This always confuses me and I’m not sure how it works. Please explain…
In: 252
At quantum scales, the electron is not actually a material “thing” like a small pebble. It’s more like a little wavelet on a surface. The amplitude of the wave at each point indicates how likely it’s actually “there” if measured so it’s a proxy for the position
But the speed of the electron is tied to it’s energy and the energy is tied to the frequency of this wave.
If you want to know exactly where the electron is you would need only one oscillation on one point. But then, you can’t read it’s frequency and don’t know its energy and speed. On the other hand, if the wave was spreading infinitely its frequency would be absolute but we can’t say where it is at all.
So whenever you have this small wavelet you can only kinda know its position because it’s spread around a volume, and the same for its frenquency.
This is exactly the same for a sound : if you want to know it’s frequency you’need a sine wave but you couldn’t tell at all when it happens. If you want to precisely know when it happens, then, there is no frequency to it, it’s just a sudden bump at a specific time.
EDIT : the observer effect is not the cause, here, the wave nature of the phenomenon is the source.
Schroedinger, Erwin, Professor of Physics!
Wrote daring equations! Confounded his critics!
(Not bad, eh? Don’t worry. This part of the verse
Starts off pretty good, but it gets a lot worse.)
‘win saw that the theory that Newton’d invented
By Einstein’s discov’ries had been badly dented.
What now? wailed his colleagues. Said Erwin, “Don’t Panic,
No grease monkey I, but a quantum mechanic!
“Consider electrons. Now, these tiny articles
Are sometimes like waves, then sometimes like particles.
If that’s not confusing, the nuclear dance
Of electrons and suchlike is governed by chance!
“No sweat though — my theory permits us to judge
Where some of ’em is and the rest of ’em was.”
Not everyone bought this; it threatened to wreck
The comforting linkage of cause and effect.
E’en Einstein had doubts, and so Schroedinger tried
To tell him what quantum mechanics implied.
Said ‘win to Al, “Brother, suppose we’ve a cat,
And inside a tube we have put that cat at–
“Along with a solitaire deck and some Fritos,
A bottle of Night Train, a couple mosquitoes
(or something else rhyming) and, oh, if you got ’em,
One vial Prussic acid, one decaying ottom
“Or atom — whatever — but when it emits,
A trigger device blasts our vial into bits
Which snuffs our poor kitty. The odds of this crime
Are 50 to 50 per hour each time.
“The cylinder’s sealed. The hours’s passed away. Is
Our pussy still purring — or pushing up daisies?
Now _you’d_ say the cat either lives or it don’t
But quantum mechanics is stubborn and won’t.
“Statistically speaking, the cat, goes the joke,
Is half a cat breathing and half a cat croaked.
To some this may seem a ridiculous view,
But quantum mechanics must answer, ‘Tis true!’
“We may not know much, but one thing’s fo,sho’;
There’s things in the cosmos that we cannot know.
Shine light on electrons — you’ll cause them to swerve.
The act of observing disturbs the observed —
“Which ruins your test. But then if there’s no testing
To see if a particle’s moving or resting
Why try to conjecture? Pure useless endeavor!
We know probability — certainty never.”
The effect of this notion? I very much fear
‘Twill make doubtful all things that were formerly clear.
Till soon the cat doctors will say in reports,
“We’ve just flipped a coin and learned he’s a corpse.”
So said Herr Erwin. Quoth Albert, “You’re nuts.
God doesn’t play dice with the universe, putz.
I’ll prove it!” he said, and Lord knows he tried —
In vain — until fin’ly he more or less died.
‘win spoke at his funeral: “Listen, dear friends,
Sweet Al was my buddy. I must make ammends.
Though he doubted my theory, I’ll say of this saint:
Ten-to-one he’s in heaven — but five bucks says he ain’t.”
(shamelessly stolen from Cecil Adams at the the Chicago Reader’s Straight Dope column).
(Edit to add): A lot of explanations here make it sound like the uncertainty principle is an artifact of observation: if the only tool you have to measure the position and momentum of a marble is by throwing other marbles at it, then clearly you can’t measure both at the same time.
This is a wonderful intuitive explanation, **and it is wrong.**
—-
So the best explanation I have ever seen for this came from [a video by 3Blue1Brown](https://www.3blue1brown.com/lessons/uncertainty-principle)—and while it’s not really geared towards 5-year-olds (the “ELI5” thing), the video presentation does walk you through the relationship between waves and the Heisenberg Uncertainty Principle (which you’re alluding to) makes the entire thing incredibly easy to understand.
Essentially the idea is this, and I’m condensing from a spectacularly well done video here—is that there is a relationship between knowing the frequency of a sound and the duration of that sound. A solid tone that lasts for a second, for example: you can determine the frequency of that sound with a high degree of certainty. But if that sound is a brief chirp, it becomes harder to know the frequency of the sound: if the chirp is less than 1/100th of a second, it can be quite impossible to determine if the sound was an C or a D on a piano.
Now electrons being waves (hand-waves at the association here), if frequency is like momentum, and time is like position, the more certain you are of the position (that is, the shorter the time), the less certain you can be of momentum (that is, frequency). If you can be certain of the position of an electron, it’s like the brief chirp that lasts less than 1/100th of a second—and it’s harder to know what the momentum is, just as it’s hard to know if that chirp was a C or a D note.
This implies, by the way, that the relationship in the uncertainty of position and momentum of an electron is **NOT** a feature of observation: it’s not just a matter of figuring out a better way to measure electrons.
It is instead, a fundamental feature of anything constructed out of waves.
But watch the video to get a full appreciation of the argument. I promise you it will be well worth 18 minutes of your life. And to be frank, I wish I had 3Blue1Brown’s video presentations when I was in college: he makes so many different concepts out of mathematics incredibly clear.
Lets say I give you a camera and tell you to take a picture of a baseball, and to find the ball’s speed and position after five seconds.
You have a few options. If you use a high-speed camera you will get the EXACT position of the the ball at five seconds, with absolutely no blur or distortion. But the ball just looks like it’s hanging there,so it’s impossible to guess the speed.
Or you could take a standard picture where the ball just looks like a smudge. You don’t know exactly where the ball was at five seconds, but you know the smudge is 10 feet long and the camera takes half a second to take a picture. From there you can tell the ball was traveling at 20 ft/s.
Now imagine every time you take a picture, a giant fan turns on and blows the ball in a totally random direction at a random speed.
Same general principle with electrons. There’s obviously a LOT more to it, but at a base level it comes down to the amount of information we can gather at one time. Every test and observation we make of that election changes its speed and trajectory.
It is really difficult to wrap your head around it, but basically the best you can do is accepting that the rules of the world are changing if things are getting smaller and smaller.
The really small things behave very differently from how we describe our world.
The biggest difference is that those really small things are not objects as we imagine a thing,like a ball. A ball would have a defined border where the ball starts and everything outside is not the ball.
But for example you can imagine a crowd of people (like a mass event). As you get closer, you notice that there’s more and more people as they stand more dense closer to the stage. There’s a point where you can say you’re totally standing in the crowd. If you move out, there’s less and less crowded people, at a point you would find people who look like lonely bystanders, isolated from the crowd. How would you tell if such person belongs to the crowd, or just passing by? What I want to say, you can never precisely draw the borders around a crowd, because there’s always a fuzzy unclear layer between the “certainly crowd” and the “certainly non-crowd”. Besides not knowing where the crowd ends, what you can do is finding the “crowdiest” part and call it the center, as a kind of point of location on the map. Like the GPS address of the crowd.
Now, the electron somehow manages to live by the same principles but without a crowd of electrons. Just like, being alone, it never has a precisely defined border, where you know the electron is inside. It’s not a ball then. It’s like a smear in the space, always a little electron-ness being somewhere outside of where you think it is.
Small side note about speed. Speed is a vectorial amount. The direction of movement *belongs* to the speed. In the everyday usage we are a bit sloppy because we say a car goes at a speed of 10 mph (or km/h or whatever you use). But in fact if we don’t know which direction the car goes, in terms of physics we do not know it’s speed.
So if we say we don’t know the speed of an electron, it means more like we don’t know which direction it goes.
Now what is happening, is that the electron, a big undefined smear is going zig-zag somewhere. If you want to see the current trajectory of the smeary stuff, you have to zoom out. But then you will have a huge smear in which the electron can be anywhere so you loose the precise position. If you want to find the “main body” of the electron within the smear (which can totally be anywhere, not in the middle), then you need to zoom in, but the more you zoom in, the less clue you have which direction the whole thing is moving.
It’s a mathematical limitation that expresses an inherent quality of quantum systems and not a consequence of the observer effect as stated elsewhere.
Let’s start with quantum mechanics is *really* weird. The only way to really explain it is that it’s pure math and completely ignores human concepts of reality.
This is related to the Heisenberg Uncertainty Principle (HUP). The typical explanation of HUP relies on the analogy that to measure something we need to hit it with something like a photon, which introduces error in either speed or position.
The flaw with this explanation is that it leaves out that the electron’s position and velocity are defined by something called a wave function. This is a mathematical equation that describes how position and velocity are related. Specifically, it’s an equation that we use to describe the motion of waves, like waves on the surface of water.
The HUP is a direct result of the wave function. The wave function quite literally makes it impossible to describe both position and velocity of any quantum particle with perfect accuracy. The closer you get to perfect accuracy of one property, the less accurate you are on the other. The HUP is quite literally a fundamental property of the universe and has nothing to do with our ability to measure it. Rather the math tells us that electrons literally don’t have a fixed position and speed. The more you fix the electron in place, the less you know about the speed and vice versa.
Imagine a marble rolling across a table and a blind person wants to know where it is and where it’s going. The blind person has a stick that he can poke the marble with, and feel when it touches. The problem is, if he pokes the marble with the stick, that has the effect of changing the motion of the marble. At the quantum level, “measuring” means interacting with something, like poking the marble with a stick. The simple act of measurement changes the thing you are interacting with, like poking the marble with a stick.
An actual eli5 answer is…
Imagine a rollercoaster. You take a snapshot when its at the top of the hill.
You can now determine its location! But you don’t know its speed. Its just a snapshot, there isnt enough information to work out its speed.
To work out the rollercoasters speed we would have to record a video or take multiple photos. Then we could measure its speed by watching how far it moved in a period of time.
But now you don’t know its location! Because its moving!! If all you have is a snapshot to measure the rollercoaster you can only ever know its location OR speed not both, because a short snapshot tells you its location but not the speed. A long one tells you the speed but confuses the location.
Another example is a ripple in a pond. To measure the speed of the ripple you would measure how many peaks and throughs pass and in how much time. If you wanted to know the exact location of a peak you would have to monitor a small section of the ripple. You cannot measure both the whole over time and a short section at the same time. Its just physically impossible.
So it basically is for electrons. Because quantum physics are waves, we have this inherent problem.
The best analogy I heard was this: Imagine you have a 1gb camera and you go to a soccer game. You can take a picture of the all in play, and you can tell exactly where the ball is on the field in the picture by looking at the lines and the background to pinpoint it’s position. But just looking at the picture you have no idea what direction it came from or it’s going. So you switch your camera and make a video of the ball. Now you can tell what direction it came from and where it’s going. But your camera is only 1gb so the resolution is terrible. The ball in the video is a fuzzy blob. You can’t pinpoint exactly where it is on the field because it’s too blurry. So you can either know exactly where the ball is, or the direction it’s coming from or going to, but never both.
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