Waves of Possibility: Amplitudes and the Born Rule
Quantum physics gives each possible outcome an amplitude, a number that can be positive, negative, or even complex. The chance of seeing that outcome is the amplitude squared. This is the Born rule, found by Max Born in 1926. Because amplitudes can be negative, two paths can cancel, which plain probabilities never can.
Why can't ordinary chances explain the double slit?
Chances, also called probabilities, are numbers from 0 to 1. They can only add up. If a photon has a 1-in-4 chance to reach a spot by path A, and another 1-in-4 by path B, plain chances say 1/4 + 1/4 = 1/2. Opening a second path should never make a spot darker.
But in the double slit, opening the second slit makes some spots darker. Some spots go fully dark. Plain chances can't do that. We need a number that can be negative, so that two of them can cancel.
- What is an amplitude?
- How do you turn an amplitude into a chance?
- Worked example: amplitudes of 0.8 and 0.6
- How do two paths cancel? Work the numbers.
- Run it: set amplitudes of 0.8 and 0.6INTERACTIVE
- Try this: hide a minus signINTERACTIVE
- Try this: let the hidden sign decideINTERACTIVE
- Is the amplitude something real, or just math?
You’ve read the opening of chapter 4. Pro unlocks the other 8 sections — plus every chapter of every course, with circuits you can run right on the page. That’s $11.99 a month, about the price of a coffee, or $99.99 a year (save 30%). The first chapter of every course, and the whole math course, stay free.