Basic Info

Physics II: Official Course Description

What are relativity and quantum mechanics, and why were they viewed as revolutionary when they were formulated in the early 1900s? How and why do relativity and quantum mechanics compel us to discard commonsense ideas about the nature of the physical world that are part of classical mechanics? Why is there not agreement on how to interpret quantum mechanics, and why does quantum mechanics even need interpretation? This version of Physics II covers Einstein's theory of special relativity and selected topics in quantum mechanics, and is designed to introduce students to some of the formalism and central results of relativity and quantum mechanics, so that they can formulate scientifically grounded answers to the above questions. Throughout the course we will start with first principles and carefully build toward key results, allowing students to see how relativity and quantum mechanics---two of the pillars of modern physics---were constructed and how they cohere as mathematically consistent and experimentally verified theories. The first half of the course will cover relativity topics including the principle of relativity, spacetime intervals and proper time, coordinate transformations, time dilation and Lorentz contraction, and relativistic energy and momentum. The second half of the course will turn toward the foundations of quantum mechanics, including: spin-1/2 particles, wave-particle duality, and Bell's inequalities and the Einstein-Podolsky-Rosen paradox. If time permits, we may cover additional topics such as blackbody radiation, the photoelectric effect, Bohr's model of the hydrogen atom, and quantum cryptography. To gain a sense of the scientific, social, and material context in which the theories of relativity and quantum mechanics were developed, we will read a number of papers and book chapters by historians and philosophers of science. This course is designed to appeal to a wide range of students: both those whose interests lie outside of science as well as those who are drawn toward the sciences or mathematics. Students who take this course should be comfortable working with mathematical abstraction. Evaluation is based on weekly problem sets, participation in weekly discussion sections, and several short reflection assignments. Meets the following degree requirements: QR and ES.

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Who/when/where

• Instructor: Dave Feldman
• Pronouns: he/him/his
• Class Meeting Times/Location: Monday, Thursday, 11:10 - 12:35, Room 103, Center for Human Ecology
• Discussion Section Times/Location: Thursday 2:35 - 4:00 or Friday 11:10 - 12:30, Turrets Straus Room (second floor).
• Help Sessions: Help Session Schedule (updated frequently)
• Individual Meetings: By appointment
• Teaching Assistants: Noelle Stringer, Alsu Shagieva

Axioms

In mathematics, axioms are propositions that are assumed to be true. The mathematician Federico Ardila-Mantilla has written four axioms that guide the work he does in education and outreach. Federico's axioms resonate strongly with me. They are:

1. Mathematical and physics potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
2. Everyone can have joyful, meaningful, and empowering math and physics experiences.
3. Math and physics are a powerful, malleable tools that can be shaped and used differently by various communities to serve their needs.
4. Every student deserves to be treated with dignity and respect.

Community Agreement

Taking the above axioms as a starting point, let's think about what type of community we want to create this term. Here is a community agreement based on one written by Federico Ardila-Mantilla.

This course aims to offer a joyful, meaningful, and empowering experience to every participant; we will build that rich experience together by devoting our strongest available effort to the class. You will be challenged and supported. Please be prepared to take an active, critical, patient, creative, and generous role in your own learning and that of your classmates.

Course Information and Advice

Course Goals

1. Stay physically and mentally healthy and maintain intellectual and personal connection during a potentially difficult time.
2. Experience the challenge, joy, and beauty of theoretical physics.
3. Gain a firm, grounded, enduring understanding of the basic elements and structure of special relativity and quantum mechanics.
4. Engage with the philosophical and ontological questions surrounding relativity and quantum mechanics. I hope you'll leave this course thinking somewhat differently about space/time, reality, determinism, and causality.
5. I want to help you improve your basic facility with algebra and functions, your problem solving skills, your ability to create and interpret different types of graphs, and your overall mathematical confidence.
6. Have fun while growing and learning.

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Course Logistics

1. There are no texts that you need to acquire for this course.
2. For the relativity part of the course I will follow the exposition in Thomas A. Moore, Six Ideas that Shaped Physics: Unit R: The Laws of Physics are Frame-Independent, McGraw Hill, 1998. You do not need to purchase the text.
3. For the relativity portion of the course I will also likely assign short videos to watch. These are videos I made when I taught the class entirely online in the spring of 2020.
4. There will be numerous other readings and videos assigned throughout the course
5. There will be two sorts of work you will do for this course:
   • Weekly Homework Assignments, described below.
   • Reflection Assignments. There will be two reflection assignments. The goal of these are for you to synthesize and explore some of the many philosophical, historical, and political questions we'll be reading about and discussion. The assignment can take any form, and should be the equivalent of a 2-3 page paper.
6. All work can be resubmitted without penalty up to (roughly) a few weeks after I return it to you.
7. Your final evaluation will be roughly weighted as follows: Weekly Homework (70%), Reflection Assignments (20%), Engagement in Discussion Sections (10%).

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Course Structure and Flow

1. I have taught the material in this course a handful of times, and taught this particular combination two springs ago. I think the class worked well then, and I'm confident that it will work well this time around.
2. We will cover special relativity (SR) for approximately the first five weeks of the course and then will turn our attention to quantum mechanics (QM). While there will definitely be consistent threads throughout, in some ways this course may feel like two separate courses. I think that's ok.
3. Some notes about math.
   • This class assumes that you have some level of comfort with basic algebra. QM and SR are areas of physics that defy common sense, so we'll need to lean pretty heavily on the mathematical formalism in some places. The math in most ways isn't harder than that of Physics I, but we'll rely on the math in a more fundamental way.
   • It is possible get a solid, grounded treatment of SR and QM without using math beyond algebra. However...
   • There are lots of fun and interesting math in QM and SR. I'll prepare a number of optional explorations for those who want to dig deeper into some of the mathematical underpinnings of QM and SR. I would strongly encourage those of you interested and/or experienced in math to give some of these explorations a try. I'm also happy to set up times outside of class to work through some more math-heavy material.
4. We will do a wide variety of things in the discussion sections: mostly discussing readings, but also we will do some exercises and explorations.

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Electronic Distractions

As much as possible, I'd like to minimize the use of laptops, tablets, and phones during our class meetings. There is good evidence that these wonderful devices can harm the learning environment, even for those who are not using their own devices and are merely exposed to the devices of others.

There is no need to ban laptops entirely—that just seems silly to me. There may be times in class when we will do exercises that require computers, and there will also be moments when we might want to grab a device and look up the meaning of a word or a historical tidbit or something. So let's use common sense and keep devices holstered except when they're needed, at which point we should use them proudly and without apology.

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Stuff about Homework

1. There will be an assignment due almost every Friday. It is essential that you do these assignments, as this is how one learns math, and also this is most of what your evaluation will be based on.
2. There will be two parts to almost every homework assignment:
   • Problems to be submitted on WeBWorK
   • Problems to be submitted on "paper" (a scanned pdf) on google classroom
3. WeBWorK is an online homework system. There are three reasons why I use WeBWorK:
   • You get instant feedback while doing the work, so you can learn right away from your mistakes. You can submit solutions many times until you get everything correct.
   • Some problems are randomized so that you will all get slightly different versions of the questions. This means that collaborating with other students will be maximally effective, since you'll have to share solution methods and not just the final answer.
   • Since the problems are automatically marked, I can spend more time helping you and won't have to spend as much time grading.
4. If you need extra time for one or two of the homework assignments, it's not a big deal. But be mindful to not fall farther behind every week.
5. I do not expect all of the homework assignments to be easy; I don't expect you to be able to sit down and do them quickly. Don't let yourself get frustrated. I strongly suggest working with others and seeking help if you need it.
6. You are strongly encouraged to work together on homework. You can also consult me, class tutors, other faculty, friends, and family. However, the homework you hand in should represent your own understanding.
7. As I plan on sending out homework assignments and other information via email/google classroom, it is important that you check your email/classroom regularly.
8. You will need access to a calculator (or the equivalent) that has scientific notation.

Discussions

We will do a lot of different things during discussion section, including discussing readings. These discussions are chance for us to explore some of the philosophical, conceptual, historical, and social aspects of relativity and quantum mechanics. The readings we do will range widely in content, style, and difficulty. There are several goals and motivations I have for discussions:

• The discussions are a chance to figure out some things together. We will be doing some readings that are sometimes difficult and subtle and, I hope, interesting. Working together we can solidify and deepen our understanding.
• In some of the discussions it will be particularly valuable to hear a diversity of opinions. I expect there will be a range of reactions and responses to some of what we read, and I think that there is tremendous value to listening to and engaging with a diversity of thought.

Expectations for class discussions:

• Prepare. Do the reading and think about it. Expect to spend an hour or two preparing, although obviously this will vary a lot from reading to reading. Take notes, write down questions, and prepare responses to any questions I might have posed.
• If you can work with a hard copy of the reading. I think it is easier to engage with a text via a physical copy, and as much as possible I don't want us to have laptops open when we meet.
• Be present. Listen to others, respond, and contribute your own ideas and questions.

We should all work to create an inviting atmosphere and ensure that there is opportunity for all to contribute. At the same time, there is no need for everybody to contribute equally. It is natural for some people to talk more than others, and I think this is normal and good. Also, I expect that students will engage and contribute at different levels, depending on prior coursework. I see this diversity of backgrounds as a strength and not a weakness; there are roles for everyone to play. Asking good questions is as important as providing answers.

Finally, it goes without saying, but I'll say it anyway: the point of discussions is not to figure out who is right and who is wrong, but to help all of us get to a deeper, and not necessarily uniform, understanding.

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Help Sessions

I will have a handful of help sessions every week. You are warmly invited and encouraged to attend these sessions. Help sessions are relaxed, informal, and hopefully fun. Things that happen at help sessions:

1. I am around to offer help on the homework.
2. Some students do most of the homework while at a help session. They work through problems alone or with others, and find it comforting to know that help is immediately at hand if needed.
3. Others do the problems at home and come to the help session with specific questions.
4. Some students work in groups at help sessions, others work more or less alone.
5. Help sessions are also a chance to ask general questions about the course. Conversations also sometimes wander into other areas: politics, the state of the world, what's for dinner, what classes are offered next term, and so on.
6. Help sessions are a great way to meet other students in the class.
7. Often there will be coffee/tea and/or snacks.

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Individual Meetings

I am happy to meet with students one-on-one. The best way to set up an appointment is to send an email. There are lots of reasons why you might want to meet with me:

1. You have some in-depth questions that there isn't time to explore in a help session.
2. You have a question that you think is too basic or you're uncomfortable asking in a help session. (You shouldn't be uncomfortable, since, as the saying goes, there are no dumb questions! But I understand that you might be uncomfortable nevertheless.)
3. You want to discuss some challenges you're facing in the class.
4. You want to talk about other classes in math or physics, or internships, senior projects, etc.

Please don't hesitate to reach out if there's anything you want to discuss. You should also feel free to reach out to the TAs.

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Diversity, Inclusion, and Belonging

It is my intent that students from all backgrounds and perspectives be well served by this course, that students' learning needs be addressed both in and out of class, and that the diversity that students bring to this class be viewed as a resource, strength, and benefit. I aim to present materials and activities that are respectful of diversity: gender, sexuality, disability, age, religion, socioeconomic status, ethnicity, race, and culture.

Learning about diverse perspectives and identities is an ongoing process. I am always looking to learn more about power and privilege and the harmful effects of racism, sexism, homophobia, classism, abelism and other forms of discrimination and oppression. Your suggestions are encouraged and appreciated. Please let me know ways to improve the effectiveness of the course for you personally, or for other students or student groups. If something was said or done in class (by anyone, including me) that made you feel uncomfortable, please let me know. You can also reach out to Provost Ken Hill, or Associate Deans Kourtney Collum or Jamie McKown.

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Statements about Academic Honesty and Hours of Academic Engagement

• I am required to remind you that: "By enrolling in an academic institution, a student is subscribing to common standards of academic honesty. Any cheating, plagiarism, falsifying or fabricating of data is a breach of such standards. A student must make it his or her responsibility to not use words or works of others without proper acknowledgment. Plagiarism is unacceptable and evidence of such activity is reported to the academic dean or his/her designee. Two violations of academic integrity are grounds for dismissal from the college. Students should request in-class discussions of such questions when complex issues of ethical scholarship arise."
• I am also required to say that: You should expect to spend 150 hours of academically engaged time on this course, or 15 hours per week. In addition to 4.5 hours per week in class or discussion section, in a typical week you'll spend 2 hours reading and preparing for class and 8.5 hours attending help sessions and completing assignments.

Schedule

Important Links

Week 01

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Week 02

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Week 03

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Week 04

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Week 05

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Week 06

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Week 07

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Week 08

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Week 09

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Week 10

The building in which we gather for this class, and all of College of the Atlantic, is located on traditional lands of the Wabanaki people. The four Native American tribes in Maine today are the Maliseet, Micmac, Penobscot, and Passamaquoddy, collectively referred to as the Wabanaki. I believe it is important to acknowledge that our presence on this land entangles us in the web of colonialism, past and present. The future, however, is still unwritten.