QED by Richard Feynman

QED: Quantum Electrodynamics / Quod Erat Dictum

Everyday properties of light:

• goes in straight lines 
• bends when it goes into water 
• when reflected from a surface like a mirror, the angle at which the light hits the surface is equal to the angle at which it leaves the surface 
• light can be separated into colors 
• you can see beautiful colors on a mud puddle when there is a little bit of oil on it 
• a lens focuses light 
• light is partly reflected in some surfaces, such as glass or water

Proven using photomultipliers (which produce an audible click each time a photon hits) and monochromatic (red, green, or blue) light:

• light is made of particles (photons) 
• partially reflective surfaces return an average of 4% of photons 
• as the thickness of a given partially reflective surface increases, the return oscillates between 0 and 8% 
• because glass has two reflective surfaces (front and back), the return oscillates between 0 and 16% 
• this cycle repeats itself at different rates for different colors, so some thicknesses return only red or only blue, or blue and red in different proportions, creating effects like rainbows in oil puddles 

Grand Principle:
The probability of an event is equal to the square of the length of an arrow called the "probability amplitude." An arrow of length 0.4, for example, represents a probability of 0.16 or 16%.

General Rule for drawing arrows if an event can happen in alternative ways:
Draw an arrow for each way, and then combine the arrows ("add" them) by hooking the head of one to the tail of the next. A "final arrow" is then drawn from the tail of the first arrow to the head of the last one. The final arrow is the one whose square gives the probability of the entire event.

Derived from the above findings:

• The arrows correspond to a metaphorical stopwatch hand; their direction is determined by the amount of time it takes for them to travel a given distance. When graphed, outliers cancel each other out, so the center of the distribution has the most influence on the final direction of the arrow / path of the light. Thus, light travels along the shortest path, and the angle of incidence equals the angle of reflection. 
• If the scope of the possible paths is limited too extremely, the time of each revolution of the metaphorical stopwatch is too short, so near-identical paths end up scattering. There is a lower limit to the size of a mirror. 
• Scraping away the parts of a mirror that bias one direction biases the light towards the opposite direction, making a previously unreflective surface reflective. This is called a diffraction grating.