IFM: Interaction Free Measurement
Answer to HW1 problemhttp://logicaltightrope.com/2013/08/13/seeing-without-looking-the-quantum-bomb/
Universe in very real sense, unknowable
E= ~hw, p=~hk; ~h = h/2pi
dx*dp \> h
If you pinpoint the position of a specific particle, then you won't be able to precisely measure its momentum.
And if you precisely measure a particles momentum, then you cannot know its exact position
Also, if we try to measure the momentum of the wave, this uncertainty shows up with how accurately we can measure it - classical mechanics fails at this point.
2.2 Feynman quote
"Yes! physics has given up. We do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible - that the only thing that can be predicted is the probability of different events.
3 Wave Particle duality
3.1.1 Wave eqation
22.214.171.124 Schroedinger Equations
A mapping between vectors; A vector function
A linear vector operator
126.96.36.199.1.2 Hilbert Space
Complex-valued linear vector space; Complete space w/ an inner product
Inner Product: generalized dot product (?)
Individual particles unpredictable; lots of them follow statistical/ probabilistic laws
3.3 Feynman quote
exhibits different behavior at different frequencies