Special Relativity

Real Special Relativity for talented high schoolers.

Online from anywhere · or in-person in Princeton, NJ

A World Through the Lens of Special Relativity

This course explores Einstein's theory of Special Relativity, one of the four Modern Physics electives in the Physics Lyceum: High School curriculum. It follows the Deep Physicsmodel that runs through the whole SoTS Physics Lyceum.

The course runs on theory, problem-solving sessions, and homework, deriving every result from Einstein's two postulates.

1. Einstein’s Two Postulates

Two statements that force everything else. The principle of relativity, and the constancy of the speed of light. Each one looks innocuous. Together, they break the classical idea of absolute time and drive every result in this course.

2. Time Dilation and Length Contraction

Why moving clocks run slow, and why moving rods contract. Time dilation and length contraction as two faces of the same spacetime structure.

3. The Relativity of Simultaneity

Why “now” is not absolute. Two events that happen at the same time for one observer happen at different times for another observer moving past them. A single phenomenon that resolves most of the “paradoxes” of relativity on its own.

4. The Lorentz Transformation and Velocity Addition

The full rules for how positions and times transform between observers. Why velocities do not simply add. Why combining two sub-light speeds can never get you to the speed of light, let alone past it.

5. Spacetime Diagrams, Intervals, and Four-Vectors

From “space and time” to spacetime as a single arena. Spacetime diagrams as the primary tool for picturing relativistic motion. Invariant intervals, worldlines, and light cones. The four-vector formalism that packages relativistic kinematics into one geometric language.

6. Relativistic Energy, Momentum, and E = mc²

The capstone of the theory. How energy and momentum behave at relativistic speeds. Conservation laws in collisions and particle decays. E = mc² as a theorem.

The specific topics, and the depth given to each, may shift depending on class priorities and the dynamics of the cohort.

How Special Relativity Is Taught in This Course

We teach Special Relativity through Bondi’s k-calculus and spacetime diagrams.

The relativistic Doppler factor (the k-factor) emerges directly from Einstein’s two postulates. From it, with algebra alone, we derive time dilation, length contraction, the Lorentz transformation, velocity addition, and finally E = mc².

Every conceptual move is first made concrete in a physical setup (light signals between moving observers, clocks on a spaceship, particles colliding at near-light speed) before being generalized.

Texts and Requirements

Primary text. Yury Deshko, Special Relativity: For Inquiring Minds (Springer, Undergraduate Lecture Notes in Physics). We work through it over one semester.

Prerequisites. Mechanics of Motion or an equivalent course elsewhere, plus algebra and geometry.

No calculus. This course is deliberately algebra-only: every result, through to E = mc², follows from the two postulates with algebra. Bondi’s k-calculus, despite the name, is not calculus.

Schedule, Tuition, and Enrollment

Schedule, tuition, and enrollment
0.75 × speed of light