Learning special relativity

Bryan J. Field
4 min readSep 29, 2021
Photo by Maks Key on Unsplash

I took a break from writing here to finish and submit the manuscript for my new book, but I am back now and eager to continue our discussions on modern physics as we put the pieces together on our way towards understanding the needs and shortcomings for a possible theory of everything. I will post more about the book when I know more.

Today, I’d like to begin our look into special theory of relativity (SR). The formal study of SR is sometimes an afterthought in even the best physics education. For fun, I’m going to tell you about the books I learned from as we go, all great mainstream books on the subject, but if you are familiar with them you’ll know that SR is a very small part of their total content.

When I first learned SR, it was taught in the last week of my three part general physics course as a few dilation equations and some notes about the conservation of mass (Fundamentals of Physics, 4th Extended Edition by Halliday, Resnick, and Walker. In the current edition SR is chapter 37 of 44). We learned SR again, in the last week of a two-part course on analytic mechanics (Classical Dynamics of Particles and Fields, 4th Edition by Marion and Thornton. SR is chapter 14 of 14 and includes a reference to relativistic rotations which is ignored in almost every other book and begins to introduce four-vectors and Lorentz transforms albeit with an imaginary fourth component). And one final time in the last week of a two part course in electromagnetism where we learned it as an introduction to four-vectors (Introduction to Electrodynamics, 2nd Edition by Griffith. SR is chapter 12 of 12. Introduces proper Lorentz transforms, relativistic mechanics, and how fields transform). Each time, the treatment was rushed (which was no fault of my wonderful undergraduate professors) but it was presented as a neat physical effect tidily summarized in three equations: time, length, and mass dilation, velocity additions, and perhaps Lorentz transformations. The idea of space and time being combined into spacetime was mentioned, but the deeper significance was not elaborated upon.

In graduate school, we did this routine again at the end of graduate mechanics (Classical Mechanics by Goldstein, 2nd Edition. SR is chapter 7 of 13 which is much more prominent) and graduate electrodynamics (Classical Electrodynamics, 3rd Edition by Jackson. Chapter 11 of 16), with no real added insight, but the homework problems became more difficult.

These shortcomings came to a head when I started to learn quantum field theory where SR is very, very important. In short, quantum field theory is the unique extension of quantum mechanics that is consistent with special relativity which was pointed out with amazing clarity and elegance by Steven Weinberg in his first volume of The Quantum Theory of Fields. Here, we learn that spacetime is much more than simply a new way of thinking of space and time, but a new foundation that needs exploration.

The general theory of relativity, our current best theory of gravity, is also built upon the idea of spacetime, but a curved spacetime. Learning to understand and work in flat spacetime can give important knowledge on how to begin the move to more complicated curved spaces.

So, if it is so important, why do we breeze over it so quickly? We will discuss the nuts and bolts of how to understand SR, what it means, and how to use it in our coming articles.

Where did such an important theory come from? Deep thoughts and childlike wonder.

A great deal has been written about Einstein and his personal life all the way back to his childhood where the seeds of what would become special relativity first started. To modernize this story a little, Einstein had a thought that many of us had while growing up — if you were driving a car at the speed of light and turned the headlights on, what would happen? In his own time, Einstein wondered what it would be like to chase a beam of light.

In physics, sometimes we wish to imagine an experiment that we cannot perform for a number of reasons. Perhaps it would be too expensive or too impractical, but what we can do is to imagine the outcome of such an experiment given the constraints of everything we actually know. This is called a gedankenexperiment which is German for “thought experiment” and although these were not invented by Einstein, they are often associated with him.

Many of Einstein’s greatest ideas, that he later worked out in painstaking mathematical detail, revolved around these kinds of thought experiments. He would try to think of a situation where the known laws of physics would lead to a paradox which meant that our understanding was either incorrect or incomplete. This way of thinking is deeply Einsteinian. If you want to think like Einstein, train yourself to think this way. Next time, we will try and think like Einstein.

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Bryan J. Field

Dr. Bryan J Field is a theoretical high-energy physicist and Associate Professor. “A Theory of Everything” (MIT Press, Spring 2023). https://www.bryanjfield.com