We could say this is relatively low uncertainty. It can't be before the rear bumper or ahead of the front bumper. That's not a perfectly well defined question because you don't know whether to measure the front, back, middle, center of mass, or average position of the car. You are shown the photo and asked where, precisely, is the car. Imagine the photographer takes a still photo. But to get the first measurements you describe, the systems in the two scenarios have to be fundamentally different prior to any measurement. However, the second part of each sentence (definite position => indefinite momentum, and vice versa) is true. The system can't simultaneously be in an eigenstate of position and momentum, so as written what you've said isn't correct. If you were to swap the measurements around and do momentum first, you'd read exactly the same momentum for all of them, but the position data would be spread.Īnd the first half of this (same momentum for each particle) is only true if the particles are initially in a momentum eigenstate. The first half of this (same position for each particle) is only true if the particles are initially in a position eigenstate. Measure position first with a position-measuring-machine and then momentum with a momentum-measuring-machine, you'll get exactly same position for each particle (within precision of your machine) and the results for momentum will be all over the place (no matter how precise you momentum-measuring-machine is). If you were to swap the measurements around and do momentum first, you'd read exactly the same momentum for all of them, but the position data would be spread. The point is that if you have a bag of very many identical particles (or measure them one after another as they come from a machine that makes them all identical), and measure position first with a position-measuring-machine and then momentum with a momentum-measuring-machine, you'll get exactly same position for each particle (within precision of your machine) and the results for momentum will be all over the place (no matter how precise you momentum-measuring-machine is). It's not fuzzy and you can't not know the property when you measure it. When you measure a position or momentum of a single particle, you'll always get a single number. People have explained what the uncertainty principle is, but it might be worth also telling you how it looks in practice, because most people don't know that. In that case, we have a pretty good idea where the wave package is, but in order to do this, we had to mix a whole lot of frequencies together, thus losing precision with regards to this observable.Īs momentum is associated with the frequency of a wave, this should help to gain some intuition for the uncertainty principle. Or, we can create a wave package by superimposing different frequencies, so as to create destructive interference at all positions except a narrowly defined interval of space. In that case, we have perfect knowledge of its frequency, but its position is totally spread out through space. For example, we can have a standing wave of uniform frequency that is uniform across all of space. This becomes more intuitive by reminding ourselves how waves and wave packages work. Rather, it tells us, that two observables, like momentum and position, do not exist beyond a certain threshold of precision. The uncertainty principle, on the other hand, has nothing to do with observation. That seems intuitive enough, after all, if we measure a quantum system by shooting photons at it, it is reasonable enough that this collision should change the state of the system. The observer effect tells us, that we cannot observe a system without interacting with it, and through the act of interaction necessarily influence it. While they may look similar at first glance, they are fundamentally different on an ontological level. That is a good question, and there is an unfortunate tendency – especially in pop-science – to treat the uncertainty principle and the observer effect) as the same thing.
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