Conceptual Science

​ In section 11-1 of the Feynman Lectures, symmetry is introduced not as a decorative or geometric idea, but as a deep principle about how physical laws behave. Feynman adopts Hermann Weyl’s operational definition: a system is symmetric if, after performing a certain operation on it, nothing observable changes. This definition is crucial because it shifts symmetry away from appearances and toward actions. What matters is not how something looks in isolation, but whether it behaves the same after a specific transformation. The opening example of a left–right symmetrical vase is deliberately simple. Rotating the vase by 180 degrees around its vertical axis leaves it indistinguishable from its original state. The important point is not the vase itself, but the logic of the test: perform an operation, then check whether the outcome is identical. Feynman uses this everyday example to prepare the reader for a more abstract application of the same idea to physical laws, which are not objects ...

​ In chapter 10-5 of  The Feynman Lectures on Physics , Feynman examines how the classical law of conservation of momentum survives the transition from Newtonian mechanics to modern physics. Rather than presenting conservation laws as immutable formulas, he emphasises that their validity depends on how fundamental quantities are defined. Momentum, in particular, remains conserved, but its meaning must be broadened to accommodate relativity, electromagnetism, and quantum mechanics. Feynman begins by revisiting the classical definition of momentum as the product of mass and velocity. In Newtonian mechanics, mass is treated as a fixed property of a particle, independent of its motion. Special relativity alters this assumption. To ensure that momentum is conserved in all inertial frames, mass must depend on velocity. As a particle’s speed approaches the speed of light, its effective mass increases, causing its momentum to grow more rapidly than predicted by classical theory. Feynman st...

​ In Chapter 10–4 of  The Feynman Lectures on Physics , Richard Feynman develops a conceptual analysis of momentum and energy through the study of collisions and related interactions. Rather than relying on mathematical formalism, the discussion emphasises physical interpretation and symmetry arguments. This approach is especially effective at the undergraduate level, where the goal is to understand not only what physical laws state, but why they must hold across a wide range of situations. The chapter begins by contrasting simple collisions in which bodies stick together or separate after an explosion with more general cases in which bodies rebound. In these latter situations, the key physical insight is that collisions are dynamic processes involving temporary energy storage. When two bodies collide and rebound, they do not instantly reverse direction. Instead, there is a brief interval during which both bodies are in contact, compressed, and momentarily at rest. At this instant ...