Connecting classical and quantum physics
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- Опубликовано: 6 сен 2024
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How does classical physics emerge from quantum physics? Bohr's key insight linking classical and quantum physics via the so-called Correspondence Principle ensures the smooth transition between these two realms and constitutes an essential notion for modern physics.
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[References]
∘ N. Bohr, On the constitution of atoms and molecules, Phil. Mag. XXVI, 1, (1913) archive.org/de...
∘ N. Bohr, On the constitution of atoms and molecules (part 2), Phil. Mag. XXVI, 476 (1913) archive.org/de...
∘ N. Bohr, On the constitution of atoms and molecules (part 3), Phil. Mag. XXVI, 857 (1913) archive.org/de...
∘ N. Bohr, On the series spectra of the elements, Lecture before the German Physical Society in Berlin (27 April 1920)
∘ P. Dirac, On the theory of quantum mechanics, Proc. R. Soc. Lond. A112, 661 (1926) doi.org/10.1098...
∘ P. Ehrenfest, Bemerkung über die angenäherte Gültigkeit der klassischen Mechanik innerhalb der Quantenmechanik, Z. Phys. 45, 455 (1927) doi.org/10.100...
[Credits]
Niels Bohr, public domain
Max Planck, by R.Dührkoop, public domain
Albert Einstein, public domain
Peter Debye, public domain
Hydrogen atom Balmer series, by MikeRun under CC BY-SA 4.0
Paul Dirac, public domain
Paul Ehrenfest, public domain
Absorption spectrum, by Almuazi under CC BY-SA 4.0
CC BY-SA 4.0: creativecommon...
Are we just gonna quietly ignore the fantastic Taylor Swift references? This is not even the first time Taylor Swift references have appeared in these videos and I am loving it!
While I try very hard not to know anything about Taylor Swift, my curiousity is piqued.
😂😂
Not to demean other yt scientists, but i think youtubers like this who actually go into the more advanced, more detailed parts of science, should deserve more views. These kinds of videos is for the more curious, those who want to know more. While other channels simplify their content quite a lot so that their viewers can understand, and i don't blame both groups of people, but i wish there are more channels like yours which wont be nerfed by the size of viewers' knowledge base. Keep it up!
Thank you for your kind comment. I agree with you that channel presenting more superficial versions of these stories are necessary; but I found myself always wanting more and wondered if there was an audience for this. Last year I decided to stop complaining about the lack of more in-depth videos and launched this channel. This is precisely the audience that I have attempted to reach: physics enthusiasts that don't shy away from some math and people with scientific background who might value some history details. I personally was never told all the dramas and interesting human aspects of these stories during my studies. Now that I have time, I decided to dig deeper, read the original papers, and I decided to share the details and found that the stories get even more fascinating.
For me it's great to have both 😃
But the really good deep ones like here are really rare.
The channel "But Why?" is similar and goes into more detail! you might also like that channel
It’s also hard to find these
@@lasarkolja9692 I guess they are complementary, I also like to watch light stories once in a while
The mathematics is really necessary, it gives us a holistic justification to how scientists arrived to their results.
Many concepts can be explained and discussed, but the math behind to supporting the claims is the most effective way to convey the message. It is the common language that can be used to challenge the ideas back and reach consensus.
Hey I am a high school student who loves to learn about physics and I have found videos extremely entertaining and easy to understand. Please continue do more, Thank you
This guy makes my day happier. Perfect video for a lazy Sunday afternoon.
Glad to hear that, enjoy!
Interesting to note that Maxwell's formula for the frequency of an orbiting, radiating electron works without a transition between states (it's stationary?), unlike the Bohr model counterpart. I see that Bohr's move of taking the limit of large quantum number N cleverly reconciles the two cases because as N gets larger the gap between levels gets smaller, so at very large N it's as if the transition isn't there and the electron just radiates while orbiting.
you got it, that's exactly Bohr's purpose on taking a large N: the gap between the two relevant energy levels approaches zero in this limit so it is like the gap is not there at all.
That's worth a coffee and a bagel
Thank you so much, your valuable and continuous support is always appreciated. Greetings to the other side of the globe.
Ever since I started watching your videos, every time more content is posted my interest in studying Quantum Mechanics and its history is rekindled. Even though my academic routine distances me from studying more physics, I get brought back to the subject, and I am absolutely grateful for the quality of the videos because they are second to none in peaking my interest.
Wow, thank you for sharing this. It means a lot when viewers appreciate the content and it is very fulfilling knowing that the videos that I enjoy so much (but also spend so much time) making can have such a positive influence on people that I do not know and might be sitting far on the other side of this planet. Thank you for your words, this keeps me motivated to continue this hobby that has connected me to an enthusiastic and vert supportive community of nerds around the globe.
I was not expecting my black and white -sometimes yellow-, physics history channel to put a colorful sponsor section in the middle of the video. Totally spooked me out, anyway good to see you're getting places with this channel.
Such an important story in Physics.. Awesome to see it covered with a lot of details well done!
Thanks, glad you liked it!
2:14 here it is! Was I the only one to guess it correctly from the community posts?
yes, you were the only one to correctly guess the topic. Good catch!
Still the most valuable channel on all of RUclips currently. Please keep them coming!
Has a mathematician I really find it hard to grasp these taylor series approximations because they seem so arbitrary and without rigour, but even worse, a lot of times they can be very easily explained by studying limits! In the case of 4:20, for example, that's just the limit of x/(e^x-1) -> 1 when x ->0, where x=hv/(kt). To get that limit in that equation, because we only have 1/(e^x-1), we just multiply and divide by x to get the result. Same with 6:40. We have (x^2)*(e^x)/(e^x-1)^2 whose limit as x approaches 0 is also easy to calculate to be 1 without any taylor approximations as a simple limit. And the same in 9:44. N(1-1/(1+1/N)^2) can be simplified to (2+1/N)/(1+2/N+1/N^2) which of course approaches 2 as N approaches infinity. No need to make dubious and arbitrary approximation, and much easier to understand and also replicate in other problems.
Also I really enjoy your content btw
I forgot to include an apology to mathematicians, but yes, you are totally right, Taylor series are not needed in the examples shown as they are just limits. It is probably due to "academic deformation" but Taylor series is the go-to way for physicists to evaluate limits. The sloppy way we use and abuse Taylor series becomes more useful when approximating functions, which I will probably need in a future video and that was another reason to introduce it here.
As a physicist with strong math skills, I am perfectly happy with the Taylor series approach, and I think it works well for others. However, I’d be interested to see how mathematicians otherwise evaluate those limits.
You can use L'Hopital's rule and you get the limits right away.
@@jkzero : Indeed, except I always worry about some of those cases where L'Hôpital breaks down (like indeterminate forms of limit quotient).
Lovely sunday, chilling after a workout and watching your wonderful video. Thank you for satisfying my need for historical stories of physics.
Wonderful! Thanks for the appreciation. BTW, love the profile pic.
I wonder if he plans on telling how the quantum theoretical picture came to be, it would be quite enlightening to see what inspired Schrödinger, Dirac and other to come up with such an elegant framework to explain quantum phenomena.
those are coming; for a long time I have been preparing the material for De Broglie (who did way more than just proposing the wavelength of matter waves) and Schrödinger to show exactly how he came up with his famous equation to hopefully debunk the myth that goes around that he just was a genius who figured it all out in his head. I blame Feynman, on his Lectures volume III, section 16-1 he said "It’s not possible to derive it from anything you know. It came out of the mind of Schrödinger."
@@jkzero Good to know you’re working on it! There is an excellent series on the mathematics of Quantum Mechanics in the channel Quantum Sense, there they derive Schrödinger’s equation from “things we already know”, might be a good reference for you. Anyways, congratulations on this series, it’s been amazing!
@@gabrielamici5540 I have seen many derivations of the Schrödinger equation but they all seem contrived to me, they use modern techniques or are unnaturally guided because we know the answer, so everything is tuned to get the right equation. Interesting but it feels like cheating. I am interested in Schrödinger's thought process with what they knew at the time.
@@jkzero Wow, that's a nice, succinct description of why I enjoy learning physics and science and math through their history so much! Its fascinating to follow along on the discovery path. :)
@@jkzero This is the first time I have encountered anyone wise enough and brave enough to criticise Feynman. I know he scored a Nobel Gong in physics, but while Feynman was a genius, the ambitious scope of his lectures meant he sometimes touched on subjects outside his core expertise. His handling of classical wave theory is a case in point. He really didn't recognise the difference between transverse and longitudinal waves. Pressure waves in a gas, whose amplitude is pressure , are not associated with any oscillation in the space dimension. I am trying to find a forum where enlightened skepticism is not dismissed as ignorance.
I always believed the Correspondence Principie on faith, and always wondered how it could be demonstrated mathematically. I never understood until now. Thanks for that.
I am convinced that most of the confusion about the conceptual ideas of modern quantum mechanics arise due to the neglect of old-quantum physics, all the key ideas arose there. Most textbooks and popular stories move from Planck quickly to Schrödinger and Heisenberg; making many key concept appear like out of a hat. Most of the very exciting physics that led to the building up of modern quantum mechanics happened before 1925. This is how I understand it and how I am presenting it in this series.
One of the few serious channels on physics. Congratulations for your amazing job, from a colleague Ph. D in Physics working as a Postdoc in Germany. I also have the surname Diaz (useless fun fact). My best wishes.
good to know that there is another Dr. Diaz in physics in Germany too; should we create a club of "Dr. Diaz in Germany"?
My goodness, this is absolutely beautiful.
Thanks, I am glad you liked it.
It is a good day when JK0 uploads a video! Especially on a sunday morning!:)
Good morning to your side of the planet and thanks for the kind comment.
@@jkzero Thanks:) Have a great sunday! Looking forward to the next video!:)
@@TimRobertsen I am right now with pen and paper calculating the details for the next video
@@jkzero Can’t wait:)
Regarding future videos, I was wondering if you might consider making a video about the weak force/interaction. I have for weeks been trying to get some understanding of it (I have no formal education on the matter) and it has been fairly difficult. In so many cases it is simply covered by “..and it is responsible for some types of radiation/decay”.
What really puzzles me about it is how it “senses” the proton-neutron-ratio of a nucleus (if it does that at all:p). And, there are so many other interesting aspects of it, chirality, time-asymmetry.
Excellent explanations. Would be nice to see how you explain Schroedingers derivation of his eq. and Heisenberg’s matrix formulation. You follow the history, pointing beautifully at how new insights came about, in a simple way yet without diluting the material. Wonderful!
Heisenberg and Schrödinger are coming, for sure; I just like to spent some time on the early (old) quantum physics. I personally believe that many of the misunderstanding on quantum mechanics or conceptual holes arise because people jump directly to modern quantum mechanics and its ad-hoc postulates without studying the early developments. Even though the old quantum physics was rapidly replaced by quantum mechanics, it is the old quantum physics that led to the conceptual jump of Heisenberg, Born, Pauli, and the others.
...I geuss this is why all the most complex problems are at molecular/microbiological scale. Think about it. If we start with "simple" quantum rules at atomic level on the one end and only observe quantum rules at their limits in macroscopis scale (our everyday scale), then there is a point were rules of quatum world become most convoluted (there are just enough atoms in the observed system that ALL the interacting effects must be calculated precisely)...
P.S. Awesome video as always...:)
Great video. Bohr's approach is fascinating. In here the circular motion of the electtron is brought to a straight movement.
Love your patience and love for physics
Very good recap!
Can you make a explanation video on how stimulated emissions was theorized? (lasers)
I cannot guarantee to be able to fulfill all the requests but I always open to collecting suggestions, thanks.
4 minutes i caught this amazing video
7 minutes😀
circ = 2pie = 2π*e = 2π*(1+1/n)^n
n , circ
1 , 12.566
2 , 14.137
3 , 14.893
4 , 15.339
5 , 15.634
etc…
Excellent and crystal clear presentation of this concept.
Glad you think so!
Another beautiful video!! ❤❤❤
One test I want to see is a tunable metamaterial for slits and the orbital energy levels. Can the defraction gradient manipulate the bands/probabilistic pathing.
One part is many body and shared mixed state and difusion. Bell and Q. cryptography point to that. Thank you for sharing the video.
Does a locksmiths pin fluidiser (lock picking gun) show quantum effects in a physical system? It's as if all of the pins end up in the state of 'unlocked' just because they are bouncing about randomly. Does this effect also apply to a jiggling sand bed where solid objects will sink just because each sand grain is bouncing about? In my limited understanding, probability and quantum physics seem to go hand in hand.
Hmmm on comparing hν to kT in (hν/kT), looking at the physical feasibility of it, can we say that the quantized mode ν is independent of temperature T? If ν grows with T, it seems like it's invalid to take that limit unless we drive the constant h itself to zero
I would not say that the frequency of the radiation v directly depends on the temperature T. A blackbody radiates all frequencies, only the peak frequency depends on the temperature.
@@jkzero Ah yes that's right
The Bohr model is essentially a classical theory, it only introduces a quantum condition selecting the possible classical orbits. A limiting case to classical physics is then natural. But with the Schrödinger theory it is quite different.
I would disagree here; classically, electrons could not maintain their orbits. The quantum rule imposed by Bohr really requires going beyond classical physics.
@@jkzero This is still not quantum mechanics, then this says nothing about the correspondance principle in quantum mechanics. Heisenberg believed it was true because he started from the correspondance principle, but Dirac proved it was false, as soon as in 1926.
@@clmasse I never said that Bohr's model was quantum mechanics, I even explicitly say that the complete theory was developed more than a decade later. I have tried to be consistent and refer to quantum physics but not quantum mechanics. I just reported what Bohr wrote in 1913, he called it correspondence principle in 1920 (also before quantum mechanics).
@@jkzero The Bohr model doesn't work and is no longer used today.
@@clmasse you are totally right; in fact, I never say that Bohr's model is valid today.
Quantum mechanics is not a theory of continuum mechanics described by an ordinary differential equation. It is a theory of quantum jumps between quantum states. The two theories should agree on matters that are both within their respective domains of applicability. It is not reasonable to say that the classical result is just a limit of the quantum result. The classical result is simply not applicable when the jumping is from one quantum state well separated from another.
Thanks for the videos. This is so interesting and helpful.
Glad you like them!
EN TODA UNIVERSIDAD SE ENSEÑA UN SEGMENTO , SE DIVIDE EL SEGMENTO Y SE PONE UN " PUNTO " , ESO ES SIMPLE PERO ES EL RETRATO DE LAS COSAS EN PEQUEÑO Y SE PUEDE CAMBIAR DE UNA BASE DISCONTINUA A UNA CONTINUA Y AHÍ COMIENZA LO QUE LOS NOBEL LLAMAN MAL CUÁNTICA
Great video again!!! really having fun with the series.
but Few questions...
What is physical significance of h going to 0? like it's more appropriately should be hv goes to 0(as proposed by u in video) but why h going to 0 at first place?
i am not able to grasp the correspondence between bohr's emmission and maxwell's emission, they are quite different in their origin except their similar looking formula in case shown in video, then why we see it as a classical-quantum correspondence?
ehrnfest theorem comes more naturally and is more digestable to me.
will you be making a detailed video on dirac's and ehrnfest version of corresponding principle?
From a mathematical point of view, h→0 is just a limit; physically h is a fundamental constant so we cannot change its value. The meaning of h→0 can be interpreted as "the angular momentum of the system, like Bohr's electrons in orbit around the atomic nucleus, is much larger than h."
The correspondence shown in the video refers to how a classical electron in orbit around the atomic nucleus described by Maxwell's equations is a particular (limit) case of the quantum description of the same physical system.
Congrats on the sponsorship 🎉
Thanks!
Let's assume and assume that we managed to "improve" Michelson's experiment (1881) so that it determined the speed in an airplane; 300, 350, 400 meters per second. Question for you: what will change in BIG SCIENCE?
Plancks law isn’t just quantum before quantum, it’s also relativistic before relativity.. probably the greatest rectus pluckus in history.
Could you explain what do you mean being "quantum before quantum"? Also, what aspect of Planck's law is relativistic?
@@jkzero well, it wasn’t real quantum mechanics with operators and Schrödinger equation.
@@DrDeuteron true, the so-called old-quantum physics was not a real theory but rather a bag of similar ideas. But what do you mean by Planck's law being relativistic?
@@jkzero e.g the CMB was emitted at 3000K, and relativisticly Doppler shifted to 2.7K, and it’s still a black body spectrum.
It's interesting that Planck first deviced a 'fit' and only then pondered over what it actually implies ...
Work your way back from reality to fundamentals
One can wonder about the other route. Start with fundamentals and see what it delivers as reality
But ... what is really fundamental?
The only absolute fundamental is Nothing
Soin the other route one should start with Nothing and ponder what is the next inevitable step.
Planck cleverly managed to find a function that notably fit the data, he used some thermodynamics arguments but there was also knowledge of what he wanted to achieve, this is what in theoretical physics is called "phenomenology." Then to explain his solution he decided to stick to thermodynamics and give up anything else. The question is what do we need to give up today to get to the next revolution. My PhD was about exploring unconventional physics when Lorentz invariance (the fundamental spacetime symmetry underlying special relativity and quantum field theory) is a broken symmetry. It was fun, but no experimental signatures exist of this.
@@jkzero Interesting 'what do we need to give up?' ... It implies we have 'too much'
As I said, if you start with Nothing ... One thing is sure, you dont have to give up anything (anymore). Therefor Nothing is a fail save fundamental starting point ... albeit a seemingly impossible one. Yet we do know there is reality so there has to be a way forward.
Maybe you could muze on this. Just for fun 👍 (I did and still do ...)
The promise is that you should be able to eventually 'connect' with known physics ...
What people don't get, is that the properties of a fluid semi dictate things like drop size under given conditions.
c being transmission speed also via Eo Uo gives the fluid qualities of "space"
Which imho is best treated as a dielectric super fluid. That real flows in this fluid cause charge, create charge.
Physics: Flows in a dielectric fluid cause charge separation.
taylor swift reference 😉
The Eherenfest theorem is F=ma
Ah yes, another Taylor’s version :) my favorite musician physicist.
If I had radiation from 10^18 atoms how would that be equivalent to the transition from N+1 to N orbital of an atom (where N is very large). I think I'm missing something in my thinking here.
The calculation is for a single atom, both in the classical and in the quantum case.
@@jkzero oh right on. Thank you.
What software or resources do you use for writing and animating equations?
All the animations are made using Manim, an open-source library on Python created by 3b1b docs.manim.community/en/stable/examples.html
I always wonder if you people know this much from your early age or you learnt this with experience. I am an undergraduate mechanical engineers passionate about physics and math😅.
I doubt anybody knows to this level too early. All of Bohr's model and consequences require high-school physics and basic algebra; however, this is only taught in college. At least in my experience, I taught all this concepts to first-year physics undergrads, that is the earliest I have seen this content covered.
Amazing!
Aw yiss intermediate physics content, none of this Arvin Ash "let's find the most confusing analogy possible" nonsense
I am glad you like the content. This channel is a mix of historical context, some calculations, and use of original sources (original papers). Many viewers have actively asked me to include calculations instead of just superficial stories and I am happy to get that audience. Analogies can be great but they can be limited and prone to misinterpretations. There are many channels that focus on that, here I include mistakes and wild guesses and do some math to show how things were discovered in the first place.
Embedding promotion for products. Ok
I voluntarily spend many hours of my free time researching, scripting, animating, recording, editing, and producing these videos, viewers watch them for free; ads fix the imbalance.
Planck derivation is incomplete. To this date nobody explained how graphite emits photons. He begins his derivation with Kirchhoff's Law of radiation. But this Law states that the radiation is independent of the nature of the walls. Kirchhoff ignored the properties of material the walls are made. It is wrong. We have almost perfectly absorbing bodies or almost perfectly reflecting ones. In a cavity made of a black body any incident radiation is converted into thermal radiation but in cavity made of a reflector radiation belongs to the surrounding and we get resonant cavity. If Kirchhoff's was right than we wouldn't have lasers, MRI and relay antennas. Dr. Jorge. I have a question. How graphite emits thermal radiation? Explain it on the level of atomic structure.
I’ll try to explain it in classical terms. In every moving atom, the nucleus gets displaced a bit relative to the electrons around the nucleus. The electrons, a charged particle, experience a new acceleration to restore their equilibrium position. Accelerating charges emit photons. Since the velocity of atoms goes up on average with temperature, the mean displacement in a given amount of time also increases. In an ensemble of atoms at a given temperature, some will move faster than others, but the fast moving ones emit higher energy, shorter wavelength radiation in order to restore the electrons to their equilibrium locations.
Quantum mechanically, electron position should be thought of as an orbital with a distinct shape and the effect of that “cloud” on the nucleus can be treated with perturbation theory.