When we force protons through a narrow slit, we are gaining certainty in their position. As we gain certainty in their position, what should happen to the certainty on momentum?
Google Heisenberg uncertainty principle
certainty of product of position and momentum is limited so the more accurately you know position the less accurately you know momentum
eg:
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/lecture-notes/MIT6_007S11_lec38.pdf
When we force protons through a narrow slit, we are essentially confining their spatial extent to a small region, which increases the certainty in their position. This phenomenon is known as wave-particle duality, where particles like protons can exhibit wave-like behavior.
By narrowing down the region in which we expect to find the protons, the uncertainty in their position decreases. According to the Heisenberg uncertainty principle, which is a fundamental principle in quantum mechanics, reducing the uncertainty in position results in an increase in the uncertainty of momentum.
The Heisenberg uncertainty principle states that the product of the uncertainties in position (Δx) and momentum (Δp) must always be greater than or equal to a certain minimum value. Mathematically, this principle is expressed as Δx * Δp >= h / 4π, where h is Planck's constant.
So, when we gain certainty in the position of protons by passing them through a narrow slit, the uncertainty in their momentum must increase. This means we would have less knowledge about their velocity or direction of motion. The trade-off between position and momentum uncertainties is a fundamental characteristic of quantum mechanics.