Boltzmann's Entropy Equation: A History from Clausius to Planck

[@thomassynths]

Correction: `log` is a transcendental function, not a trigonometric function. (Side note: all the trig funcs are transcendental.) Transcendental means that the function cannot be described by a polynomial.

[@Kathy_Loves_Physics]

Thank you for clarifying. I had never heard of the term transcendental functions (The problem of learning my math solely to help me with my physics). I wish I could fix my videos after publishing.

[@profjoshtan]

While this is true, one can, of course, derive the logarithm using only trigonometric functions via infinite series! :)

[@thomassynths]

@@profjoshtan Sure, but the same can be said about using infinite polynomials. So to be more pedantic, the addendum is "finite polynomial". (Can also talk about coefficients needing to be a "rational" field, such as real rationals, complex rationals, etc... but simplifying here for the non-mathies.)

[@thomassynths]

@@Igdrazil Fair enough. I've yet to read Wildbergers Rational trig, though I'm a fan of his channel.

[@nasseemmuttur778]

@@Igdrazil , interesting to follow your debate. Am no mathematician nor physicist but just have an inerest in physics among many other subjects. I never stop learning. Greetings from Mauritius.

[@Trp44]

The real joy you bring is not dependent on anything you say… you are electricity… I enjoy so much your grasp of truth

[@sonarbangla8711]

Extremely beautifully and masterfully explained by Kathy. Why Plank's equation was engraved on Boltzmann's tomb stone is one of paying respect out of indebtedness on the part of Plank, perhaps saddened by the death of a great man and teacher. Kathy you video sounded like music to my ears. Thank you.

[@sherafgankhan9327]

Madam you are awesome. Ive been out of university since 1999, working as an electrical engineer now. Your videos make me go back in time and question what i have learned. In a good way! Thank you for your videos...

[@pieteruys2032]

As a student one of the subjects in my final undergraduate year was Statistical Mechanics. I was hugely impressed by the sheer brilliance of the reasoning involved. it is an intellectual tour de force. Thank you for presenting this history

[@michaelzumpano7318]

I’m so glad you don’t shy away from a little math.

[@Yuki_Matsumoto_7]

Absolutely delightful. Thank you very much for your thorough and comprehensive research. I'm currently self studying Statistical mechanics and the relationship between quantum mechanics and statistical mechanics often confused me (mainly because of the intercalation of them, I was unsure if what ideas and/or experimental results inspired the respective equations). Although this is not a university Lecture and you didn't explain the maths, trust me that you really helped me a lot in my studies.

[@jackd.ripper7613]

Bassi. You are just friggin' awesome. The most underrated channel on KZbin.

[@Kathy_Loves_Physics]

Thanks - blushing now

[@Kathy_Loves_Physics]

Jack, I decided to start with the life of Planck as that got the most votes AND I am going to Bologna in June to study more about Laura Bassi's life so I will probably make the video about her in July. I wrote more about it (and her) on Patreon: www.patreon.com/posts/my-next-video-is-33502544

[@anonymous.youtuber]

Thanks for these very interesting stories. So often the historical context is missing from the teachings, which is a pity because it makes the study of science so much more colorful. It really struck me that the quantization concept emanated from kinetic gas theory, up until now I was made to believe it was only considered to explain the discrete character of spectral lines in relation to atomic theory. Your videos are so enlightening. Respect !

[@jamesboulger8705]

I worked very hard to understand the historical context because it helps tremendously if you write on these subjects.

[@MrHARRYGOODNIGHT]

The historical point of view also aids in the overall technical understanding of the subject. Kudos.

[@SustainableDreams]

Back after a PBS vid. Go get ‘’em Gal! Your narrative surpasses the pros! Thanks for being awesome!

[@lawrencedoliveiro9104]

4:42 Maxwell’s equations were derived very much from the experimental work of Michael Faraday. Faraday was a gifted experimenter, but he lacked the mathematical background (indeed, any kind of formal education) to make theoretical sense of his own empirical numbers.

[@jaybingham3711]

Adding even more issues of dubious attribution to the mix as today's referenced Maxwell equations are actually Heaviside-Hertz derived equations.

[@profjoshtan]

From watching this, I have come to appreciate for the first time why we focus on Boltzmann's H-theorem in spite of it not quite doing what many physics teachers who teach it claim it does. In classes where the H-theorem is taught, it is often argued that it proves the second law of thermodynamics. A bit of judicious searching the internet will find all sorts of debunking of that claim and, indeed, it does not *quite* do such a thing. But it is weird that it is a topic, then, in so many statistical mechanics courses. Why this weird theorem that doesn't really have much practical application beyond its cute result? Well, one possible answer struck me when watching this video. This is the work that Planck identified as being the first invocation of the logarithm in relation to statistical mechanical properties. So it is an homage to primacy rather than anything truly fundamental. This is why I like this channel. In my physics education, I was taught superficial anecdotes about a lot of this history which gave almost hagiographic accounts of discovery and scientific advancement. Kathy approaches the subject from a much more contextual approach that uncovers some of the weirdness and arbitrariness that still infects our choice for approaching physics to this day. Thank you for this channel!

[@tariqjadoon2301]

Explaining the history just makes learning about science so interesting. Awesome!

[@wim0104]

Your work should be on the freshmen curriculum for every STEM course! I was lucky to have a physics and an optical physics instructor much like this, starting from the basics and open our eyes.

[@mapifisher]

Thanks so much for this awesome history! Didn't know how spoiled I was when you were putting out videos regularly.

[@ericreiter1]

I love you Kathy. Curious of your references, sources.

[@BrightBlueJim]

I find myself becoming deeply absorbed in your articles, with an ever-increasing enthusiasm. Keep it up - you are a gem.

[@jgboyer]

My sentiments exactly, Kathy is enlightening!

[@manuelhe46]

I’m reading Schrödinger’s What is Life and this really helps the background

[@skshum]

Kathy makes physics history fun to listen and learn. Thank you

[@neuronerd5211]

Love, love, love! And your enthusiasm is also the best. I've always thought that physicists have the best sense of humor.:))

[@Kathy_Loves_Physics]

I often think we have the worst sense of humor but I may know too many physicists 🤣

[@jakelabete7412]

Your 'lectures' are absolutely delightful.

[@dougieh9676]

Love Boltzmann ❤️❤️❤️ I’ve been obsessed with Thermodynamics for sometime now. It’s both fascinating and disturbing. Can’t get enough!!! RIP Ludwig!!! The world wasn’t ready for you in your time but your ideas are common knowledge now. More Thermodynamics pretty please. ❤️

[@martingrillo6956]

As I don't like Entropy that much, I cannot consider this episode the best of all the more than good ones you created. It's a bit too much content for a single video to me. Keep up adding your excellent work. Cheers

[@afifakimih8823]

So all of those years we were wrong!! From today I will introduce students Boltzmann entropy equation is actually Planck Entropy equation. And Thanks to this channel, I learn many truth about Science!!

[@ogbanugot6078]

This was so good. Please do Bohr's model and then Planck. But I'll probably watch all four if you do them.

[@petematthews9346]

I had to laugh when I heard "…but we already have a Planck's constant." Reminds me of Euler-how many things are named for or attributed to him? My favorite comment about Euler was that all of the things attributed to Euler should be named for the second person to have discovered them. Anyway, thanks for the wonderful survey of the history of the Thermodynamic Laws.

[@enricolucarelli816]

Wow! From Spain, all my respect and gratitude. I always thought that the historical development of knowledge is an essential ingredient towards its comprehension. Your videos are amazing 👏👏👏👏

[@jesussanchezherrero5659]

Yo también

[@artdonovandesign]

That was an incredible and mesmerizing video! Thank you, Prof. and... What is that beautiful painting on the wall?

[@aletheia4581]

Wow! I've just discovered this channel. Amazing piece of history. Amazing piece of work by Kathy. I think it is important to understand the historical context of physics, which is often disregarded, as we pursue of the fundamental laws of nature.

[@Kathy_Loves_Physics]

Glad you liked it

[@exwhyz33]

Your videos (all of them) are nothing short of fascinating, not least for the amount of work you put into finding the facts and their lineage - Thank you very much.

[@Andres-is3lj]

best physics channel on youtube. Rare passion for thermodynamics right here

[@nassehk]

I really enjoy your videos. As a metallurgist these names and formula were my bread and butter at school but I never knew the history behind them. Thank you and please keep up the good word.

[@Tom-sp3gy]

Please make a video on Edwin Hubble and George Lamaitre and how Mr Hubble didn’t believe in the Doppler effect explanation of redshift

[@mariocanedo196]

A video on Bohr's model would be awesome!

[@demeloalex]

Thank you! So clarifying! Your explanations shine like a sun in my mind! 🙏🙏🙏

[@macroman52]

Now try explaining Boltzmann's H-theorem, which (under certain assumptions of randomness) shows that a function H (related to entropy, as Planck agreed) always increases for a collection of molecules undergoing collisions. I understand it was controversial since it appeared at first to be based only on Newton's laws for collisions, which are time reversible, yet it gave an irreversible law. One of Lorentz's students, c1900, wrote a paper on this, trying to explain, for hard sphere collision dynamics, where the irreversibility comes from. As I remember it, that paper looked at how tiny changes in the initial conditions led to large changes in the outcome of collisions.

[@footshot13]

Oh, the contributions of the female species. Through your efforts to highlight those fundamentals the bulbs would not be as bright and ( I too have no dog in the race.)But thanx the subject is enjoyable, and you make it so. William Dupree

[@bobvar72]

This was pretty awesome! Great history here. I always thought Boltzmann came up with it. My respect for Planck grows even further.

[@Anna_Swamy_Nageshwar]

my respect grown h times

[@bobbymcgeorge]

Ooooh Kathy, you are spoiling us! Another fantastic entropy video - many thanks!

[@Kathy_Loves_Physics]

Anything for you Robert

[@anjinsantaipan4393]

Love your videos explaining the history and especially all the interplays between the main characters. Well done and please keep it up!

[@Jhopsssss]

I don't understand what it means for "absorbing less heat at lower temperatures to be equivalent to absorbing more heat at higher temperatures." What is equivalent between them? I can't seem to find answers through google. Great videos by the way! :)

[@picksalot1]

Only recently discovered your videos. Been enjoying them. It's important to get the history right. Thanks

[@KevinOrePflucker]

Very nice explanation, thank you for the video. I'd like to add that the reason the scientific establishment in Vienna (not Germany) didn't like the idea of molecules was that they were influenced by the instrumentalist philosophy of Ernst Mach. For them, the unobservable entities proposed in scientific theories (e.g. molecules) were just "useful instruments" to explain sensorial phenomena and said nothing about reality itself. Thus, they opposed the treatment of molecules as real entities and didn't accept any further formulations on them, such as Boltzmann's. All of this also had a political aspect, as the newborn Austrian bourgeoisie knew it had to incentivize science to be able to compete with the rest of Europe but at the same time feared the atheist and atomist materialism of socialdemocrats, which threatened their power. Instrumentalism was for them a perfect solution.

[@KevinOrePflucker]

For instance, the alderman who you mention honored Boltzmann's grave, Julius Tandler, was a social democrat.

[@Kathy_Loves_Physics]

Thank you for that amazing analysis. I know nothing about philosophy but it is fascinating how philosophy and politics can alter science.

[@rayoflight62]

Yes. If you note, all the current of neo-positivists headed by Wittgenstein declared that the entire realm of reality was exclusively based on what could be perceived, and made one big cauldron of tought - only theories. As a philosopher, I consider the neo - positivism a form of obscurantism, which placed a toll -albeit limited - on the progress of science and philosophy.

[@rayoflight62]

Guess why. As a scientist and representative of the Government, he determined that tobacco, to give the best smoking experience, had to be added 4% water. He was formally executed for selling adultered goods to the populace.

[@a1m1i1r1g1a1l]

love your videos, show them to my students. thank you

[@Kathy_Loves_Physics]

a1m1i1r1g1a1l I’m so glad. What kind of classes may I ask?

[@j.raimundosilva2101]

Your channel is great and unique!!! I just got here and i'm marveled with the context you put to scientific discovery and how people made the theories. Thanks and keep up this great work, it's not easy to find these informations. It would be good if you put your sources on the vídeo description for those willing to research on their own as well.

[@timjohnson979]

Great video as always, Kathy. Please do all the videos you mentioned. The order is not important, just their stories.

[@Kathy_Loves_Physics]

Will do Tim. Don't know how long it will take me but I will definitely make all 4 videos.

[@lechj9351]

@18:01. Please, correct me, if I am wrong. I believe that the charge of an electron cannot be determined using the Boltzman constant because they both are fundamental quantities, not related to each other through any equation. The slide does not demonstrate that Planck used k to find e.

[@mikebellamy]

This is clear, accurate and informative.. well done. Not spoilt by the shadow of faulty reasoning brought into the subject of entropy by naturalists confusing it to push their philosophy. (nonsense like entropy is not disorder or information is entropy) Although she uses the Wikipedia which is totally confused about the definition of entropy and the second law the quotes used are all ok except one tiny detail. (it confines macrostates to gases only)

[@josesaldivar655]

What you must do is to learn the paper by Bokrzmanb so you know who did the equations at least on words. Similar things among Euler and Bernoulli in fluids.

[@klingeron5929]

These videos are incredibly interesting and unique, thank you

[@SudaNIm103]

This was my favorite video of yours so far!

[@PabloMayrgundter]

Bohr. Tho, I'd love to see Gibbs to have this taken to the modern era. He also influences the development of radio which might help with your upcoming vid on TV. Cheers! Great work :)

[@9613ENKI]

thank you. this kind of historical context makes clearer even the math of thermodynamics. great video.

[@meow75714]

Hi Kathy, Great video. How do you get access to all the historical references and papers? Can you find them all online?

[@rasmusfriberg5520]

Fantastic work on scientific history. You should actually write a book on all your insights of the scientific history. You just made me realize that Planck is an even greater scientist than i thought. It is also easier to understand why he came to the conclusion: "Science advances one funeral at the time"

[@JagdishCVyas]

Enlightning story on Boltzmann's constant. Thanks.

[@hansvetter8653]

Great story telling! Thank you!

[@billclinton6040]

I had to take statistical thermodynamics as an undergrad. It was one of the last courses I took long after I had studied thermodynamics from a non-statistical or classical point of view. The professor was really good and made what could've been a horribly confusing topic somewhat comprehensible. I always marveled at that class because despite its name, the class devoted a big chunk discussing quantum mechanics (we basically derived Schrodinger's Equation from statistical thermodynamics). So, in a bizarre twist, even though I was not a physics major, I have had at least an intro to quantum mechanics. And for what it is worth, that class was much easier than my class on electromagnetism. Anyway, perhaps it was explained (I don't recall though), but now I understand the link between statistical thermodynamics and quantum mechanics and Planck's role. Max Planck's name was mentioned all throughout that course, and I grew to marvel just how brilliant that man must have been. I still have my notes and textbook from that class (even though it has been decades) because many of the derivations we did were quite literally works of art. I too have struggled to understand entropy. I know this comment is way late, but I think a follow up to this video that includes Claude Shannon's thoughts on entropy is definitely in order.

[@stauffap]

I can't believe i've never seen your channel! I have loved videos about the history of scientific discoveries for years! This video especially was very interesting :)

[@h2energynow]

Awesome loved all the illustrations.

[@brucejackson4219]

Well presented amiga.

[@meegangalante5224]

Hello! Do you have any information on where I can find those german 50 pages of equations?

[@valipearuna6372]

I can clearly see the passion you have for physics... Keep up the good work Do some episodes on classical mechanics

[@minioasislibrary5222]

Kathy, thanks for your interesting video ! this is awesome ! you explained the history that always skip in the class...

[@NG-we8uu]

Very good presentation thanks

[@itsevilbert]

I always thought that Television was invented by the Scottish engineer John Logie Baird, but Farnsworth did make it practical by being all electric instead of being a mostly mechanical device. Anyhow I vote for Laura Bassi, just because I've never heard their name before. Great video as always, thank you.

[@Kathy_Loves_Physics]

Count Dracula you are right. Technically Baird invented the first television and Farnsworth invented the fist all electric television and I should have said it that way (but the “television” invented by Baird is a far cry from what we think of as televisions whereas Farnsworth’s vision was pretty far reaching and advanced).

[@tomasb7645]

WOW, EXTREMELY well done. Abstract info enmeshed in practical context makes learning easy and fun; you obviously do this well Kathy!!! THANK YOU for sharing your talent and this great stuff.

[@jonathanjackson7047]

Great videos. As a grad student, we would take courses in Statistical Mechanics and Thermodynamics without any of the historical background. It's very interesting to see the evolution of these ideas and how people were thinking about things. As an idea for a future video, I'd love to know how Newtonian mechanics progressed into Lagrangian and Hamiltonian mechanics. We use the later extensively, but I'm not at all sure of how they were formulated. They seem to pop up out of nowhere in Mechanics courses like magic.

[@shambulardo]

I don't mind your arms moving all over. At first it bothered me I must confess. Now I couldn't care less. The content and its delivery (pace, style, graphhics, etc) are absolutely captivating. Seriously, I don't mind. It's a part of the package that's totally fine with me.

[@Stafford674]

I have only just discovered your channel. It is awesome.

[@225rip]

You put so much energy into your videos.

[@Richardj410]

I just found your channel. Thank Thank You. Oh my this is wonderful. Alas how could anyone give these a thumbs down.

[@ulotrichous]

This was a terrific video! Thank you Kathy! I vote for Bassi too.

[@Kathy_Loves_Physics]

Glad you liked it. Now I don't know what I would prefer to win as I want to make all 4 videos next. Hrmm.

[@Kathy_Loves_Physics]

I decided to start with the life of Planck as that got the most votes AND I am going to Bologna in June to study more about Laura Bassi's life so I will probably make the video about her in July. I wrote more about it (and her) on Patreon: www.patreon.com/posts/my-next-video-is-33502544 (you don't have to be a Patron to read the page)

[@orialtman6176]

I want to hear you tell all of these stories! But if I have to choose, let's hear Bohr's Model. Your explanations of the history really gives my chemistry class the context it's missing to understand it.

[@Kathy_Loves_Physics]

I will get to all of them eventually - promise.

[@codemant5224]

I love your videos soooo much! Great information and charming enthusiasm!!

[@Kathy_Loves_Physics]

Codeman T thanks.

[@climbeverest]

Madam you are incredible!! I am loving all your videos, please before history of physics melts away, continue what you do please

[@Kathy_Loves_Physics]

Thank you so much I’m not worried about the history melting away as much as me melting but thanks for the nice comment

[@climbeverest]

@@Kathy_Loves_Physics please I am loving Dirac and the start of positron, if you find more, please, also debroglie, planck, anyone who lived on the cusp 19-20th century, after 50s I think physics became so complicated, thanks!

[@mahaswetabhattacharya5823]

Neils Bohr Model would be good.

[@Kathy_Loves_Physics]

I was just amazed at how many people waxed poetic about Bohr and his model. I definitely will do this video - maybe not right away but definitely.

[@Kathy_Loves_Physics]

OK this will be the video after Planck's life, so pretty soon

[@pedzsan]

A KZbin video titled "What is the Ultraviolet Catastrophe?" also talks about Plank and the problem first encountered with black body radiation and the concept that energy must be quantized.

[@Pedritox0953]

Wonderful video Kathy!

[@swangleewatanakarn7701]

Love your video. Thank you for post it here.

[@wellesmorgado4797]

Thanks for communicating this point the public! These 2 articles by Swendsen (doi: 10.1119/1.2174962 & 10.3390/entropy-e10010015), I believe at least the second one is open, might be of interest by showing how Boltzmann true entropy definition helps to get rid of Gibbs' paradox.

[@TenzinLundrup]

Thanks for this video. I shall now call k, Planck's first constant (usually attributed to Boltzmann). Planck not only introduced it but determined its value.

[@ihbarddx]

Wonderful presentation. You asked for suggestions for future topics. I would like to suggest Newton's Second Law. In another video, you mentioned (in passing) that it wasn't originally F=m*a. Physics teachers become combative whenever I mention this. No one else on KZbin (that I can find) has addressed the issue. Perhaps you would be good enough? In any event, thank you for your good work!

[@johndii2194]

If you split water with electrolysis into Hydrogen and Oxegen then recombine the two back to water do you get the same water?

[@dougr.2398]

Log ( a • b ) = ( log a ) + ( log b ). The logarithm function maps multiplication onto addition (for the positive real numbers).

[@meibing4912]

Super interesting. Had no idea: Boltzmann constant = Planck's constant = Bohr's constant. (turns out first naming these things is very important, have a friend who is very close to solving the the Collatz conjecture or 3x + 1 problem - already told him to make sure that the solution (if/when cracked) will be called xxx's equation).

[@MattMcIrvin]

I always wondered how Boltzmann managed to work that out without quantum mechanics, which is the only way you even have a hope of thinking about discrete microstates. That it was really thought up by Max Planck when he was on the verge of introducing quanta makes a lot of sense.

[@petercalkins3011]

Kathy; Thank - You, Thank - You, Thanks - You. Your videos are on par with Bronowski's "Ascent of Man" and CalTech's "The Mechanical Universe". Please relate your basis of thermodynamic articles to Einstein's work on Brownian Motion. On another related topic, please bring to life the zeitgeist of the debate between the proponents and opponents surrounding the existence of molecules. The debate that is not appreciated today.

[@ai6mk897]

This is by far the best explanation of entropy but I think it is very unfortunate that "disorder" is used, even Planck used it. Personally I think it's lead to most of the confusion about entropy. I'm also a bit puzzled how the "log" instead of "ln" was carved on his gravestone. Anyone know ?

[@zetacrucis681]

Physicists use log to denote the natural logarithm (base e) and log₁₀ to denote logarithm base 10, while mathematicians use ln and log, respectively. Logic being that the natural logarithm should be the default logarithm or log for short.

[@ai6mk897]

@@zetacrucis681 Thanks for your reply. I'm an electrical engineer, so I've been exposed to both Physics and Mathematics, but I've never noticed that before. As I understand, it was added to the gravestone after his death, so I thought it was just a typo. Could have even saved the cost of the extra letter, a la Curb your enthusiasm. If what you say is true, perhaps it's time for Physicists to bite the bullet and adopt what I considered to be the "standard" notation; log=base 10 and ln=base e, as is assumed on my venerable HP-41C. Of course other bases can be used, but they must be written explicitly as logxx

[@zetacrucis681]

@@ai6mk897 There is no real consistency even within disciplines. Some mathematicians will also use log for the natural log and some physics texts (especially for high school and early undergraduates) will use ln. And in information theory the default log is sometimes base 2. Depends on the author. These inconsistencies rarely cause confusion because it's usually clear from context which log base is being used (and often it's not even relevant to what's being discussed).

[@ai6mk897]

@@zetacrucis681 Zeta, thanks for your reply, again. I also forgot to mention that we also used loge to denote base e. BTW, great first name. I well remember ZETA was the UK's entry into the Nuclear Fusion scam in the 1950's.

[@exxzxxe]

Agree with J. Ripper (below); you are a gem Kathy!

[@Kathy_Loves_Physics]

Aww thanks

[@burtonsankeralli5445]

I first heard of Boltzmann from the work of Bronovski ... The Ascent of Man... There he credited Boltzmann with playing a key role in getting the very existence of atoms accepted failing this physics may have been set back 100 years.

[@jbflores01]

Fascinating!... as always! Finally found the source of why Quantum Mechanics was created!

[@speckofdust272]

Really great delivery that I greatly enjoyed ... more please 👍🙏👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻

[@Kathy_Loves_Physics]

You got it!

[@polyrhythmia]

So it was Thirring who was guilty of "name dragging". Interestingly, "Einstein's Constant" doesn't seem to have caught on. I'm wondering about the Stephan-Boltzmann constant. Looks like Planck was the first to tame infinities. These stories are really interesting as I had never thought of entropy as being related black body radiation.

[@Sandcat87]

Been on KZbin since 2007 and never bothered to subscribe to anyone but holy smokes, that was awesome! Do them all, I'll watch them all. Fantastic explanation of a side I'd never known before (read Louisa Gilder's Age of Entanglement, which picks up more or less where you leave off here). Fantastic! Thanks

[@Kathy_Loves_Physics]

Wow what a lovely compliment (and I guess I need to check out the Age of Enlightenment book)

[@daleronsin4756]

Do you know of any contributions in Magnetics by a Dr. Fuller? First EE phd from Stanford, cohort of Lawrence

[@camilorivera4685]

Thanks Kathy. Greetings from Colombia.

[@Kathy_Loves_Physics]

Camilo Rivera you are welcome. Cheers from San Francisco

[@christianduval8374]

Can we have a video about deriving PV=nRT starting from a probabilistic standpoint?

[@rienzitrento8397]

Do all of them . Really interesting thanks

[@sarahspocksocks]

I want all of what you suggested as the new video, but I want to hear about Niels Bohr's musical approach extra much!

[@Kathy_Loves_Physics]

The life of Planck won the contest but Bohr's model will be next, promise.

[@TheMrgoodmanners]

this channel is just awesome!

[@Kathy_Loves_Physics]

Thanks