1. Quantum Uncertainty Project Leader: James Arnemann Members: Jesus Gallegos, Jose Castro, Matthew Constantino

2. Classical World Waves and Particles DeterministicContinuous Quantum World Particle-Wave Duality ProbabilisticDiscrete

3. What is Quantum Uncertainty? You cannot know both the momentum and the position of a particle with exact certainty ΔpΔx≥ħ/2 (uncertainty principle) Δp = Change in momentum Δx = Change in position ħ = h/2π

4. Now, Some Magic

5. First Experiment: Polarizers ½ of unpolarized light will go through a polarizer polarized in one direction No light polarized in one direction will go through a polarizer in an orthogonal (perpendicular) direction 0 prob. light comes thru

6. First Experiment: Polarizers When a slanted polarizer is inserted, half goes through that one, and half goes through the third ½ prob. light comes thru ¼ prob. light comes thru 1/8 prob. light comes thru

7. Second Experiment: Laser Laser pointers make dots Δx

8. Second Experiment: Laser When a laser passes through a slit, its position changes There is an uncertainty in position (Δx) This causes uncertainty in momentum (Δp) If Δx gets small, Δp must be bigger Remember ΔxΔp must be larger than or equal to ħ/2

9. Second Experiment: Laser But, when the light does pass through the slit… Δp

10. Second Experiment: Laser The smaller Δx is the bigger Δp must be The smaller the slit the more the light spreads

11. In Conclusion… In Conclusion… ΔxΔp≥ħ/2 (uncertainty principle) We can never know both variables with complete certainty In trying to measure the position, we inevitably change the momentum and vice-versa It took a whole lot of math to understand this however, math is a tool to help us conceptualize these abstract ideas