Deep Physics: Special Relativity for Talented High Schoolers, Princeton
Real Special Relativity, taught through Bondi’s k-calculus and spacetime diagrams. For talented high schoolers.
A World Through the Lens of Special Relativity
At high speeds, space and time do things classical physics has no answer for.
Classically, time runs at the same rate for everyone, fast or slow, here or there. In Special Relativity, a clock on a fast spaceship runs slower than a clock on Earth. Not metaphorically. Less time genuinely passes on board, for the clock, the atoms inside it, anyone riding along.
Classically, a meter stick is a meter long for everyone. In Special Relativity, a meter stick flying past you is shorter than one at rest. Not “looks shorter.” Is shorter, in your frame.
Classically, two events at the same time happen at the same time for everyone. In Special Relativity, two events you call simultaneous are not simultaneous for someone moving past you. Both of you are right.
Classically, velocities add: shine a flashlight from a rocket moving at half the speed of light, and the beam should fly at 1.5 c. In Special Relativity, the light leaves at c, for everyone watching. Not c plus the rocket’s speed. Just c.
Special Relativity is the theory that makes sense of all of this. One of the most thoroughly verified theories in physics, and the foundation on which everything from particle accelerators to GPS satellites depends.
This course teaches you what physicists know, from Einstein’s two postulates to E = mc².
You will:
- Derive the Lorentz transformation from Einstein’s two postulates, with algebra alone.
- Predict what happens to clocks and meter sticks at relativistic speed.
- Resolve the twin paradox and the pole-and-barn paradox by reasoning from the postulates.
- Compute relativistic energy and momentum in collisions, and derive E = mc² yourself.
By the end, you will think about Special Relativity the way a physicist thinks about it.
What You Will Actually Understand
By the end of the course, you will understand six core ideas of Special Relativity.
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. Both derived from the relativistic Doppler factor (the k-factor), using Bondi’s k-calculus. Not two separate phenomena. Two faces of the same underlying 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, derived from k. 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 you prove yourself, not a slogan to memorize.
The specific topics, and the depth given to each, may shift depending on class priorities and the dynamics of the cohort. The destination, a working understanding of Special Relativity from Einstein’s two postulates to E = mc², stays the same.
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, follow 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.
Primary text: Yury Deshko, Special Relativity: For Inquiring Minds (Springer, Undergraduate Lecture Notes in Physics). We work through it over one semester. Students purchase their own copy; the book is not included in tuition.
Schedule, Pricing & Enrollment
Formats: Fall, Spring, and Summer semesters.
Schedule, format, tuition, refund policy, and transcripts apply to every Lyceum course. They live on the Physics Lyceum: High School overview.
To enroll, schedule a call. We confirm fit, prerequisites, and the right semester.
Part of the SoTS Physics Lyceum
Special Relativity is one of eight semester-long physics courses in the SoTS Physics Lyceum: a multi-year curriculum in Princeton, NJ.
Mechanics of motion. Mechanics of bodies and fluids. Waves and oscillations. Thermodynamics. Electricity and magnetism. Optics and atomic structure. Special Relativity. Quantum mechanics.
The Lyceum is built on the Deep Physics methodology.