Quantum mechanics: describe everything as waves

Wave: abstract mathematical description

To get real-world properties, apply mathematical operations on wave fxn

• Position: Amplitude^2

  • Gives you a probability distribution of where the particle might be

No idea if quantum wave is real or just mathematical abstraction

• Quantum realm (waves) → Our world (particles)

• Measurement barrier divides these two realms, and when we measure we collapse the wave function into one location

• "Measurement problem" = one of our gaps in knowledge

Double slit experiment: particle wave duality

• Get interference pattern when electrons fired one at a time

• When measure, goes down to localized particle.

Basically just the adding together of waves

Being "two places at once" just means equal probability of being at 2 locations

Two electron waves meet, interfere with one another and get mixed up

Mathematically: one wave fxn that describes everything about both electrons

• Inextricably linked no matter distance

• Measurement on one particle correlated with measurement on another

Einstein troubling ("faster than light communication?")

• But can't use it to communicate info b/c measurements give random results

Non-locality: link over distance

Position given by amplitude

• Uncertainty comes from various amplitudes

Momentum given by wavelength

• Also uncertainty from varying wavelengths

• If you make a wave with only one position, then don't know momentum (wavelength) because there's only one!

If you make a wave with constant wavelength, then the particle can be anywhere (infinite sine wave!)

• Every wave other than a sine wave is a sum of a bunch of waves (which means many wavelengths)!

Not an issue with measuring apparatus: fundamental property of universe