Uncertainty Principle
Measure position vs momentum tradeoff. Builds on Wave-Particle Duality.
You have a single electron. Using advanced equipment, you measure its position with extreme precision — you know EXACTLY where it is, down to 0.01 nanometers.
What can you say about the electron's momentum (speed) at that instant?
The momentum is completely uncertain! This isn't about bad instruments — the electron literally doesn't HAVE a definite momentum when its position is precisely known. This is Heisenberg's uncertainty principle: Δx·Δp ≥ ħ/2.
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Squeeze the position wavepacket to make it narrow (precise position). Watch the momentum spread explode! You can't have both precise at once.
Δx·Δp ≥ ħ/2
The more precisely you know WHERE something is, the less you can know about where it's GOING.
A proton's position is fuzzy enough to overlap a neighbour's even when it lacks the energy to climb the barrier between them — this tunneling is what lets the Sun fuse hydrogen
Even at absolute zero, particles still jiggle — perfect stillness would violate the uncertainty principle
Quantum tunneling in nanoscale transistors is a major challenge for making chips smaller
“The universe keeps secrets — not because we can't measure well enough, but because some things are genuinely undetermined.”
Uncertainty Explorer
Shape a quantum wavepacket. See the position-space and momentum-space representations simultaneously. Squeeze one and watch the other spread.
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Make the wavepacket as narrow as possible in position. The momentum distribution becomes almost flat — the particle could be moving at ANY speed! Now spread the position out — the momentum becomes sharp.
A narrow wavepacket in position space is a sum of many sinusoidal waves (Fourier decomposition). Each sine wave represents a different momentum. More waves = more localized position = more uncertain momentum.