Uncertainty principle it's uses and abuses
The Uncertainty principle is another of the abused concepts from Quantum Mechanics.
First a the formula, next it's theory, then applications, and lastly it's abuses.
I'll post the formula/principle since people who often abuse it don't actually know it. And with this formula and principle, we can get some applications.
Where A and B are operators and [A,B] is the commutator.
Now take position [x] (x.) and momentum [p] (i(hbar.)d/dx.)
[x,p]= xi(hbar) d/dx-i(h-bar.)dx/dx
Sub into the formula
The most commonly known formula, the Heisenberg uncertainty principle.
Notice how it does not depend on the method of measurement! No matter how far along our technology goes, we will not build a machine that will eliminate the principle.
The Schrodinger equation (Time independent.)
Give the wave function Y. This is where the wave properties of matter come from.
Now picture a wave.
Now if it was represented thusly: ________/\/\/\/\/\/\/\/\/\/\/\/\_____
As you can see it has a wave-length. If I were to ask you the wave length it is easily measured. And since the momentum is related to said wave length (De-Broglie formula
it is not a stupid question.
But what if I asked you where the wave was? Now that's a stupid question. It's spread over such a wide wavelength that it's extremely difficult to know preciously where it is!
Now what if the wave looked like this: __/\_____ that 'bump' moves along.
I can ask you where the wave is, you can give me a position. But what about the wavelength? It's not oscillating so it is very difficult to pin point a wave length.
Observing the particle collapses the wave function as in the second form ergo making momentum difficult to pinpoint.
That is the basic principle behind the Heisenberg uncertainty.
Now, what do we do with it?
Well, we can use the principles in to explain things such as Quantum tunneling, electron orbits, vacuum fluctuations etc....
For example, an electron can travel through a barrier. Why? Because we cannot know for certain where the damn thing is! If we could, then we would know that it's on one side of the barrier! Note however, the barrier must have certain properties that the wave length can penetrate the barrier.
You may have read about these in high school chemistry, s and p orbitals and such. Where the s-orbital is a sphere and p-orbital is like two dumbbells. These shapes are the shape of the probability functions meaning the electron is somewhere in those orbits, but thanks to the uncertainty principle, we don't know where exactly. This gives atoms, particulary hydrogen atoms some interesting properties.
For, vacuum fluctuations the uncertainty doesn't just apply to position and momentum, but also to time and energy. This means that 'virtual' particles can appear for a short time and then fade out without violating conservation laws.
Now for it's abuses. The most common one is that it denotes we cannot know everything. This is untrue, in fact by the examples above, it tells us things we wouldn't have known otherwise.
Yes, there are several small ones. Here is a starting point for the relevant info on that:
And here is a quantum computer in action: