electron for each proton, and then by 109 , since there are far more particles (such as photons and neutrinos) in space than in luminous matter.

Problem 4PE If a galaxy is 500 Mly away from us, how fast do we expect it to be moving and in what direction?

Problem 5CQ If some unknown cause of red shift—such as light becoming “tired” from traveling long distances through empty space—is discovered, what effect would there be on cosmology?

Problem 4CQ Another known cause of red shift in light is the source being in a high gravitational field. Discuss how this can be eliminated as the source of galactic red shifts, given that the shifts are proportional to distance and not to the size of the galaxy.

Problem 6PE Our solar system orbits the center of the Milky Way galaxy. Assuming a circular orbit 30,000 ly in radius and an orbital speed of 250 km/s, how many years does it take for one revolution? Note that this is approximate, assuming constant speed and circular orbit, but it is representative of the time for our system and local stars to make one revolution around the galaxy.

Problem 5PE On average, how far away are galaxies that are moving away from us at 2.0% of the speed of light?

Problem 7CQ If the cosmic microwave background radiation (CMBR) is the remnant of the Big Bang’s fireball, we expect to see hot and cold regions in it. What are two causes of these wrinkles in the CMBR? Are the observed temperature variations greater or less than originally expected?

Problem 6CQ Olbers’s paradox poses an interesting question: If the universe is infinite, then any line of sight should eventually fall on a star’s surface. Why then is the sky dark at night? Discuss the commonly accepted evolution of the universe as a solution to this paradox.

Problem 7PE (a) What is the approximate speed relative to us of a galaxy near the edge of the known universe, some 10 Gly away? (b) What fraction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than 0.9c .

Problem 8CQ The decay of one type of K -meson is cited as evidence that nature favors matter over antimatter. Since mesons are composed of a quark and an antiquark, is it surprising that they would preferentially decay to one type over another? Is this an asymmetry in nature? Is the predominance of matter over antimatter an asymmetry?

Problem 9CQ Distances to local galaxies are determined by measuring the brightness of stars, called Cepheid variables, that can be observed individually and that have absolute brightnesses at a standard distance that are well known. Explain how the measured brightness would vary with distance as compared with the absolute brightness.

Problem 9PE Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital speed using the following information: The mass of the galaxy is equivalent to a single mass 1.5×1011 times that of the Sun (or 3×1041 kg ), located 30,000 ly away.

Problem 10PE (a) What is the approximate force of gravity on a 70-kg person due to the Andromeda galaxy, assuming its total mass is 1013 that of our Sun and acts like a single mass 2 Mly away? (b) What is the ratio of this force to the person’s weight? Note that Andromeda is the closest large galaxy.

Problem 8PE (a) Calculate the approximate age of the universe from the average value of the Hubble constant, H0 = 20km/s ? Mly . To do this, calculate the time it would take to travel 1 Mly at a constant expansion rate of 20 km/s. (b) If deceleration is taken into account, would the actual age of the universe be greater or less than that found here? Explain.

Problem 11CQ If the smallest meaningful time interval is greater than zero, will the lines in Figure 34.9 ever meet?

Problem 10CQ Distances to very remote galaxies are estimated based on their apparent type, which indicate the number of stars in the galaxy, and their measured brightness. Explain how the measured brightness would vary with distance. Would there be any correction necessary to compensate for the red shift of the galaxy (all distant galaxies have significant red shifts)? Discuss

Problem 11PE Andromeda galaxy is the closest large galaxy and is visible to the naked eye. Estimate its brightness relative to the Sun, assuming it has luminosity 1012 times that of the Sun and lies 2 Mly away.

Problem 12CQ Quantum gravity, if developed, would be an improvement on both general relativity and quantum mechanics, but more mathematically difficult. Under what circumstances would it be necessary to use quantum gravity? Similarly, under what circumstances could general relativity be used? When could special relativity, quantum mechanics, or classical physics be used?

Problem 12PE (a) A particle and its antiparticle are at rest relative to an observer and annihilate (completely destroying both masses), creating two ? rays of equal energy. What is the characteristic ? -ray energy you would look for if searching for evidence of proton-antiproton annihilation? (The fact that such radiation is rarely observed is evidence that there is very little antimatter in the universe.) (b) How does this compare with the 0.511-MeV energy associated with electron-positron annihilation?

Problem 13PE The average particle energy needed to observe unification of forces is estimated to be 1019 GeV . (a) What is the rest mass in kilograms of a particle that has a rest mass of 1019 GeV/c 2 ? (b) How many times the mass of a hydrogen atom is this?

Problem 13CQ Does observed gravitational lensing correspond to a converging or diverging lens? Explain briefly.

Problem 14PE The peak intensity of the CMBR occurs at a wavelength of 1.1 mm. (a) What is the energy in eV of a 1.1-mm photon? (b) There are approximately 109 photons for each massive particle in deep space. Calculate the energy of 109 such photons. (c) If the average massive particle in space has a mass half that of a proton, what energy would be created by converting its mass to energy? (d) Does this imply that space is “matter dominated”? Explain briefly.

Problem 15CQ What are gravitational waves, and have they yet been observed either directly or indirectly?

Problem 15PE (a) What Hubble constant corresponds to an approximate age of the universe of 1010 y? To get an approximate value, assume the expansion rate is constant and calculate the speed at which two galaxies must move apart to be separated by 1 Mly (present average galactic separation) in a time of 1010 y. (b) Similarly, what Hubble constant corresponds to a universe approximately 2×1010 -y old?

Problem 16CQ Is the event horizon of a black hole the actual physical surface of the object?

Problem 17CQ Suppose black holes radiate their mass away and the lifetime of a black hole created by a supernova is about 1067 years. How does this lifetime compare with the accepted age of the universe? Is it surprising that we do not observe the predicted characteristic radiation?

Problem 16PE Show that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.

Problem 17PE The core of a star collapses during a supernova, forming a neutron star. Angular momentum of the core is conserved, and so the neutron star spins rapidly. If the initial core radius is 5.0×105 km and it collapses to 10.0 km, find the neutron star’s angular velocity in revolutions per second, given the core’s angular velocity was originally 1 revolution per 30.0 days.

Problem 18CQ Discuss the possibility that star velocities at the edges of galaxies being greater than expected is due to unknown properties of gravity rather than to the existence of dark matter. Would this mean, for example, that gravity is greater or smaller than expected at large distances? Are there other tests that could be made of gravity at large distances, such as observing the motions of neighboring galaxies?

Problem 18PE Using data from the previous problem, find the increase in rotational kinetic energy, given the core’s mass is 1.3 times that of our Sun. Where does this increase in kinetic energy come from?

Problem 19CQ How does relativistic time dilation prohibit neutrino oscillations if they are massless?

Distances to the nearest stars (up to \(500 ly\) away) can be measured by a technique called parallax, as shown in Figure \(34.26\). What are the angles \(\theta_{1}\) and \(\theta_{2}\) relative to the plane of the Earth's orbit for a star \(4.0 ly\) directly above the Sun? Equation Transcription: Text Transcription: 500 ly 34.26 theta_1 theta_2 4.0 ly

Problem 21CQ Lacking direct evidence of WIMPs as dark matter, why must we eliminate all other possible explanations based on the known forms of matter before we invoke their existence?

Problem 20CQ If neutrino oscillations do occur, will they violate conservation of the various lepton family numbers ( Le , Lµ , and L? )? Will neutrino oscillations violate conservation of the total number of leptons?

Problem 20PE (a) Use the Heisenberg uncertainty principle to calculate the uncertainty in energy for a corresponding time interval of 10?43 s . (b) Compare this energy with the 1019 GeV unification-of-forces energy and discuss why they are similar.

Construct Your Own Problem Consider a star moving in a circular orbit at the edge of a galaxy. Construct a problem in which you calculate the mass of that galaxy in kg and in multiples of the solar mass based on the velocity of the star and its distance from the center of the galaxy.

Problem 22CQ Must a complex system be adaptive to be of interest in the field of complexity? Give an example to support your answer.

Problem 22PE What is the Schwarzschild radius of a black hole that has a mass eight times that of our Sun? Note that stars must be more massive than the Sun to form black holes as a result of a supernova.

Problem 23CQ State a necessary condition for a system to be chaotic.

Problem 23PE Black holes with masses smaller than those formed in supernovas may have been created in the Big Bang. Calculate the radius of one that has a mass equal to the Earth’s.

Problem 24PE Supermassive black holes are thought to exist at the center of many galaxies. (a) What is the radius of such an object if it has a mass of 109 Suns? (b) What is this radius in light years?

Problem 24CQ What is critical temperature Tc ? Do all materials have a critical temperature? Explain why or why not.

Problem 25CQ Explain how good thermal contact with liquid nitrogen can keep objects at a temperature of 77 K (liquid nitrogen’s boiling point at atmospheric pressure).

Problem 26CQ Not only is liquid nitrogen a cheaper coolant than liquid helium, its boiling point is higher (77 K vs. 4.2 K). How does higher temperature help lower the cost of cooling a material? Explain in terms of the rate of heat transfer being related to the temperature difference between the sample and its surroundings.

Problem 25PE Construct Your Own Problem Consider a supermassive black hole near the center of a galaxy. Calculate the radius of such an object based on its mass. You must consider how much mass is reasonable for these large objects, and which is now nearly directly observed. (Information on black holes posted on the Web by NASA and other agencies is reliable, for example.)

Problem 26PE The characteristic length of entities in Superstring theory is approximately 10?35 m . (a) Find the energy in GeV of a photon of this wavelength. (b) Compare this with the average particle energy of 1019 GeV needed for unification of forces.

Problem 28CQ Discuss whether you think there are limits to what humans can understand about the laws of physics. Support your arguments.

Problem 27CQ For experimental evidence, particularly of previously unobserved phenomena, to be taken seriously it must be reproducible or of sufficiently high quality that a single observation is meaningful. Supernova 1987A is not reproducible. How do we know observations of it were valid? The fifth force is not broadly accepted. Is this due to lack of reproducibility or poor-quality experiments (or both)? Discuss why forefront experiments are more subject to observational problems than those involving established phenomena.

Problem 27PE If the dark matter in the Milky Way were composed entirely of MACHOs (evidence shows it is not), approximately how many would there have to be? Assume the average mass of a MACHO is 1/1000 that of the Sun, and that dark matter has a mass 10 times that of the luminous Milky Way galaxy with its 1011 stars of average mass 1.5 times the Sun’s mass.

Problem 28PE The critical mass density needed to just halt the expansion of the universe is approximately 10?26 kg / m3 . (a) Convert this to eV / c 2 ? m3 . (b) Find the number of neutrinos per cubic meter needed to close the universe if their average mass is 7 eV / c 2 and they have negligible kinetic energies.

Problem 29PE Assume the average density of the universe is 0.1 of the critical density needed for closure. What is the average number of protons per cubic meter, assuming the universe is composed mostly of hydrogen?

Problem 30PE To get an idea of how empty deep space is on the average, perform the following calculations: (a) Find the volume our Sun would occupy if it had an average density equal to the critical density of 10?26 kg / m3 thought necessary to halt the expansion of the universe. (b) Find the radius of a sphere of this volume in light years. (c) What would this radius be if the density were that of luminous matter, which is approximately 5% that of the critical density? (d) Compare the radius found in part (c) with the 4-ly average separation of stars in the arms of the Milky Way.