Physics 320Symmetries in Nature

Block 8, Spring 2016

Instructor:

Brooks Thomas Email: bthomas @coloradocollege.edu Office: Olin 259 Phone: (719) 389-6750

General Course Information

Symmetry principles and conservation laws have long played a fundamental role in our understanding of the universe. Indeed, symmetry is ubiquitous in the natural world. It manifestsitself in the regular atomic structure of crystals, in the periodic motion of clock pendulums and vibrating molecules, in the spiral structures of seashells and galaxies, and in the conservation laws which apply to energy and electric charge. Over the last century, physicists have even come to see the four fundamental forces through which matter interacts as manifestations of different underlying symmetries of nature.

In this course, we will characterize the different kinds of symmetries which manifest themselves in the natural world and learn how to describe them using the mathematical language of group theory. Along the way, we will see how symmetry principles can be applied to solve problems in physics, geology, biology, chemistry, and other related fields. Finally, we will explore the fundamental relationship between symmetries and conservation laws which lies at the heart of contemporary physics.

Being able to understand the material in this course requires a solid background in Newtonian mechanics, thermodynamics, and electromagnetism at the level covered in Physics 241 and Physics 242, as well as a familiarity with special relativity and quantum mechanics at

the level covered in Physics 251. Moreover, it also requires a solid mathematics background including an understanding of calculus at the level of Math 129, which is a prerequisite for these prerequisites. If you do not feel comfortable with this background material, we strongly recommend that consider taking a different course this block. Finally, I also ask that you join this course with a will to think, to ask questions, to make mistakes, and to try out ideas.

Components of the Course

The course will consist of class meetings, readings from a variety of different texts, an excursion to the Baca Campus, some homework activities and assignments, two take-home exams, and a final project. These are described more fully below.

Class Meetings: Class meetings will be held each Monday – Friday from 9:00 AM – 12:00 PM during the

first three weeks of the block in Barnes 217. The one exception will be during the first week of the block, from Wednesday, April 20th – Friday, April 22nd, when the class will be making an excursion to the Baca Campus. Class meetings will not be held during the fourth week of the course. Rather, you will be meeting with me individually to work on your final projects.

Class meetings aren't only about lecture. On most days, we will also have other class activities that are meant to help you understand the material. Come to these class meetings prepared to ask questions. If you don't understand something from the reading, chances are thereare others who don't understand it either. Your preparedness for and active participation at class meetings represents a non-trivial portion of your final grade for this course. Moreover, it is not unusual for exam questions to be based on these activities, so make sure you understand them.

Readings and Texts:

Over the course of the block, we will be drawing from a wide variety of sources, including my own notes and slides, which I will be distributing throughout the block. For this reason, there is no single required textbook for this course. However, there are many texts that I would recommend for those who are interested in additional background material. For example, you may find it useful to consult a textbook on mathematical methods in physics. For this, I would recommend the following:

• Mathematical Methods in the Physical Sciences, 3rd ed., by Mary L. Boas.

• Mathematical Methods for Physicists, 7th ed., by George B. Arfken, Hans W. Weber, andFrank E. Harris.

In addition to a general mathematical-methods text of this sort, there are a number of good mathematics textbooks which focus more heavily on topics related to symmetry and group theory.

• Contemporary Abstract Algebra, 9th ed., by Joseph Gallian.

• Symmetry: An Application to Group Theory and its Applications, by Roy McWeeny.

Furthermore, since group theory plays an important role in particle physics – as we shall see by the end of this course – a number of practicing particle physicists have written textbooks on group and representation theory for students of the field. Fortunately, many of these texts are very well written and provide good introductions to group theory in general:

• Lie Algebras in Particle Physics, 2nd ed., by Howard Georgi.

• Group Theory in Physics, by Wu-Ki Tung.

Finally, since we will be discussing many of the topics (special relativity, quantum mechanics) covered in Modern Physics, it would be useful to have a modern-physics textbook handy for reference. There are many such textbooks, but the one which I would recommend are:

• Modern Physics , 3rd ed., by Kenneth Krane.

• Modern Physics for Scientists and Engineers, 2nd ed., by John R. Taylor, Chris Zafiratos,and Michael Dubson.

• The Feynman Lectures on Physics, Volume III, by Richard P. Feynman, Robert B. Leighton, and Matthew Sands.

Homework Activities and Assignments:

Homework assignments will be assigned throughout the course as a way of giving you additional practice applying the physical and mathematical principles we cover during course meetings and showing you some further interesting consequences of the fundamental ideas. Some of these homework assignments will be more traditional (working through problems), some will be a bit more unorthodox. I strongly encourage you to work with other students in the class on homework assignments. It is one of the most productive ways to study, and working with other people to solve problems is a big part of how science is really done. The classroom will remain open throughout the day as a place for you to work together on homeworkproblems.

Exams:There will be two exams given during the course, both of which will be take-home

exams. One of these exams will be distributed at 12:00 PM – i.e., at the end of our class meeting– on Wednesday, April. 27th; the other at 12:00 PM on Monday, May 9th. Each exam is due the following morning at 9:00 AM.

Final Project:In addition to the homework and the exams, I also want you to have the opportunity to

explore your own interests and to gain a deeper appreciation of the symmetry principles that we're covering in this course and how they relate to those interests or to your chosen field. To that end, you will be undertaking a final project in this course in which you will delve more deeply into a topic of your own choosing. This topic can be drawn from physics, biology, chemistry, geology, or any other field as long as it involves the symmetry principles we will be covering in this course in a substantive and meaningful way. You will need to approve your topic with me by Thursday, April 28th. If you are not sure what topic you're interested in

pursuing, I would be happy to meet with you and discuss possible ideas before that date.Your final project will have two components: a slide-based presentation (created using

PowerPoint, OOImpress, Beamer, etc.) and a formal paper. Your presentation will be delivered to other members of the class during a special presentation session on Thursday, May 5th from 1:00 – 3:00 PM. It should be about 15 minutes in length. Public presentations are a part of just about every career in science and engineering – and in a lot of other situations in life as well – sogetting practice preparing and giving one will be valuable no matter what you want to do. I strongly encourage you to meet with me ahead of time to discuss your presentation.

Your formal paper should be at least 8 pages in length. It should include an abstract and bibliography. A preliminary draft of your paper is due by 5:00 PM on Saturday, May 7th. You will need to schedule a Skype meeting with me Monday or Tuesday in order to discuss your preliminary draft. Plan on this meeting taking around 30 minutes. A final draft of your paper is due by 5:00 PM on Wednesday, May 11th.

Baca Excursion:Both in order to provide us with a broader opportunity to see how the symmetry

principles we'll be studying in this course manifest themselves in nature and in order to spend some concentrated time focusing on those principles, we will making an excursion to the Baca Campus during the latter half of the first week of this course. We will be departing from Barnes Hall at 7:00 AM on Wednesday, April 20th and returning on Friday, April 22nd at around 6:00 PM.

Before our departure, you must sign the student agreement form stating that you have read and will abide by the policies set for by Colorado College for the Baca Campus. In particular, you should be aware that the Baca Campus is a dry campus (no alcohol is permitted anywhere on the premises). Your signed form must returned to me by no later than 4:00 PM on Monday, April 18th.

Meals at Baca are provided by the Desert Sage Restaurant. If you are on a Colorado College meal plan, you will have meals deducted while attending Baca. If you are not on a meal plan, you will have your student account billed per meal. If you are not on the meal plan and feelthat you cannot afford this expense, you should contact Student Accounts. If you have any food allergies or other dietary restrictions, it is your responsibility to let me know what those are by nolater than 4:00 PM on Monday, April 18th in order that arrangements can be made with the DesertSage.

Further information about the Baca Campus, the facilities there, and the guidelines for personal conduct can be found on the Colorado College website at:

• https://www.coloradocollege.edu/offices/fieldstudy/the-baca-grande/ If you have any questions about these policies or have any concerns about the Baca excursion, please let me know as soon as possible.

Grading and the Honor Code

Course Grade:Your grade in the course will be determined by the following criteria:

Class Participation and Homework 35%Take-Home Exam 1 15%Take-Home Exam 2 15%Presentation 15%Final Paper 20%

Office Hours:My official office hours, during which I am guaranteed to be in my office, are Monday –

Friday from 2:00 – 3:00 PM. However, you are encouraged to stop by my office at any time if you have questions about any aspect of the course. You may not always find me, however, if you drop by unannounced, so if you are unable to drop by during these official office hours, you may also call or email me to make an appointment to meet at some other time.

Honor System: When working on homework problems or activities, I wholeheartedly encourage you to

work with other students in the course. However, the final problem write-ups should be your own work. The same applies to your presentations and final papers. You are not permitted to work together on the take-home exams or to consult with anyone else about them until all exams have been turned in. However, while working on a take-home exam, you may freely refer to your notes, all handouts and other materials distributed in class, a modern-physics textbook of your choice, and a table of integrals. You may also use a graphing calculator and Wolfram Mathematica.

Other Useful Information

Laptops and Wolfram Mathematica: Wolfram Mathematica is a software package for symbolic computation. It is a powerful

numerical tool that is used broadly by the natural sciences, and it is a tool that we will be usingthroughout this course. If you have little or no experience using Mathematica, don't worry: oneof the goals of this class is to familiarize you with this computational too.

While Mathematica is commercial software, a home-use license is available at no cost to all students at Colorado College. This license allows you to download and install a copy of Mathematica on your laptop or home computer. For assistance in getting Mathematica installed on your computer, contact Weston Taylor in ITS by email at Weston.Taylor@ColoradoCollege.edu or by phone at (719) 389-6159.

I wholeheartedly encourage you to bring a laptop computer to class. Moreover, as we will be using Mathematica while staying at the Baca campus (where there is no wifi connection),it is important that you install Mathematica on your laptop before we depart for Baca and that you bring a laptop along on the excursion. If you do not have a laptop to bring to class orto Baca, please let me know. Laptops can be checked out from the circulation desk at Tutt Library and are can also be made available from AV services directly with instructor approval.

Accessibility Services:If you experience a disability and are requesting accommodations for this course, please

speak with me privately as soon as possible so we can discuss how best to put accommodations in place. If you haven't already done so, please connect with Accessibility Resources, the office

responsible for coordinating accommodations and services for students with disabilities. Accessibility Resources is located in Armstrong 211 and can also be reached at (719) 227-8285.

Please note if you are requesting accommodations that it is your responsibility to provide me with an official letter from Accessibility Resources which outlines what those accommodations are. I cannot provide accommodations until you provide me with such a letter. Moreover, it is important that you provide me with this letter well in a timely manner, so that I am able to make the appropriate arrangements.

Communication:This syllabus, a list of homework assignments and activities, and other course materials

will be posted on the course web page, which can be found at

• https://faculty1.coloradocollege.edu/~bthomas/PC320-block8-2016/PC320-block8-2016.html

In addition, I may also occasionally use Canvas in conjunction with this course – primarily to send emails to the class as a whole, but potentially for other functions as well. The canvas page for the course is

• https://canvas.coloradocollege.edu/courses/15441

It will often be necessary for us to communicate additional information (scheduling changes, clarifications about homework problems, etc.) to the class as a whole. When we do so, we will use your official Colorado College email addresses for all course-related email correspondence, so make sure to check your CC email regularly.