Although I didn’t collect the statistics, I am certain my unit on special relativity is the favorite of more of my students than any other. This might be because it is usually the last unit. However, I am convinced it would be popular regardless of its placement in the course sequence. Many students have never encountered time dilation, length contraction, and the relativity of simultaneity. These facts about the way the world works are mind blowing. Students that are familiar with special relativity seem to get even more excited when they find out they will be studying it.
Student response and interest are the reasons I almost always included a unit on special relativity after the AP test. I also tried units on quantum theory and chaos theory at the end of the year. These went well but I always went back to special relativity. The math is simpler and there is a large amount of educational and cultural material produced by others to draw from. It can be intimidating to teach something that is so hard to understand at the same level we understand other concepts in physics. When students tell me they don’t understand special relativity even though they are trying hard, I tell them they need to broaden their concept of what understanding is. Since we don’t travel at speeds where the effects of special relativity are noticeable, we cannot expect to understand them as we do falling objects and applied forces.
My success with special relativity prompted me to promote it to other teachers. I have found that not only do many teachers not cover it, they don’t want to. I believe there are several reasons for this. They have not taken a special relativity class, they may be reluctant to teach something not found on standardized tests, or they feel unprepared to answer student questions about it. Although most of these things were true for me, I plunged ahead anyway. The incredible student response motivated me to read more about it and to seek out ways to answer their questions. As the years passed I added things to make it more interesting. I found multiple ways to explain the same concepts. I found ways to either answer their tough questions or explain why their question was unanswerable.
When I needed to develop more curriculum for my Fusion/Astrophysics Teacher Research Academy workshop at Lawrence Livermore National Laboratory, I immediately thought about doing special relativity. LLNL paid me to develop slides for the workshop. This made it easier to share with other teachers. I have heard good feedback from teachers that used the slides. This webpage is a depository for those slides and many more resources from my special relativity unit. It also has some details about how I use it. Please feel free to use these resources and share them with others.
My primary resource was the Conceptual Physics for High School textbook by Paul Hewitt, second edition. That is also the book my students were assigned to read. I also relied heavily on Relativity Visualized by Lewis Carol Epstein. Lew’s other book, Thinking Physics, was also very helpful for this and many other physics topics. There are many, many other resources for a teacher preparing to teach special relativity. Spending time with college textbooks, popular science books, and YouTube videos will be worth it. To help those wanting to use the slides in class, below are YouTube videos of my narration of the slides for students who were absent. Watching them will give you more information about how I use them in class than what you will find in this post.
I begin the unit with a showing of the “Journeys in Space and Time” episode in the original Cosmos series. It can be found on YouTube. It is based on the “Travels in Space and Time” chapter in the Cosmos book but includes topics from other chapters. That might explain the difference in titles. I recommend introducing the episode with a brief talk about who Carl Sagan was and some of his accomplishments. I say he was a frequent talk show guest and parodied on Saturday Night Live. I end my introduction with one of the highest compliments, he was a great teacher. While watching the video students earn a few points by answering the questions on a sheet I provide them. My experience is that students really enjoy the episode, it opens their minds to many big ideas that they have not encountered before. You can almost feel the chills they get when he says “We are star stuff that has taken its destiny into its own hand.” It is not unusual to have them applaud at the conclusion. After we switched to block schedule we had time to discuss the last question on the sheet, “What do you think Carl means by “a critical branch point in history”?” It seems we too often find ourselves at such a branch.
The assignment after the video builds on the part about interstellar travel. They read an article from the Planetary Report, the publication by Carl Sagan’s Planetary Society. The article and questions are below but you might try finding a more up to date article. On the other hand, interstellar travel is still about as far into the future as it was when this article was published in 2003!
See the narration Part 1 YouTube video for details about the second day of instruction. We end the first block schedule day with Paul Hewitt’s cartoon about what is known as the twin paradox. Hewitt and I take the standard approach to resolving the twin paradox. This says that the twin that accelerated was the one that ends up not aging as much. Here is the Hewitt video:
Some people object to this explanation and carefully describe how the traveling twin ages less even when the acceleration is discounted. They then resolve the paradox with an example where the twins never meet again! Not very satisfying in my opinion. You can decide for yourself by watching Don Lincoln’s excellent video below.
The notes on the Twin Trip slide give the script of a little dialogue I have with myself after the Hewitt cartoon. I recorded myself playing the role of a fictional Albert. I start the recording and have a conversation with myself. I suggest you record yourself doing the Albert part. This is a technique I have used for many years in other contexts. Whenever there was a question I would hope a student would ask, I would record ahead of time asking it myself. The trick is to keep the things you say live short so the timing is easier. I even used this technique in a skit for our Fractured Follies teacher talent show one year.
See the narration in the Part 2 YouTube video for details about the third day of instruction. The discussion about the finite speed of light would fit well in a unit on light too. I have been telling my story about the alien space mirror for decades, before light echoes were a thing. As Michael Faraday said, “Nothing is too wonderful to be true, if it be consistent with the laws of nature.” The part about the 3 spaceships is direct out of Lewis Epstein’s book, “Relativity Visualized”. At the time of this writing it appears it is difficult to find a used copy of this gem for a reasonable price. I recommend you study the slides and my narration well before discussing it in class.
After reading the fictional book “Einstein’s Dreams” by Alan Lightman, I looked for a way to include it in the special relativity unit. The book contains very short chapters that describe a dream Einstein had where time works in a different way. In some dreams time works as it really does but the effect is exaggerated. In others things work backwards such as entropy decreasing with time. I obtained the audio book and play selected chapters in class. I post a pdf of each chapter for students that miss class. Students jot down a few notes and at the end of the unit write their own dream. It is a great way to inject some creative writing and many students love it. I only require their story to be about 2/3 of a page but many write a lot more. Some will talk to me after class about their idea and be very enthusiastic about it. I have collected some from each year and might publish them at some point. Here is one from 1997:
In this world, time travels more slowly when one is surrounded by hot temperatures rather than cold temperatures. The village people in Ecuador experience life at a slower rate than those souls that meander in Iceland. When a young girl in Florida bathes in her backyard, she is, in actuality, growing older at a slower rate. An Alaskan lumberjack, a crab catcher in the Yukon, and a fisherman searching for fish off the coast of Nova Scotia would all grow older while their relatives living in California remain young, bursting with vitality. It is because of the way time works that drive some into burning pits of fire believing that its intense capacity of heat will bring about their immortality. Madness permeates the most prominent cities of the world. Many run to their heated houses, packing up their belongings, and jump on the first flight to the warmer areas in hope of capturing unceasing youth. Tropical Islands are more populous than ever and cities, like Moscow, have literally been abandoned due to the coldness of their unbearable winters. Life is much different in this world. Skiing would be considered a pastime. The Eskimos in Alaska will go through generations much faster. When two lovers get caught up in a moment of heated passion, they are, in fact, extending the rate in which they live. Finding heat and being in warm area is a way of life, and essentially a part of everyone’s life. – Tina Chang
The audiobook is available for about $10 and the book can be found used for a few dollars. The chapters I use are April 14 – cycles of time, April 26 – time slows with altitude, May 11 – entropy, May 29 – time slows with speed, June 3 – morning and evening people, and June 9 – laters and nows. The last chapter has been a reading on the AP English Literature test multiple times. My students were very excited and rushed to tell me after their test. I mention this when I introduce the assignment so they might take it a little more seriously. After we listen to a chapter we have a short discussion. They come up with some great observations. For example, in the time slows with altitude chapter, some students realize that the Earth’s rotation would result in a faster speed at higher altitudes, causing this effect. I add that general relativity predicts time slows with stronger gravity, causing the opposite effect. Some students use this device for their own dream. I have a lot of stories where people are living on the bottom of the ocean so time will go slower!
See the narration in the Part 3 YouTube video for details about the fouth day of instruction. I recommend you download the Mr. Tompkins video from YouTube, delete the audio, and add your own. The story can be found for free on Google Books and by searching “mr tompkins in paperback pdf”. I have had students do a dramatic narration with several students playing different parts. I also like the “Quantum Jungle” story and have read that in class.
The Mechanical Universe for High School video on special relativity is a great way to summarize the unit. It goes over some of the ideas with a different example. It also introduces spacetime diagrams. I prepare students for the video by drawing a distance vs time graph for a person standing still, walking away from the origin, and walking toward the origin. I then draw the same thing with time on the vertical axis and distance on the horizontal. That is a spacetime diagram. The lines showing the motion form a cone. If it was a graph of a light pulse, it would be called a light cone. I use the last part of the video to introduce the idea of relativistic mass. This concept has fallen out of favor because of cranky particle physicists. Even Hewitt removed the idea from later editions of his book. In my opinion it is fine to include it at the high school level. The thought experiment in the Mechanical Universe video that develops the idea is really good and there is nothing wrong with it. The concept of relativistic mass can cause problems when interpreting certain particle physics experiments so it has been widely discarded. I just warn my students about this and caution them to not insist upon it if their physics professor balks at the idea. Don Lincoln addresses this issue in another great video. Notice how he backs off his initial dogmatic statement about relativistic mass in the end.
I would really like to hear Don Lincoln explain Hewitt’s trolley and electric motorcycle thought experiment. However, I won’t hold my breath while I wait!
Throughout the special relativity unit I am usually asked repeatedly by students questions that begin with, “if you were traveling at the speed of light …”. I stop them and explain that we will get to that but need to develop more ideas first. The “Faster than Light?” slides are for this discussion. I show the idea that as you add to your speed, observers see the extra distance you travel diminish as space contracts and the time it takes increase as time dilates. Thus they don’t see you add to your speed as much as you measure. This effect is more prevalent the faster you go. Not a proof but they can follow the logic. It is a lot like the Zeno’s paradox where you keep halving the distance to a destination, always approaching but never quite getting there.
The pole and barn paradox is optional. I suggest you read up on it before showing it to your students. There are MANY videos and discussions about it posted online. It is also called the ladder and barn paradox or just ladder paradox. I used animations from a program called RelLab that simulates scenarios using special relativity. It was orphaned by an OS update many years ago. The video of my take on this paradox got a nice mention on BoingBoing.net: https://boingboing.net/2015/12/10/gravity-visualized-with-a-big.html
I end with a short discussion about time travel. During the special relativity unit I mention how time travel is not only real, it is compulsory. We must always travel into the future. Special relativity dictates that we can travel into the future at a different rate than others if we move at a high speed relative to them. This discussion is about travel into the past. I mention that physicists like Nobelist Kip Thorne have worked on the problem and shown it may be possible with extremely advanced technology. The constraint is that you cannot travel back any further than the time that the time machine was constructed. That solves the “where are the time travelers?” argument. Since we haven’t built the time machine yet, there can be none. If you are curious about this, I recommend Thorne’s book “Black Holes and Time Warps, Einstein’s Outrageous Legacy.” If there is time at the end of the semester, I show the 1999 Nova episode, Time Travel. It is hard to find so I posted it on YouTube: https://youtu.be/XWvd0OFtPA0. The Saturday Night Live skit, “Timecrowave” is perhaps the best skit they have ever done. After watching it, I tell my students I am working on a washer/dryer that works the same way. However, I am not sure if I should put my dirty clothes in the washer or the dryer first!
I can’t guarantee all the links on the last slide still work but it is worth finding out. The MIT “A Slower Speed of Light” game has potential for classroom use. It always made me motion sick! If you are reading this far I hope that means you are serious about teaching a unit on special relativity. Your students will be glad you did.