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The Quantum of Change
1 Minimum action – quantum theory for poets
The effects of the quantum of action on rest
The consequences of the quantum of action for objects
The effect of the quantum of action on motion
The surprises of the quantum of action
Transformation, life and Democritus
Randomness – a consequence of the quantum of action
Waves – a consequence of the quantum of action
Particles – a consequence of the quantum of action
Curiosities and fun challenges about the quantum of action
The dangers of buying a can of beans
A summary: quantum physics, the law and indoctrination
2 Light – the strange consequences of the quantum of action
How do faint lamps behave?
What is light?
The size of photons
Are photons countable? – Squeezed light
The positions of photons
Are photons necessary?
Interference: how can a wave be made up of particles?
Interference of a single photon
Reflection and diffraction deduced from photon arrows
Refraction and partial reflection from photon arrows
From photons to waves
Can light move faster than light? – Real and virtual photons
Indeterminacy of electric fields
How can virtual photon exchange lead to attraction?
Can two photons interfere?
Curiosities and fun challenges about photons
A summary on light: particle and wave
3 Motion of matter – beyond classical physics
Wine glasses, pencils and atoms – no rest
No infinite measurement precision
Flows and the quantization of matter
Fluid flows and quantons
Knocking tables and quantized conductivity
Matter quantons and their motion – matter waves
Mass and acceleration of quantons
Why are atoms not flat? Why do shapes exist?
Rotation, quantization of angular momentum, and the lack of north poles
Rotation of quantons
Silver, Stern and Gerlach – polarization of quantons
Curiosities and fun challenges about quantum matter
First summary on the motion of quantum particles
4 The quantum description of matter and its motion
States and measurements – the wave function
Visualizing the wave function: rotating arrows and probability clouds
The state evolution – the Schrödinger equation
Self-interference of quantons
The speed of quantons
Dispersion of quantons
Tunnelling and limits on memory – damping of quantons
The quantum phase
Can two electron beams interfere? Are there coherent electron beams?
The least action principle in quantum physics
The motion of quantons with spin
Relativistic wave equations
Bound motion, or composite vs. elementary quantons
Curiosities and fun challenges about quantum motion of matter
A summary on motion of matter quantons
5 Permutation of particles – are particles like gloves?
Distinguishing macroscopic objects
Why does indistinguishability appear in nature?
Can quantum particles be counted?
What is permutation symmetry?
Indistinguishability and wave function symmetry
The behaviour of photons
Bunching and antibunching
The energy dependence of permutation symmetry
Indistinguishability in quantum field theory
How accurately is permutation symmetry verified?
Copies, clones and gloves
6 Rotations and statistics – visualizing spin
Quantum particles and symmetry
Types of quantum particles
Spin 1/2 and tethered objects
The extension of the belt trick
Angels, Pauli's exclusion principle and the hardness of matter
Is spin a rotation about an axis?
Rotation requires antiparticles
Why is fencing with laser beams impossible?
Spin, statistics and composition
The size and density of matter
A summary on spin and indistinguishability
Limits and open questions of quantum statistics
7 Superpositions and probabilities – quantum theory without ideology
Why are people either dead or alive?
Macroscopic superpositions, coherence and incoherence
Decoherence is due to baths
How baths lead to decoherence – scattering
How baths lead to decoherence – relaxation
Summary on decoherence, life and death
What is a system? What is an object?
Is quantum theory non-local? A bit about the Einstein–Podolsky–Rosen paradox
Curiosities and fun challenges about superpositions
Why do probabilities and wave function collapse appear in measurements?
Why is h necessary for probabilities?
Summary on probabilities and determinism
What is the difference between space and time?
Are we good observers?
What relates information theory, cryptology and quantum theory?
Is the universe a computer?
Does the universe have a wave function? And initial conditions?
8 Colours and other interactions between light and matter
The causes of colour
Using the rainbow to determine what stars are made of
What determines the colours of atoms?
The shape of atoms
The size of atoms
Relativistic wave equations – again
Getting a first feeling for the Dirac equation
Curiosities and fun challenges about colour and atoms
A tough challenge: the strength of electromagnetism
A summary on colours and materials
9 Quantum physics in a nutshell
Physical results of quantum theory
Results on the motion of quantum particles
Achievements in accuracy and precision
Is quantum theory magic?
Quantum theory is exact, but can do more
A Units, measurements and constants
The meaning of measurement
Planck's natural units
Other unit systems
Curiosities and fun challenges about units
Precision and accuracy of measurements
Limits to precision
B Numbers and vector spaces
Numbers as mathematical structures
Other types of numbers
From vector spaces to Hilbert spaces
Mathematical curiosities and fun challenges
Challenge hints and solutions