The Heisenberg’s Uncertainty Principal 101

The Heisenberg uncertainty principal is often in texts about Quantum Mechanics said to be that the more you know about a particles position the less you can know about its speed(although it’s actually momentum, which is speed times mass but for the sake of simplicity I’ll only use speed here). This isn’t completely true since the uncertainty principal can be applied to many other situations. But what it basically says is that, in the world of particles(on subatomic levels), if you want to know more about one thing, you’ll have to forfeit knowledge about another thing. But lets start with the example above:

We start of with a simplified billiard ball analogy; if you have a billiard ball and wants to know it’s position you could shoot another billiard ball at it and watch it’s trajectory. Its trajectory will depend on where it hit the other billiard ball(if it was a direct hit or if it just nudged it) and also the speed of the other billiard ball , so by watching its’ trajectory you can find out the other billiard balls’ position and speed.

If you have a particle and want to know its position you would shine some light on it to see were it is. If we considered light to be waves, then as normal waves do we could say that the light would shatter and form ripples around the particle. But now we want to know which way the photon went(just like in the double slit experiment) so then the light wave collapses into a photon and it can’t spread out around the particle, it has to go one-way or another, so which way will it go? This is where the uncertainty comes in; there is no way of telling exactly which way the photon will go or exactly what speed it will have. There is just a set of chances that it will go one way or another. So therefore you can’t get an exact answer of the particles’ position or speed since there are allot of different scenarios where the photon would have some chance of gaining a similar speed and position as the one you may observe in an experiment. This is one thing that creates uncertainties when looking for a particles position.

Now, the same thing goes for the particle that the photon will hit, since we now know that matter particles also behave as waves. So when the incoming photon collides with the particle it will give the particle a recoil which also will send it of in a random direction and at a random speed because of its’ wave like character.

If you want to know the particles’ position better you would use light with smaller wavelength, an increase in the wavelength is also an increase in the energy in the photon so this means that it will hit the particle harder. The thing is that if the photon hits the particle very lightly it will move away in a more uncertain way then if the photon would hit it very hard, in which case the particle would be set on the move in a much more predictable way and thereby you’ll know it’s direction and therefore it’s destination better.
You can again think of normal billiard balls, if you only nudge the billiard ball the force in it’s movement will be so small that any little disturbance in the rug will alter it’s trajectory thereby making it hard to predict, but if you hit it hard it will take a large obstacle to stop or alter it’s direction of motion. The same goes for particles, if the photon hits it very lightly it will be more easily affected by outside forces the if it were hit very hard.
Now back to the photon and the particle; if you smack the photon harder into the particle you’ll send it of flying which means that you’ve altered it’s speed allot and in a uncertain fashion. However if you just nudge the particle its’ speed will hardly change and so it will be more uncertain. BR> So then you can see that this is sort of a trade off between position and speed.

But you shouldn’t think that it is only because we “touch” the particle that this behaviour occurs. Say we put a particle in a shrinking box, the more the box shrink the better we know the particles position(since then we’ve narrowed down the places were it can exist). But we don’t interact with it so therefore we shouldn’t change its momentum. Wrong. The smaller the box gets, the more energetic and unpredictable the particles motion gets. This is because, as in black body radiation, the particles wave length has to fit between the sides of the box. So as the box shrinks the wave length has to get smaller and smaller, and a smaller wave length leads to higher energy values, thereby the chaotic motion. So there’s no way to get around it.

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