This is a superb, highly detailed account of a topic that is usually glossed over. There are far too many videos on youtube that 'pretend' to explain a topic, but ultimately leave you feeling empty because they have explained nothing. This is the first time that I have seen (and understood) a detailed derivation of the ultraviolet catastrophe and Max Planck's route to a solution. Genius. Thank you for taking the time to make this video.
that's the difference between explaining what the topic is about and explaining the topic in depth, a video with the same title could've just been 10 minutes explaining that it's something about infinite amount of uv, which wouldn't fit in the current model, and a simplified explanation without all the maths involved (i.e. put the math in a magic black box). imo both are valid explanations, as most people in the audience don't need the maths, and if they do they now know what to search.
@@nono-bn3sm that's a valid point, but we would still like to try 😂 I'm not a math person...but I still wach this stuff....a good 35% of it honestly makes sense to me lol
It’s unbelievable that most text books skip over the detailed math behind the ultraviolet catastrophe. For gods sake this is the origin of quantum mechanics. This is similar to Newton’s observation that apple falls, or Einstein’s derivation of consequences caused by the constant speed of light. You can’t just say speed of light is constant, then something is wrong, therefore time slows down when speed is up. The details are extremely important. Because this detail is skipped, I had the feeling that quantum mechanics is dropped out of nowhere for a long time.
@@deangel9128 It's ironic how you automatically call everyone who doesn't believe in _your_ god, atheists. For the record, I'm an agnostic, and NO, it's not the same thing.
As someone who studied physics, this is by far the most thorough and yet simply explained video on this topic. It was always glossed over in both my modern physics and quantum courses, thus its significance glossed over. Thank you for this!
I have never heard anyone as good. It is like I am back at my final year of high school when I have a lightbulb moment where I realise I can convert most equations by substitution and a few other tricks like sums and difference and sine^2 + cos^2 = 1.
I am bowled over by the depth and clarity of the presentation. When I was studying engineering at the Indian Institute of Technology, the instructor spent a half hour on this topic, skipped the Raleigh -Jeans derivation entirely, and went straight to Planck's formulation. I was dissatisfied at that time with the transition but, after decades, have finally found a satisfying exposition. Thanks so much. I am certainly going to subscribe.
This is the third time I very carefully went over this presentation. My compliments and immense gratitude to the author, especially for rigorous derivation and historical content - simply amazing !!!!
Many here will probably know that when Planck was deciding whether to seek a PhD in Physics, one of his advisors told him not to do it because, after Maxwell and Boltzmann, everything that could be discovered in Physics already had been. Around the same time, the great telescope builder George Ellery Hale was told that his desire to build bigger and bigger telescopes only resulted in counting more and more stars and we already knew that space was filled with them. So, bigger telescopes were a waste of money.
@@lkytmryan Except that Hale's big telescopes had the resolution to allow the measurements of the distance to galaxies outside our own. That ended up proving that the universe was made up of galaxies and that the same galaxies were moving at a rate proportionate to their distance, which showed that the universe was expanding. Can't do that with small, low resolution telescopes.
@@jmchez Not to be argumentative but what difference does it really make? The stars are so far away and completely out of reach. Other than as a source of wonder and amazement, nothing about stars will ever have the slightest practical affect on any of our lives. I'm not saying that I don't understand why people would want to investigate the stars, I just really don't see how it matters to anyone beyond astronomers in any practical sense.
@@lkytmryan because usage of the correct theoretical apparatus enabled us to create an atomic bomb, for example? I'm not saying that with the help of astronomy we can also create some kind of WMD, rather that such discussions about practical applications of fundamental research are irrelevant. Knowing how world works will naturally produce practical applications, even the most unexpected ones
@@lkytmryan We can see how the other galaxies are moving, and this movement has let physicists and cosmologists deduce a lot of things. For example, the accelerating expansion of the universe revealed, after some calculation, that there must be large amounts of some form of energy in the universe that we can't see directly. They call it "dark energy" because so far, it's invisible to us. But its effects on the universe can be seen using a powerful telescope. Or radio telescopes that let us investigate the cosmic background radiation, revealing a lot about stuff that happened after the big bang. What will these discoveries lead to in practice? I don't know yet, because they're still pretty recent. Remember that quantum mechanics (about to turn 100 years old soon!) was once mostly of interest just to theoretical physicists, until it led to the invention of semiconductors which are now the fundamental building block of all our electronics. Or Einsteins's special and general theories of relativity, which much later made the invention of GPS possible, for example. Maybe 100 years from now there will be some ubiquitous technology which was only possible to invent because of dark energy, I don't know.
My mind blew up and then reformulated itself... you are never to old to confront your long forgoten nightmares and finally see a glimer of light that says all is not lost. I will now go back to the begining, a time I left behind 40 odd or more years ago and perhaps enjoy a stress free journey where not completely understanding is OK but enjoying the trip non the less. Thank you.
when you watch this kind of scientific explanation, by someone who thoroughly understands their subject, it shows you how little you, as an average person, actually understand, but it was enjoyable
Absolutely fantastic video, this was the only one I could find that actually explained why the UV catastrophe occurred and how planck's constant solved it. And you derived everything using maths and physics I (mostly) knew, where my physics teacher refused to even go near this topic. Many thanks!
I thought TH-cam was going to give me some historical background noise that I could relax to and learn about. What I got instead was mini PTSD back to my days of getting a B.S. in Math, where I had feelings of "Oh, I think I get it." and "Wait, could you back up and explain that whole thing again?" and also "Wait, how did you get that equation?". It's like hanging onto a pole for dear life while a tornado barely misses you on it's path of destruction, your house is gone and you got a broken leg or two, but you're still alive. Alternatively, it's like getting shitfaced at a club and being sober enough to get home, but there's puke in your pockets and you'll never fully remember what questionable things happened that night. All this writing and similes aside, I enjoyed watching this video despite the migraine, hunger, and the feelings of loss and confusion that ensued afterward. Good shit, buddy.
😂😂😂😂😂😂😂😂😂😂😂 You are legend man. I sympathize with you. Still appreciate you going through this trauma. I am myself a graduate in physics. So I understand what you are saying :)
I took Calculus 30 years ago. The best part of this video was actually seeing Calculus used. I've been a software engineer since and I have never used Calculus before! Seriously, great video. You break things down well and you have an easy to listen to voice. I especially enjoy your pronunciation of "but."
Yeah I studied 30 years ago which involves lots of Calculus, but my career was also digital. I did an introductory computer course when I was 12, so 1979, and had one of the few 'light bulb' type moments in my life - I knew, in a flash really, that anything that was information, which in our modern world is lots of stuff, would be digitised. I was at the approx beginning of a revolution probably more profound than the industrial revolution.
I've studied this stuff, but I finally feel I understand it after this video. I've long been confused by mixing up quantisation of energy levels in atoms with Planck's idea. I understood how the Schrodinger equation gave rise to discrete energy levels for bound electrons, and that the difference in energy levels gave rise to the discrete frequencies associated with spectral absorption and emission lines. Having encountered these concepts before Planck's black body function, I'd always assumed that the solution to the ultraviolet catastrophe was something to do with quantisation of frequencies. But there's still an infinite number of frequencies or vibrational modes, even though the frequencies are limited to stationary wave values. I've finally realised that Planck's solution was to quantise the amount of energy in _each mode_ ! With classical waves of a given frequency the amplitude is continuously variable, so the energy is too. I finally get that the energy _within any mode_ for EM waves is _not_ like that. It's split across a discrete number of quanta. Then the energy conservation principle dictates how the energy is statistically distributed across the modes, just like with the Boltzmann distribution for gases in statistical mechanics. Essentially the discrete number of quanta plays the same role as the discrete number of molecules in a gas. (Which probably explains why I've heard the term "photon gas"). Eureka! In turn, I've realised Einstein didn't _discover_ quantisation with his analysis of the photoelectric effect, it was already there in Planck's work. Einstein simply intuited that energy was transferred to electrons in the same discrete quanta.
I had a prof who studies history of physics. He told us that Planck called quantization a final act of desperation. His quanta aren't real quanta bc he used them as a binning mechanism, each quanta containing a continuum of frequencies that happen to be grouped together. What Einstein did was abandon the continuum aspect and say that the quanta of their math is indeed a true reflection of reality, that quantization isnt just some mathematical trick but a real feature of the smallest scales of reality.
@@johnr797 makes you wonder what the next big problem will be after someone cracks the theory of everything... I mean, realistically we won't need theoretical physics anymore, it'd be a race for applied science!
This was fascinating and an extraordinarily well-done presentation, marred only by some need to pause a few times to allow my dense brain to catch up, to make sure that I truly understood. Haven't been hit by that feeling (the "slow down, you move too fast" feeling) in a while. Thank you.
And it was a 40 minute video! I had to do the same thing, honestly. It just goes to show that a lecture's worth of math is barely enough time to discuss these complicated phenomena in any detail, even when you already know the foundations in calculus.
@@robertwatson818 that's straight up wrong. Essentially every breakthrough has been based on research from other individuals, even many (most) of Einstein's discoveries were analysis of other scientist's data and conclusions.
I wanted to say thank you from a true layman. I do not even have a High School Diploma but the way you explained the problem and the solution step by step was fascinating to me. The math was way above me but the way you presented it made it very interesting to follow. Excellent work. I can only hope you are some kind of teacher to the future generations.
I'm a college graduate with a science degree and the math was over my head as well. Don't worry, there was a lot of representation of different branches of mathematics in there. I surely got more out of the math than you did, but this video is wonderful in that it doesn't matter much to the overall understanding of the bigger picture. This really was a great vid.
As a mere biologist, much of this flew over my head, but I can still recognize a superb science video when I see one. I would love to make videos like you someday, but for my field
I learned this topics in a physics seminar a few years ago and roughly have an idea of what's going on in this video. My limited mathematics capabilities at the time did not permit me to understand it in full detail. Thanks for the wonderful presentation, allowing me to revisit this topic with greater depth and getting a more comprehensive understanding!
I know this is a joke but to be fair, Newtonian physicists probably were like that as well. They understood everything _up to_ the end of the 19th century.
@@kondrahtiz7370 Nono I meant they understood every part of physics that was discovered until the late 19th century, then they had their minds blown with general relativity
the thing about the box n the cat and superPosition is exactly the act of not understanding unless making the measurement ...quantum physics as I get it is an exercise of explaining how exactly things aren’t understood(??!?!!) *unless measured which inturn affected the outcome anyway
I know just enough maths to barely understand what its saying but nothing about Physics that this is still black magic to me. It's just enough familiarity that this video is the best thing I know to fall asleep to.
You put a lot of work into this video.Probably more than 99% of other youtube videos out there.This is really professional and well thought out you are certainly getting a like from me.
16:36 Oh wow, it is at this exact moment that Quantum Mechanics was born. As a Chemist I don't know much about the mathematical details of QM but this is the basic principle behind Quantum Chemistry that you will find again and again, especially in Spectroscopy, Electron Orbitals, Bond Oscillations etc.
Wow, I never knew this was how the theory of energy quantization came into being. So well explained, thanks. It's going to take me a couple more watches to digest the math - but this is the first time the math I've learned has made it possible for mde to understand something I really wanted to understand.
You’ve explained the concepts in this video in a much simpler way than my high school physics teacher did. You break everything down into bite sized pieces, making it a lot easier to understand. I loved physics as a teenager but never got into it because it was never explained to me in a way that made sense to my brain.
This is really neat. I... honestly understand almost nothing of this, but it's very interesting and what parts I did get were amazing. Thank you for your hard work and a terrific video :)
I recommend you to come back some time after and see it again. I have definitely learned more stuff along the way and in the second watchthrough I was then constantly trying to remember or predict the next steps! I definitely felt I learned so much
33:05 Am I the only one hearing the reference: "All that is gold does not glitter, Not all those who wander are lost; The old that is strong does not wither, Deep roots are not reached by the frost. From the ashes a fire shall be woken, A light from the shadows shall spring; Renewed shall be blade that was broken, The crownless again shall be king." LotR, JRR Tolkien
Just going into my 2nd year of A level and this video really helped answer some questions I had about how some of the equations I've learned came to be. Thank you for this amazing video!
The best video on this topic. I have been searching for the right explaination to me for couple of days but i was not satisfied. Finally this video took me to the satisfactory zone. Thanks! Love from Bangladesh 🇧🇩
This is an excellent video, and goes very in-depth in mind-bending ways for which I'm grateful. For everyone who, like me, didn't realize that this video contained only a very thin (in some ways) and rather convoluted (in other ways) introductory synopsis to set the stage for the rest of the video: The Ultraviolet Catastrophe refers to the realization of the "catastrophic" difference between the mathematical prediction (made via the Raleigh-Jeans Law) of a blackbody's energy output based on its light's wavelength vs. the real-world observations. The real-world observations revealed that at shorter wavelengths (going towards ultraviolet), a blackbody's emitted energy was *far* below what the Law predicted. An uppity physicist named Max Planck (who wasn't even a Lord or a Sir or *anything*) made his own mathematical predictions and theoretical models based strictly on the observed data, and in so doing realized that energy is quantized, meaning split into discrete sections (rather than just being a smooth transition up the energy scale). Think of it like this: physicists thought the Universe's energy ran on analog signals like a record player, and Max Planck revealed that energy is delivered similar to digital music, in discrete bits and levels. This realization upturned every apple cart in the physics world at the time, and was considered a "catastrophe" for anyone who thought we were even remotely close to figuring out how the Universe works. Further explanations just to help anyone who might get lost in the wonderful details in this video: a "blackbody" is a useful physics model in the same vein as an "infinite flat plane with zero friction" from high school physics. It is an object that only emits light due to its temperature, regardless of any other property (like charge, radiation from particle decay, phosphorescence, etc.). Make a blackbody hot, it will start to emit light. Blackbody radiation is the reason why hot metal glows. In other words, the concept of a blackbody was the first realization among physicists that, for any object that is so hot it emits light (from an incandescent lightbulb all the way up to stars), there are fundamental and invariable correlations between energy output, brightness, and color wavelength. Scientists noticed that, as a blackbody got hotter, it would both get brighter and its emitted light would increase in frequency (meaning it would have a smaller wavelength). Two scientists named Lord Raleigh and Sir James Jeans, using the best mathematics and theoretical thinking of their day, made a mathematical prediction of how the emitted wavelength of a blackbody can tell us about its energy output. This sort of prediction, if accurate, would be very useful for figuring out the temperature (and through that, many other properties) of objects we can't yet get close to, like stars out in space, our own sun, or even our neighboring planets. Their mathematical prediction was at first very useful, and became called the Raleigh-Jeans Law. Unfortunately for those two (but fortunately for everyone else), as scientists began testing this mathematical concept against real-world observations, they realized that the Raleigh-Jeans Law worked great for "long" wavelengths (< 10^5 GHz) in the infrared spectrum, but as the wavelength got shorter into the range of visible and then ultraviolet light, the amount of energy output observed was *far* less than the Law predicted. Enter a young upstart physicist named Max Planck. Out of frustration, he made the try-hard move of just brute-forcing an equation and set of theoretical models out of the observed data. In so doing, he created the mathematical and theoretical concepts that led to the discovery of quantum mechanics, and, as I believe is stated somewhere in this video, physics students have been cursing Planck's ingenuity ever since. This video goes into superb mathematical and theoretical detail as to how Planck ended up rustling the jimmies of pretty much all his contemporaries. Thanks for reading! If I'm wrong in any particulars, please let me know and I will happily correct them. I'm no scientist, only an enthusiastic amateur learner. Hope this helps some folks!
I just want to thank you, and many others, including those who made this video, for giving me back my passion in science again. When I was at school, I was top of my year all the time in science and stuff. So when I was ready to go into my senior years, I did Physics/Chemistry/and 3 Unit Maths (advanced Maths, I guess)... HOWEVER. My heart was broken when I discovered that I was Mathematically/Numerically Dislexic. That is to say, Formulas, quadratic equations and all that stuff just looked like gobblygook. More importantly, I just couln't understand wht was going on regarding the written work. This crushed me, I was going to fail maths... And the further I got into Physics, I knew this mathermatic dyslexia would hamper my learning there, too... As for Chemistry, well, that was a bit different. The Irony being that it was the elements that were the numerals, and somehow this made the formulas more "tangible", and not an "abstract" thought, so to speak. I never finished high school. But my passion for chemistry always went with me, probably because I had a great teacher who, even though I was failing and skipping school, always welcomed me in the class, as I always paid attention. I failed the tests, but I think he understood that there was something going on with me that was hampering my thirst for knowledge. Because I never played up when I went to class. And he never made me feel like a fool. Anyhow the last 5 years I have been getting back into all these scientific fields again. Not for a career, or for academics. Just as that that young boy who whose wide eyed curiosity saw him read science encyclopedias on the weekend, when his friends were all playing games, or sports, or chasing girls. It's these vides that are great. I am not going to say I understand it all. But now, at least, I can comprehend it all more better. Visualize some of it. And it's thanks to people like you in the comments, and the makers of these channels and videos. And a good teacher, one who shows empathy, or compassion, can lay the seeds to a persons quest for knowledge. As an adult, I got into rave culture, stoner culture ect. My nickname with my friends was Dr. Gonzo. Because I could explain to them why taking an MDMA pill is a dangerous idea of you are on SSRI's. I wasn't just a know it all, I was someone who could be counted on to say "you know what, I dunno. I'll find out. But I wouldn't do it", when it came to the psycho-pharmacoligical playground. Anyhow, As a 44 year olf, I have bpu chemistry to the side. The only Acid Base Extractions I do now are German HardTrance DJ sets.Thanks to the Net, I now am learning all ther is to know about Physics, Classical and Quantum. I feel like that 14 year old boy again. Sorry for rambling, but I just had to let you know that these deeds are really apreeciated by some. Oh, and I have had a rum or two.... So excuse the grammatical errors, in which I am sure there are a few
@@RogueBoyScout: Compliments upon realizing that Your personal intellectual and emotional defects have been maintainable through the application of chemical and alcoholic molecules. You have found Your place in existence.
That was a fantastic post, thank you. *Now* I understand what the background is for the video, which makes it a lot more understandable, even if the math involved is way over my head.
Imagine if someone told the flat earth people that the sun is really a hyperdimensional jeans cube with the hole only seemingly appearing to us as a sphere of plasma while in reality being a pinhole in the side of a hot, massive hypercube on another plane of perception. I hope one of them reads this comment now.
I don't think a lot of regular people know that a 4th dimentional circle would look like a floating ball to us Usually flatards like a simple explinations that not only don't need you to know anything, but require you to be uneducated to believe. With complex conspiracies and explanations like that to justify problems with their Flat Earth An example is when trolls explained the sun as a floating spotlight with a magic shape-shifting lampshade and the stars are fairly lights on a dome, but said with diagrams so it seemed legit It's definitely possible just gotta word it so it explains a problem and it'll become a flatard fact. Maybe it'll teach regular people watching debunking videos a thing or 2 about higher dimensions
Your statement is irrelevant to any flat earth concepts.the so called flat earth has been not surprisingly distorted by the scientific community.the description of the sun as you described is simply not specific to the capernicus model of the universe..the so called flat earth theory is more correctly described as fixed realm model of the universe.the earth by this design is a unique realm , the celestial bodies actually exist in the 4th dimension of vibration yet are observed and also influence the 3rd dimensional earth realm...so get your tin foil hats ready as both flat earth and capernicus global concepts are erroneous
@@showtale8325 Not sure if its directed at me but i am gonna assume it is until proven otherwise and going to assume you believe the unique realm conjecture. When people talk about the Flat Earth society they are not talking about thought experiments from the 1500s or space-time being flat... they are talking about people in modern day who belive the Earth is flat, they exist, they're not hard to find...if you cant be bothered to go to the community then check out the channels Logicked or CHL and you'll find dozens. It's an unfortunate reality but it doesn't mean it's a hoax from the scientific community to invalidate your idea. If you believe something no one studying the concepts believes, maybe instead of it being apart of a conspiracy, maybe you're wrong If the Earth was flat in 3 dimensions and we lived in a 4D universe, there would be twice as much space for gravity tp travel theough. Meaning gravity would fall at the cube of distance instead of the square like we observe. Being flat in 3 dimensions doesn't necessarily mean there's a 4th, it just means there's 3 dimensions and they're flat Fairly certain the theories that predicted we had higher dimensions were disproven in 1910. Then replaced w theories we almost had higher dimensions, but the universe didn't meet the requirements for them to form so they collapsed in on themselves (that's why they are called vibrations). Each time those hypothisises get systematically disproven people come up w even smaller and harder to find dimensions... so if you believe in higher dimensions you're like 110 years behind
@@insertyourfeelingshere8106 excuse my ignorance I am not a theoretical physicist, I am simply a medical student interested in astrophysics. But doesn’t the theory of relativity and gravitation already relies on the fact that we are 3 dimensional beings living in a 4 dimension universe? That gravity itself is a curvature in the four dimensions of spacetime? Isn’t that notion accepted till this day? What about string theory that stipulates that we live in a universe of 12 dimensions. I understand that string theory hasn’t been proven but it hasn’t been fully disproven (yet) either. Doesn’t all of this go against your point that believing in hyperdeminsions is archaic in nature?
This is very good. So nice to see a thorough explanation devoting most of the time to the wrong explanation and not be afraid of formulas or mathematics.
Wow this is the best physics video I have seen on yotube! History, rigorous math, comparison with experiments. It was simply amazing! Thanks for putting this out.
Every single time I watch this video, it gives me chill🥶 Max Planck was truly a genius, I don't think he has anything less than Einstein. One of the best video's in TH-cam imo❤️
This is the best video explaining the Ultraviolet Catastrophe in great detail and how the culmination of classical physics represented by the Rayleigh-Jeans model fails and what motivates the need for modern Quantum theory.
I know most of this from having studied physics for a while, but sadly my professor had some type of aversion to quantum mechanis, so even when discussing electro dynamics he carefully circumvented any and all discussion of things related to quantum mechanics. Looking back that was kind of impressive on it's own, but obviously this compartmentalized approach left out most important connections and ultimately made the topic harder to understand. I had other reasons for dropping out, but I made the final call during one of his lectures, when he reiterated again how any quantum related explanations would have to wait another two years and I just realized I couldn't keep it up for that long.
TH-cam obviously think i like catastrophes. But this video piqued my interest, because a catastrophe is just a word. I wanted to see what is behind it and you nailed the explanation. Thank you!
Same here. YT recommended it because I binge watch aircraft catastrophes.😂 But although it is impossible (for me) to follow every equation in this video in realtime, I enjoyed the greater picture: That Max Planck laid the foundation to Nils Bohr‘s atom model etc., and now I know more about how the Planck constant was derived.
I agree, I also loved the synthesis of the problem and the derivation of the equation. Even though their concept of continuous energy was wrong but their grasp on mathematical physics was remarkable and unchallenged.
I wonder how they validated this. They proved that jeans box is a black body. Then they made some theory on Jeans cube which included things valid only for the cube (integer number of waves between walls) and got an impossible prediction. But why they projected prediction on all black bodies? Ok there is a Jean's box radiation problem, I admit. But why telling it is general black body problem?
@@0masuk0 In short, because experimentally all blackbodies show the same results. The real beauty in physics is that we take complex things, simplify them, calculate those simplified "models" and get the theoretical solution. Then we try to use that solution to different things, from simple ones to more complex ones and compare them with experiments. If the experiments match - great, it seems that our model is good. If the experiments show a discrepancy with theory... well, let's try to change theory. The point that Planck's blackbody radiation theory matches the Sun is a neat example. Of course, it doesn't match it completely... the Sun's radiation curve has dips at some wavelengths... so we expanded the theory to explain the absorption of gases... Also, lightbulbs have the same curve... incandescent ones even without dips in it...
I think this video is the first I've watched that really puts Planck's work into perspective, humanity would of been in a really tough spot if he hadn't introduced all these fundamentals that solved the massive problems classical physics was being presented with.
This topic is notoriously hard to explain without the mathematical derivations. I don't think there is a better explanation out there then this. Thank you so much for this contribution.
I've been searching for a logical explanation of blackbody radiation-derived quantum concept. I found it nowhere else other than this video. What an effort. Thank you
Admittedly, I was expecting a discussion of the ultraviolet divergence of quantum field theory (amateur physics student, math nerd by training); but this is a nice introduction to the birth of quantum mechanics.
Ultraviolet catastrophe is a name stuck to this situation in the history of physics, when theory predicted infinite thermal radiation of bodies and it made no sense and people were scratching heads. People then thought they are inch close to completing the physics as science. They thought they just needed to solve two paradoxes: ultraviolet catastrophe and Maxwell equations being not invariant for switching to other (moving) system, including stupid prediction of light speed being constant in all inertial systems. Then boom: quantum physics and relativity are the answers.
@@0masuk0 : The phrase "ultraviolet catastrophe" is also sometimes used to describe the appearance of infinities in quantum field theory as zero is approached, which is what I was referencing in my comment. I was talking about a mild ambiguity of the terminology.
What a great explanation at the start. I wonder why none of my physics or chemistry teachers at high school couldn’t have explained the origin of Plancks work instead of just dropping the constant on us out of thin air in quantum theory. Neither did text books do it well back then. I think it was dur to the fact that even for teachers they felt uncomfortable with the ideas and really didnt understand them enough to explain them with confidence as they did the much older laws of people like Boyle firmly grounded in tbe classical idea of the atom consisting of particles behaving in a newtonian way. Thanks again
Although this explanation is clearly at a deeper and more fundamental level, there was no need to ‘drop Planck’s constant’ out of thin air when doing high school physics. A relatively simple experiment to find the turn on voltage for different colours of LED’s will produce results which allows students to produce a straight line through the origin graph which reveals that the energy of a photon is directly proportional to the frequency of its light. The constant of proportionally in this case is the value of the gradient of the straight line which has the value of Planck’s constant. Thus E =hf and hey presto Planck’s constant is introduced but in a context which students can grasp.
@@arnesaknussemm2427 I fear when I did physics and chemistry in the 60s leds weren’t around and the curriculum never included determining plancks constant
@@lyntoncox7880 lol fair point. They are incredibly useful nowadays for introducing this constant in a tangible and relatively straight forward way. That’s progress :)
An ideal strategy to explain, it looks as you tell a story (All the details in a precise way, step by step chronologically, including all the concepts and ideas and all the mathematical proofs and demonstrations).
I still find it quite mysterious how the frequency /wavelength in these cases concern only integer values in the denominator, its a deep link between math and physics
The video covered this, but it's easy to miss. The short answer is that only standing or _stationary_ waves are allowed inside Planck's box. These are ones with wavelengths that divide evenly into twice the width of the box. That's where the integer values come from. It's the same reason that only standing waves are allowed on a guitar string -- because the string is pinned at both ends, so the wave displacement has to be zero there. In the case of the Planck cavity, a similar boundary condition is the result of Maxwell's equations. The electric component of an EM wave is an oscillation in the electric field. A non-zero field at the wall boundary would produce a force on the electrons there that would be dissipated by conduction along the wall. So such waves would be rapidly damped. Only waves with a zero of the electric field at the wall boundary will be propagated. This effectively pins the ends of the wave, resulting in only stationary waves. It's a little more complicated since the waves obviously don't only bounce in one dimension like a guitar string, but by considering that component of the EM field normal to the wall, along with the geometry of the setup, it works out to the same thing.
@@ps200306 the stationary wave explanation falls down if the object is not a cube. it probably was and is the classical 'explanation' of the time, but subsequent discoveries perhaps lead closer to the truth - that the discrete wavelengths are a result of discrete electron orbitals.
@@edwardlewis1963 , the resonant cavity description can be extended to cavities of any shape using Kirchoff's law of thermal radiation, and a thought experiment where a cuboid cavity is coupled to one of arbitrary shape. Note that the stationary wave description in Planck's formulation is only used to establish the density of states (or modes) as increasing with the square of frequency. The same result can be derived from the Schrodinger equation with suitable boundary conditions. It works out the same as the resonant cavity description and has nothing to do with discrete electron orbitals _per se._ (Consider that plasmas are good examples of black bodies, and their electrons are unbound). In fact the resolution of the ultraviolet catastrophe has nothing to do with the discretisation of allowed wavelengths, but with the quantisation of the allowed energy at any given wavelength. That's the crucial step that allows the quanta to be treated exactly like molecules in the Maxwell-Boltzmann distribution.
@@ps200306 Stationary waves are, by construction, insulated from the walls. So it seems like those are precisely the ones that would be absent inside of the box. For there to be a thermal equilibrium, there's no problem with waves getting absorbed and emitted continuously. In fact, it's necessary that it happens to some degree. (The density of states would still work out the same).
What an interesting problem nicely exposed. Well done, you got my instant sub. Planck must have been thrilled to realise the enormous implications of his discovery despite of the many years of failure, which makes it even more compelling. I'm quite positive that we are yet to discover many implications of his theory. Videos like this definitelly deserve more attention as they elegantly manage to achieve what school failed: Genuine interest for domains once though too hard or too useless to understand. Someone told me once "Learn math now, you won't have time or interest for it later." - boy was that person wrong.
The Stephan Boltzmann law is strangely the most counter intuitive. Temperature being a measure of kinetic energy one would never at first intuit that intensity would grow as the 4th power of T.
I cannot emphasize enough how effective the teaching style of this video is where it combines all the necessary topics in a storytelling manner while keeping an endgoal in mind. All the physics classes i’ve taken would teach topics like blackbody radiation, wien’s displacement law, wave function, etc. etc. until we just felt like we were jumping from one topic to another without ever drawing a connection/motivation through them all. I feel exhilarated now knowing that all these ideas were individual puzzle pieces that eventually fell in right places, but at the same time I feel so so frustrated that the university lecturers failed to help us understand the big picture.
This is suspiciously similar to a lecture I had while doing my physics degree. I'll share a tip from my quantum mechanics lecturer, "anytime I see the words 'obviously' or 'clearly' in a description I start to worry". Me too boss Thanks for the refresher course, well spoken, well done, but no more obviouslies or clearlies please ;-)
@@vyor8837 Not if it's part of a training exercise for firefighters. It's obvious this is desirable and clearly no problem. Sometimes the building NOT being on fire is a problem, humans have been working on this for millennia lol
One of my physics professors told a story (quite possibly apocryphal) about one of his physics professors giving a quantum mechanics lecture and stating that "It is trivial to show that (some complicated function) can be reduced to (some simpler function)" then continuing for bit, pausing, and then staring at the blackboard. The professor then left the lecture hall, leaving the students milling around in confusion. 40 minutes later he returned to the hall sweating slight and with mussed hair, and announced. "I was right. It is trivial!"
I love this channel does not shy away to get into the nitty gritty. I hope that someone does similar videos about molecular biology. I think this could ease the fears and highlight the risks about vacciantion. So much in our comlicated world is decided based on how it feels to one's gut
👏👏👏👏👏👏 SUPERB👏👏👏👏👏 Excellent description of what can be considered the birth of quantum mechanics. I have seen the deduction of Planks formula in many books and classrooms, but this one overrides them all. I can not imagine a clearer and better explanation. Thank you very much!
35:57 "we find the following rather ghastly expression" Your sensitivity to the moment the student's mind collapses in despair genuinely helps this all go down a lot more easily!
The story why steel wasn’t invincible when heated up! Such a question laid the bridge to quantum mechanics! Planck and later Einstein and the revolution were kicked in( the short story)
I loved this video when I first watched it, and I'm definitely going to watch this reupload as well in the next few days (a quick refresher is never a bad thing), but for now I'm just gonna leave a thumbs up :) Really love your way of explaining things!
38:05. "When Planck plotted his energy density function..." ...it just occurred to me that he couldn't just open his MacBook Air and type "ipython" and "plot(f, h*f.....)..."... I mean how long did it take to plot back in the day? 5-th powers, exponentials.... how did he know what h was without scipy.constants.h ?
Certainly longer than just calling plot(), but probably not as long as you would think. As they say, practice makes perfect and in the days before calculators (never mind computers), people who did this kind of work had a _lot_ of practice doing those kind of calculations.
We were still plotting by hand in my calculus course... wasn't all that long ago, under 15 years ago. And we did learn how to calculate the exponentials and logs and all that, though my memory fails to recall it without a refresher.
Time to watch a 40 minute video on a subject I have ZERO advanced or even passable knowledge in just because T sounds interesting and the narrator’s voice sounds really really nice and well spoke.
The solution of that catastrophe was truly marvelous. I like how you named the expansion of the universe as the vacuum catastrophe. It made me think that maybe it also will be solved.
This is a superb, highly detailed account of a topic that is usually glossed over. There are far too many videos on youtube that 'pretend' to explain a topic, but ultimately leave you feeling empty because they have explained nothing. This is the first time that I have seen (and understood) a detailed derivation of the ultraviolet catastrophe and Max Planck's route to a solution. Genius. Thank you for taking the time to make this video.
that's the difference between explaining what the topic is about and explaining the topic in depth, a video with the same title could've just been 10 minutes explaining that it's something about infinite amount of uv, which wouldn't fit in the current model, and a simplified explanation without all the maths involved (i.e. put the math in a magic black box).
imo both are valid explanations, as most people in the audience don't need the maths, and if they do they now know what to search.
Yes yes....explain the topic...made total sense to me! lmfao 😂
most videos aren't highly detailed because most people wont understand or have the time to watch the whole thing
@@nono-bn3sm that's a valid point, but we would still like to try 😂 I'm not a math person...but I still wach this stuff....a good 35% of it honestly makes sense to me lol
@@mobilegamersunite getting 35% means you failed a test so understanding 35% would mean you basically understand none of it
It’s unbelievable that most text books skip over the detailed math behind the ultraviolet catastrophe. For gods sake this is the origin of quantum mechanics. This is similar to Newton’s observation that apple falls, or Einstein’s derivation of consequences caused by the constant speed of light. You can’t just say speed of light is constant, then something is wrong, therefore time slows down when speed is up. The details are extremely important. Because this detail is skipped, I had the feeling that quantum mechanics is dropped out of nowhere for a long time.
Cuz If we were talking about quantum physics with our friends in 9th grade for real, we probably would have went home and built time machines
What do you expect, this is high shool level physics involving college level math.
"For god's sake".
God has nothing to do with it.
Because you know, there is no god...
@@hippyjason It's ironic how it's always atheists talking about God
@@deangel9128 It's ironic how you automatically call everyone who doesn't believe in _your_ god, atheists. For the record, I'm an agnostic, and NO, it's not the same thing.
As someone who studied physics, this is by far the most thorough and yet simply explained video on this topic. It was always glossed over in both my modern physics and quantum courses, thus its significance glossed over. Thank you for this!
Why am I understanding this... where were you when I was in physics class. You are brilliant!
I have never heard anyone as good. It is like I am back at my final year of high school when I have a lightbulb moment where I realise I can convert most equations by substitution and a few other tricks like sums and difference and sine^2 + cos^2 = 1.
I am bowled over by the depth and clarity of the presentation. When I was studying engineering at the Indian Institute of Technology, the instructor spent a half hour on this topic, skipped the Raleigh -Jeans derivation entirely, and went straight to Planck's formulation. I was dissatisfied at that time with the transition but, after decades, have finally found a satisfying exposition. Thanks so much. I am certainly going to subscribe.
Very glad to hear that you enjoyed the video. Thanks for taking the time to leave a comment, much apprciated
physics is becoming like religion, people talking about the same stuff for many years
TH-cam must think very highly of me.
Lololol
I think TH-cam is trying to troll me.
I study colours and love this stuff. I thought I was getting a very specific recommendation.. I guess not
you’re here aren’t you
A like for your sense of humour 😂😂
This is the third time I very carefully went over this presentation.
My compliments and immense gratitude to the author, especially for rigorous derivation and historical content - simply amazing !!!!
You're very welcome!
Many here will probably know that when Planck was deciding whether to seek a PhD in Physics, one of his advisors told him not to do it because, after Maxwell and Boltzmann, everything that could be discovered in Physics already had been.
Around the same time, the great telescope builder George Ellery Hale was told that his desire to build bigger and bigger telescopes only resulted in counting more and more stars and we already knew that space was filled with them. So, bigger telescopes were a waste of money.
Well he wasn't really wrong. The best telescope in the world pointed at a star shows a speck of light. It does seem a bit pointless.
@@lkytmryan Except that Hale's big telescopes had the resolution to allow the measurements of the distance to galaxies outside our own. That ended up proving that the universe was made up of galaxies and that the same galaxies were moving at a rate proportionate to their distance, which showed that the universe was expanding. Can't do that with small, low resolution telescopes.
@@jmchez Not to be argumentative but what difference does it really make? The stars are so far away and completely out of reach. Other than as a source of wonder and amazement, nothing about stars will ever have the slightest practical affect on any of our lives.
I'm not saying that I don't understand why people would want to investigate the stars, I just really don't see how it matters to anyone beyond astronomers in any practical sense.
@@lkytmryan because usage of the correct theoretical apparatus enabled us to create an atomic bomb, for example?
I'm not saying that with the help of astronomy we can also create some kind of WMD, rather that such discussions about practical applications of fundamental research are irrelevant. Knowing how world works will naturally produce practical applications, even the most unexpected ones
@@lkytmryan We can see how the other galaxies are moving, and this movement has let physicists and cosmologists deduce a lot of things. For example, the accelerating expansion of the universe revealed, after some calculation, that there must be large amounts of some form of energy in the universe that we can't see directly. They call it "dark energy" because so far, it's invisible to us. But its effects on the universe can be seen using a powerful telescope.
Or radio telescopes that let us investigate the cosmic background radiation, revealing a lot about stuff that happened after the big bang.
What will these discoveries lead to in practice? I don't know yet, because they're still pretty recent. Remember that quantum mechanics (about to turn 100 years old soon!) was once mostly of interest just to theoretical physicists, until it led to the invention of semiconductors which are now the fundamental building block of all our electronics. Or Einsteins's special and general theories of relativity, which much later made the invention of GPS possible, for example. Maybe 100 years from now there will be some ubiquitous technology which was only possible to invent because of dark energy, I don't know.
My mind blew up and then reformulated itself... you are never to old to confront your long forgoten nightmares and finally see a glimer of light that says all is not lost. I will now go back to the begining, a time I left behind 40 odd or more years ago and perhaps enjoy a stress free journey where not completely understanding is OK but enjoying the trip non the less. Thank you.
when you watch this kind of scientific explanation, by someone who thoroughly understands their subject, it shows you how little you, as an average person, actually understand, but it was enjoyable
This is really wonderful STEM-to-STEM exposition. This is a hard level to hit square in the nuts, and you did it. Well done sir.
Thanks for the comment, glad you liked it
Absolutely fantastic video, this was the only one I could find that actually explained why the UV catastrophe occurred and how planck's constant solved it. And you derived everything using maths and physics I (mostly) knew, where my physics teacher refused to even go near this topic. Many thanks!
Thanks for the feedback and kind words of encouragement, much appreciated
There is a bit more to this: th-cam.com/channels/DmikjslWwIlxJDpiimuQ3w.html
whenever i feel i am a smart human being, i just watch your video and it put me where i belong which is to be humble again..
The Ultraviolet Catastrophe sounds like a band from the 60s.
I claim that
Tim Hecker has a great album by this name, hence the reason I'm watching this now.
@@karisdarkness Tim hecker is the truth
@@karisdarkness waww I
Yeah, they're good.
I thought TH-cam was going to give me some historical background noise that I could relax to and learn about. What I got instead was mini PTSD back to my days of getting a B.S. in Math, where I had feelings of "Oh, I think I get it." and "Wait, could you back up and explain that whole thing again?" and also "Wait, how did you get that equation?". It's like hanging onto a pole for dear life while a tornado barely misses you on it's path of destruction, your house is gone and you got a broken leg or two, but you're still alive. Alternatively, it's like getting shitfaced at a club and being sober enough to get home, but there's puke in your pockets and you'll never fully remember what questionable things happened that night.
All this writing and similes aside, I enjoyed watching this video despite the migraine, hunger, and the feelings of loss and confusion that ensued afterward. Good shit, buddy.
😂😂😂😂😂😂😂😂😂😂😂
You are legend man. I sympathize with you.
Still appreciate you going through this trauma.
I am myself a graduate in physics. So I understand what you are saying :)
Would have loved to have seen Plancks "Holy Fook!" expression when he first plotted his function and found it matched experiment.
It was a cheat and it took a long time for him to realize that he was right.
@@treborobotacon Yep, "lets just say that exists a constant called h which fits our needs", it was a wondrous cheat anyways
Schitzel schnitzel!
I took Calculus 30 years ago. The best part of this video was actually seeing Calculus used. I've been a software engineer since and I have never used Calculus before! Seriously, great video. You break things down well and you have an easy to listen to voice. I especially enjoy your pronunciation of "but."
Yeah I studied 30 years ago which involves lots of Calculus, but my career was also digital. I did an introductory computer course when I was 12, so 1979, and had one of the few 'light bulb' type moments in my life - I knew, in a flash really, that anything that was information, which in our modern world is lots of stuff, would be digitised. I was at the approx beginning of a revolution probably more profound than the industrial revolution.
I've studied this stuff, but I finally feel I understand it after this video. I've long been confused by mixing up quantisation of energy levels in atoms with Planck's idea. I understood how the Schrodinger equation gave rise to discrete energy levels for bound electrons, and that the difference in energy levels gave rise to the discrete frequencies associated with spectral absorption and emission lines. Having encountered these concepts before Planck's black body function, I'd always assumed that the solution to the ultraviolet catastrophe was something to do with quantisation of frequencies. But there's still an infinite number of frequencies or vibrational modes, even though the frequencies are limited to stationary wave values.
I've finally realised that Planck's solution was to quantise the amount of energy in _each mode_ ! With classical waves of a given frequency the amplitude is continuously variable, so the energy is too. I finally get that the energy _within any mode_ for EM waves is _not_ like that. It's split across a discrete number of quanta. Then the energy conservation principle dictates how the energy is statistically distributed across the modes, just like with the Boltzmann distribution for gases in statistical mechanics. Essentially the discrete number of quanta plays the same role as the discrete number of molecules in a gas. (Which probably explains why I've heard the term "photon gas"). Eureka!
In turn, I've realised Einstein didn't _discover_ quantisation with his analysis of the photoelectric effect, it was already there in Planck's work. Einstein simply intuited that energy was transferred to electrons in the same discrete quanta.
Glad you found the video useful! Thanks for leaving a comment
I had a prof who studies history of physics. He told us that Planck called quantization a final act of desperation. His quanta aren't real quanta bc he used them as a binning mechanism, each quanta containing a continuum of frequencies that happen to be grouped together. What Einstein did was abandon the continuum aspect and say that the quanta of their math is indeed a true reflection of reality, that quantization isnt just some mathematical trick but a real feature of the smallest scales of reality.
Excellent comment that takes it a little further and clarifies some details. Thanks for that, ps!
You’re an excellent teacher. If that is your profession outside TH-cam, your students are incredibly lucky.
"Theoretical physicists wanted more"
They always do.
Thats how the black mesa incident happened
@@dr.dapper120 nothing some applied science couldn't solve. All it took is a bit of mass and the right amount of acceleration.
Those ungrateful bastards
Theoretical physicists, ammirite? You give 'em a Unified Field Theory and all they can say is "this isn't a Grand Unified Theory!"
@@johnr797 makes you wonder what the next big problem will be after someone cracks the theory of everything... I mean, realistically we won't need theoretical physics anymore, it'd be a race for applied science!
This was fascinating and an extraordinarily well-done presentation, marred only by some need to pause a few times to allow my dense brain to catch up, to make sure that I truly understood. Haven't been hit by that feeling (the "slow down, you move too fast" feeling) in a while. Thank you.
My pleasure, glad you enjoyed it
And that's why I like videos.
And it was a 40 minute video! I had to do the same thing, honestly. It just goes to show that a lecture's worth of math is barely enough time to discuss these complicated phenomena in any detail, even when you already know the foundations in calculus.
We need another Max Plank to solve the gravity catastrophe and create a new branch of physics
Maybe gravity is quantized
Entropic Gravitation using Hawking's information paradox leads the way in new research.
@@robertwatson818 no one invented any original idea dude.
@@robertwatson818 then how did they study
@@robertwatson818 that's straight up wrong. Essentially every breakthrough has been based on research from other individuals, even many (most) of Einstein's discoveries were analysis of other scientist's data and conclusions.
I wanted to say thank you from a true layman. I do not even have a High School Diploma but the way you explained the problem and the solution step by step was fascinating to me. The math was way above me but the way you presented it made it very interesting to follow. Excellent work. I can only hope you are some kind of teacher to the future generations.
You're very welcome! Thanks for taking the time to leave such a positive comment, it means a lot
I'm a college graduate with a science degree and the math was over my head as well. Don't worry, there was a lot of representation of different branches of mathematics in there. I surely got more out of the math than you did, but this video is wonderful in that it doesn't matter much to the overall understanding of the bigger picture. This really was a great vid.
@@CeesaX The video only used high school math with a little bit of calculus… Did your college not teach math or what
As a mere biologist, much of this flew over my head, but I can still recognize a superb science video when I see one.
I would love to make videos like you someday, but for my field
I learned this topics in a physics seminar a few years ago and roughly have an idea of what's going on in this video. My limited mathematics capabilities at the time did not permit me to understand it in full detail. Thanks for the wonderful presentation, allowing me to revisit this topic with greater depth and getting a more comprehensive understanding!
Glad it was helpful! Thanks for the kind feedback
I understood EVERYTHING up untill "Towards the end of the 19 century...".
Ah, eighteenth century, simpler times.
I know this is a joke but to be fair, Newtonian physicists probably were like that as well. They understood everything _up to_ the end of the 19th century.
not understanding was discovered
@@kondrahtiz7370 Nono I meant they understood every part of physics that was discovered until the late 19th century, then they had their minds blown with general relativity
the thing about the box n the cat and superPosition is exactly the act of not understanding unless making the measurement ...quantum physics as I get it is an exercise of explaining how exactly things aren’t understood(??!?!!) *unless measured which inturn affected the outcome anyway
This is, by far, the best treatment of this topic on TH-cam. Bravo.
Glad you enjoyed it, thanks for taking the time to leave a comment
The cube concept created by James Jeans was further expanded upon with the Sweatpants Sphere, theorized by Martin Sweatpants in 1946.
Looking forward to the bell bottoms conjecture.
James kept em high and tight
Luther Leggings has entered the chat
All research conducted at local Walmarts
An alliteration like James Jeans is would have been even better. Like "[...] theorized by Sebastian Sweatpants in 1946 [...]"
I know just enough maths to barely understand what its saying but nothing about Physics that this is still black magic to me. It's just enough familiarity that this video is the best thing I know to fall asleep to.
You put a lot of work into this video.Probably more than 99% of other youtube videos out there.This is really professional and well thought out you are certainly getting a like from me.
Thank you!
It still has mistakes included,
I wanted to work it out for myself but by telling us what Max Plank said he gave away the answer. That should have had a spoiler alert.
This is one of my favorite physics stories. It’s challenging to understand, and it is such a innocuous setup for a major physics revolution
16:36 Oh wow, it is at this exact moment that Quantum Mechanics was born. As a Chemist I don't know much about the mathematical details of QM but this is the basic principle behind Quantum Chemistry that you will find again and again, especially in Spectroscopy, Electron Orbitals, Bond Oscillations etc.
Wow, I never knew this was how the theory of energy quantization came into being. So well explained, thanks. It's going to take me a couple more watches to digest the math - but this is the first time the math I've learned has made it possible for mde to understand something I really wanted to understand.
You’ve explained the concepts in this video in a much simpler way than my high school physics teacher did. You break everything down into bite sized pieces, making it a lot easier to understand. I loved physics as a teenager but never got into it because it was never explained to me in a way that made sense to my brain.
Damn you learned this in highschool?
Physics student here, this is quite literally how this was presented to me in the first Quantum Physics lecture I attended. Well done.
This is really neat. I... honestly understand almost nothing of this, but it's very interesting and what parts I did get were amazing. Thank you for your hard work and a terrific video :)
Glad you enjoyed it!
It’s an excellent start to delving deeper!
I recommend you to come back some time after and see it again. I have definitely learned more stuff along the way and in the second watchthrough I was then constantly trying to remember or predict the next steps! I definitely felt I learned so much
33:05 Am I the only one hearing the reference:
"All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be king." LotR, JRR Tolkien
*"...All that glisters is not gold..."*
William Shakespeare
For whatever reason, I think of Dark Souls.
Yes.
"There's a lady who's sure all that glitters is gold............"
Stairway to heaven. Not a fan. Can’t remember the lyrics. Better clues fuckers. Fuck history fr. Shits gay af
Just going into my 2nd year of A level and this video really helped answer some questions I had about how some of the equations I've learned came to be. Thank you for this amazing video!
Very glad to hear it! Good luck with your 2nd year of A-Level :-)
The best video on this topic. I have been searching for the right explaination to me for couple of days but i was not satisfied. Finally this video took me to the satisfactory zone. Thanks! Love from Bangladesh 🇧🇩
Full stop dude, this is up there with the best of the youtube educators.
You should do videos on transport phenomena (heat, mass, momentum)
I finally get the understanding of how discreet energy comes into play in explaining black body radiation. Excellent explanation.
This is the best description of Blackbody Radiation I've ever seen. Well done.
This was one of the first topics we covered in my Chemistry degree, genuinely fascinating
You just watched a decent chunk of undergrad Quantum Mechanics course done in 40 mins...and much clearer than I experienced
Not gonna lie, I was expecting a low quality video but this was actually great 👍🏼
This is an excellent video, and goes very in-depth in mind-bending ways for which I'm grateful.
For everyone who, like me, didn't realize that this video contained only a very thin (in some ways) and rather convoluted (in other ways) introductory synopsis to set the stage for the rest of the video:
The Ultraviolet Catastrophe refers to the realization of the "catastrophic" difference between the mathematical prediction (made via the Raleigh-Jeans Law) of a blackbody's energy output based on its light's wavelength vs. the real-world observations. The real-world observations revealed that at shorter wavelengths (going towards ultraviolet), a blackbody's emitted energy was *far* below what the Law predicted. An uppity physicist named Max Planck (who wasn't even a Lord or a Sir or *anything*) made his own mathematical predictions and theoretical models based strictly on the observed data, and in so doing realized that energy is quantized, meaning split into discrete sections (rather than just being a smooth transition up the energy scale). Think of it like this: physicists thought the Universe's energy ran on analog signals like a record player, and Max Planck revealed that energy is delivered similar to digital music, in discrete bits and levels. This realization upturned every apple cart in the physics world at the time, and was considered a "catastrophe" for anyone who thought we were even remotely close to figuring out how the Universe works.
Further explanations just to help anyone who might get lost in the wonderful details in this video: a "blackbody" is a useful physics model in the same vein as an "infinite flat plane with zero friction" from high school physics. It is an object that only emits light due to its temperature, regardless of any other property (like charge, radiation from particle decay, phosphorescence, etc.). Make a blackbody hot, it will start to emit light. Blackbody radiation is the reason why hot metal glows. In other words, the concept of a blackbody was the first realization among physicists that, for any object that is so hot it emits light (from an incandescent lightbulb all the way up to stars), there are fundamental and invariable correlations between energy output, brightness, and color wavelength.
Scientists noticed that, as a blackbody got hotter, it would both get brighter and its emitted light would increase in frequency (meaning it would have a smaller wavelength). Two scientists named Lord Raleigh and Sir James Jeans, using the best mathematics and theoretical thinking of their day, made a mathematical prediction of how the emitted wavelength of a blackbody can tell us about its energy output. This sort of prediction, if accurate, would be very useful for figuring out the temperature (and through that, many other properties) of objects we can't yet get close to, like stars out in space, our own sun, or even our neighboring planets. Their mathematical prediction was at first very useful, and became called the Raleigh-Jeans Law.
Unfortunately for those two (but fortunately for everyone else), as scientists began testing this mathematical concept against real-world observations, they realized that the Raleigh-Jeans Law worked great for "long" wavelengths (< 10^5 GHz) in the infrared spectrum, but as the wavelength got shorter into the range of visible and then ultraviolet light, the amount of energy output observed was *far* less than the Law predicted.
Enter a young upstart physicist named Max Planck. Out of frustration, he made the try-hard move of just brute-forcing an equation and set of theoretical models out of the observed data. In so doing, he created the mathematical and theoretical concepts that led to the discovery of quantum mechanics, and, as I believe is stated somewhere in this video, physics students have been cursing Planck's ingenuity ever since. This video goes into superb mathematical and theoretical detail as to how Planck ended up rustling the jimmies of pretty much all his contemporaries.
Thanks for reading!
If I'm wrong in any particulars, please let me know and I will happily correct them. I'm no scientist, only an enthusiastic amateur learner. Hope this helps some folks!
I just want to thank you, and many others, including those who made this video, for giving me back my passion in science again. When I was at school, I was top of my year all the time in science and stuff.
So when I was ready to go into my senior years, I did Physics/Chemistry/and 3 Unit Maths (advanced Maths, I guess)... HOWEVER. My heart was broken when I discovered that I was Mathematically/Numerically Dislexic. That is to say, Formulas, quadratic equations and all that stuff just looked like gobblygook. More importantly, I just couln't understand wht was going on regarding the written work. This crushed me, I was going to fail maths... And the further I got into Physics, I knew this mathermatic dyslexia would hamper my learning there, too...
As for Chemistry, well, that was a bit different. The Irony being that it was the elements that were the numerals, and somehow this made the formulas more "tangible", and not an "abstract" thought, so to speak. I never finished high school. But my passion for chemistry always went with me, probably because I had a great teacher who, even though I was failing and skipping school, always welcomed me in the class, as I always paid attention. I failed the tests, but I think he understood that there was something going on with me that was hampering my thirst for knowledge. Because I never played up when I went to class. And he never made me feel like a fool.
Anyhow the last 5 years I have been getting back into all these scientific fields again. Not for a career, or for academics. Just as that that young boy who whose wide eyed curiosity saw him read science encyclopedias on the weekend, when his friends were all playing games, or sports, or chasing girls.
It's these vides that are great. I am not going to say I understand it all. But now, at least, I can comprehend it all more better. Visualize some of it. And it's thanks to people like you in the comments, and the makers of these channels and videos.
And a good teacher, one who shows empathy, or compassion, can lay the seeds to a persons quest for knowledge. As an adult, I got into rave culture, stoner culture ect. My nickname with my friends was Dr. Gonzo. Because I could explain to them why taking an MDMA pill is a dangerous idea of you are on SSRI's. I wasn't just a know it all, I was someone who could be counted on to say "you know what, I dunno. I'll find out. But I wouldn't do it", when it came to the psycho-pharmacoligical playground.
Anyhow, As a 44 year olf, I have bpu chemistry to the side. The only Acid Base Extractions I do now are German HardTrance DJ sets.Thanks to the Net, I now am learning all ther is to know about Physics, Classical and Quantum. I feel like that 14 year old boy again.
Sorry for rambling, but I just had to let you know that these deeds are really apreeciated by some.
Oh, and I have had a rum or two.... So excuse the grammatical errors, in which I am sure there are a few
@@RogueBoyScout: Compliments upon realizing that Your personal intellectual and emotional defects have been maintainable through the application of chemical and alcoholic molecules. You have found Your place in existence.
That was a fantastic post, thank you. *Now* I understand what the background is for the video, which makes it a lot more understandable, even if the math involved is way over my head.
Imagine if someone told the flat earth people that the sun is really a hyperdimensional jeans cube with the hole only seemingly appearing to us as a sphere of plasma while in reality being a pinhole in the side of a hot, massive hypercube on another plane of perception. I hope one of them reads this comment now.
I don't think a lot of regular people know that a 4th dimentional circle would look like a floating ball to us
Usually flatards like a simple explinations that not only don't need you to know anything, but require you to be uneducated to believe. With complex conspiracies and explanations like that to justify problems with their Flat Earth
An example is when trolls explained the sun as a floating spotlight with a magic shape-shifting lampshade and the stars are fairly lights on a dome, but said with diagrams so it seemed legit
It's definitely possible just gotta word it so it explains a problem and it'll become a flatard fact.
Maybe it'll teach regular people watching debunking videos a thing or 2 about higher dimensions
Your statement is irrelevant to any flat earth concepts.the so called flat earth has been not surprisingly distorted by the scientific community.the description of the sun as you described is simply not specific to the capernicus model of the universe..the so called flat earth theory is more correctly described as fixed realm model of the universe.the earth by this design is a unique realm , the celestial bodies actually exist in the 4th dimension of vibration yet are observed and also influence the 3rd dimensional earth realm...so get your tin foil hats ready as both flat earth and capernicus global concepts are erroneous
Lol. You don't even realize what you just stated . 👍
@@showtale8325
Not sure if its directed at me but i am gonna assume it is until proven otherwise and going to assume you believe the unique realm conjecture.
When people talk about the Flat Earth society they are not talking about thought experiments from the 1500s or space-time being flat... they are talking about people in modern day who belive the Earth is flat, they exist, they're not hard to find...if you cant be bothered to go to the community then check out the channels Logicked or CHL and you'll find dozens. It's an unfortunate reality but it doesn't mean it's a hoax from the scientific community to invalidate your idea. If you believe something no one studying the concepts believes, maybe instead of it being apart of a conspiracy, maybe you're wrong
If the Earth was flat in 3 dimensions and we lived in a 4D universe, there would be twice as much space for gravity tp travel theough. Meaning gravity would fall at the cube of distance instead of the square like we observe. Being flat in 3 dimensions doesn't necessarily mean there's a 4th, it just means there's 3 dimensions and they're flat
Fairly certain the theories that predicted we had higher dimensions were disproven in 1910. Then replaced w theories we almost had higher dimensions, but the universe didn't meet the requirements for them to form so they collapsed in on themselves (that's why they are called vibrations). Each time those hypothisises get systematically disproven people come up w even smaller and harder to find dimensions... so if you believe in higher dimensions you're like 110 years behind
@@insertyourfeelingshere8106 excuse my ignorance I am not a theoretical physicist, I am simply a medical student interested in astrophysics. But doesn’t the theory of relativity and gravitation already relies on the fact that we are 3 dimensional beings living in a 4 dimension universe? That gravity itself is a curvature in the four dimensions of spacetime? Isn’t that notion accepted till this day? What about string theory that stipulates that we live in a universe of 12 dimensions. I understand that string theory hasn’t been proven but it hasn’t been fully disproven (yet) either. Doesn’t all of this go against your point that believing in hyperdeminsions is archaic in nature?
It's also the name of the metal band I'm starting with a bunch of physicists
This is by far the best black body video on TH-cam and deserves more love! Max Planck, Raleigh and Jeans were sharp dudes.
This is very good. So nice to see a thorough explanation devoting most of the time to the wrong explanation and not be afraid of formulas or mathematics.
I get it and then I lose it then I get it then I lose it ... it’s like my understanding is a wave !
🤷🏻♂️
But, which wave started first !!!??
Wow this is the best physics video I have seen on yotube! History, rigorous math, comparison with experiments. It was simply amazing! Thanks for putting this out.
Glad you liked it!
Wow. Back to the second year of college, but without the stress.
Replying to comments 11 months after uploading a video, that’s what taking real passion in your work looks like.
Every single time I watch this video, it gives me chill🥶
Max Planck was truly a genius, I don't think he has anything less than Einstein. One of the best video's in TH-cam imo❤️
This is the best video explaining the Ultraviolet Catastrophe in great detail and how the culmination of classical physics represented by the Rayleigh-Jeans model fails and what motivates the need for modern Quantum theory.
I know most of this from having studied physics for a while, but sadly my professor had some type of aversion to quantum mechanis, so even when discussing electro dynamics he carefully circumvented any and all discussion of things related to quantum mechanics. Looking back that was kind of impressive on it's own, but obviously this compartmentalized approach left out most important connections and ultimately made the topic harder to understand.
I had other reasons for dropping out, but I made the final call during one of his lectures, when he reiterated again how any quantum related explanations would have to wait another two years and I just realized I couldn't keep it up for that long.
I wasn’t expecting a 40 minute adventure into this, but I’m happy I did! Really great video
Glad you enjoyed it!
Very well done and educational video! I learned a lot from this lecture, in spite of having studied graduate level physics for many years. Good job!
Glad you enjoyed it!
TH-cam obviously think i like catastrophes. But this video piqued my interest, because a catastrophe is just a word. I wanted to see what is behind it and you nailed the explanation. Thank you!
Same here. YT recommended it because I binge watch aircraft catastrophes.😂 But although it is impossible (for me) to follow every equation in this video in realtime, I enjoyed the greater picture: That Max Planck laid the foundation to Nils Bohr‘s atom model etc., and now I know more about how the Planck constant was derived.
Fantastic. Thanks for this. Clearest explanation of how Plank used quantization to solve the ultraviolet catastrophe, perhaps anywhere.
My favourite part is how they used that Jeans box to create a blackbody because they knew this was the simplest way to study the phenomenon.
I agree, I also loved the synthesis of the problem and the derivation of the equation. Even though their concept of continuous energy was wrong but their grasp on mathematical physics was remarkable and unchallenged.
I wonder how they validated this. They proved that jeans box is a black body. Then they made some theory on Jeans cube which included things valid only for the cube (integer number of waves between walls) and got an impossible prediction. But why they projected prediction on all black bodies? Ok there is a Jean's box radiation problem, I admit. But why telling it is general black body problem?
@@0masuk0 In short, because experimentally all blackbodies show the same results. The real beauty in physics is that we take complex things, simplify them, calculate those simplified "models" and get the theoretical solution. Then we try to use that solution to different things, from simple ones to more complex ones and compare them with experiments. If the experiments match - great, it seems that our model is good. If the experiments show a discrepancy with theory... well, let's try to change theory. The point that Planck's blackbody radiation theory matches the Sun is a neat example. Of course, it doesn't match it completely... the Sun's radiation curve has dips at some wavelengths... so we expanded the theory to explain the absorption of gases... Also, lightbulbs have the same curve... incandescent ones even without dips in it...
This is genius work. So detailed that and perfectly presented. TH-cam needs more creators like you.
I think this video is the first I've watched that really puts Planck's work into perspective, humanity would of been in a really tough spot if he hadn't introduced all these fundamentals that solved the massive problems classical physics was being presented with.
This topic is notoriously hard to explain without the mathematical derivations. I don't think there is a better explanation out there then this. Thank you so much for this contribution.
I've been searching for a logical explanation of blackbody radiation-derived quantum concept. I found it nowhere else other than this video. What an effort. Thank you
Admittedly, I was expecting a discussion of the ultraviolet divergence of quantum field theory (amateur physics student, math nerd by training); but this is a nice introduction to the birth of quantum mechanics.
Ultraviolet catastrophe is a name stuck to this situation in the history of physics, when theory predicted infinite thermal radiation of bodies and it made no sense and people were scratching heads. People then thought they are inch close to completing the physics as science. They thought they just needed to solve two paradoxes: ultraviolet catastrophe and Maxwell equations being not invariant for switching to other (moving) system, including stupid prediction of light speed being constant in all inertial systems. Then boom: quantum physics and relativity are the answers.
@@0masuk0 : The phrase "ultraviolet catastrophe" is also sometimes used to describe the appearance of infinities in quantum field theory as zero is approached, which is what I was referencing in my comment. I was talking about a mild ambiguity of the terminology.
Elegant, beautiful and consistent line of thought
Thank you kindly!
What a great explanation at the start. I wonder why none of my physics or chemistry teachers at high school couldn’t have explained the origin of Plancks work instead of just dropping the constant on us out of thin air in quantum theory. Neither did text books do it well back then. I think it was dur to the fact that even for teachers they felt uncomfortable with the ideas and really didnt understand them enough to explain them with confidence as they did the much older laws of people like Boyle firmly grounded in tbe classical idea of the atom consisting of particles behaving in a newtonian way. Thanks again
Glad you enjoyed it, and thanks for taking the time to leave a comment, much appreciated
Although this explanation is clearly at a deeper and more fundamental level, there was no need to ‘drop Planck’s constant’ out of thin air when doing high school physics. A relatively simple experiment to find the turn on voltage for different colours of LED’s will produce results which allows students to produce a straight line through the origin graph which reveals that the energy of a photon is directly proportional to the frequency of its light. The constant of proportionally in this case is the value of the gradient of the straight line which has the value of Planck’s constant. Thus E =hf and hey presto Planck’s constant is introduced but in a context which students can grasp.
@@arnesaknussemm2427 I don't think anyone is disagreeing with you. But this is a video about the ultraviolet catastrophe.
@@arnesaknussemm2427 I fear when I did physics and chemistry in the 60s leds weren’t around and the curriculum never included determining plancks constant
@@lyntoncox7880 lol fair point. They are incredibly useful nowadays for introducing this constant in a tangible and relatively straight forward way. That’s progress :)
This is the very best explanation on standing waves that I have ever seen. And we all know it is the basis of determining the orbitals. Great Job!
An ideal strategy to explain, it looks as you tell a story (All the details in a precise way, step by step chronologically, including all the concepts and ideas and all the mathematical proofs and demonstrations).
Subscribed after less than 20 seconds because i just knew this was going to be good
I love how in my general thermodynamics course my professor bored me to sleep with this stuff and yet im interested af in this video
I can relate.
I still find it quite mysterious how the frequency /wavelength in these cases concern only integer values in the denominator, its a deep link between math and physics
The video covered this, but it's easy to miss. The short answer is that only standing or _stationary_ waves are allowed inside Planck's box. These are ones with wavelengths that divide evenly into twice the width of the box. That's where the integer values come from. It's the same reason that only standing waves are allowed on a guitar string -- because the string is pinned at both ends, so the wave displacement has to be zero there.
In the case of the Planck cavity, a similar boundary condition is the result of Maxwell's equations. The electric component of an EM wave is an oscillation in the electric field. A non-zero field at the wall boundary would produce a force on the electrons there that would be dissipated by conduction along the wall. So such waves would be rapidly damped. Only waves with a zero of the electric field at the wall boundary will be propagated. This effectively pins the ends of the wave, resulting in only stationary waves.
It's a little more complicated since the waves obviously don't only bounce in one dimension like a guitar string, but by considering that component of the EM field normal to the wall, along with the geometry of the setup, it works out to the same thing.
@@ps200306 the stationary wave explanation falls down if the object is not a cube.
it probably was and is the classical 'explanation' of the time, but subsequent discoveries perhaps lead closer to the truth - that the discrete wavelengths are a result of discrete electron orbitals.
@@edwardlewis1963 , the resonant cavity description can be extended to cavities of any shape using Kirchoff's law of thermal radiation, and a thought experiment where a cuboid cavity is coupled to one of arbitrary shape. Note that the stationary wave description in Planck's formulation is only used to establish the density of states (or modes) as increasing with the square of frequency. The same result can be derived from the Schrodinger equation with suitable boundary conditions. It works out the same as the resonant cavity description and has nothing to do with discrete electron orbitals _per se._ (Consider that plasmas are good examples of black bodies, and their electrons are unbound). In fact the resolution of the ultraviolet catastrophe has nothing to do with the discretisation of allowed wavelengths, but with the quantisation of the allowed energy at any given wavelength. That's the crucial step that allows the quanta to be treated exactly like molecules in the Maxwell-Boltzmann distribution.
@@ps200306 Stationary waves are, by construction, insulated from the walls. So it seems like those are precisely the ones that would be absent inside of the box. For there to be a thermal equilibrium, there's no problem with waves getting absorbed and emitted continuously. In fact, it's necessary that it happens to some degree. (The density of states would still work out the same).
My Friend recommended your channel, now I can't stop watching your videos :) I hope you upload more!
Never stop making videos bro. You have no idea how much I needed this!
What an interesting problem nicely exposed. Well done, you got my instant sub.
Planck must have been thrilled to realise the enormous implications of his discovery despite of the many years of failure, which makes it even more compelling. I'm quite positive that we are yet to discover many implications of his theory.
Videos like this definitelly deserve more attention as they elegantly manage to achieve what school failed: Genuine interest for domains once though too hard or too useless to understand. Someone told me once "Learn math now, you won't have time or interest for it later." - boy was that person wrong.
Thanks for the feedback!
Thank you for revealing the maths behind this magic, that Planck performed, in an understandable way! Clever guy that Planck.
Glad you liked it!
His heroic son was executed for the plot to assassinate Hitler
The Stephan Boltzmann law is strangely the most counter intuitive. Temperature being a measure of kinetic energy one would never at first intuit that intensity would grow as the 4th power of T.
I cannot emphasize enough how effective the teaching style of this video is where it combines all the necessary topics in a storytelling manner while keeping an endgoal in mind.
All the physics classes i’ve taken would teach topics like blackbody radiation, wien’s displacement law, wave function, etc. etc. until we just felt like we were jumping from one topic to another without ever drawing a connection/motivation through them all. I feel exhilarated now knowing that all these ideas were individual puzzle pieces that eventually fell in right places, but at the same time I feel so so frustrated that the university lecturers failed to help us understand the big picture.
Then wasting time defining basic terms like "intensity" as if we are in grade school.
This video is freaking brilliant. Such a great explanation. I've been literally studying this topic for years. Slightly obsessed
I'm going back to watching goats get scared and fall over
I got recommended a video of a goat getting scared and falling over right after reading this comment
This comment should be pinned to the top of the comment stream with a gold star.
Thanks for the laugh, sir!
So funny. Lol
🤣🤣
🤣😂🤣
This is suspiciously similar to a lecture I had while doing my physics degree. I'll share a tip from my quantum mechanics lecturer, "anytime I see the words 'obviously' or 'clearly' in a description I start to worry". Me too boss
Thanks for the refresher course, well spoken, well done, but no more obviouslies or clearlies please ;-)
are you commenting this in a Tottenham game interval? ;-)
"The building being on fire is clearly an obvious problem."
@@vyor8837 Not if it's part of a training exercise for firefighters. It's obvious this is desirable and clearly no problem. Sometimes the building NOT being on fire is a problem, humans have been working on this for millennia lol
One of my physics professors told a story (quite possibly apocryphal) about one of his physics professors giving a quantum mechanics lecture and stating that "It is trivial to show that (some complicated function) can be reduced to (some simpler function)" then continuing for bit, pausing, and then staring at the blackboard. The professor then left the lecture hall, leaving the students milling around in confusion. 40 minutes later he returned to the hall sweating slight and with mussed hair, and announced. "I was right. It is trivial!"
@@Pax_Veritas well, no, the goal in that case is still to make sure the building doesn't stay on fire.
Possibly the best physics video I've seen on TH-cam
That is very kind of you to say, and thank you for taking the time to leave a comment. Glad you enjoyed it!
I love this channel does not shy away to get into the nitty gritty. I hope that someone does similar videos about molecular biology. I think this could ease the fears and highlight the risks about vacciantion. So much in our comlicated world is decided based on how it feels to one's gut
Risk vaccination has changed due to mRNA. Which does nothing to combat the actual pathogens and wrecks havoc on your cells
thankful there are resources like this for a student in a small physics program, the UV catastrophe never really clicked in until now!
"So lets do that" needs to be the channel tagline.
You know... I was just asking myself this exact thing
This channel is revolution for me 🗿 thanks again! Keep growing buddy.
Cheers
👏👏👏👏👏👏 SUPERB👏👏👏👏👏 Excellent description of what can be considered the birth of quantum mechanics. I have seen the deduction of Planks formula in many books and classrooms, but this one overrides them all. I can not imagine a clearer and better explanation. Thank you very much!
ive been listening to this for 25 minutes. i only just relized that i dont care... thats how i know this is a good video!
Thank God that u uploaded it again ..I was worried
I needed this video two years ago...
It's comforting being back at school when things weren't so tough. I want to go back. Though I would be rather a Brian Johnson-lookalike by now.
This is the greatest explanation of the problem of blackbody radiation that I have come across throughout my career; this is awesome! Thank you.
35:57 "we find the following rather ghastly expression" Your sensitivity to the moment the student's mind collapses in despair genuinely helps this all go down a lot more easily!
The story why steel wasn’t invincible when heated up! Such a question laid the bridge to quantum mechanics! Planck and later Einstein and the revolution were kicked in( the short story)
I loved this video when I first watched it, and I'm definitely going to watch this reupload as well in the next few days (a quick refresher is never a bad thing), but for now I'm just gonna leave a thumbs up :)
Really love your way of explaining things!
Glad you enjoyed it!
38:05. "When Planck plotted his energy density function..." ...it just occurred to me that he couldn't just open his MacBook Air and type "ipython" and "plot(f, h*f.....)..."... I mean how long did it take to plot back in the day? 5-th powers, exponentials.... how did he know what h was without scipy.constants.h ?
Certainly longer than just calling plot(), but probably not as long as you would think. As they say, practice makes perfect and in the days before calculators (never mind computers), people who did this kind of work had a _lot_ of practice doing those kind of calculations.
Slide rules are still useful
We were still plotting by hand in my calculus course... wasn't all that long ago, under 15 years ago. And we did learn how to calculate the exponentials and logs and all that, though my memory fails to recall it without a refresher.
The experts argue with experts. I only hear wind chimes.
Time to watch a 40 minute video on a subject I have ZERO advanced or even passable knowledge in just because T sounds interesting and the narrator’s voice sounds really really nice and well spoke.
The solution of that catastrophe was truly marvelous. I like how you named the expansion of the universe as the vacuum catastrophe. It made me think that maybe it also will be solved.