(Original post by FireGarden)
The uncertainty principle applies in a sense to all objects, not just quantum scale things, if you are proper fussy about things.
Here's a scenario where we can determine the uncertainty principles relating of position and momentum, without having to be considering quantum weirdness:
We have a ball floating through space; and now we wish to find its momentum, and where it is. First, position. We wish to measure position at a time t, and we want to measure the position as quickly as possible, cause in the time taken to measure position, (say, dt), the particle will move v*dt (so we get some inherent uncertainty), so ideally, we would be like to measure in zero time. But then, if you have no time, then we can't know v, and hence can't know momentum (as P=mv).
On the other hand, for momentum, P=mv, so to find P we must have m (take that as a given) and v, but to know v we must measure distance travelled and time elapsed. The issue here is, though, if you want this value to be precise
, then you must measure over infinite time. Anything less, and you will
have some measure of uncertainty - you're ignoring some portion of it's existence! So if that's how you get precise
momentum, how can you get position simultaneously? You can't at all. It will take on all possible positions in it path as you measure momentum! In the classical world, we have approximations that are by no means exact, and if you were to take out a quantum ruler and clock, will find them wildly varying around the true values (if you could know them).
When it comes to quantum, there is an added isse (and why it's so important to the theory); There is unavoidable
uncertainty. Measure position in an instant or momentum over an infinite amount of time if you wish, but that relation is saying you still won't know it precisely. Another, and in my opinion much more interesting uncertainty principle, is for energy and time. Now that
has some serious