Physics (Feynman Lectures)
Richard Feynman's physics, one big idea at a time — for curious K-12 minds.
Atoms in Motion
If you had to pass on just one sentence of scientific knowledge to the next generation, it would be the atomic hypothesis: all things are made of atoms —…
Read →Basic Physics
Before about 1920 we thought we understood the world: a three-dimensional stage, things changing in time, and particles pushed and pulled by forces like…
Read →The Relation of Physics to Other Sciences
A poet once said, 'The whole universe is in a glass of wine.' Look closely enough and it is true. The swirling liquid and evaporating alcohol are…
Read →Conservation of Energy
There is a law that, as far as we know, is never broken: energy is conserved. But what is energy? Imagine a child with 28 indestructible blocks. Each day…
Read →Time and Distance
Time is what a clock reads; distance is what a ruler reads. But how do you measure the age of the Earth or the distance to a galaxy? You cannot use a…
Read →Probability
We make guesses because we rarely have all the information. Probability is a system for making better guesses. Picture a drunk man taking steps at…
Read →The Theory of Gravitation
For centuries the motion of the planets was a mystery. Kepler found the pattern — planets trace ellipses, sweeping out equal areas in equal times — but…
Read →Motion
The world is always changing — how do we describe change precisely? The ancient Greeks tied themselves in knots over this. The answer required a new…
Read →Newton's Laws of Dynamics
Newton gave us a program for predicting the future. His second law, F = ma, is really a rule about change: it does not tell you where something is, but…
Read →Conservation of Momentum
Newton's third law says that for every action there is an equal and opposite reaction: push on me and I push back just as hard. A wonderful consequence…
Read →Vectors
The laws of physics do not care whether you run an experiment here or there, facing north or facing east — they must be the same regardless of how you…
Read →Characteristics of Force
What is a force? Saying it equals ma is only a definition; the real content of Newton's laws is that forces have simple, independent properties. The…
Read →Work and Potential Energy (Part A)
When a force moves an object, we say it does work, transferring energy. For some forces, like gravity, the work to move from A to B does not depend on…
Read →Work and Potential Energy (Conclusion)
The power of potential energy is that it lets us use conservation of energy directly. For a conservative force — gravity, or an ideal spring — the sum of…
Read →The Special Theory of Relativity
Nature has a strange rule: the speed of light is the same for all observers, no matter how fast they move. This simple fact has enormous consequences. If…
Read →Relativistic Energy and Momentum
If space and time are relative, other quantities must change too, and Newton's laws need modifying. An object's mass increases with its speed; as it…
Read →Space-Time
Minkowski said it best: space by itself and time by itself fade into shadows, and only their union survives. We live in a four-dimensional world. An…
Read →Rotation in Two Dimensions
Spinning motion can be described with perfect analogs of ordinary straight-line ideas. Instead of distance we use angle; instead of velocity, angular…
Read →Center of Mass; Moment of Inertia
A thrown wrench tumbles in a complicated way, yet one special point — the center of mass — flies in a simple parabola, as if all the mass were…
Read →Rotation in Space
In three dimensions, rotation gets wonderfully counter-intuitive. Torque and angular momentum become vectors. Push on the axis of a spinning gyroscope…
Read →The Harmonic Oscillator
The simple back-and-forth of a mass on a spring is one of the most important problems in all of physics, because its equation of motion shows up…
Read →Algebra
Mathematics is the language of physics and algebra is its grammar. Starting from simple counting and a few rules, we abstract them and demand they keep…
Read →Resonance
Push a child on a swing at just the right moments and she goes higher and higher — that is resonance. A system with a natural frequency responds…
Read →Transients
Strike a bell and it does not instantly ring a pure tone; first there is a complicated 'clank' before it settles. That start-up behavior is a transient.…
Read →Linear Systems and Review
Many systems are 'linear,' which simply means double the cause and you double the effect. The magic of linear systems is superposition: break a…
Read →Optics: The Principle of Least Time
Here is a completely different way to see physics. Instead of saying light bends because it hits water, we can say light checks all possible paths from A…
Read →Geometrical Optics
Using least time we can understand lenses and mirrors. A converging lens is thicker in the middle, so light through the center travels a shorter distance…
Read →Electromagnetic Radiation
An accelerating electric charge disturbs the electric and magnetic fields around it, and Maxwell's equations say that disturbance spreads outward as a…
Read →Interference
Light is a wave, and waves can add up or cancel out. Crest meets crest and they build a bigger wave — constructive interference. Crest meets trough and…
Read →Diffraction
When light passes through a small opening it spreads out — that is diffraction. It looks like a separate effect from interference but is really the same…
Read →The Origin of the Refractive Index
Why does light seem to slow down in glass? The light itself is not slowing; rather, its electric field makes the electrons in the glass jiggle, and those…
Read →Radiation Damping; Light Scattering
An accelerating electron radiates light, and therefore radiates energy, so it must be losing energy — an effect that acts like a friction, or 'radiation…
Read →Polarization
Light is a transverse wave: its electric field oscillates perpendicular to the direction it travels. Polarization is simply the direction of that…
Read →Relativistic Effects in Radiation
When a source of radiation moves near the speed of light, spectacular things happen. The radiation gets beamed into a narrow forward cone and its…
Read →Color Vision
Color is not in the light itself — it is in your eyes and brain. Your retina holds three kinds of cone cells, each most sensitive to a different range of…
Read →Mechanisms of Seeing
The eye is far more than a camera; the retina is part of the brain, and a great deal of computation happens there before any signal leaves the eye.…
Read →Sound. The Wave Equation
Sound is a wave of pressure ripples traveling through a medium like air. We can derive the equation governing it — the wave equation — directly from…
Read →Beats
Add two sound waves of slightly different frequencies and you get a wave at the average frequency whose loudness pulses up and down. Those pulses are…
Read →Modes
When a wave is confined — like a wave on a guitar string — it cannot have just any frequency; it is forced into specific patterns called modes, each with…
Read →Harmonics
For a simple vibrating string, the mode frequencies are whole-number multiples of the lowest one — these are the harmonics. The particular mixture of…
Read →Waves
Here we meet some of the richest wave phenomena in nature. When something moves faster than the waves it makes — a boat on water or a jet in air — it…
Read →Symmetry in Physical Laws
There is a deep, beautiful link between the symmetries of the universe and its conservation laws. Because the laws are the same everywhere (symmetry…
Read →Electromagnetism
Matter is held together by enormous electrical forces, but they are so perfectly balanced between positive protons and negative electrons that we never…
Read →Differential Calculus of Vector Fields
To talk about fields that vary from point to point, we need a new calculus and a special operator. The gradient of a field points the way of steepest…
Read →Vector Integral Calculus
Differential laws describe what happens at each point; integral laws describe the overall behavior. Gauss's theorem says the total flux of a field…
Read →Electrostatics
The world of stationary charges runs on two simple laws. First, electric field lines start on positive charges and end on negative ones, so the total…
Read →Application of Gauss' Law
Gauss's law is a powerful shortcut for finding electric fields where there is symmetry, avoiding hard integrals. For a uniformly charged sphere, symmetry…
Read →The Electric Field in Various Circumstances
When conductors are present, charges shuffle around until the surface is all at one potential, which makes problems tricky. A clever fix is the 'method…
Read →The Electric Field in Various Circumstances (Continued)
The equations of electrostatics turn up far beyond charges. For two-dimensional problems there is a powerful method using functions of a complex…
Read →Electrostatic Energy
It takes work to push charges together against their repulsion, and that work is stored as potential energy. But where is the energy? A very useful idea…
Read →Electricity in the Atmosphere
On a clear day there is a downward electric field of about 100 volts per meter in the air — the Earth itself is negatively charged. This drives a small…
Read →Dielectrics
Put an insulating material — a dielectric — into an electric field and the field inside it weakens. This is because the field polarizes the atoms,…
Read →Magnetostatics
Magnetostatics studies the magnetic fields of steady currents. Two laws rule it: magnetic field lines never start or stop but form closed loops, and the…
Read →The Vector Potential
Just as the electric field comes from a voltage, the magnetic field can be derived from a 'vector potential.' Is it a real field or just a math…
Read →Induced Currents
Faraday discovered that a changing magnetic field creates an electric field — the principle of induction. Move a magnet near a wire loop, or change a…
Read →The Maxwell Equations
This is the great moment of synthesis. Maxwell noticed the known laws of electricity and magnetism were inconsistent with conservation of charge, and…
Read →The Principle of Least Action
Like mechanics, all of electrodynamics can be summed up in one powerful principle: least action. The motion of a charged particle and the behavior of the…
Read →AC Circuits
The laws of electromagnetism let us analyze alternating-current circuits. For smoothly oscillating voltages and currents there is a beautiful trick using…
Read →Waveguides
To send high-frequency waves like microwaves from place to place you cannot just use wires — they would act as antennas and radiate the energy away.…
Read →The Kinetic Theory of Gases
A gas is a vast swarm of tiny molecules in constant, random motion, and its properties follow from that picture. Pressure on the container walls is just…
Read →The Principles of Statistical Mechanics
Kinetic theory generalizes into a powerful framework: statistical mechanics. Its core is Boltzmann's law — in a system at thermal equilibrium, the chance…
Read →The Brownian Movement
Watch a tiny smoke particle under a microscope and you see it jiggle in a jerky, random dance — Brownian motion. It is direct, visible proof that atoms…
Read →Applications of Kinetic Theory
Statistical ideas reach far and wide. The rate a liquid evaporates, the way electrons boil off a hot filament, the ionization of a hot gas, and the speed…
Read →Diffusion
Open a bottle of perfume in the corner of a still room and the scent eventually spreads everywhere — that is diffusion. No force pushes the molecules…
Read →The Laws of Thermodynamics
Thermodynamics rests on a few sweeping laws. The First Law is conservation of energy: you cannot get something for nothing. The Second Law is deeper…
Read →Illustrations of Thermodynamics
Thermodynamics is abstract but yields surprising, exact relationships between the properties of materials. For example, it can prove that heating a…
Read →Ratchet and Pawl
Imagine a tiny paddle wheel in a box of gas, attached to a ratchet that lets it turn only one way. Won't random molecular hits be rectified into useful…
Read →Inside Dielectrics
A material can polarize in two ways. In nonpolar molecules a field distorts the electron cloud to induce a dipole; in polar molecules like water, which…
Read →Reflection from Surfaces
The laws of reflection and refraction can be derived straight from Maxwell's equations by matching the fields at the boundary between two materials. This…
Read →The Internal Geometry of Crystals
Most solids are crystals: their atoms sit in a regular, repeating three-dimensional lattice. That hidden geometric order is responsible for a crystal's…
Read →Tensors
How do you describe a material that behaves differently in different directions? A single number is not enough, and often neither is a vector — you need…
Read →The Magnetism of Matter
Most materials are only weakly magnetic. Paramagnetism happens when atoms carry permanent magnetic moments that a field tends to line up, slightly…
Read →Paramagnetism and Magnetic Resonance
Treated with quantum mechanics, paramagnetism reveals that atomic magnetic moments can only point in a discrete set of directions relative to a field.…
Read →Ferromagnetism
Ferromagnetism is the strong magnetism of iron. It springs from a purely quantum effect, the 'exchange interaction,' which makes the spins of electrons…
Read →Elasticity
Elasticity is the way solids deform under stress and spring back when it is released. For small deformations, the strain (fractional change in size) is…
Read →The Flow of Dry Water
Fluid dynamics studies liquids and gases in motion. The simplest case is an ideal fluid — incompressible and with no internal friction — playfully called…
Read →The Flow of Wet Water
Real fluids have viscosity — internal friction — which makes things much harder and far more interesting, and is the source of drag on a moving object.…
Read →Curved Space
Einstein's general relativity gives a new view of gravity: not a force, but a property of space-time itself. Mass and energy curve space-time, and…
Read →Quantum Behavior
Here is the heart of modern physics, and it is a true mystery. Send electrons through two slits and they arrive one by one, like particles — yet the…
Read →The Relation of Wave and Particle Viewpoints
The wave and particle natures are two complementary sides of one reality, tied together by Heisenberg's uncertainty principle: you cannot know both a…
Read →Probability Amplitudes
Quantum mechanics never predicts a single outcome with certainty; it predicts probabilities, computed from a new kind of number called a probability…
Read →Identical Particles
There is a strange, beautiful rule for identical particles like electrons or photons. If a process can happen two ways that differ only by swapping two…
Read →Spin One-Half
Particles carry an intrinsic angular momentum called spin. The electron is a spin-one-half particle, meaning its spin along any axis can only be +half or…
Read →The Dependence of Amplitudes on Time
How do quantum states change over time? The amplitudes to be in different base states evolve according to equations governed by a grid of numbers called…
Read →The Ammonia Maser
The ammonia molecule is a perfect real-world two-state system: its nitrogen atom can sit on either side of the plane of three hydrogen atoms, and quantum…
Read →The Hyperfine Splitting in Hydrogen
Even hydrogen's ground state is not a single level. The magnetic moments of its electron and proton interact, and the energy differs slightly depending…
Read →Propagation in a Crystal Lattice
How does an electron move through the perfectly regular lattice of a crystal? It has some amplitude to tunnel, or hop, from one atom to the next, and…
Read →Semiconductors
Energy bands explain insulators, conductors, and semiconductors. In an insulator, a band is completely full and a big gap separates it from the next…
Read →The Dependence of Amplitudes on Position
So far we described states by amplitudes for a set of discrete base states. But to describe a particle that can be anywhere in continuous space, we…
Read →Symmetry and Conservation Laws
The deep link between symmetry and conservation, first seen in classical physics, is even more profound in quantum mechanics. If a system is unchanged by…
Read →Angular Momentum
In quantum mechanics angular momentum is quantized: its component along any axis can only take a discrete ladder of values separated by whole units.…
Read →The Hydrogen Atom and the Periodic Table
Solving the Schrodinger equation for hydrogen was one of quantum theory's first great triumphs. It correctly predicts the atom's discrete energy levels —…
Read →The Schrodinger Equation in a Classical Context: Superconductivity
Superconductivity is a spectacular, large-scale quantum effect. Below a critical temperature, some metals lose all electrical resistance and expel…
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