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Quantum Uncertainty. Project Leader: James Arnemann Members: Jesus Gallegos, Jose Castro, Matthew Constantino. Classical World Waves and Particles Deterministic Continuous Quantum World Particle-Wave Duality Probabilistic Discrete. What is Quantum Uncertainty?.

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Quantum Uncertainty

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## Quantum Uncertainty

Project Leader: James Arnemann

Members: Jesus Gallegos, Jose Castro, Matthew Constantino

Classical World

• Waves and Particles

• Deterministic

• Continuous

Quantum World

• Particle-Wave Duality

• Probabilistic

• Discrete

### 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

### First Experiment: Polarizers

• ½ ofunpolarizedlight 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

### First Experiment: Polarizers

• When a slanted polarizer is inserted, half goes through that one, and half goes through the third

1/8

prob. light comes thru

½ prob. light comes thru

¼

prob. light comes thru

### Second Experiment: Laser

• Laser pointers make dots

Δx

### 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

### Second Experiment: Laser

• But, when the light does pass through the slit…

Δp

Δp

Δp

Δp

### Second Experiment: Laser

• The smaller Δx is the bigger Δp must be

• The smaller the slit the more the light spreads

### 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