This always confuses me and I’m not sure how it works. Please explain…
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I’m by far an expert but the way I see it is as follows: the act of measuring disrupts the electron because it is so small. Measure the position and you disrupt the speed like if you were to pin it down
We can easily see the position of a car by looking at it. We can pretty easily measure the speed of a car by just watching how far it goes in a certain amount of time.
But looking at things requires bouncing photons off of it. That’s fine when it’s a car. But for something as small as an electron, a single photon can easily just yeet the electron to who knows where.
Edit: This is the observer effect. Check out the other replies explaining the uncertainty principle.
By measuring the position you disturb the wave function so that it has a sharp peak where you found it, and wiggles around zero everywhere else, since it can now be expressed as a sum of a wide range of wavelengths (via CFT) which are all nonzero at the peak. So its second derivative is highest at the measured position. In the Schrodinger equation that second derivative corresponds to “kinetic energy”(kinda sorta) which means the electron is going to high-tail it out of there and since its function is built by a wide range of wavelengths you can’t accurately determine how fast it’s going.
If you do it the other way you get a nice sine wave composed of one wavelength (or at least a n narrow range), so there are peaks all over the place destroying your knowledge of its position.
It’s an inherent property of things that are waves.
Technically it’s momentum and position. Speed will always be C (the speed of light).
Momentum is: how much mass you have and how fast you’re moving.
At these scales, everything is too small to have anything like a physical surface. It is instead a sort of fuzzy area of energy that vibrates.
In your mind’s eye, I want you to draw a single wave.
The height of that wave is its energy. which is also how much energy/mass it has, which is also its momentum.
The width of that wave is its position.
Now we conduct our experiment:
Since what I’m trying to look at is a few orders of magnitude smaller than light itself , I have to use something else. So we use another electron.
You can fire one of two types of electrons. Low energy and high energy.
Your low energy electron will have a long wavelength that does not go up very high. The high energy electron will have a very short wavelength but a very high peak.
If I use the low energy electron it will definitely hit the electron I’m looking for, but I won’t know exactly where. Also, when it “bounces off”, the amount of energy it has will have a slightly different amount that I can measure. So I will have a good idea of how much energy for more momentum I’ve imparted to the electron in question but I don’t know exactly where it’s at.
If I use the high energy electron, having a much shorter wavelength means I can get a very high level of precision about where that other electron is. however, since it has so much momentum or energy once I hit it the other electron now has a bunch of energy. And I can’t know how much energy was imparted to it without hitting it with *another* electron.
It makes a sort of intuitive sense if you just look at the two different wave types: wide and flat Vs short and high.
Wide and flat: A lot of positions to the left and right (position) not many positions up and down(momentum).
Short and tall: few positions to the left and right(position) a lot of positions up and down (momentum)
Sorry I rambled.
As others said, if you measure its position you mess up its speed. You can measure how much time it takes for an electron to get from place A to place B, but you can’t measure it at any one place without stopping it. If you measure it in any way, you mess it up.
What’s the chance you’ll accidentally move a car if you put measuring tape on it? Zero.
What’s the chance you’ll accidentally move a coin if you put measuring tape on it? Higher than a car.
What’s the chance you’ll accidentally move a human hair if you put measuring tape on it? Almost guaranteed.
Well, with electrons it’s basically the same but even more. Take even one measurement and you certainly disrupted the electron somehow (changed it’s position or speed), so if you take the other measurement, the first one is already invalid by then, hence you can’t know both at the same time.
Electrons don’t always behave like particles. Sometimes they behave like waves. Rather than the Bohr model of an atom, where the electron orbits the nucleus like a planet around a star, Schrodinger’s equation gives orbitals as regions of high probability of the electron existing. The means the electron could be found in multiple places, based on that equation (which is related to its motion – so if we know the motion we can’t know the location).
If we combine multiple equations for motion (meaning we no longer know which one is the true motion) then these probable locations combine through interference (constructive and destructive, the way light does through diffraction) and this can result in one area of 100% probability – so we know where it is but as above we no longer know its motion.
Imagine you want to take a photo of a car in absolute darkness: like trying to take a “photo” of an electron is.
On realistic scales, you can use a flashlight to send photons to the car, so that the light bounces back to your camera.
Do the same for an electron, and you’ll quickly notice that the size ratio photon-electron is much larger than the size ratio photon-car.
Now, imagine you scale back up the electron to the size of a car, and follow the same scaling for the photon you send to the car for it to bounce back on your camera. To “scale”, throwing photons at an electron is the same as throwing cannonballs to a car. Those will bounce back towards your gigantic camera, but at the tradeoff of sending the car out god knows where.
“If I say they [electrons]>behave like particles I give the wrong impression; also if I say they behave like waves. They behave in their own inimitable way, which technically could be called a quantum mechanical way. They behave in a way that is like nothing that you have seen before. Your experience with things that you have seen before is incomplete. The behavior of things on a very tiny scale is simply different. An atom does not behave like a weight hanging on a spring and oscillating. Nor does it behave like a miniature representation of the solar system with little planets going around in orbits. Nor does it appear to be somewhat like a cloud or fog of some sort surrounding the nucleus. It behaves like nothing you have seen before.
There is one simplication at least. Electrons behave in this respect in exactly the same way as photons; they are both screwy, but in exactly in the same way….
The difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, “But how can it be like that?” which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it. There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I think I can safely say that nobody understands quantum mechanics. So do not take the lecture too seriously, feeling that you really have to understand in terms of some model what I am going to describe, but just relax and enjoy it. I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possible avoid it, “But how can it be like that?” because you will get ‘down the drain’, into a blind alley from which nobody has escaped. Nobody knows how it can be like that”
-Feynman
If this helps, it’s a matter of precision that applies to everything.
Someone used a car example, so we’ll go with that. When we measure the position of a car. We probably use inches.
But if you wanted to measure the position of a car down to .00000000000001 inches EXACTLY, how would you do it? Well you’d have to hold the car perfectly still, right? Well how fast was it going? We can’t measure that because we stopped the car. Okay, now speed. Again we want down to .0000000000001 mph exactly. If you want to know exactly how fast the car is, it helps to have to put it on a test track where you know exactly where to point your radar gun.
So we have this thing where because electrons are so small and so fast, we cannot measure speed without affecting the location and we cannot measure location without affecting the speed. So at a given moment, we can know one but not the other.
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