What is the Heisenberg Uncertainty Principle?
2 Answers
It says that certain factors of a phenomenon are complementary: if you know a lot about one of the factors, you know little about the others.
Heisenberg talked about this in the context of a particle with a certain speed and location. If you know the speed very precisely, you wont know much about the location of the particle. It also works the other way around: if you know the location of a particle precisely, you won't be able to accurately describe the velocity of the particle.
(Source: what I remember from chemistry class. I'm not entirely sure if this is correct.)
For a quantum mechanical (itty-bitty/subatomic) particle such as an electron, the Heisenberg Uncertainty Principle applies in a significant manner so as to assert that:
#color(blue)(sigma_xsigma_p >= h/(4pi))#
What this says is that the product of the position's standard deviation
This is the main statement---that the more precisely you know the position of an electron, the less precisely you know its momentum, and vice versa.
Or, you could say that you can't observe both at the same time with good certainty.
Alone, they may be under
For the electron using a "Particle in a Box" model (electron/particle in a chemical system/box), for example, it has been determined that:
#color(green)(sigma_xsigma_p = color(blue)(h/(4pi))sqrt((n^2pi^2)/3 - 2))#
where
You can tell that with the lowest value using
#[color(blue)(sigma_xsigma_p) = h/(4pi)sqrt((pi^2)/3 - 2)] color(blue)(>= h/(4pi))#
since:
#[sqrt((pi^2)/3 - 2) ~~1.136] > 1#
In contrast, the uncertainties for normal objects like baseballs and basketballs are so low that we can say with good certainty what their positions and momenta are, mainly due to their size, giving them negligible wave characteristics.