Could someone explain the Heisenberg uncertainty principle from a layman's point of view?

Caveat: this could be completely wrong, The way it was explained to me is that it’s like trying to state where a bullet that has just been shot is located. You can tell me where it is at any given moment, you can track it, but when you point out where it is, it is gone.

Disclaimer, I’m a chemist, not a physicist, so this is probably somewhat incorrect. But it should be be close. Also not sure how great this will be as far as ‘layman’s terms’, but I’ll give it a go.

No, it’s different than that. The explanations above both fall into what’s known as the ‘hidden variable hypothesis’, which is generally not accepted in physics (it is also known as the hidden variable fallacy). The hidden variable hypothesis says, simply, that we can know all those quantities, we’re just not good enough at finding them yet, essentially. Alternately, and closer to the name, there is some hidden variable that determines those values, and if we find it we could know the other variables exactly.

As I mentioned, this is not correct according to our current understanding (and it mostly due to incomplete understanding/explanation of quantum physics by educators shakes fist). It also doesn’t help that it was espoused by Albert Einstein (he definitely had his biases). The problem is that, again as far as we understand quantum mechanics, it literally doesn’t make sense to know a particle’s location and momentum exactly, as you mentioned, @LostInParadise. It’s not that we can’t know it, it’s that there is nothing to know. Most of this, to my understanding, is because of quantum field theory, which states that particles essentially just don’t exist at all, but are actually momentary fluctuations of the fields in the form of waves (for example, the Higgs Boson is so hard to find because while the Higgs Field is everywhere, actually disrupting it enough to cause it to form a ‘particle’ is very difficult because of how the field works). And while we can cause something we see as a ‘particle’ to exist, we haven’t actually done that. We’ve just localized the field to such an extent that we’ve caused it to act in a way as to ‘look’ like a particle. But it’s still a wave in a field. The ‘wave-particle’ duality is, as far as we know now, in itself a fallacy. It’s not a duality, just all waves that we mistook for particles.

Soo.. how do you measure the ‘location’ of a field or a wave? Especially, given quantum mechanics, that these fields never cease to exist, they always stretch out to infinity getting weaker and weaker as they go. You could measure the center of the field, but what does that mean? Some fields don’t even have a center. Electrons, for instance, when bound to an atom can’t even exist at the ‘center’ of their field. It has what’s called a ‘node’, and it’s part of why we have atoms at all; the center of the atom is the nucleus, and you can thank this effect that all atoms everywhere don’t immediately have their protons and electrons pull together and cancel each other. If you can measure the center, is that the ‘location’ of the particle? And the problem comes that, from a certain distance out, you can make a good estimate as to location of a field or speed of a wave. But as you get closer and closer, these measurements make less sense.

Lets take the ocean. You can point to to ocean, but what exact point in the ocean is ‘the ocean’? Is there a single point? Does it, as a whole, have a speed? You could, say, measure the speed of the earth and call that the speed, but is that true for all points of the ocean? Same for a wave. You can look at a wave, and point at a wave, and even measure it’s speed. But where is the wave, exactly? Where does it start and stop, compared to the ocean as a whole? You can measure it’s speed, but what are you measuring, exactly? The speed of the crest? The trough? What about when it enters a harbor, and bends? How about when it crashes? Do you take the average speed? The fastest? And as soon as you pick a single ‘location’ to measure the speed, you’ve lost sight of the whole, because asking the question of the whole requires losing focus of individual points, and vice versa.

Hence, (finally), the uncertainty principle. We can’t know both exactly, because knowing it wouldn’t make sense based on their actual existence. We can compromise on one and focus in tightly on a single variable, but to do so requires ignoring other parts of the system in order to even let you consider a single point.

If you measure the position of a particle, you will change its momentum. If you measure the momentum of a particle, you will change its position. You can measure with accuracy one or the other, but not both.

You wound me, sir.

@BhacSsylan , Thanks, that helps, but it still leaves a little unclear what we mean by the location and momentum of a particle. Perhaps the full explanation requires a bit more mathematical detail.

The location and momentum of a particle refers, usually, to the general area of a wave, or the area of the most disturbance of the field, and how that moves (going back to ocean waves, we’d be trying to find the biggest peak in the wave and how fast that’s traveling, or trying to find the average across the whole wave). The problem being when you zoom in there is no particle, only field, but from a distance you can still measure that wave in a general sense because it’s a disturbance you can measure.

Another example i guess would be swarms. Not the best since they are made of distinct units, but go with me here. Say, a swarm of mosquitoes. As it moves, if they’re dense enough, you can see them. You can measure the position and velocity of the swarm, because you can see it as a whole. And even if they’re a few mosquitoes outside the main dense part, you can sort of ignore them and focus on the bit you can really see. So, that gives you the general position and momentum. But if you try to drill down and see specifics, it become nonsensical to ask about a single position, because in most of the swarm it’s empty space.

Again, not the best, since then you can take the individual mosquitoes and look at those, which isn’t true of quantum mechanics, but maybe that helps? >.>

See if this makes sense. Using your swarm analogy, if I step back a distance, I can get a fix on the movement, but the location is spread out. If I zoom in, I can get a fix on the location, but I have much less of an idea from the local movement of where the swarm as a whole is headed.

It is a little like watching snowflakes during a snowstorm. If you fix on an individual flake, you will see local air currents moving it in all directions. It is not immediately apparent that it is headed downward. By widening your view, you can get a better idea of the downward drift.

Yep! Pretty good :). The only thing I’d say to keep in mind is that while in these cases you can actually find the snowflake or mosquito (snowflake is the much nicer example >.>), you have to remember that in quantum mechanics it really is the drift or the swarm that is the important thing (since, as far as we know, there is no deeper level). But it sounds like you’ve got it :-).

@BhacSsylan Sorry, I was just answering quickly.