[Physics] How to particles travel in a straight line

heisenberg-uncertainty-principlemomentumquantum mechanicswave-particle-dualitywavefunction

A particle can be set off in a certain direction by giving them momentum. Momentum is a vector, so the particle heads off in a specific direction. But the wave function of the particle allows it to obtain other momentum values, which would steer the particle on a different path. How then can we "shoot" electrons and other particles in straight lines? How can they maintain their momentum in the face of quantum uncertainty?

Best Answer

The uncertainty principle's restriction on the minimum spreads in position and momentum is really small. An electron can be confined to a region in both position and momentum space that's extremely small compared to anything human-sized, but still have more than enough spread to obey the uncertainty principle.

To give you an idea of how small this is, $\hbar=1.05457173 × 10^{-34} J\cdot s$, so an electron with a standard deviation in it's position of 10 micrometers ($10^{-5}m)$ has a minimum uncertainty in it's velocity of about $6 m/s$. Electrons in any sort of beam are usually travelling at some appreciable fraction of the speed of light ($3 \times 10^{8} m/s)$, so this uncertainty is tiny.