What’s the underlying principle on why you can’t know the position and momentum of a particle at the same time? Is there an explanation? I don’t have any knowledge of calculus or the math behind anything so I’m asking here, thanks!
In: 57
The Heisenberg Uncertainty Principle doesn’t say you can’t know the position and momentum of a particle at the same time; that kind of holds in normal, non-quantum mechanics.
How do you measure how fast something is going?
You take two points, you measure the distance between them, and measure how long it takes the thing to get from one to the other.
So in order to measure how fast something is going it needs to be moving. Which means it has to be at two different points. So how can you measure both how fast something is going *and* where it is?
Now it turns out we can get around that problem using limits, and get a kind of instantaneous speed, to the extent that makes sense.
———-
So what does the Uncertainty Principle say? To [quote Wikipedia](https://en.wikipedia.org/wiki/Uncertainty_principle):
> the uncertainty principle states that the more precisely the position of some particle is determined, the less precisely its momentum can be predicted from initial conditions, and vice versa.
In quantum mechanics things don’t take exact, predictable values. Instead, when you measure something about a system, the answer you get will be based on a probability distribution, with an average value and an uncertainty (or standard deviation). You might find it has one value, but it might have a different value, and there is no way to predict that (beyond using probability tools).
The Uncertainty Principle puts a hard limit on how small these uncertainties can get; specifically, if you multiply two of them together you get a minimum value. This means that you can never get either of them down to 0, but also the lower you get one the higher you get the other – the more you can lock down where something is, the harder it is to lock down how fast it is going.
If you want to visualise this, imagine a bubble of air trapped under a thin sheet of plastic; it has a certain fixed volume that you can’t squeeze it below. So if you try to squeeze it one way you can make it narrower, but it will spread out in another direction. You try to squeeze it that way and it will spread out in the first direction. No matter what you do, you will get some spread-out-ness in all directions.
As for “why”, why questions are always tricky in physics, because the answer ultimately boils down to “because that’s the way the universe appears to work.”
>What’s the underlying principle on why you can’t know the position and momentum of a particle at the same time? Is there an explanation?
*You* can’t know, because the universe itself doesn’t know.
When you start getting into quantum mechanics, you leave this reality behind and enter a new one. They’re both valid–and this has been proven beyond a shadow of a doubt–but at the large scale we’re used to, the quantum effects aren’t visible.
When you get down into *very, very* small scales, the universe looks very different. Particles don’t *have* a well-defined position and momentum, they’re sort of smeared out across a relatively wide range of possible positions and momentums. Those quantities are tied together, but so is that uncertainty. The more you force the universe to define one, the more uncertain you are about the other. This isn’t a measurement issue–it’s literally impossible to precisely define both of those quantities, because doing so would eliminate the uncertainty.
It has to do with wave particle duality. In reality, all matter (and photons) are both a wave and a particle at the same time. In quantum physics, you use a wave function to define a particle, which is basically a graph of the probability a particle is in a given space at a given time. Now, when an observation is made of a particle, its wave function collapses down to a very small space where that particle can be, but you have no idea where that particle was in it’s wave function a moment ago, so it may have needed to move very far in a very short time, or maybe it only needed to move a little bit to get there, but you can’t know where it was previously without having collapsed the wave function earlier, which would change your later observation. (Note: and observation can be any sort of interation the particle takes, not necessarily a measurement) I cant really think of a good analogy for a certainty momentum, but I can tell you about an experiment. When you cool helium down to very near absolute zero (ie the momentum gets very close to 0) it will actually leak out of whatever container it’s in. That’s because the position becomes less certain than the size of of the container and it can quantum tunnel through the walls of the container. Sorry that second part isn’t really an explanation why, but I did my best. Fun fact: the uncertainty principle also works with energy and time. The more certain we know a particle’s energy state, the less certain we are about how long it will last in that state and vice versa.
Small particle is too delicate that any attempt to measure one characteristic, it inevitably change the other. People has always been try to shoehorn light as a particle, however, at this scale, classical concept like momentum may not even applicable anymore.
Let me give you a simple analogy: the only way we can measure certain things is by bouncing photons off of them. And if it’s small enough or light enough or fast moving enough, once you bounce a photon off of it, it’s no longer where it was.
I like to think of it like a camera with different shutter speeds. Imagine you’re taking photos of a sports game. People are running fast, so you turn to a very high shutter speed, meaning that each photo is a very small fraction of a second. These photos give you a very clear view of the players, and you can make out a lot of details. But they’re static, and you can’t really tell who’s doing what.
You lower the shutter speed until each photo takes like 2 seconds. Now everybody is just a featureless smear, because your measurement was over a long time. You can’t tell anything about the individuals. BUT, you can measure the lengths of the smears and tell exactly who was moving what direction and how fast, based on their relative lengths.
I’ll do my best. Basically, it’s math. Every particle is described by a math problem, its wave function. That function is a mathematical expression that describes the particle in its entirety.
When we want to know something about that particle, we use an operator, a math operation applied to that function to give us an answer. Not all operators give us an answer that makes sense.
Heisenberg uncertainty principle basically states that there are operators that can’t be applied to the same function at the same time. If we change the problem to make one operator work, the other stops working. Position and momentum are only one example of operators that can’t coexist. There are others.
So basically a big problem with Quantum physics is that there are a lot of things that cannot be accurately observed due to issues of scale. Note this is not the Heisenberg uncertainty but a different principle although it is technically the cause of it.
Because of this inability to know, the mainstream branch of quantum physics basically went “what if we just forget about even trying to figure out what is actually happening in physical reality and just focus on creating mathematical models to predict the outcomes that will occur from whatever is going on. ” The result is convenient, but also not very satisfying as it tends to provide all sorts of contradictions and excuses.
The Heisenberg uncertainty is basically just a side effect of the math that comes from this situation which limits the amount of information you can have about a particle or wave creating a level of uncertainty in any calculation.
You’re in a room. I give you a stick and throw a ball at one of the walls and it starts rolling across the floor. Now I blindfold you and tell you to find out where the ball is.
Obviously your first instinct to is to swing the stick around and eventually you’ll feel yourself hitting the ball-congrats you’ve found the ball! But now that you’ve hit the ball, you have absolutely no idea where its gone( you did not know how fast it was going in which direction before you hit it) so now you have to find the ball all over again.
This is Heisenburg’s uncertainity principle: you cant find the exact position of a microscopic particle without changing its momentum and vice versa.
Scientists today are acutely aware of the phenomenal capacity of quantum information processing. For this reason they try in a great hurry to construct so-called “quantum computers”.Since quantum information processing is a natural capability of the Universe since its very beginning, it is highly likely that the Universe itself is already using it.Unfortunately, the fundamental quantum information processing of the Universe itself is banned from consideration here on Earth.In the beginning of the 21st century science firmly believes that the basis of all quantum processes in the Universe is chaos.Belief in chaos and randomness of quantum processes was initiated by some famous people in the past century, who failed to imagine an explanation for “apparently random” behavior of elementary particles such as electrons.As a result of this glaring lack of imagination, the so-called “uncertainty principle” has been adopted as a foundation of all sciences on Earth.The uncertainty principle, in its essence, brutally averages-out all traces of the quantum information processing of the Universe and estimates “probabilities” of some primitive set of locally averaged quantum events.The most famous critic of the uncertainty principle as a way to describe the fundamental activity of the Universe was Albert Einstein, who insisted that “God does not play dice”. Unfortunately, like all his contemporaries, he failed to imagine and propose a plausible explanation for apparently random behavior of elementary particles such as electrons. In the absence of intelligent critics, the uncertainty principle gained the status of a sanctified dogma that is not even allowed to be questioned.However, quantum-domain information processing in the Universe continues and will continue everywhere, no matter how many authorities and laureates choose to deny it…
Latest Answers