Physics 120 Reading Homework Assignment #1-2 Name:______
Due: Sunday 10 PM, January 28, 2018
(This is a double assignment covering the first two weeks of class.)
Please insert your name where indicated in the upper right-hand corner of this page. Expected length of answers is anywhere between a few sentences (if concise) to a short paragraph for each numbered question. Please expand this word-file and insert your answers in-place below.
Feel free to discuss questions and concepts with other students from the class. This is encouraged. However, when you sit down to answer the questions in the homework assignment, you must submit your own answers. Please copy this word file and enter your responses below each question. Be concise but complete.
Your completed homework assignments must be uploaded on Canvas by the specified due date and time in order to receive credit.
1) a) Give some (at least three) of the misconceptions that are common about the Big Bang and expansion of the Universe.
The Big Bang was an explosion that occurred within our universe.
When the universe expands, it must be expanding into some existing space.
Big Bang theory explains what caused the Big Bang.
The Big Bang theory tells us with certainty that the Universe was once a single point.
b) Give three tests of Big Bang Cosmology, the conclusion from each and how each supports the model.
Expanding Universe: The Big Bang Theory predicts that, apart from local movement between galaxies, other galaxies should be moving away from ours at a velocity proportional to the distance to our galaxy. This is what observations have confirmed, with distance objects moving approximately 70 km/sec away from us for every million parsecs between the objects and our galaxy.
CMB: Given the high temperatures and energies in the early universe, we should see some remaining evidence of this state. This was confirmed in 1965 with the discovery by Penzias and Wilson of the Cosmic Microwave Background (CMB), a nearly perfectly uniform radiation in the microwave light spectrum coming from every direction in the universe. This background has a distribution of photon energies perfectly consistent with the thermal radiation of some material around 2.7 K. The uniformity of the radiation is consistent with it originating in an early state of the universe, before stars and galaxies formed.
Light Nuclei: Big Bang Cosmology predicts that the universe had a very dense early state, dense enough for primordial protons and neutrons to frequently fuse into light nuclei such as Helium (2 protons and 2 neutrons) and Deuterium (1 proton and 1 neutron). The observed quantities of these light nuclei in the present universe is consistent with this prediction.
2) How did Edwin Hubble first determine that the Milky Way was not the only galaxy in the Universe? Describe how he used Cepheid variable stars to do this and to determine that the Universe is expanding. Explain what it means when we say “the farther away in space we can see, the farther back in time we view.”
He hypothesized that Andromeda, then thought by many to be a nebula within our own galaxy. He estimated the distance to Andromeda using Cepheid variable stars, which vary in brightness periodically. It was known then how the period of Cepheid stars related to their brightness, which allowed Hubble to calculated the distance to Cepheid stars in Andromeda using their apparent brightness from Earth, finding Andromeda to be approximately 1 million lightyears away from Earth, too far to be within the Milky Way.
When Hubble used this same method to measure the distances to other galaxies, he found that the farther away the galaxy, the more its light was redshifted. This indicated that the farther away a galaxy is, the faster it is moving away from us (sidenote: Andromeda is in fact blueshifted, meaning that it is approaching our galaxy. This is possible because the gravitational attraction between galaxies in a galaxy cluster is strong enough to avoid being separated by the expansion of space). This is consistent with a universe that is uniformly expanding.
Due to the finite speed of light, as we look at objects at greater distances, the light from those objects has taken more time to reach us, meaning that we are looking farther into the past. This statement would be true even in a universe that wasn't expanding.
3) What role does matter have in determining the evolution and the possible fate of the Universe? Describe the evolution of the Universe implied by each of the curves in the graph labeled “Expansion of the Universe” on page 3 of the WMAP reading.
The densities of matter and dark energy in the universe determine the evolution
The effect of matter on the universe is to decelerate expansion and force the universe through gravity towards contracting. Dark energy has an opposing effect. The curves in the WMAP graph show four different possibilities:
1. (Orange) A universe with mass density greater than the critical density, leading to a universal contraction.
2. (Green) A universe with the critical mass density, whose expansion is decelerating.
3. (Blue) A universe with more than the critical mass density, whose expansion is decelerating less than the critical density universe.
4. (Red) A universe with matter and dark energy adding up to the critical density, whose expansion is decelerating at first, but eventually accelerates due to dark energy.
4-5) a) Describe how quantum mechanics is necessary for inflation to have occurred in the early Universe.
A key component of the inflationary theories is that the Universe quantum-tunneled out of a false vacuum state, which would be impossible in a classical theory.
b) Explain the origin of this rapid expansion (i.e. inflation) of the Universe.
In the old Inflationary Scenario, the inflation was driven by the high energy density of whatever field was stuck in a false vacuum. In the new Inflationary Scenario, inflation is driven by a quantum field slowly transitioning to a true vacuum state.
c) What propelled the expansion (i.e. forces, energy or something else)?
The inflation is driven by the high energy density of the field responsible for inflation. General Relativity tells us that a Universe that is dominated by the energy of a field (as opposed to kinetic energy of matter) will expand exponentially.
d) What is the primary advantage of the “new inflationary scenario” over the standard inflationary scenario according to Trefil?
The primary advantage of the “New Inflationary Scenario” is that it does not necessarily allow the universe to freeze into separate domains, which would create topological defects such as cosmic strings and magnetic monopoles, which have not been observed.
6) Name two problems with the Big Bang Theory (not the TV show!) that are resolved by inflation, and how inflation purports to resolve them.
Any two among:
The Horizon Problem: Observed correlations in the Cosmic Microwave Background occur over large distances than should be possible by Special Relativity: one area of space cannot effect another if light hasn't had time to reach the other. Inflation explains these long range correlations because, prior to Inflation, those regions of space were actually much closer than we calculated without inflation.
Magnetic Monopoles (the lack thereof): Modern cosmology predicts the production of magnetic monopoles (particles that act like either the North or South end of a magnet) in large quantities in the early Universe. However, no such monopole has ever been observed. Inflation explains this problem because the rapid expansion of the universe would reduce the density of magnetic monopoles to the extent that we might never observe one.
The Flatness Problem: All measurements indicate that our universe is flat, while General Relativity predicts that any deviation from flatness would grow over time. This would imply that the density of matter and dark energy in the early Universe was extremely finely tuned to the critical density, a seemingly unlikely coincidence. Inflation explains this because any curvature would be flattened out by the rapid inflationary period.
The Galaxy or Structure Formation Problem: inflation may also explain the formation of structures in the Universe, as a consequence of the sudden “amplification” over galactic scales of small quantum fluctuations present in the small Universe before inflation.
7) What is the difference between a phase transition of the first kind and that of the second kind. Give an example of each.
A phase transition of the first kind is one in which energy is necessarily released or absorbed during the transition, while a transition of the second kind has no sudden change in energy. Some examples of the first kind include water condensing (releasing energy), ice cubes melting (absorbing energy), and dry ice (frozen CO2) sublimating. Examples of transitions of the second include a ferromagnet transitioning between a magnetized and demagnetized state, a liquid such as liquid Helium becoming a superfluid, and a superconductor entering/exiting a superconducting state.
8) The GUT era must have been fascinating.
a) Please give the time‐span that Trefil associates with this era, the forces and particles that were expected to be active at that time.
Trefil associates this era with the timespan between 10^(-43) seconds (the Planck time) and 10^(-35) seconds. In this era, the electroweak and strong forces are combined into a single force, mediated by what Trefil refers to as X-bosons.
b) Which force “freezes” at the end of this era (please give the forces before and after this freezing)?
Before the end of this era, the Universe is driven by two forces: the GUT force and the gravitational force. After the end of this era, the GUT force freezes into the separate electroweak and strong forces, leaving the Universe with three forces.
9) The Universe was hotter earlier to the extent that particle creation occurred early. How can more massive particles be created more easily when it is hotter? What are some general constraints on the masses and types of particles that can be created at a given time for a given energy (e.g. based on conservation laws)?
Hotter temperatures correspond to higher average kinetic energies of particles. In collisions between individual particles, this energy can be converted into mass (E=mc2) in the form of new particles. The more energy there is, the more massive the particles that can be created. In order to create a particle, the extra kinetic energy of the colliding particles must be more than the mass of the new particle. An additional constraint is that the creation of any matter particle must be balanced with the creation of an antimatter particle. For example, in order to form a proton from the collision of two high energy protons, an anti-proton would need to be created at the same time.
10) a) Which topics did you find particularly complicated and had difficulty understanding? What specific questions do you have about this (these) topic(s)?
Any answer receives credit.
b) Which topics did you find particularly interesting and would like to discuss further in class? Any specifics or questions that you wish to add on each topic?
Any answer receives credit.