Quantum Wave Functions: What's Actually Waving?
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- čas přidán 11. 05. 2024
- The most mysterious aspect of quantum mechanics is the wave function. What does it have to do with probability and statistics? Let's find out. Also, check out Brilliant for 20%: brilliant.org/ScienceAsylum
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Taking the quantum brick road.
"Do I turn right or left here?"
"Yes."
Michael Price
This is a technically correct answer. The actual question that shows the weirdness of quantum mechanics is:
"Did you turn left and right?"
"Yes."
Same answer if you ask a computer scientist.
It depends, do you have a Heseinberg license? Lol.
wow never noticed that meme is a superposition but yes it is
@@donwald3436 Computer scientist does both and tells you which one you did....unless there was a loop, and he blows his stack instead...unless Win95, in which case, BSOD.
A side note for those interested in the math: We don't use sine and cosine just because "they look wavy." We use them because there's a piece of mathematical machinery called the Fourier transform which let's us write _any_ periodic (aka wave) function as the sum of sine and cosine functions. It's incredibly convenient to be able to represent _any_ possible wave function in terms of just two relatively simple functions, so that's why we use them. 3blue1brown did a video explaining how the Fourier transform works for anyone who wants to know the details: czcams.com/video/spUNpyF58BY/video.html
Discrete Fourier transformations in signal processing has to be the hardest maths I’ve had to do in university. Typically I tend to be able to make a mental image of what I’m doing in maths and make my own way of understanding it, but my mind couldn’t make sense of these, I had to stupidly learn these by heart.
@@cedmelancon that totally sucks.
what learning by heart means?
@@ankitaaarya
"Learn by heart" is an English 'idiom' that means "rote learning"...
It's like navigating in a city in a foreign country where you cannot read ("understand") street signs, but learn to get around "mechanically" from memory.
That's your fish feed for the day. (A reference to another English idiom that begins: "Give a man a fish; you feed him for...")
The "fishing lesson for your lifetime" gift is to point out to you that you are connected to the World Wide Web, and can search out answers to questions like this for yourself...
Happy fishing!! :-)
A side-side note for those who are really interested: Sine and cosine may be particularly nice functions with this property, but there are an infinite number of alternative bases that can look arbitrarily weird which all have an analog to the fourier transform.
Picking sine and cosine is exactly analogous to the choice of basis in finite dimensional vector spaces, that is to say entirely arbitrary and without consequences. So to be perfectly correct, we use sine and cosine entirely because we like sine and cosine. For some people that might be because "they look wavy".
It can also be explained by the fact that all waves can be simplified into an infinite series of right triangles, in the same way a line is an infinite series of points, hence the sudden appearance of trigonometry.
your skills on teaching are the most outstanding qualities a person can have.
this is what I like about these videos. Even if you don't learn anything profoundly new sometimes, when you see a good animation changing from one aspect to another, two previously separate things get connected and it clicks. A new level of understanding!
Static diagrams just aren’t enough sometimes.
_“The events are probabilistic. The probabilities are deterministic.“_
Oh, I like that! Where is that from?
The Science Asylum My old QM professor from college. 1974.
I'm stealing it.
In more lay-terms: What happens to a quantum particle is completely up to probability; it might be here or there, it might be going this fast or this slow. That probability is set in stone, which means we can tell what the probability is if we measure.
We can always tell what a quantum particle might be doing, we can never predict what it will actually do. (Kinda like a crazy relative. You know what they CAN do, you never know what they WILL do.)
probability of a event of a wave to occur at sea surface is 1, but to know exactly when and where is deterministic. not sure of that example fits the above statement
Descartes is at fault here, he was the one who coined "imaginary numbers" as a derogatory term. Gauss knew better and named them lateral numbers.
Yeah, I mean, technically speaking, all numbers are imaginary... but these are the names they have now. We're stuck.
Which goes to show, people who haven't taken a class about them and think complex numbers are a hoax are putting Descartes before the course.
... I'll show myself out....
How "real" are real numbers, anyway?
Descartes also had that pesky duality problem. Princess Elisabeth of Bohemia asked him some good questions about it.
@@ScienceAsylum natural numbers are real. the others... i'd say not...
This is the best explanation of quantum wave functions that I ever seen. I've seen a lot of videos from a lot of CZcamsrs and this is the only one that is actually understandable by non physicians. Great work!
totally agree with you
You mean "physicists" ... (physicians are medical practitioners) ..
@@88feji no, only doctors understand wave functions
@@kylecesar6347 😂😂
Not only did this help me understand quantum mechanics better, it helped me understand probability and statistics better, or gave me ideas for how to convey it to others. There's a lot of power in the term "skinny rectangles" especially for helping students transition from discrete probability distributions to continuous ones.
Those skinny rectangles are one of the most basic concept in calculus 👀. Adding them all up is how integrals work 😁.
Skinny rectangles = Calculus by stealth. Nice job Nick :)
Archimedes was pulling that trick thousands of years ago.
I read that this is an old concept, known as infinitesimals, mathematicians just didn't like it very much because it wasn't very rigorous.
Skinny rectangle infinitecimals are beginners beliefs. Calculas outgrown a lot from this now a days.
@@william41017 not true. Calculus was informal for more than a century. Cauchy, Weierstrass, and others made it rigorous when they needed to but the smartest minds often cheat a little.
You have to do the "skinny boxes" method for mathematical models if you are using a spreadsheet EG calculating the voltage on an analogue integrator.
This is the most intuitive explanation I've seen so far for laypersons like me. I've seen so many videos say, basically, "You get the probability by squaring the wave function." OK, so what exactly _is_ the wave function? "It's a probability thing." Which doesn't feel very helpful.
@Fuert Neigt He's got a ton of really amazing videos. Don't forget to subscribe!
@Fuert Neigt _anything_ you say? hmm...
How was his answer any different? He did expand on it more but his final answer was of course the same, that it's a probability thing
Tom, You should know there is more to this story. Intelligent people have long ago figured out that Quantum theory is all BS. Same with everything that the so called "genius" Einstein said. All total BS. Keep that in the back of your mind when things seem weird, this is the reason.
@@xiaoxiao-kg5np classical (pre-Einsten and pre-Quantum) models do not explain observed phenomena. Is there a different model you can offer, or is this just filed under "who knows?"
This might be the best layperson-accessible video on quantum mechanics I've ever seen
That was a great description of the QWF. The graphs really clicked the issue into my mind. I love the humour and general presentation of the video. Keep up the excellent work, videos like this should be compulsory in all physics courses. Cheers
Underrated moment in this video was when Nick made sense of why we use sine and cosine: they make shapes that look like waves. Like, you need something to look wavy? Here, use this. Doesn't matter what that wavy thing is, but this will get you a pretty good picture of it on your graph, bud. Thanks.
You're welcome :-)
Fourier to the rescue!
Yeah, that's basically it. A more calculus-based perspective on this (which is the math we use to calculate these wave functions in quantum mechanics) is that a sine or cosine wave is "proportional to its own second derivative." Basically, they are curviest at their own peaks, in a very precise way.
This was a great explanation. It's all gradience, until it isn't.
@@ScienceAsylum A probability distribution is just another way of saying "We don't know what happens on a smaller scale". We have to be humble & say "I don't know what the constituents of this wave is, or if any", & continue doing science. I wish you would have added this in your video, physicist need to be more honest about the data to avoid confusion... sometimes "I don't know" is the right answer.
Waaait, what? Yesterday i was searching something on this topic and meanwhile i was thinking "man, i really hope the science asylum will release a video on this". Nice
Glad I could deliver :-)
@@ScienceAsylum can you do a video explaining how the waves of two (or more) separate particles can interact with each other? I understand the nature of the quantum wave, but how can the waves from different particles interact to create the interference pattern, especially when they are separated by time like in the double slits experiment?
You're his clone you, just don't know it.
Max Born is one of the unsung heroes in science, 'cause his interpretation in 1926 of wave function as a probability function was groundbreaking at that times!
Surely his greatest contribution is Olivia Newton John.
he did get a nobel prize for that. there is no unsung here. if you want to know about an unsung hero then look for S.N Bose.
Wait - Max Born or Max Bohr? Oh, it’s Neils Bohr…oops
@@GeokinkladzeWait..what? I don’t get the connection…?
I looked it up - she’s his granddaughter from his daughter Irene. Well, I’ll be damned - definitely his most important contribution to humanity!!! 😂
This was by far one of the best explanation of the wave function i have ever seen.
I clicked on the video for science and stayed for ..........
SCIENCE!!!!!
Your explanation is amazing !!!
for me , this is your best video..... quantum mechanics looked simple in this
I felt so.
I have to say, I watch a lot of physics videos on CZcams. Yours are great but the thing I like the most about them is that somehow you manage to figure out exactly the question I have, title the video as i would, and cover exactly what I needed to know to feel like I got my answer. Well done! At least for me, which may mean nobody else gets any of it. Hmmm. Well, I luv ya, so you have that!
This is the greatest quantum video ever explored in youtube video or any platform. You just hit it. Thank u thank you so much Nick.
damn, that boxxy reference brought ME down to memory lane.
Ah yes queen boxxy
@@addajjalsonofallah6217 aaand it's 2008 again!
Very happy to see you after a long time explaining Quantum wave function. Your explanation is absolutely amazing.
I don't know if I learned anything, but I do enjoy how you present your material. You are a great teacher.
This madman is teaching about the basic idea of integration without letting the people watching the video know (which is probably good since you are trying to explain quantum wave functions in a simple way at the same time). Also, I finally noticed that 3Blue1Brown plushie on your shelf, nice!
[bernhard riemann, stroking his beard in begrudging acknowledgement like a kung-fu master]
@@nibblrrr7124 lol
Love your videos. You go straight to the point, and cut the bullsh*t metaphores or theoretical explanations. It's very refreshing. Thanks !
Ur really best sir 💯
No one explained me quantum mechanics that deep and well
I absolutely love you man, may you live a long life. You make science exponentially easier! Thank you so very much
Nick you're getting better and better. Just loved your video. Best explanation I've seen since learned this in 1993!
Maybe it's because I've learned complex nos before unlike many things you talk about, but you explained this topic extremely well.
In my opinion, this is one of your best videos yet! I love your, hmmm, "energetic" style 😂
Good job taking us one baby-step at a time through a complex subject.
Such a great video Nick. I love your vids they are always conceptually rich and plenty of good questions
I've said this before, but the thing I really love about your videos is that I always learn at least one new thing! This time, it was that the square involved in the Born rule is a *complex* square. I've seen many people write about the Born rule informally in comments here and there, but not ONE person has ever made that clear. Thank you!
You're welcome 😊
As Richard Feynman said, "The prize is in the pleasure of finding the thing out, the kick in the discover"... Ya this video gives that required kick....
He also said...
If you think you understand quantum mechanics, you don't understand quantum mechanics.
- Richard P. Feynman
@@jcf20010 stupid quote
@Jerry Perry I under stand it. The quote works on different levels. Kind of like this one:
"You can observe a lot by just watching."
-- Yogi Berra
I really love how you animated the electron as trying to be at every position at the same time, but still keeping it as a particle. That is the best visual representation of a wave particle duality I ever saw.
Indeed!
thank u so much for taking care of my curiosities so well, have just fallen in love with this channel
You're a lsegend for that one fam.
You answered all my questions.
Thanks brodaaa 🤜🤛
Awesome work yet again Nick - thank you!
Android Robot kicking the "i" - LOL !
lol.. yeah
Kicked that i right in its a.
What else should it do? :D use it? Come on...
cheeky
I forcefully convinced myself that I understood the video. Thanks for your super awesome explanation. Nobody does it better than you.
that square of wave function was ground breaking realization for me, thanks, exactly what i needed
Not the first one, but I'm certain I'll love it. Love from Nepal!!
When you say at the end “Until then, it’s ok to be little crazy” I really feel very reassured. 😆
It's one of the best videos I have ever seen..makes understanding things way simpler..thanks!
You are a life saver. Keep making these and adding the humor. Saved me from tears over chemistry
Shit has started to become real on this channel , you are getting sponsors . Finally!!
I think I've watched about every video on the wave function. This is the first or at least best I've found in showing how it actually works-what is actually does. I know how F=MA works, and I knew the wave function is the quantum analog of the F=MA, but I could not understand how the wave function predicted the future state. I did not until now understand about the different inputs for each property. I would like to more about what those inputs actually are so I can understand how it operates better. But this video advanced my non-math physics learning quite a bit. Thank you.
The imputs are displacement, time and frequency
This was a fantastic video. I've been studying machine learning lately, and this actually helped with understanding some of the underlying mathematical concepts there, as well.
Cool!
Thank you for reinforcing that this is a mathematical function and not a physical property. No one has put it in those words and that is the concept I have struggled to grasp
Really this channel is so underrated! It deserved more subscribers. Let's make it popular!
Quantum Mechanics has always seemed to be really strange... but you make it sound much simpler than I made it out to be. Thank you for showing the connections between probabilities, complex numbers, and integration to understand how those functions work. Awesome job! Although Quantum Mechanics will almost certainly still be a challenge, you made it seem less terrifying. So thank you for that.
You're welcome 😊 Glad I could help
The _math_ of QM isn't actually that hard to understand -- it's all just calculus, linear algebra, linear differential equations, and basic probability theory. And, while those can certainly be challenging when you're first learning them, it's all standard math that's covered in a typical undergrad math or physics degree and is nothing specific to QM in particular. The truly challenging part is distinguishing between and relating the math, the experimental results, and the various interpretations. It's figuring out what, _if anything,_ the math actually tells out about individual particles that's so hard.
Thanks that was one of the most comprehensive explanations I have heard.
We are currently doing intro to quantum in lecture now. Really up-to-date with my physics study! ❤️❤️❤️❤️
One comment i would make is to show an example of a textbook picture of the cos and the isin and relate to the actual rotating wave function.
Other than that, this is one of the best explanations I've encountered as to what the wave function "means"
I love that *transform* sequence! I imagine inserting such clip into our software at work... ;)
The whole vid is great too, of course.
It's a nod to the Adam West Batman transition 😊
Dude, your videos are AWESOME! Keep it up man! Greetings from Bulgaria.
thank you so much. really it help me a lot. keep going on for spreading nice information like this.
Mind totally blown this is what everyone means when they say it's the square of the wave function that gives any meaning to a quantum state
Exactly.
Isn't the square of the amplitude of a mechanical wave (or even EM wave) its energy?
Is there an energy - probability equivalence?
I remember Noether said energy and time have a symmetry, etc. But I don't remember the details.
These quantum probabilities aren't just from functions of time (?)
.. anyway, just rambling. Good observation.
@@NoActuallyGo-KCUF-Yourself You're right that the square of the amplitude is the energy, but that only applies for physical waves.
Wave functions are basically mathematical constructs used to describe probabilities, not actual physical properties like displacement or field strength.
This was great! And the dance music made it seem like a party.
this video helped me a lot to develop the idea of wave function as i am newly introduced to this..thanks
One of the best and beautiful explanations about quantum mechanics on the title: quantum wave function.
Nice boss👍
ohh yeah, great to see edutubers that aren´t afraid of showing the math, specially for my current introduction to quantum mechanics course xdxd. Instant subscription and if you can talk about Hilbert spaces that would be awesome!!!
Yesss, I'd also love to know what's the deal with Hilbert spaces.
Or to get away from QM, how the heck do you (even begin to) describe spacetime curvature in numbers for GR? Or, how does Hamiltonian mechanics work, and how is it different from Lagrangrian?
And anything along the lines of your recent div-curl-Maxwell/Heaviside episode would be _amazing_ - visualizing the important consequences of mathematical equations (though I realize that format is a tall ask ^^)
This man just casually explained the entirety of high school level maths in a single 11 minute video.
Still killin'it, Nick. Thanks a million.
Nick, You mean you are not just going through the science experiments books and do another video that 50 other youtubers are doing over and over? I do love your fresh view on things. Keep it up. You have insights that are worthy.
If I'm not adding something new to the community, what's the point?
wow just found this channel today, goldmine! Its been hard being stupid but interested in what smart people are interested in, i've seen a few of your videos now and been able to follow everything, gotta say thats a first after many years of youtube, well done man! (And you're funny, 5:47) They say you dont really understand something until you can explain it easily, so you must *really* understand what you're talking about! unlike most other youtubers!
Made my day to see a new upload from the asylum
Mine too
narrator dru ditto!
I just love your thought process and sense of humor, makes learning so much more engaging and fun! Although I got lost at complex square so going to research more about that, if you can do a video on how quantum wave function relates to quantum entanglement I will love to know more!
Quantum Entanglement: czcams.com/video/hiyKxhETXd8/video.html 🤓
An excellent way to explain it. Thanks for the hard work you put in this video
"i" really get your joke.
Good one.
justa actually, that's about the only thing I did get. I watch his great vids for humility with a snippet of once and a while " ah ha "
underrated!
i^2 don't.
@@tiny_toilet Jay does, but he's an electrical engineer.
I've got a feeling, after you assemble all your best explanations in its best sequence, I will FINALLY UNDERSTAND HOW THIS WORLD WORKS!
OMG! So as soon as Science Asylum finishes producing all its videos, you'll take over the world!
@@aniksamiurrahman6365 That was the plan!
THIS IS AWESOME OMG IVE BEEN SO CONFUSED FOR SO LONG THANK YOU
Definitely this video helped me a lot to have a better understanding of quantum wave functions. For real, congratulations for your work, your videos are simply fantastic !
Ps. I'm in the other side of the globe (Brazil) sat in my couch learning with you such complex concepts as quantum mechanics and relativistic physics that not long time ago just a really small select group of people could have access...its a great time to be alive !
Great video as always. Measurables go in, probability comes out, with Hizenberg limitations on certainty. No need for observers, or consciousness, or any woo whatsoever.
The understanding of the behavior of the quantum particle as a probability without any understanding of where it comes from is derived from the quantum wave function. This is true and no need for any speculation to assert that. However, where does the quantum particle arise from? Or perhaps another question would be what is the nature of the quantum particle? Not what is the behavior of the quantum particle but what is it actually made up of? We called a wave but what does that mean as being defined in terms of its make up. Not advocating for woo here but it still doesn’t answer some important questions.
@@lopezjraul My opinion is that a quantum particle is best understood as a discrete deposit of energy into a quantum field. This is pretty far down the philosophy of science rabbit hole, but the only remaining undefined term is ‘energy’ and that is both basic, yet does not have a formal definition. If we accept ‘energy’ then the definition is also acceptable. All my opinions.
I love your content. your videos help me escape my crippling depression for a short time & for that I thank you. I have a question about the perspective of a photon. from the perspective of a photon does time stop?
You could say that, but I think it's more accurate to say the photon can't possibly have a perspective. Nothing traveling at the speed of light can. A perspective requires a rest frame and photons don't have one.
Love your videos. They help me to explain Quantum Mechanics to others. You do not have to have a college degree to understand your videos. Thanks for all you research work and simplifications.
Neat. I get a little more understanding of the world from every video. And all this came about from realizing light came in quanta ? Amazing.
Can you use some details from this video to explain the Pauli Exclusion Principle?
this one was bit extra crazy :) i like it . laughted loudly around 6:00 - 6:20
Love the humor very descriptive. A friend of mine always tells me the wave function doesn't make sense but it does and this may be his explanation
Amazing.
how a 10 min video can explain more than phd quantum mechanics professers who took 7 years. keep going :D
9:42 Absolutely!
Hey, just wanted to let you know that this is fucking brilliant and one of the most "intuitive" descriptions on the topic I've ever seen
This video helped me a lot in understanding the wave function. Very good .
There is very less Probability that someone do not like your video.
Its not so Complex task to subscribe and share your videos.
Its time to get Real and start understanding the physics from this channel.
Quantum mechanics hurts my brain in a fun trippy way
Quantum mechanics entangles my brain a PARTICULarly fun way.
My head feels wavy 😖
This is Quantum mechanics for dummies to pro! Beautiful!
Wow where was this video during my exams?? I literally mean it. It solved My all doubts I had.
You have some of the best explanations I have come across to date. I'm happy that some wave function collapsed and I found my self here.
So THAT's why I had to learn calculus!
I've been watching your videos for about 2 years and yeah I have really learnt a lot
And till now I've been ''crazy'' so far🤪🤪🤪🤪
👍👍👍👍👍for ur channel
Okay
I still do have the following questions;
1. Where the heck does the energy come from in the process of nuclear fission and fusion???????😰😰 Mass defect or nuclear binding energy????
2. Nothing....
that's all
3..........''let's all be craz😜😜🤪🤪🤯🤯🤯
Yes, the energy released during fission and fusion is nuclear binding energy... sort of. Technically, nuclear binding energy is negative (a loss). A bond is loss of energy that traps particles together. Here are a few videos explaining that if you haven't seen them:
Nuclear Fusion Explained: czcams.com/video/LKUPAk5049M/video.html
What EXACTLY is a Bond? czcams.com/video/mFKCW_D2oE4/video.html
Bonds Do NOT Have Energy! czcams.com/video/g39nwNm0Xfw/video.html
This one was painful, but I still love the videos. Keep them coming.
Brilliant as always! Amusing and highly informative.
"bouncing squirrels arent the only waves in nature"
i learned something today
Nick: "did this help you understand quantum mechanics a little better?"
Me: LOL... like I come here for understanding 🤣
My god you are the best explainer among CZcams 😌😌
I love your channel! It's really fun to watch, learn, and also hurts my brain too, but that's fine that's how I learn.
Awesome man. Even I'm starting to understand the horrible quantum probabilities.
*_The Born Rule_*
starring Matt Damon as - no wait, wrong Bourne
Thank you for explaining without using the slit experiment. That worked nicely for me. Cheers!
Glad it helped! 🤓
I am so grateful for all you have done for us!