Reading relativity

Recommended reading (mostly free) about Einstein's universe, for people with a variety of math backgrounds

Online, I run into a lot of laypeople who are curious about black holes or the big bang, as well as people with more of a background in philosophy, engineering, or one of the sciences. Often they have great questions, but haven't been looking in the right places to get clear, reliable information. Laypeople are often reading magazine or newspaper popularizations, or watching videos, and many of those treatments are inaccurate. People with more of a STEM background may be looking at presentations that are old-fashioned or that make the subject look more mysterious than it is. This blog post is my attempt to provide a reader's guide to relativity, with options that allow you to decide how much you want to try to digest at once, and at what math level.

Because I love free information, I've tried to list mostly free articles and books, but when there's a non-free book that I think is outstanding, I've included it. Some of the links are to materials written by me (Ben Crowell). The list is broken down into headings by general topic, and then each heading lists resources at different mathematical levels. Of the books that are not free, many can be borrowed for free by clicking through on the links to the Internet Archive.

Spacetime diagrams, relativity of time, the light cone

This is a topic that is inherently pretty easy to discuss without a lot of math. The resources below are all ones that use only easy math.

• General relativity from A to B, ch. 1-4 (Geroch) - Borrow online from the Internet Archive. A gen ed textbook. The initial chapters are set up to avoid the necessity of un-learning anything in order to understand general relativity. Not much contact with experiment. (3 hrs)
• Spacetime diagrams and the relative nature of time (Crowell) - A short introduction (20 min).
• Relativity for poets, ch. 1-2 (Crowell) - A longer textbook-style introduction for a gen ed college class (90 min).
• An illustrated guide to relativity, ch. 1-3 (Takeuchi) - A gen ed textbook (90 min, not free). Non-threatening style, with cute cartoons.
• It's about time, ch. 1-8 (Mermin) - A gen ed textbook with a more dry style. (3 hrs, not free)

The metric

With easy math

• Why can't you go faster than the speed of light? -- An explanation without equations or fallacies. (Crowell) - As suggested by the title, the emphasis in this short article is on explaining why superluminal speeds are impossible, but I accomplish that by developing from scratch, in a visual style, the relevant facts about the metric. I gloss over some details, which are presented in more detail in the Euclid meets Dalí article (below). (20 min)
• Relativity for poets, ch. 4 (Crowell) - A very short textbook-style introduction for a gen ed college class. This assumes that you already know quite a bit of relativity from the earlier chapters of the book, so the metric is presented as an afterthough: simply a different set of mathematical tools for expressing the same ideas. (20 min)
• Euclid meets Dalí: the metric in Einstein's theory of relativity (Crowell) - This article assumes only some basic previous knowledge of spacetime diagrams (like this), and presents the metric as a foundation for relativity. This is pitched at people without a college-level STEM background, but it will be helpful to have had something like a high school precalculus or physics class. (60 min)

Sophomore STEM level

• Modern physics (Crowell), sec. 1.3 (20 min)

With calculus, designed for an upper-division class for physics majors

• Spacetime physics, ch. 1-3 (Taylor and Wheeler) - Borrow online from the Internet Archive.. An older college textbook for physics majors. A nice physical presentation. Emphasis on coordinates. (3 hrs)
• Introduction to spacetime: a first course on relativity, ch. 1-2 (Laurent) - Available used for about $35. A dry mathematical treatment. Coordinate-free. (90 min)
• Special relativity, ch. 1 (Crowell) - Mixes coordinate-based and coordinate-free approaches. (1 hr)

The Lorentz transformation, combination of velocities

With easy math

• Relativity for poets, ch. 3 (Crowell) (90 min).
• An illustrated guide to relativity, sec. 3.4, ch. 4-6 (Takeuchi) - (90 min, not free). Non-threatening style, with cute cartoons.
• It's about time (Mermin) - Ch. 2 and 4 are Mermin's unusual presentation of combination of velocities. (2 hrs, not free)

Sophomore STEM level

• Modern physics (Crowell), ch. 4 (1 hr)

With calculus, designed for an upper-division class for physics majors

• Spacetime physics, chapter titled "Special Topic L" (Taylor and Wheeler) - Borrow online from the Internet Archive.. (3 hrs)

Momentum, energy, and E=mc²

With easy math

• Relativity for poets, ch. 5-6 (Crowell) - These are my lecture notes that were really meant to supplement the other books used in a gen ed course on relativity. The treatment of this topic is a little thin to stand on its own. (60 min)
• Relativity: A Very Short Introduction, pp. 35-42 (Stannard) - Borrow online from the Internet Archive. Available used for about $4. A serviceable but old-fashioned presentation.

Sophomore STEM level

• Modern physics (Crowell), ch. 6 (1 hr)

With calculus, designed for an upper-division class for physics majors

• Spacetime physics, ch. 7-8 (Taylor and Wheeler) - Borrow online from the Internet Archive.. (2 hrs)
• Special relativity, ch. 4 (Crowell) (1 hr)

General relativity

With easy math

• General relativity from A to B, ch. 5-8 (Geroch) - Borrow online from the Internet Archive. A gen ed textbook. Out of date and out of touch with experiments and observations, but still worth reading. (8 hrs)
• Relativity for poets, ch. 7-14 (Crowell) - These are my lecture notes that were really meant to supplement the other books used in a gen ed course on relativity. The treatment of general relativity is a little thin to stand on its own. (4 hrs)

With calculus, designed for an upper-division class for physics majors

• Gravity: An Introduction to Einstein's General Relativity (Hartle) - Not free. Used copies are available for about $40
• Spacetime physics, ch. 9 (Taylor and Wheeler) - Borrow online from the Internet Archive.. A one-chapter presentation at the tail end of a book on special relativity. (1 hr)
• Exploring black holes: introduction to general relativity (Taylor and Wheeler) - A cool book that uses only basic calculus and introduces general relativity solely though black holes. Unfortunately, used copies seem to cost at least $75.

Graduate level

• Spacetime and Geometry: An Introduction to General Relativity (Carroll) - As far as I know, this is the best option right now at the graduate level, since the old standards (MTW and Geroch) are 40 years out of date. There is an earlier, shorter version that is available for free on arxiv.

Cosmology

With easy math

• Heart of Darkness: Unraveling the Mysteries of the Invisible Universe (Ostriker and Mitton) - Borrow online from the Internet Archive. A nice historical treatment that is fairly up to date. Assumes no knowledge of relativity.
• Relativity for poets, ch. 13-14 (Crowell) - Designed to supplement Ostriker and Mitton by doing a little more math and making more of a connection to students' prior knowledge of relativity.

With calculus, designed for an upper-division class for physics majors

• General relativity, ch. 8 (Crowell)

Ben Crowell, 2023 Jan. 4

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