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Symmetry as a Test of Physical Law

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​ 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 ...
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Momentum Reconsidered: From Newtonian Particles to Relativistic Fields and Quantum Waves

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​ 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...
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Compression, Rebound, and Recoil: A Conceptual Study of Momentum and Energy

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​ 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 ...
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Riding Along with Feynman: Galilean Relativity and Conservation of Momentum

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​ Chapter 10-3 is a carefully staged piece of reasoning in which Feynman is less interested in announcing a law than in showing how one earns the right to believe it. The passage reads almost like a laboratory notebook written for the reader, with the air trough playing the role of both experimental apparatus and philosophical device. By invoking Galileo’s struggles with friction and then immediately “fixing” them with modern technology, Feynman situates his argument historically while also making clear that his conclusions rest on controllable, repeatable experiments rather than abstract postulates. The air trough is not decorative: it is what allows motion to persist unspoilt, so that reasoning about collisions can proceed without constantly apologising for real-world imperfections. Methodologically, Feynman begins with the most symmetrical situations imaginable. Equal masses, starting from rest, driven apart by an internal explosion; equal masses approaching one another with equal s...
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Conservation of Momentum: Feynman’s Conceptual Route to a Universal Law

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​ Richard Feynman’s discussion of conservation of momentum in Chapter 10-2 of  The Feynman Lectures on Physics  is a careful construction of a universal physical law from simple but deeply constrained ideas. Rather than presenting momentum conservation as an axiom, Feynman shows how it follows naturally from the mutual character of forces and from the symmetry properties of space and motion. The result is not merely a rule for solving problems, but a statement about what kinds of change are possible in nature. The starting point is the recognition that forces between particles arise through interaction and are inherently reciprocal. When two particles interact, each influences the other, and the changes produced by these influences are linked. The significance of this reciprocity becomes clear when one considers the system as a whole rather than focusing on individual particles. Changes in motion can occur internally, but when all interacting particles are considered together,...
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Newton’s Third Law: “Action Equals Reaction”

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​ In Chapter 10-1 of  The Feynman Lectures on Physics , Feynman situates Newton’s Third Law within a broader methodological discussion concerning the limits of analytical and numerical approaches in classical mechanics. While Newton’s Second Law provides, in principle, a complete prescription for determining motion from known forces, Feynman emphasises that practical and conceptual considerations motivate a deeper examination of the laws themselves. Analytical solutions, where they exist, reveal general structures of motion - parabolic trajectories under uniform acceleration, harmonic oscillations described by trigonometric functions, and elliptical planetary orbits - that numerical methods, though powerful, do not naturally expose. These solutions contribute not merely computational efficiency but conceptual understanding. Feynman then contrasts such analytically tractable systems with those that resist closed-form solutions. Even modest increases in complexity, such as deviations...
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Feynman, Orbits, and the Power of Doing It Step by Step

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​ By the time we reach Chapter 9–7 of  The Feynman Lectures on Physics , the tone of the book has subtly shifted. Feynman is no longer primarily concerned with finding elegant analytical solutions. Instead, he is showing us how physicists actually wrestle complicated systems into submission. The subject is planetary motion, but the deeper lesson is about method, approximation, and the quiet power of Newton’s laws when they are allowed to operate incrementally. Feynman begins by pointing out that techniques which work beautifully for simple systems, such as oscillating springs, do not transfer neatly to planets moving under gravity. The force law is different, and that difference matters. A planet does not experience a restoring force proportional to its displacement. Instead, the force depends on its distance from the Sun in a way that makes the mathematics stubbornly resistant to tidy solutions. Rather than fighting this, Feynman changes strategy. The core idea is to stop thinking...
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