The Heisenberg Uncertainty Principle: Position vs. Momentum
1 · Predict
If you confine an electron to a smaller and smaller region of space (reducing the uncertainty in its position), does the minimum possible uncertainty in its momentum shrink too, or grow?
- It grows — position and momentum uncertainty trade off against each other; confining position more precisely forces momentum to become less certain.
- It shrinks along with position uncertainty.
- Momentum uncertainty doesn't depend on position uncertainty.
2 · Set Up
- Open the heisenberg-electron preset and press Reset.
- Enable the minimum-momentum-uncertainty readout.
- Set the position uncertainty Δx for each trial and record the minimum possible momentum uncertainty.
3 · Collect Data
| Position uncertainty Δx (nm) | Momentum uncertainty Δp (×10⁻²⁵ kg·m/s) (×10⁻²⁵ kg·m/s) |
|---|---|
| 0.05 | |
| 0.1 | |
| 0.2 |
Plot Δp (y-axis) against 1/Δx (x-axis) for your three trials. Is the line straight through the origin?
4 · Analyze
- For one trial, compute Δp_min = ℏ/(2Δx) using ℏ = 1.055×10⁻³⁴ J·s. Compare to the table.
- Explain why the product Δx·Δp_min is exactly the same (ℏ/2) in every trial — the uncertainty principle sets a fixed lower bound on the PRODUCT of the two uncertainties, not on either one alone.
5 · Extend
- The uncertainty principle isn't about clumsy measuring instruments disturbing a particle — it's a fundamental property of quantum states themselves, true even with perfect measuring equipment. Explain why 'measurement disturbance' is a common but incomplete way to describe this principle.
- For a baseball (much more massive than an electron), confining its position to within a millimeter still gives an absurdly tiny minimum momentum uncertainty compared to its actual momentum. Explain why quantum uncertainty is only noticeable for very light particles like electrons.
The Physics Behind This Experiment
Heisenberg Uncertainty Principle
Position and momentum can never both be known with unlimited precision simultaneously: Δx·Δp ≥ ℏ/2, where ℏ = h/2π. A more precisely known position forces momentum to become correspondingly less certain.