The de Broglie Equation and Why There Is No Wave-Particle Duality
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- เผยแพร่เมื่อ 1 มิ.ย. 2024
- The wave-particle duality seems to used all the time to explain quantum mechanics to the public, but it is one of my pet peeves. It represents an outmoded way of thinking (old quantum theory), which is replaced by our current understanding of the wavefunction (new quantum theory). I explain how to use the wavefunction to explain one of the most important experiments in quantum mechanics: the double slit experiment.
Update on my life: I'm going to start a PhD! Same place as the masters, on quantum computing. Very very excited. But don't worry, I'm determined to make time for this channel throughout my remaining studies. In fact, expect some videos on quantum comp in the not too distant future (well, at least not too distant compared to the time scales I work on. Don't hold your breath or anything. That will end badly).
Understanding Quantum Mechanics series: th-cam.com/users/playlist?list...
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Did anyone notice I completely changed how I produce the videos? No? That's good- I wanted them to have the same style. I no longer draw physical pictures/ write on a whiteboard/ physically move things and take photos. Instead I bought a Cintiq (which I could afford using the TH-cam ad revenue I've gotten (I started putting ads on in the last year)), so everything is drawn onto there (in the program Sketchbook Pro) and then hundreds and hundreds and hundreds of these images are edited together in iMovie.
I was about to ask how u make ur videos ^^ well now I know. Also, do you really make hundred of drawing for one video?
Welcome back :)
I did notice that the audio sounded different. Or maybe that was just in my imagination.
The audio was just different because I recorded it about 5 times and was unhappy with it. In the end I just gave up and uploaded whatever.
you da besst
e^(it) := cos(t) + isin(t) isn't just some arbitrary definition. It's the only complex definition of the exponential that preserves its defining property (the derivative of exp is itself) as well as its Talyor expansion.
It's pretty much the only natural non-trivial why of defining exp. That's why any properties it might have are allowed to be interesting.
She is clearly a physicist and not a mathematician.
I like Tristan Needham's discussion of the issue in Visual Complex Analysis. He says that presenting the formula as a definition is a "low blow to Euler, reducing one of his greatest achievements to a mere tautology." He says that d e^kx/dy = ke^kx is a defining property of the exponential function. "Let us cling to this property by insisting that it remain true if k=i so that
d e^it/dy = i e^it." He then presents a proof of the formula based on a moving particle and a 90 degree rotation caused by i. So it's not an arbitrary definition, it's something that we cling to. I really like Needham's language here.
I've never been satisfactorily convinced that the 'e' is required. Clearly some expression with a^ix = cos(x) + i sin(x) is true, but it was never obvious that 'e' was necessarily the correct choice (although it is the obvious natural choice). I'm willing to be given a quick demonstration of why e.g. using a=2 messes things up.
The derivative of a^ix would be i*ln(a)*a^ix. That's why e is the natural choice orelse you would get a^ix = cos(ln(a)*x) + i sin(ln(a)*x), which of course is true and does exactly the same thing, but the ln(a) term is kind of in the way.
Recap: d/dxe^ix = i*e^ix
d/dx(cos(x) + i sin(x)) = -sin(x) + i cos(x) = i(cos(x) + i sin(x))
If you use some other number a instead of e you will get an ln(a) term when you differentiate.
You start by deriving the Taylor series of e^x. Then you include i. After simplifying you have some terms that still have i in them and others that don't, so you separate those terms into two series. Those two series happen to be the same series for cos x and isinx.
www.math.toronto.edu/mathnet/questionCorner/epii.html
You do a very good job at composing and orating these lectures. I’m not sure why these types of videos suit you so well, but you have a talent for capturing your audiences’s attention and keeping people engaged.
So happy to see you back on TH-cam! I was so afraid you had given up! And as usual, such awesome explanations! The relationship between position space and momentum space is much clearer to me now.
Here's a small comment about the awesomeness of e^{i\pi} + 1= 0. Euler did not define e^{i\theta} as a point on the circle. He defined it based on the Taylor series e^x = 1+x+x^2/2+x^3/3!+..., and by then replacing x by i\theta. Following his footsteps, it is then almost spooky that e^{i\theta} gets to be decomposed into the back-then well-known trig functions. Of course, these days, we have a much more geometrical interpretations, but this interpretation was not really available to Euler.
Just want to say how much I enjoy your videos! I hugely respect how you simplify such complex mathematics to reveal the simple intuition behind it. Your videos have really helped me as a conceptual aid when studying such topics (I especially loved your video on Fourier series) and inspire me to research more advanced topics in Physics. Please keep your videos coming!
The fact that someone as daft as me can understand any of this speaks volumes about how you explain things
Seconded
Sorry if it sounds condescending but it is a good example of Dunning-Kruger. I am doing my PhD in the field of quantum chemistry and this stuff is really mind-bendy. And it's not just the math thats hard, its the concepts that are unituitive. So the more you understand the less you understand. If that makes sense?
This pleases Mike Hock the way most people explain quantum mechanics gives people a sense of understanding rather than an actual understanding. I suppose it's kind of hard to give people an actual appreciation of quantum mechanics without going into the maths like in in this video she didn't explain that momentum is a Fourier transform of position or that the superposition principle comes from the fact that the Schroedinger equation is a linear partial differential equation. Likewise my understanding would not be as in depth as yours.
Thank you so much. It's been two years since I last did calculus and you're really helping me get a handle back on what I used to know.
Hey... we missed you! Welcome back!!!! I'm definately going through the previous video to follow properly in this one...
Your videos are very enjoyable to watch. You allow science to be understood in a meaningful and relatable way like no one that I have ever seen before. What you are doing for the world is more than you will ever know.
Ohh... I waited for so long! Thanks! I'm glad that you're back!
So glad I subscribed!
Good luck on the PhD. You'll have over 30,000 fans behind you all the way.
Wow! Just found you. What a brilliant set of videos you have produced. Love your way of describing and analysing subjects. Have already seen two of your videos and they were instant likes! Love you. Keep it up. Subscribed.
Thank-you! I totally agree - this idea of 'wave-particle duality' is not only one which doesn't actually make sense in many cases (where the wave function doesn't look anything like what you would classically call a 'wave'), but it also makes coming to the correct conclusion about certain experiments incredibly difficult.
Yes you are a Genius ! Love your videos ! You are able to explain these difficult concepts better than anyone else on TH-cam. Thanks for taking the time to do it !!!
Interesting videos, finding them a good place to start since they leave so many new questions. Thanks for your time and effort.
You are like the Vi Hart of physics.. I like it.
That is unacceptably flattering.
And absolutely accurate ;)
+Looking Glass Universe Actually of the two of your styles I personally prefer yours.
Téssio Fechine collab! Collab! Collab!
Yay! Welcome back. Perfect timing, my brain was getting hungry for good physics videos. I appreciate all the time and effort you must put into these.
I'm so glad you didn't go hungry then :) And I appreciate that your generous enough to say that me not making videos for months was actually perfect timing, rather than laziness!
Thanks for your return on your videos! When I saw you weren't posting any more for like a year I thought it was a pitty because I wanted more haha. It seems it brought some discussion though, but don't worry, people should be here for physical explanations, rather than for mathematical demonstrations. I'm glad you just got the will to continue helping in spite of the bad commentaries you could get. I started following you after watching de Fourier series video, they are really helpful!
I'm so glad that you're back! Thank you for your awesome videos!
Awww, thank you :)!
wow, MIND BLOWN! great work there, completely changed my perception of quantum entities once again. I love you!
Thanks for your awesome video again! I was really hoping you didn't stop making them. They inspire me a lot.
I think the real mystery to QM, that makes people think it sometimes behaves as a particle, is because the energy of a wave manifests itself in a single spot, and not somewhere else. The wave moves through a slit or slits and moves anywhere on the screen with different energy densities anywhere. But then.. it lands on a single spot, and not anywhere else where the wave has been. Now why is that I wonder? Why does this energy wave which is everywhere, suddenly releases all its energy on just a single random spot and not anywhere else?
Just went back through and watched basically all of your videos. Thank you for making these. They make me even more excited for my physics minor (which I will stuff with as many quantum mechanics classes as possible). I totally understand how hard simple tasks can be when you worry about them (GAD sucks) so if anyone ever acts like they're entitled to some perfect explanation of one of the most complex fields of physics for watching a 15 second ad just tell them to screw off :).
Thanks for another great video. Always good stuff and the best ones out there on the subject if you ask me. Good luck with the PhD, i'm sure you will get it done!
Welcome back. We missed you. And congratulations on completing your masters degree!
Great presentation. This is the first 'Looking Glass Universe
' I see. This has a particular level of mathematics not usually used in You Tube physics videos and I like it. Looking forward for more!
Ahhhhh Welcome back! I was so excited when I got the notification.
holy hell , I almost thought you had given up! Glad to see you here again , i was like "oh riiight, thats the channel that was missing on my youtube updates".
Well the good side of this hiatus is that now im at university and stuff is getting clearer (mathematically speaking, you do the concepts pretty awsomely as always) with my current explorations on algebra and calculus (but still a long way untill the quantum world.)
Good luck with your PhD! and if my calculations are not wrong , see you next year for the uncertainty video :)
Such awesome videos. Seriously. You explain things extremely well.
Thanks for coming back Alice!
Amazing as usual ! Clear, precise, funny ! And what about your voice and intonation ? A kind of magic...so captivating. One of the best series i've ever seen. Thanks !
You have no idea how excited I was when I got the email alert for this video! I'm pretty sure I managed to follow along with the general premises, although my lack of a calculus background made some of the more technical parts a little tricky. I'll probably have to watch it again at some point...
Also, at 8:26, I totally feel your pain. When we're filming, sometimes my brother accidentally skips a step, and since it's all one take, by the time we notice it's too late to do anything about. Fortunately, the pace we do things at means that it's closer to 4 seconds than 12, but still, it's always a frustrating realization in the editing process.
And the animations look great! I noticed they were a little different, but I just assumed you'd gotten new markers or a new board or something. It's incredible that you got such a similar look to your old style out of an animation program!
Also, congrats and good luck on the PhD! Looking forward to the quantum computing stuff: It's an area I have some vague semi-understanding about, but every explanation I've seen has wound up creating more questions than it answers, so I'd love to see a good deep dive on the topic.
Anyway, all that aside, awesome video, and great to see you back! I hope it's not a 11 more months before your next one!
It's not spinning but rather Vibrating at different FREQUENCY the difference in Vibration at that point is the mass and the additive is the Wave function.Delta represent the particles energy at point x Represent a Eigenvalues or a translational SYMMETRY of particles wave spin determine the INTERGER value of Spin as ELECTRIC magnetic and Isoelectric valies
I know this comment is five years old, but wow, 12tone, you watch these videos too? :) I absolutely love your videos
got so excited when I saw the notification that you uploaded a new video! welcome back :}
Thank you, that's very sweet!
its great to find someone who actually makes sense when speaking about wave particle duality
Thank you for this video. After watching videos on the double slit experiment I was baffled by why we were so sure it was still a particle. Clearly wave can explain both results. Thank you!
I just love your voice! And the fact that you are talking about QM is only an added bonus!
YAY! You're back! I thought you quit.
Welcome back and thanks for the video!
nooo, I'm just very very very very slow. I'm sorry! It's good to hear from you though :)
Oh my god! You're back! And just in time to stimulate my lame brain for university which starts in a couple days. Honestly, I get most excited when I see your videos appear in my sub box. Thanks for coming back!
Good luck!!! What are you studying?
+Looking Glass Universe
Chemistry
I feel like you're the type of TH-camr who would reply to comments even if you had 10M subscribers lol. Anyways, welcome back! Hope university (or whatever you said you were doing) went well, and I look forward to the new (well, redone/revamped lol) vids coming soon
All the best :D
All the very best with Chemistry (I really mean that. I ran away from chemistry with my tail between my legs in uni. So difficult!)
Ahaha. I really try with the comments. But even when I have this few a comments it gets very quickly overwhelming.
Omg glad you have returned!
Well this is someone I haven't seen in my sub box in a long while, welcome back!
Yup! And thank you, glad to be back :P
As an occasional viewer, I enjoy your videos as my preferred channel for QM.
One point that I would like to clarify, is that the wave function doesn’t describe a physical model, though in this case, I can surely understand why it seems that way.
To see why imagine if particles were in a probability state instead of a superposition state. To calculate the probability (or coefficient) of each state, you would still be required to treat the problem like a superposition state because that’s the only way we can calculate probability states. i.e. any individual state probability could not be calculated without the context of all possible states that add up to 1.
So you would be using the same wave equations if it was for probability or superposition. Therefore the equation doesn’t define the physical cause and effect of the system.
Mathematical models can only determine results as values despite being a very intuitive model of a wave with all of its states defined. Only logical models can explain understanding of the theory such as requiring superposition.
So as you stated, the dual slit wave interference results were the logical basis for treating superposition as real. The Heisenberg Uncertainty Principle and the mathematical models also helped support the superposition conclusion.
The observer effect was the logical basis for particle/wave duality.
Warning:
Below, is a logical model that can explain QM in a way that may seem absurd at first, but then makes so much sense you will probably feel disillusioned.
It is not accepted science.
The dual symmetry logical model:
At the beginning of time the properties of space and time flipflop at time = 0 at the Big Bang.
⇒ Entangled matter/antimatter pairs were created moving in opposite directions in time but not space.
Applying Noether’s first Therem where conservation laws are the basis for symmetry which CPT (Reverse Charge, Polarity, and Time) symmetry provides:
...-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, +7, +8, +9...
Figure 1: New BB model, Dual Light Cones over a dual timeline of positive and negative time.
Opposite time lines seperated by the Big Bang could just be treated as positive timelines since there would be no way to reference the other side. With both domains moving in the directions of increasing entropy. CPT symmetry would tell us that their would be no way for a local oberver to distinguish which domain they were in. Since both time domains are locked in hidden entanglement they would exist like two sides of the same coin, sharing a single determinism and all observers existing in both frames would be controlled by a shared free will and each only ever aware of a single universe.
The particles would interact with opposite charges causing rotations in the same direction as if dual orbiting stars, matter/antimatter particles would act in a virtual dual orbit as if in close proximity with their hidden partners, yet they would be seperated by dimensions of time, safe from self annihilation though interacting through their EM fields and charges, creating EM waves.
To see why they would have the same spin, imagine rotating one cone over the other and you would note that all left/right polarity and spin would synchronize. Also remember that while they exist in 180° time shift, they still occupy the same space as the other, if viewed in the x domain. The only differences between them would be opposite charge and their orbits would be 180° phase shifted from each other.
We can now see that the twisted worldlines create a tightly twisted pair loop, that would be modeled as infinitessimal loops between the pairs in hidden extra dimensions along their world lines just as is the case for string theory.
Ideal for long distance propagation accross the Universe. They would exhibit mysterious properties of spin, magnetic dipole moments, and seem to have wavelike properties when entangled, due to each particle passing through a different slit in their symmetrical domains.
Yet if observed, then entanglement would break, waves would collapse, just like a switch creating an opening in a circuit.
Why the differential loop makes sense out of the Universe in reference to all known Theories.
1. Properties of time and space are flip floped at time = 0 in the BB theory
2. Noether’s first theorem states that conservation laws require a symmetrical differential Universe based on conservation laws which are the conservation of mass, charge, and spin in equal and opposite Universes.
3. CPT Symmetry requires symmetry in all three: +/-charge, L/R polarity, and +/-Time which creates dual universes that are impossible to tell apart by the observers in them.
4. Accounts for the missing antimatter.
5. Explains lack of evidence for matter > anti-matter
6. Provides the logical model that explains Quantum Spin, dipole moments, matter/antimatter properties in the Durac Equation, dual rotation in the Schroedinger equation.
7. It provides the logical model that make sense out of all Quantum weirdness
8. Unifies all Quantum Wierdness effects to the dual Helix model.
9. Dual light cones complete the conics analog.
10. Dual time lines complete the numberline analog.
1. +/-square roots results
2. -1 = +1 using sqrt(i)
3. complex numbers
4. rotation into the complex plane.
11. It provides the logical model that explains
1. Black Hole paradox
2. matter/antimatter annihilation at SoL/EH for conservation of information paradox.
3. negative energy for ER bridge,
4. positive energy for Hawking Radiation
5. Reverse time at FTL speeds in ER Bridge.
12. It provides the logical model for one of the two hidden loop dimensions in string theory.
This answered my question from the Born Rule video, about when complex numbers might appear in the coefficients, as well as why.
"It's not integral." -- made me smile. :)
Glad to have you back!
The paradox comes not from the fact that it looked like a particle with a single slit...waves do the same thing as you described. The paradox comes from the fact that photons come in discrete packets and are measured at a single point, which isn't the behavior of classical waves, which are always continuous.
Not true. _Standing_ waves (e.g. the waves created by plucking a guitar string) are _always_ quantized.
Yes that's also what I thought. The actual paradox is when the wave pattern emerges using the double slits, but the wave pattern is "painted" by individual dots.. did I get that right?
came in for this comment. exactly what I thought at the end of the video. It doesn't explain anything at all that paradox at all
glad to see you back, i thought you had given up :)
I'm excited to see some quantum computing videos. I've done a little homework on my own, but more information from a student of the topic will be exciting!
That's so cool you're reading it on your own! I really recommend the notes by David Mermin (www.lassp.cornell.edu/mermin/qcomp/CS483.html) if you haven't seen them. I'm making sure you have some material because honestly it may be a few months till I can make these quantum videos.
wow you are back after a long time. missed you.
You are awesome and your vids are always really fascinating :)
I'm so glad you like them- really!
It did not sufficiently explain why there is no wave particle duality
i believe the implication of the video is that de broglie's idea of particle wave duality (involving a wave guiding an electron particle) was usurped by schrodinger's wave function (which is now defined as a wave which tells us about the particle, i.e. de broglie says there's a wave AND a particle involved while schrodinger's wave is simply used as a mathematical tool which tells us about the particle's physical behaviour)
Manuel Odabashian particles and waves are classical concepts. Before QM, the duality was that under certain circumstances an electron behaved like a wave and in others like a particle. A huge problem. Then came along quantum mechanics providing the solution. It is neither wave nor particle, it is a quantum particle.
Can you tell me what is a quantum particle? Or you are just using some words to say it. Because I don't know what is a quantum particle.
That's the problem... it is not intuitive. The math points to it but it isn't something we CAN imagine.
I agree, and personally I find a huge flaw in that classical interpretation: how would you explain quantum tunneling? The particle clearly can exist in a non particle state somehow, otherwise there would be no tunneling it would just bounce off or get absorbed like you'd expect.
Thank you for this video! And congrats for your PhD!
This was wonderful. Subscribed
I love your videos soooo much!!!! Quantum Mechanics I hold dear to my heart and I consistently reference your videos!!! :)
Thank you so much and you are absolutely wonderful!!
My goal is to come up with a solution to the double slit experiment
Hey! It's good to hear from you :) Thanks so much for the encouragement!
+Looking Glass Universe I remember telling you I wanted to angle mirrors and try and detect which slit the particles go through for the DSE, but now I was thinking about using sound, I would like to set up sensors on the 2 slits and back panel where the particles land, instead of visually looking at the slits and collapsing the wave function, I would like to see if sound would work on detecting which slit the particles go through and if it would maintain the interference pattern, know what Im saying? Each slit would have a different tone when it would be triggered when the particle passed through telling us which slit it went through without visually looking and collapsing the WF, I would also put sound triggers on the back panel where the interference pattern takes shape, almost like the keys on a piano to match up with the interference pattern what do you think?
Very very interesting stuff! It sounds a lot like the questions Einstein would ask Nils Bohr. I think that the interference pattern will collapse as quantum mechanics says- but showing that will be mathematically tricky. Either way, it would be very interesting and useful to think about these questions.
I would really love to see a video on particles being measured or observed.
welcome back... We've missed you
I missed you
welcome back *~*
Quantum computing? How exciting! Looking forward to it.
Welcome back. Great to read about you going for a PhD. You can totally do it! You mixed up the colors blue/red parts at 7:30. Answers: 1. Not now, sorry. I completely lost track of QM, was reading other stuff (Eliezer Yudkowsky). But he confirmed what my feelings about QM were as he briefly wrote about it (as if he were some authority on QM, and as if we should trust "authorities"). 2. Nils was simply wrong in this. 3. I am pretty good again, finished a 36 pages long "paper" as final draft three weeks ago (it took me four months of research and work to finish and since it is no real academic material and I am lazy, I decided not to cite any sources), will present it hopefully until the end of September. I have to prepare another presentation for an event in two weeks, I already agreed to it (which I now regret). I bought a new flat, painted today the last room (ok, kitchen not done yet as well), moving in hopefully soon, lots of work. Finally finished a big project at work and the next one is already lurking behind the corner. No time or money for vacation. I should stop writing.
yay you're back! :D
Hi I like your teaching style! The identity e^ix is not just a definition I think though. It is derivable both from the power series representation of e^x, and by relating cosx+isinx to a function "z" taking the derivative and then solving the resulting differential equation. It is not like somebody just said lets define e^ix= cosx+isinx and left it at that. It is a mathematical identity. They are the same function.
That's not what you find in textbooks, but if you took it as definition, rather than power series, with cos and sin defined so as to coincide with their usual definitions, then you could _prove_ that this coincides with function obtained from the usual power series definition, and extend it to all complex numbers via e^(x+iy)=(e^x)(e^(iy)) to get a function on the whole complex plane which satisfies the usual power series for exp(z). [ In set theory, the equivalent forms of the axiom of choice are an example to bear in mind: one can take ZF together with any equivalent form of the axiom of choice, and the resulting axioms prove exactly the same results no matter which equivalent form you choose. On the other hand, something like Lebesgue measure agrees with more naïve measures on the real line where the more naïve measure is defined, but gives meaningful measures to other subsets of the real line. Usually when there are equivalent ways to do things, one way will emerge as the 'standard' way, with others being derived from it. But there is nothing inherently wrong with taking Euler's formula as a definition for complex exponentiation, in the sense that the results are any different from defining it the usual way. ]
Great work. I myself have been very uncomfortable with the duality thing. When I explained the double slit experiment to a friend he wanted to know why wave function does not collapse at the double slit arrangement, as there can be information transfer from electron to the double slit arrangement. I answered that in a real experimental set up all electrons need not end up at the screen as some may get measured at the part of the arrangement where there is no slit. Which, in Copen Hagen language means that the wave function can indeed collapse before it reaches the screen.
My friend also asked if wave function can collapse without a conscious observer. I said yes to it and pointed out that wave function collapse happens at the screen too.
I just want to know if I have erred in anything I said above. Basically the question is, 1)why the electron doesn't collapse at the double slit arrangement itself, 2) do we need a conscious observer to collapse wave function.
Great videos! Superb explanation, kudos.
Very interesting and superb presentation. It gives new ideas.may be 5years. Old but I feel satisfied.
Well done!
Hi! First of all, great channel, and great explanation of the wave function! There is one phenomenon, i still only can explain with the wave-particle duality: the photoelectric effect. Short and bad summary: I light a metal plate with blue light and i can measure a current, i light it with red light i measure no current. I can increase the energy density of the red light as far as i want, there will be no current. I only understand this with the wave-particle duality. Light is a electromacnetic wave but there are also light particles, photons. One electron can only absorb one photon, so a single photon must have enough energy to kick out the electron from the atomic shell. The energy of one photon is correlatets to its wavelengh, so i need light with the right wavelength for the photoeletric effect.
I dont know, if you read comments from older videos of your channel, but i would be really happy if you could explain how this works without the wave-particle duality. And sorry for my bad english.
Finally! You're Back after so Long : )
Can you upload videos a lot more often?
Welcome back!
Great video, keep it up!! :)
Thanks for making these videos and don't stop making these videos too! 😁
Ahaha! Yup, I won't :D
Great to hear that! Oh yeah by the way, will you be making any videos on entanglement in the near future?
Definitely on the hit list!
+Looking Glass Universe that's awesome!
Very good, thanks for explaining it to us, the guys on the street.
Thank you, this is invaluable.
Nice explanation. Is this hypothesis related to the Broglie-Bohm pilot wave interpretation or is it applicable for the Copenhagen interpretation as well?
Great explanation of the wave function.
No problem with your lovely whiteboard drawings, nice sense of humor too.
I am a layman with a 3rd year high school education, but I am interested in all things science now, especially gravity.
My latest interest is what is a photon, and QM is necessary to understand it.
I am looking for De Broglie's thesis now, lol
Good luck with your Phd.
@4:40 The phase theta is a function of the shift delta and the momentum p. You didn't justify why the phase is directly proportional to the momentum. They might be inversely proportional, for example. Right?
deBroglie taught that there are no particles - only waves. And that matter always acts like a wave and only sometimes acts in a manner that can be solved using particle simplifications. Just like Newton's laws are specialized simplifications of Relativity. Relativity is always true and sometimes Newton's equations can be used to make calculations simpler. We don't say there's a Newton-Einstein "duality." Particle approximations in QM are merely a simplification of wave behavior. Wave behavior is always true, just as Relativity is always true.
Maxwell proves the point. Maxwell solves essentially the same wave equation without the nonsense of trying to introduce particles. Photons often behave like particles, yet Maxwell makes no attempt to solve the photonics-particle. Everything is a wave. When Physicists do likewise with Schrodinger, a giant leap in understanding will occur. Physics hasn't advanced for a hundred-years, due in large part to the mystification and obfuscation of particle probability distribution functions. Solve Schrodinger's matter equation as a pure wave function and win your Nobel Prize.
Tom Noyb But photoelectric effect? How do you explain that with waves?
Quantization of energy can only be explained by the wave equation. This quantization is derived explicitly in the case of a hydrogen atom's potential well. Electrons exist only in quantized states within matter and knocking electrons out of those quantized states can only be explained by that same wave equation. Numerically, through computer simulations, the wave equation can be solved for higher elements and compounds to show the same quantization. Thus, quantization arises from boundary conditions of the wave equation and not from the frequency of light.
Many, if not most physicists seem confused on this point. E=hf is always quantized by by the potential well of matter. Whether deriving the source of light or the photoelectric effect at the termination of light, quantization is always a question of boundary conditions of the wave equation. Blackbody radiation is likewise derived by the potential well of a cavity within matter. Potential wells are nothing more than boundary conditions and boundary conditions are applied within wave equation solutions. Particle models explain nothing about quantization. Particle models assert quantization, but can't explain the source of it.
Photoelectric effect demonstrates the potential well of atoms making up the electrode. Work-function of materials is defined by boundary conditions of the wave equation of those atoms. Note that these boundary conditions arise within the context of the wave equation and only the wave equation. Thus, virtually every facet of electrodynamics that can be solved, can be solved by the wave equation. Some cases and problems are more easily solved using a particle model, but the particle model is merely a simplification of the ever-present and always true - wave equation.
I don't really get where this rant is going. Quantization arises due to the wave nature of a particle and you do realise that a particle is merely a wave packet right?
Tom Noyb I'd actually like to add the idea that the electromagnetic field behaves as a perfect fluid.. Which allows for quantisation.
You see, the perfect fluid has evenly distributed energy which represents a particle. The electromagnetic field has randomly distributed energy, making it a wave. They are completely dependant on each other to exist. You cannot have something acting as a particle if nothing acts as a wave.
@@sumsar01 - So what you are saying is particle = wave (packet). Does a particle = a wave? Not where I come from. Look, there are no particles. Not in the entire universe - not one single particle anywhere. Everything is a wave. Just as Newton simplifies Relativity or ray-tracing simplifies Maxwell - everything is a wave and sometimes a particle "model" (and it is only a model) simplifies calculation and thought process.
Thank you so much for this wonderful series! Loving it. Though I am pretty lagging behind(well several years :p ), just to bring it to attention to anyone who is watching it. At 8:18, the wavelength should be lambda = h/p. It can be proved following the derivation steps used in this video.
One thing I am unsure of is why there should only be one momentum eigenstate (up to a phase change) for each value of the momentum. Why couldn’t there be a full eigenspace for each momentum value, which would allow different distributions for a particle’s position, even when it has precisely the same momentum?
What if you had a wave function in two variables, one for position and one for momentum, what would be the problem?
Would the time evolution not be linear, so it doesn’t work for that reason?
Or is it just not what we experimentally observe?
As someone who has studied quantum physics for quite some time, I must point out two glaring mistakes. 1) the wave-particle duality stems from many things, not just the equation mentioned in the video. We have observed photons (and even small molecules) exhibit both particle and wave-like behaviour, but it completely depends on the system. This is why wave-particle duality came to be. 2) Where you state that a particle can be a "smeared out wave" is actually our closest explanation yet of what..."things" (I won't call them particles) are, thanks to QFT; stating that "things" are simply oscillations in a field relevant to that "thing". A wave packet so to speak, with no defined beginning or end.
You're back! Why did you go away for so long? :( :( :( we missed you!! :(
So happy to see you back! My own view of the so-called wave/particle duality has more or less followed what you just presented. But I still get confused by the nature of light. I am told it's a photon. I am told it's an electromagnetic wave. I am told it's associated with a wave function. Which is it?
Read that you are getting your PhD focus in quantum computing. I was curious what your undergrad and masters were in if you don't mind? I'm in undergrad right now finishing an electrical engineering degree with applied/computational math and computer engineering minors. I've had a large interest in quantum computing and would love to work on it in the future. I was just curious of the path you took to get into quantum computing?
At around the 8:00 mark how do you know that the complex function f(x) will give you that coil shape? Is the rest of your explanations true in general or just when the particle is in a momentum eigenstate?
Actually I think I get it. f(x) is just the complex exponential exp(i*theta) and the coil is just its complex graph on the x-axis. So the integral at 6:47 is just a fourier transform. Is that right?
Welcome back :)
Thank you!!
All the talk about wave-particle duality got me to thinking. Yesterday, I went to the beach to watch the eclipse. I was standing in the water which had some fairly big waves. I stood there and felt the waves go past me. As the waves past by me, I moved up and down. I felt a small force in the direction of the wave, but not much. Near by where I was standing, there was a shallow area. When the waves came into this region, they began to break. When I stood there, the waves that went past me that were breaking felt much different than the waves that were not breaking. In fact, the breaking waves felt more like "particles" hitting me and pushing me more forcefully in the direction of the wave. These waves hurt a little. Waves only have particle duality when the "break". Think if a tsunami. The tsunami only causes damage when it hits the shallow waters. If you were in a boat in the middle of the ocean and a tsunami when by, you would feel a small up-down motion as it went past, but that is it. Only when it hits the shore do you notice a tsunami. This, I believe, is what is happening with light waves, for instance, when they enter a particle. Travelling through space, they are waves. Absorption into an atom is analogous to the breaking wave. IMHO of course.
Soooooo basically everything may in fact be a particle, but the wavefunction that describes it (whatever that means physically lol) spreads out to form the diffraction pattern observed? Is that to say that the double slit experiment is like quantum tunneling in action and the particle just ends up in one of the bands because reasons?
Note: I have no formal knowledge of higher quantum physics. All I know is that we can superpose atomic orbitals to describe MO's and use that to do cool stuff in chemistry (aka I am a chemist, not a physicist)
Quick question about the deBroglie wavelength which has never been answered to me satisfactorily. How can the wavelength, which is a distance, which is invariant at non-relativistic speeds, be proportional to the velocity of a particle, which is defined relative to a moving observer? Do observers see different interference patterns depending on their state of motion?
for matter the frequency is non-zero even when momentum is zero, and
wavelength is infinite under those conditions. If velocity increases,
frequency changes only slightly as it is dominated by the large rest
mass energy, but wavelength rapidly decreases. This is not intuitive and bears to relation to light wavelengths, www.researchgate.net/publication/293043649_%27Leading_clocks_lag%27_and_the_de_Broglie_wavelength
What a good question. I think it's got to depend on the momentum relative to the apparatus measuring it. e.g. in the double slit, the speed relative to the slits.
Maybe you pointed it before, haven't seen the other videos, but really just the psi is the wave-function. Using bar-ket notation is slightly different. So |psi> isn't just the wave-function, especially since the wave-function by itself would be an unobservable... Anyway nothing else, and ya... I hope what I wrote makes sense, (it does in my head!) it's such a small point and it''s just something I've noticed a lot of other places too...
Great video
But when you observe from which slit the particles are coming from, you don't get an interference pattern anymore. How do you explain that?
Phewww, was holding my breath since your last video. Was wonderful to finally breath again. Luckily either your video was really clear or the brain damage I suffered has rendered me a savant because it made perfect sense. I promise not to hold my breath for the juicy quantum computing videos, even though it is such a fascinating topic.
As for the questions, not sure.
I don't quite understand what Bohr is saying, but his emphasis on including the particle model seems unnecessary. It's a useful model in a variety of situations, but if it can also be described by waves (perhaps impractically) whilst the wave model cannot be explained by particles, it would seem to indicate that waves are more fundamental. Waves is just a model though too right? Aren't they really like 'perturbations' in a field?
So is it accurate that the double-slit results are just the result of a superposition of the wave function created from 2 single slits? And that the wave function from a single slit is due to electron diffraction? And that the electron diffraction is due to the interaction of Coulomb forces between the electron and the material creating the slit?
I always understood that the duality meant that a particle acts particle-like when we see it at the wall but wave-lile when it passes through the slits and interferes after that - it's a particle when measured and nowhere else.
I'm a bit confused regarding the double slit experiment. I thought It could be observed matter properties when a detector was placed and then t would behave like wave when it was not being observed.
I read a little bit of QED by Richard Feynman (reason being because Richard had an amazing ability of explaining things in an easy to understand way) and he theorised a lot of experiments using a method similar to the one you described here. He said you can think of the particle as a single hand clock and as it travels the hand moves around at insanely high speeds, but when you stop to observe the clock at a certain point in time, it will have its hand in a certain position. I'm guessing this is similar to its phase.
Through looking at dozens of general quantum physics videos on youtube this is the first one that describes the movement of particles in a similar fashion. Albeit you go into a lot more mathematical detail than Feynman did on his speeches to the public.
I hope your view gets spread to dispel the misconception of wave-particle duality.
So, am I getting this wave heuristic right by imagining that the "particle" behavior is just a trace left by the action of the waves moving past, and that what had been called particles were behaving as waves the whole time? Your diagram of the two-slit experiment seems to suggest that the "particle" pattern is merely the trace of waves moving past, so therefore the particle wave duality is a misunderstanding of the expression of energy across dimensions of the time element? (the moire pattern of waves is the energy as 2 or 3D - the particle is a 1D trace) -- Am I Getting this right?
I wonder what hapopend to her original video "Intro To Quantum Mechanics" mentioned in this video above. I remember it from a while ago. It was great. It seems someone removerd quite a few of her earlier videos. I wonder why?
Hopefully because she realized that she was talking total nonsense.
Well worth the wait.
I'm so relieved at least someone thinks so. I've actually been working (mostly worrying) on this video for a couple of months.
Also, thanks for checking in with me periodically- I really do appreciate it, and it's very motivating.
Looking Glass Universe
Judging from the other comments, I'd say that lots of people think so.
They're a little mixed in terms of the feelings toward the video itself. Expected though, it's a very tough one.
Looking Glass Universe
Thank you; that's a very sweet thing to say. I just wish I could offer some real help (not that you need any).
@Looking Glass Universe I don't know if this will make any sense but Heisienberg's uncertainty principle states that to accurately test an electrons position it must be bombarded with some quanta of light energy, and therefore the better you know it's position the worse you know it's velocity? And the lesser wavelength of light energy we bombard it with the more it impacts the momentum of the electron or other particle. Do you think we could theoretically eliminate that uncertainty entirely by measuring the impact of the electrons mass on the space time around it? By impact I mean the gravitational waves created by its inertial mass moving through space time. Not that we could technologically do it soon but couldn't that theoretically work, and provide us with both position and velocity? (If I got any physics wrong please don't grill me too hard haha)
Wait so one single wave function describes both the position and momentum probability distribution for a given particle? There isn’t a separate one for each?
Hi! Came across your video, very well made! But it seems that the formula given at the end, De Broglie wavelength should be = h/p instead!
Hi LGU, loved the video! We still teach the idea of wave-particle duality because its much easier to visualize for students without the mathematical background to imagine superposition of momentum or position states (Grade 11). The wave property of matter IS simply that it has an associated wavefunction (and not a delta? function for its position and momentum?) But its hard to explain that. Do correct me if I'm wrong =)
yeeeeeee we're back! :D
Yesssss! Finally :D
Thank you for this amazing video. Could you explain more what is a wave function and how does it look for a particle with well defined momentum and well defined position. And what those values mean when traveling thought space with time?
A particle doesn't have a wave function. Worse than that: particles don't exist. A wave function describes a quantum mechanical ensemble, i.e. an infinite repetition of the same quantum experiment, just like a probability function describes the infinite repetition of the same random experiment.