Thank you for watching! I hope you enjoyed this one as much as I enjoyed making it. I'm thinking about what story from the history of mathematics to tell in my next video, so please drop a comment if you have a suggestion!
@@johngutwirth7706 exactly! if a professor would not teach a physics class and allow a student in that class to play their boombox … WHY do it here? i can’t watch this video because the music is too loud
A very good video. In terms of interesting problems, I would like to see you do a video on fluid flow. I am talking about the Navier Stokes equation. This equation governs things as complex as our weather, yet we still do not know if there exists a closed form solution to this differential equation.
@@krwada Thank you for watching! I will give this some thought. At the moment, I aim to make videos that involve both a mathematical concept and a historical or human story. By any chance are there any books that you'd recommend which discuss the history of the study of fluid flow/the Navier Stokes equation? I would be interested to read more if you do have a suggestion.
Whether gravity is fictitious (just an artefact of accelerated frames) or real (contains tidal forces that cannot be co-ordinate transformed) is the same as asking whether geometry is flat or curved was Einstein's key insight! Riemann probably never thought in his wildest dreams that his math would be useful to model curved spacetime. That's incredibly insane. Thanks for this wonderful video, Ben. I loved how the video slowly put all the pieces together. Wow! Also, thanks for the shoutout. Cheers!
Thank you Mahesh! And also thank you for making such a great series of videos elegantly explaining the fundamental intuitions behind relativity. They've helped me understand the concepts more clearly as I'm sure they have helped many others as well.
@user-ky5dy5hl4d Hi, and thank you for taking the time to watch my video! You are right that there are nuances to this - and even controversies - that I did not convey in the video, both for the sake of time and in order to give an overview to a less knowledgeable viewer. For example, in my summary of Einstein's thought experiment about the astronaut in outer space. There are some other things that you mention here which I'm not quite sure how they relate to this video. Can you recommend any books or articles that other viewers might find useful to learn more?
Well for example the proof of the Pythagorean theorem. The proof itself is completely rigorous and you can read more about it here: www.newyorker.com/tech/annals-of-technology/einsteins-first-proof-pythagorean-theorem I think what you’re responding to there could be the way that I keep referring back to the Pythagorean theorem itself as I walk through the reasoning of the proof, as a way to help a less knowledgeable viewer stay oriented.
@user-ky5dy5hl4d Galilean Relativity would like a word lol And Paul Gerber published E=mc^2 15 years before Olinto De Pretto and 17 before Onestone. But SR and GR are both ad hoc anyway.... both have been debunked already but the mathemagicians and cult of newton can't handle it lol Acceleration is a GUESSTIMATE and Descartes Momentum is better than it. Newton did a goodjob on Mass but Universal Gravitation and overreliance on the Mean Value Theorem meant it was always doomed to fail lol
Thanks! There were others as well who I didn't mention, for simplicity's sake. A few other mathematicians who helped Einstein with the math are mentioned by others in the comments. One more person who I didn't fit into the video (again, for time/simplicity reasons) was Michele Besso. This was Einstein's close friend during his time working at the patent office. In Einstein's paper on Special Relativity, the only person he thanks is Besso, with whom he took many long walks where they talked through the ideas together.
Wow Ben! This must've been a huge undertaking. Amazing video, full of wonderful visual explanations and put together extremely well. Great music choices, great story. Love the addition of the interview with Professor Alex K! You should be very proud of this.
Thank you Joel! I learned a lot making this and I'm proud of the result. I definitely appreciated your notes at the end on some of the finer adjustments too.
"This was when Einstein came upon what he later called the happiest thought of his life. He imagined a painter falling from the side of a building-" This made me laugh
I’m glad it made you laugh! I think it’s funny too. There were a few variations of this story that floated around in the press at the time (eg did he actually SEE a painter falling, or did he just imagine it?), but the basic idea of Einstein envisioning a thought experiment similar to this is pretty solidly in the typical telling of the story at this point. It’s possible though that Einstein was having a bit of a laugh to some degree at the expense of the reporter - don’t forget that he WAS more than just a little bit of a troublemaker…
@@bensyversen LIAR, Read Einstein's own book on relativity instead of getting your science not from DUD like Laurence kraus or the nutter neil tyson de grasse.
One of the greatest achievements of this short video is it allows me to see all these great historical figures in the overall context. We all know Riemann hypothesis, the Hilbert list of problems etc. But now I can directly connect all these geniuses and see them in the great spacetime of the cosmos.
Besides Minkowski and Grossman, Einstein also received help from Constantine Caratheodory, a Greek Mathematician considered one of the best of the 20th century. Caratheodory researched and wrote his PhD under the supervision of Minkowski at the University of Gottingen.
Wow I will look him up, thank you. I knew that Einstein consulted with other mathematicians as well, but I didn't encounter their specific stories in most of the sources that I consulted.
Dirac needed the help of Weyl and Oppenheimer for his famous Dirac equation. Leibniz published calculus before Newton did. And consulted the works of Fermat and Descartes before publishing the error-riddled masterpiece Principia Mathematica. There is no such thing as a "lone" genius. Einstein's "problems" in mathematics didn't stop him from predicting stimulated and spontaneous emission; nor entanglement; nor Bose-Einstein Condensates; etc. And in your video, you make a glaring omission: the REASON Einstein BEAT Hilbert to the final field equations of General Relativity is precisely because Einstein understood the necessity of a coordinate system that was generally covariant - Hilbert did NOT grasp this until it was too late (even though as the premier mathematician of his day, he should have known this). The video does a great job of humanizing Einstein, foibles and all, while treating the other characters with a deference that they don't deserve. Michelle Besso deserves a bit of a shout out for helping Einstein as well. For instance, you make no mention of the fact that it was Einstein's openeness to share his ideas with Hilbert after Hilbert invited Einstein to Gottingen to give lectures on relativity theory that LED to Hilbert trying to "nostrify" Einstein's work. You also don't make it entirely clear that it was more likely than not that Hilbert had copied ideas from Einstein from reading a preprint of his November 1914 paper. You'd think Hilbert, not Schwardschild, would have come up with the first exact solutions to GR. And you'd think Grossman, as the professional mathematician, would have identified general covariance as a necessary framing for making use of a coordinate system, but they did not. You should also do a deep dive on how Heisenberg needed Max Borns MATH and how Born, not Heisenberg, but matrix mechanics into quantum theory. Also do a deep dive on how Einstein got about 33% of the way to what is now known as The Schrodinger Equation, and that without Einsteins direct help, Schrodinger likely never gets to discover the very thing he's most famous for (as Schrodinger always acknowledged). Or how Max Born credited Einstein with the idea of probability waves. It's become en vogue to declare all the "help" Einstein got as a way to humanize him. However, the opposite is also true. Einstein GAVE a lot of help to scientists who took his ideas without attribution and he often gets overlooked for ideas he came up with. De Broglie is a great example. He took Einsteins equations in his 1906 - 1909 papers on quantization of energy and applied them to a gas of electrons, rather than photons as Einstein had done, and got matter waves. Or how Einstein predicted the boson (which really should be called an Einsteinion) after Schrodinger completely misunderstood Bose's paper so thoroughly, Einstein had to write a letter to Schrodinger showing an example of the new quantum statistics (e.g. 1/3 instead of 1/2).
@@feynmanschwingere_mc2270 Hi, thank you for watching my little video and for taking the time to write this very thoughtful comment. You are certainly right on these points about the people and information that I left out of my video. In fact, I very much wanted to include something about Besso, AND more detail about Einstein and Hilbert's relationship. However, this video's runtime of 30 minutes very much pushed me to my limit as a fledgling video creator, so I had to cut fairly ruthlessly, keeping the total number of historical "characters" introduced in my narrative at 6 (Einstein, Minkowski, Grossmann, Riemann, Hilbert, Eddington) and leaving out any detail that would provide more refinement to other people involved besides Einstein. (As far as the discussion of WHY Einstein beat Hilbert, it is a fascinating detail but I thought that it could be a little bit too "in the weeds" for a general audience). Do you have any favorite books or resources that you would recommend to viewers who are interested in learning more about these figures and the relationships that you describe?
@@feynmanschwingere_mc2270Poincaré contributed to SR by suggesting that the physics should be the same for all observers, regardless of the reference frame. When discussing GR and SR, people always omit his name. Remember, this is the backbone of RT, as it uses coordinate and Lorentz transformations to preserve Poincaré's "principle."
@@bensyversen you set a high bar too early. no pressure 😉 your style is really good. It’s “accessible” but not condescendingly “dumbed down” like I’ve seen. It’s a tough concept at once but you break it into pieces that explain it in chunks.
@@nadionmediagroup Haha, yes I've thought about that. :-0 This one took me four months to make if you include the time spent figuring out the concept/framing of the story. Now it's time for a few shorter, more concise videos I think!
@@bensyversenyeah, I could tell. I just watched your archimedes video and clicked on this one and had to check that I was on the same channel cuz the lengths were so different
@@nathan9901 Yeah. Seems like people are voting with their eyeballs and telling me that shorter is better, at least for now. Gonna stick with shorter and more concise videos for the next few.
This is the most informative piece I have ever seen about AE. I was amazed to learn of his initial disdain of higher level math and of his intuitive use of the axiomatic method. Congratulations to Ben and the team for creating this gem!
Omg! This adds such a depth to the development of Einstein’s theories that I have never seen. I love this addition of seeing what he saw as a child, that lead him to develop theories and then having others expand upon those theories and leading him to appreciate math he had previously found unhelpful. It really digs into the importance of how we educate our youth. Something I am passionate about. I hated math. Same situation you mention in this video, how am I ever going to use this complex math in my life? What is the point on learning this? Later in life I grew to appreciate that same math when I grew fascinated by naked eye Astronomy. First looking at stars. Constellations. And eventually planets. And I wanted to know how we figured it out. Thousands of years ago. Without calculators or computers. Just smart people seeing a problem, and the math couldn’t explain discrepancies with a theory and observations. This was such a treat finding this video! Thank you for making it and sharing it! Brilliant!
Thank you so much for this extremely kind comment! I'm really glad to hear that the big themes that I was thinking about while making this video resonated so well with you!
I'm not a scientist. I have only a layman's grasp of the basics of all of this. But I too was baffled by the mysterious merging of Einstein's theory and the miraculous math that supports it. How on earth did this 'just happen'? This video really sheds light on the whole thing. Thanks Ben and Alex.
Overall, The video quality was great and the information presented is a brief summary of the history of physics and maths and how the latter provides the foundation for the former. I thank you and Mr Alex for separating some time from your busy schedules to make this well-produced and informative video. I hope to see more such collaborative videos by you. You deserve more attention than youtube has allocated for you. Alex Kontorovich's role in this video was similar to Minkowski's role in Einsteins work. I am proud of him for advocating Mathematics in such a happy and exciteful way.
Thank you very much! The math world is lucky to have as excellent a communicator as Alex Kontorovich around, and I was thrilled by his participation here.
I remember a moment during a tutoring session nearly a decade ago when you gave me the best explanation of the number "e" - and years later, when teaching logs and "e", I still attempt to replicate your demonstration of a random accountant trying to continually compound interest with an obsolete gear/lever machine until his arm nearly fell off (of course, I add my own dramatic flair)! Anyway, fast forward to this week, when one of my more curious students came to me asking me a LOT about "e" and its discovery and significance and oh so much more. Naturally - pun intended - I thought of your work, and that this might be an interesting topic for a future undertaking of yours!
@@bensyversenI’m coming back a day later because I vaguely remember when I was dozing off to dream land last night that there was some other recommended channel in the video you said to check out but can’t seem to find it.
@@mcnugget9999 oh, the channel Float Head Physics (linked in the description) has some very good videos going into more detail on things like special relativity, exploring it in a way that I think can help people understand the intuition behind the ideas.
This was so great!!! Our history of innovation is just thrilling. I loved seeing the ways people worked together to do something no one ever thought possible!
28:46 even more ironic and interesting is that the brilliant Bernhard Riemann while a student at university was assigned in a sense a doctorate thesis research topic to formulate a generalized geometry that would extend beyond classic Euclidean "flat" geometry. Riemann as this young student was not particularly happy or interested to be working on this topic of research but ventured forward none the less thus developing this new field of mathematics known today as Riemannian geometry.
You deserve way more subscribers! This video put together so many loose ends flopping around in my head, so many pieces now fitting together, the space time interval, and general relativity, it's all starting to make sense! Keep up the stellar work, please!
@@bensyversenas a hobby, we kind of gave up of gave up on shortening the proof of Fermat’s last theorem. The CDC 6600 counter-example won’t likely work for the Collatz Conjecture, and I’m glad I wasn’t a maths major.
Keep showing the world such fundamental break downs of the scientific stories making up our world today. Awesome work Ben ! Really places many scientific aspects together in a coherent framing as allowing far more people to efficaciously apperceive & cognitively grasp. Such important information.
That is very kind of you, thank you! (Personally, I think that there are definitely better, more complete explanations of space-time out there than mine, but I'm very happy to hear that you found it helpful!)
Excellent Video! This is a Netflix worthy documentary! One small note - I think it would be better if u included the Michelson-Morley experiment on how the speed of light is constant in all reference frames to explain how Einstein got his postulate for special relativity
Thank you for your very kind comment! As far as the Michelson-Morley experiment, this was one of the juicy historical tidbits that I came across in researching this video that I had to leave out for time purposes: It’s actually unclear whether Einstein was familiar with the Michelson-Morley experiment at the time that he wrote his 1905 paper (the physics taught at Zurich Polytechnic at the time that he attended was somewhat dated, and when he worked at the patent office he had a hard time keeping up with the latest research because the library was closed by the time he got off of work). Einstein himself said different, slightly conflicting things over the years: physics.stackexchange.com/questions/89375/did-einstein-know-about-the-michelson-morley-experiment/89379#89379
There are two reasons why I love this historical tidbit so much: 1) It reminds us that history is messier than just connecting the dots chronologically. Human elements played a role back then, just like they do in our own lives. 2) Like so many of us, Einstein was once a 20-something with a day job and a dream (and a pregnant girlfriend, but that's a whole other story that I also had to leave out of the video...), and sometimes his day job got in the way of his dream.
@@bensyversen In my opinion there is no proof in the Michelson-Morley experiment or for that matter any other experiments that I have seen that the speed of light is constant in all reference frames. In every one I have seen it is the "Two way" speed that is measured as far as I can see. It is my opinion that the speed of light is probably constant but from a constant stand still meaning that any moving observer should see the speed being slower (red shifted) if you are moving away from it's origin and faster if you move towards it's origin. The time dilation is correct I believe. That has to do with time keeping that on the very small scale (in the atoms) must have to do with the electro magnetic propagation speed. Time itself is a different story i believe. I believe it only exist right now. Time gone only exist as a memory and the future is yet to come but that is philosophy. That any body's time moving at any speed should go slower than my time if I am the observer I believe is wrong. If not then a light beam emitted from my point of view should move away from me with the speed of light even though I might be moving nearly as fast in the same direction.
This video presents the common narrative used by most pop-sci stories about (what was eventually named) Special Relativity which leaves out a lot of important details about the theory itself, and the context Einstein was working in as he developed it... _and the actual problem Einstein was trying to solve_ You highlighted that in the introduction of Einstein's paper on the "Electrodynamics of Moving Bodies" but didn't explain what problem Einstein was referring to. It's actually a very important detail for understanding Special Relativity. I'm actually falling asleep at the moment and can't focus on writing this comment right now. To summarize what I was going to say in a lot of words, what someone really needs to understand is: • Inertia (yep, Newton's first law of motion, and Galilean Relativity) • Classical electromagnetism (Maxwell's equations and the Lorentz force) Special Relativity is a direct logical consequence of this. Furthermore, nobody was surprised by Einstein's 1905 papers on electrodynamics. Lorentz, Fitzgerald, Larmor, Poincaré, et al. had already figured out the same thing over the previous 20 years (in a tremendously convoluted roundabout way). The reason why Einstein didn't explain anything like why the speed of light is constant for all observers, _is because everyone already knew that_ ! Maxwell figured that out in the 1860's (arguably the experimental measurements going back to Rolmer in the 1700's also indicate a constant propigation velocity for light). The controversy over Special Relativity at the time it was published was about whether or not it was actually a new idea. There were at least four other theories of relativity by other people at the time. Most people credited Poincaré until Poincaré said that Einstein's theory was completely unrelated to his theory of relativity. I've actually read Poincaré's papers, and it's stunning, because it's what gets used to explain Einstein's Special Relativity in pop-sci videos about Einstein... which brings me back to my original thesis... The stories you hear, outside of an actual physics class, in the popular media _is the old Lorentz-Larmor luminiferous aether theory_ with the word "luminiferous aether" crossed out. That's why everyone who hears these stories thinks: "Why isn't there an aether? It sounds like there should be an aether." The source of pop-sci explanations of Special Relativity are _other_ pop-sci explanations of Special Relativity, and not modern physics textbooks. So these pop-sci stories haven't been corrected since the 1920's. I have a lot to say about how badly Relativity gets presented, but I'm currently falling asleep right now, so I'll have to write it later.
HI thank you for writing. You’re right that there are a lot of details left out. That’s by design - this video is intended as more of an overview/starting point than any kind of definitive word, especially as it relates to the details of what’s known as special relativity. The broad outline and conclusions about originality that I convey are mostly based on the Walter Isaacson biography(certainly you’d probably categorize that as pop sci), but I’ve also listed in the description a number of other resources that I consulted, esp with regards to things like Minkowski’s work. I invite you to write again with more detail on your perspective, and I would ask that you also point the audience towards reputable resources where they can learn more if they are interested. Thanks again!
@kingZ3ro I haven't forgotten about this; I have just been very busy with other stuff and not... you know, writing stuff in TH-cam comments. Most of the explanation is about _inertia_ specifically _how_ it works. Inertia is fundamental to the very core of Einstein's Relativity. Also, electricity and magnetism. Special Relativity *_unifies_* electricity and magnetism into _electromagnetism_ (This *is* the actual reason Einstein created "Special Relativity" as it's now called.)
@@juliavixen176 Understandable, people have stuff to do But about the unification of electricity and magnetism, I'm probably missing something here, but wasn't the whole point of Maxwell's laws to prove that electricity and magnetism were two sides of the same coin? If so what was then the need for special relativity to unify them? Sorry if this sounds like a dumb question.
@kingZ3ro There's a "problem" with Maxwell's Equations. There's nowhere to stick a velocity term... You know how a moving electric current creates a magnetic field, and a moving magnetic field creates electric current? How does the magnet know it's moving? Moving _with respect to... what_ ? If Alice and Bob are looking at some electrically charged whatevers, and Alice stands "at rest" on the surface of the Earth, while Bob rolls by in a tain car in a straight line at constant velocity. Bob has two electrically charged balls sitting on a table, at rest, inside the train. From Bob's point of view, the electric charges are _not_ moving, and so there's no magnetic field. Alice watches the train with Bob and his electric charges moving in a straight line at constant velocity. From Alice's point of view, the electric charges _are_ moving... so Alice will see a magnetic field... right? So, is there a magnetic field or not? Who is correct? Anyway, the solution is to invent Special Relativity.
By using animation, right brained ppl like me can finally understand mathematics. I feel like I'm really learning for the first time in my 57 years. Thanks for your effort to educate the masses who want to learn.
Great work. It’s easy to get blindsided by Einstein’s unfathomable genius and forever that he was standing on the shoulder of giants and collaborating with other masterminds to put together the puzzle of space time
This was lovely to watch; I am shocked to find out that Einstein wasn’t a mathematician. It’s so much more accurate to call him a logician with a focus in theoretical physics.
To be clear, he was an excellent mathematician by the standards of most of us “regular people”, but for general relativity he definitely needed to call in help. There were other mathematicians he consulted too besides Grossmann but I left them out for simplicity’s sake.
@@bensyversen oh absolutely, I love math and I couldn’t imagine wrangling Riemann’s stuff. But for some reason I always thought of Einstein as this math-focused genius, where his Theory of Relativity came from investigating math and seeing how it bumped up into physics and the cosmos. It’s super interesting to see that it was the other way around. Obviously the math is very advanced and complex and necessary, but the math theory was developed separately, and the implementation of the math came from the physics. And all of that was building not just on knowledge of physics, but overwhelmingly on a foundation of logististical prowess. Obviously Einstein was brilliant, and his knowledge of Physics and Math was incredible. But this is the first I’ve heard of him as a logician and I absolutely love knowing that about him.
Very good production. Melvyn Bragg in his BBC Radio 4 'In Our Time' repeatedly marvels at how abstract maths or things done just because someone thought about doing it often turn out to be part of or essential too later developments in science and / or technology.
Ben, this was a very enlightening and enjoyable treatment of Einstein. Keep up the good work. By the way, the music was just fine for me. It added to the excitement of the presentation to me. Especially when watching it later in the evening.
Thank you very much! And thank you for the comment about the music. I’m glad you enjoyed it. I definitely plan to continue including music in my videos, though I’ve identified some ways that I can improve my skills to make it more effective going forward.
@@bensyversen The stuff is interesting enough without music. But if you "must" have it, keep it on very low level, barely audible. It will still have some effect subconsciously!
Really excellent video!! I remembered an anecdote about Einstein"s trip to Italy. Back from there he was asked by a Journalist what he had enjoyed best of it, at which he answered: "Maccaroni and Tulio Levi Civita" who was one of th few mathmen that mastered the absolute differential. calculus or diferential Geometry without which you can't figure GeneralRelativity. Regards!
Speaking of math coming before physics, David Hilbert is the same Hilbert who created "Hilbert spaces", essentially the general abstraction of dimensional space, with possibly infinite dimensions, that lies at the heart of the math of Quantum physics.
Good video and clear explanation! Will try to find out more explanations & understanding of the Theory of Relativity in your other videos, hopefully! Pls cut down the voume of the background music at the beginning. It was hard to concentrate, so as to hear the voiceover.
Thank you! Yes I am aware of the music issue. I can’t make changes after upload to this one but I’m working to improve my sound design for my upcoming videos.
Dirac needed the help of Weyl and Oppenheimer for his famous Dirac equation. Leibniz published calculus before Newton did. And consulted the works of Fermat and Descartes before publishing the error-riddled masterpiece Principia Mathematica. There is no such thing as a "lone" genius. Einstein's "problems" in mathematics didn't stop him from predicting stimulated and spontaneous emission; nor entanglement; nor Bose-Einstein Condensates; etc. And in your video, you make a glaring omission: the REASON Einstein BEAT Hilbert to the final field equations of General Relativity is precisely because Einstein understood the necessity of a coordinate system that was generally covariant - Hilbert did NOT grasp this until it was too late (even though as the premier mathematician of his day, he should have known this). The video does a great job of humanizing Einstein, foibles and all, while treating the other characters with a deference that they don't deserve. Michelle Besso deserves a bit of a shout out for helping Einstein as well. For instance, you make no mention of the fact that it was Einstein's openeness to share his ideas with Hilbert after Hilbert invited Einstein to Gottingen to give lectures on relativity theory that LED to Hilbert trying to "nostrify" Einstein's work. You also don't make it entirely clear that it was more likely than not that Hilbert had copied ideas from Einstein from reading a preprint of his November 1914 paper. You'd think Hilbert, not Schwardschild, would have come up with the first exact solutions to GR. And you'd think Grossman, as the professional mathematician, would have identified general covariance as a necessary framing for making use of a coordinate system, but they did not. You should also do a deep dive on how Heisenberg needed Max Borns MATH and how Born, not Heisenberg, but matrix mechanics into quantum theory. Also do a deep dive on how Einstein got about 33% of the way to what is now known as The Schrodinger Equation, and that without Einsteins direct help, Schrodinger likely never gets to discover the very thing he's most famous for (as Schrodinger always acknowledged). Or how Max Born credited Einstein with the idea of probability waves. It's become en vogue to declare all the "help" Einstein got as a way to humanize him. However, the opposite is also true. Einstein GAVE a lot of help to scientists who took his ideas without attribution and he often gets overlooked for ideas he came up with. De Broglie is a great example. He took Einsteins equations in his 1906 - 1909 papers on quantization of energy and applied them to a gas of electrons, rather than photons as Einstein had done, and got matter waves. Or how Einstein predicted the boson (which really should be called an Einsteinion) after Schrodinger completely misunderstood Bose's paper so thoroughly, Einstein had to write a letter to Schrodinger showing an example of the new quantum statistics (e.g. 1/3 instead of 1/2).
Hi, thank you for watching my little video and for taking the time to write this very thoughtful comment. You are certainly right on these points about the people and information that I left out of my video. In fact, I very much wanted to include something about Besso, AND more detail about Einstein and Hilbert's relationship. However, this video's runtime of 30 minutes very much pushed me to my limit as a fledgling video creator, so I had to cut fairly ruthlessly, keeping the total number of historical "characters" introduced in my narrative at 6 (Einstein, Minkowski, Grossmann, Riemann, Hilbert, Eddington) and leaving out any detail that would provide more refinement to other people involved besides Einstein. (As far as the discussion of WHY Einstein beat Hilbert, it is a fascinating detail but I thought that it could be a little bit too "in the weeds" for a general audience). Do you have any favorite books or resources that you would recommend to viewers who are interested in learning more about these figures and the relationships that you describe?
Einstein's Pythagorean Theorem uses scale-symmetry, and that's what gave him relativistic intuition. Wish I could show him my d=(c-b)/a base scale. Maybe he could've used it for simpler gravity math. Thanks for the insight that a cone is Thales Theorem with infinitely sized radii.
@29:40 The TL:DR is.. Nothing, I ramble aimlessly. I love the point being made here, about the mathematicians coming up with their crazy stuff, no one paying much mind to it, for decades, until one day someone realizes it's exactly what is needed to explain something else. I like learning about how "we" know what we know (yes, "we" is doing a _lot_ of lifting here), and how the kernel of an idea can be picked up, put down, and eventually end up sidelined, possibly for years, before finding its way to someone who is at the right place, and time, to be able to recognize it is a missing piece of a breakthrough puzzle. It happens a lot, and it's nuts how often someone has come up with something that didn't find a practical use in their niche area of expertise, but turned out to be in some way central to the progress of another, sometimes long after the original author/ creator has shuffled off this mortal coil. I read a few of the speeches/ talks, articles and interviews that Einstein did, and something he made a point to discuss, more than once, was the importance learning the history of, and reading good works in the philosophy of science. It seems like it should be a no brainer, really, but some really nerdy people are bizarrely blinkered. Einstein seemed to consider this knowledge to be key to future progress. I personally think that the "shut up and calculate" contingent of modern physics, those who have been vocal about their disdain for the notion of philosophy having merit, at all, are possibly some of the most confused people on the planet, right now. It is hilarious to hear several someones who aren't even a little bit your practical, hands on, experiment devising/ conducting type of physicist, snarking that philosophy is garbage because you can't further the fields of physics, by (paraphrasing), sitting in a chair thinking really hard about things. Like, uh, projection, maybe? Or, seriously confused about the fundamental nature of what it is that they're doing when they're trying to solve problems by sitting on their arse, thinking really hard about things? I know ostensibly the idea is that their work will lead to something that a testable hypothesis can be created from, that will have practical use, progress the field and what have you, but until that time, they're just engaging in using very, very advanced math to represent the values of processes and physical constants, involved in very complex ways, which are derived using the axioms of mathematics, an understanding of the nature of the interactions, and by thinking really hard about it all... It's really complicated, logically rigorous and robust, very niche, tunnel visioned philosophy, really. Point is, Einstein was obviously correct to point out how important it is to learn and understand how progress and breakthroughs happen. If you pay attention to history, there is a predictable pattern of breakthrough - Flurry of progress and understanding - over confidence in some newly created concepts/ notions (s) that emerge, - hubris - academics chasing their own tails while inexplicably doubling down on defending a very obviously incompatible idea /or three - Philosophically inclined contributors begin to converge on concepts that lead directly to the next paradigm shifting breakthrough - Flurry of progress.... and on it goes. We need a few more academics with outlooks like our happy math genius here, embracing the philosophical and using it as the invaluable tool it has been, I think there is a shift already happening, away from the philosophically phobic view, which fills this rambling moron's heart with joy -
@@bensyversen The Pythagorean space-time interval was fascinating. Consider me a very uneducated enthusiast, so I likely get quite a bit wrong. This past week I got interested in Heron's Formula for the area of a triangle and found the sum of 4-d cubes subtracted from the sum of 4-d prisms. x^2+y^2+z^2 - (ct)^2 reminded me of that sum of volumes minus other related volumes. My flawed intuition would suggest adding, not subtracting, that fourth element in the space-time interval. Wonderful food for thought. I have much to learn.
@@johnnyragadoo2414 Yes, I agree that the space time equation feels a bit counter intuitive. Here's a video that does a good job around 5:40 of visually explaining the fundamental invariance that it preserves, when they represent it by areas of the figures being shown being preserved as the shape is stretched. Subtracting the (ct)^2 term is what leads to the hyperbolas you see: th-cam.com/video/uVxL8Q4bpqc/w-d-xo.html
I gave this a thumbs up primarily because of the mathematician's statement at the end that mathematics approximates the universe, it doesn't govern it. I really detest the phrase "governing equations". Equations don't govern anything. They describe, and usually only approximately. Kudos.
Now the next step is figuring out how general relativity and quantum mechanics fits together and once again time is the key. General relativity and quantum mechanics will never be combined until we realize that each individual observer is observing them both at different moments in time. Because causality has a speed limit (c) every point in space where one observes it from will be the closest to the present moment. When one looks out into the universe they see the past which is made of particles (GR). When one tries to measure the position of a particle they are observing smaller distances and getting closer to the present moment (QM). The wave property of particles appears when we start trying to predict the future of that particle. A particle that has not had an interaction exists in a future state. It is a probability wave because the future is probabilistic. Wave function collapse is what we perceive as the present moment and is what divides the past from the future. GR is making measurements in the observed past and therefore, predictable. It can predict the future but only from information collected from the past. QM is attempting to make measurements of the unobserved future and therefore, unpredictable. Only once a particle interacts with the present moment does it become predictable. This is an observational interpretation of the mathematics we currently use based on the limited perspective we have with the experiments we choose to observe the universe with.
Haha yes I’ve heard feedback that the music was too loud. My bad. I will definitely be sharing my mix with a few unbiased sets of ears before I publish the next one.
One more thing which could be mentioned (but not essential in an overview) is that Rieman tensor was not suitable for solving the problem. This requested to switch to Ricci tensor (Rieman's is a matrix of matrices, while Ricci's is a matrix of scalars, to simplify a bit) while subtracting 1/2 of the Ricci scalar (the trace of the tensor) including the metrics (g(μ)(ν)). To do this he had to ask for the help of Tullio Levi Civita, who would teach Einstein this kind of math. Einstein had really to delve in complex mathematics to solve his problem!
Thank you! Yes the story is more complex than the format of this video really allows room for. In addition to Tullio Levi Civita, other commenters have also highlighted Constantine Caratheodory's contribution to Einstein's understanding of the mathematics involved.
I was reading about Eddington and his full story along with another guy who was on a similar mission and it was a huge accomplishment with many obstacles. According to the story I read Einstein even had time to make some type of correction to his prediction before the final results had been made. I wish I could remember where I found it.
Yes there was a whole earlier expedition that I really wanted to include in the video but left out due to time and relevance. Basically, there was a solar eclipse happening in 1914 in the Crimean peninsula, which was a part of Russia at that time. Einstein found a young German astronomer named Erwin Freundlich and helped arrange the funds to set up the expedition (I think he even paid some out of pocket). Freundlich and team arrived in the Crimea several weeks before, and then World War I broke out. Since Germany and Russia were now enemies, the team was arrested and their equipment confiscated. (They were eventually sent home) This was all lucky for Einstein though, because his prediction at that point was wrong. It was basically in line with the prediction that would have come from treating light as a particle with mass using the Newtonian model. I read about this in the Walter Isaacson biography of Einstein, but here is a more detailed article on the topic: www.machinedesign.com/automation-iiot/article/21835940/how-wwi-saved-einsteins-theory-of-relativity
![The most beautiful equation in math, explained visually [Euler’s Formula]](/img/n.gif)
Thank you for watching! I hope you enjoyed this one as much as I enjoyed making it. I'm thinking about what story from the history of mathematics to tell in my next video, so please drop a comment if you have a suggestion!
Why the loud music?????👎👎👎
@@johngutwirth7706
exactly!
if a professor would not teach a physics class and allow a student in that class to play their boombox … WHY do it here?
i can’t watch this video because the music is too loud
A very good video.
In terms of interesting problems, I would like to see you do a video on fluid flow. I am talking about the Navier Stokes equation. This equation governs things as complex as our weather, yet we still do not know if there exists a closed form solution to this differential equation.
@@krwada Thank you for watching! I will give this some thought. At the moment, I aim to make videos that involve both a mathematical concept and a historical or human story. By any chance are there any books that you'd recommend which discuss the history of the study of fluid flow/the Navier Stokes equation? I would be interested to read more if you do have a suggestion.
Hello there, i quite enjoyed your video. One side note: the back ground music is sometimes a little bit too loud. greeting :)
Whether gravity is fictitious (just an artefact of accelerated frames) or real (contains tidal forces that cannot be co-ordinate transformed) is the same as asking whether geometry is flat or curved was Einstein's key insight! Riemann probably never thought in his wildest dreams that his math would be useful to model curved spacetime. That's incredibly insane. Thanks for this wonderful video, Ben. I loved how the video slowly put all the pieces together. Wow!
Also, thanks for the shoutout. Cheers!
Thank you Mahesh!
And also thank you for making such a great series of videos elegantly explaining the fundamental intuitions behind relativity. They've helped me understand the concepts more clearly as I'm sure they have helped many others as well.
@user-ky5dy5hl4d Hi, and thank you for taking the time to watch my video! You are right that there are nuances to this - and even controversies - that I did not convey in the video, both for the sake of time and in order to give an overview to a less knowledgeable viewer. For example, in my summary of Einstein's thought experiment about the astronaut in outer space. There are some other things that you mention here which I'm not quite sure how they relate to this video.
Can you recommend any books or articles that other viewers might find useful to learn more?
Well for example the proof of the Pythagorean theorem. The proof itself is completely rigorous and you can read more about it here: www.newyorker.com/tech/annals-of-technology/einsteins-first-proof-pythagorean-theorem
I think what you’re responding to there could be the way that I keep referring back to the Pythagorean theorem itself as I walk through the reasoning of the proof, as a way to help a less knowledgeable viewer stay oriented.
@user-ky5dy5hl4d Galilean Relativity would like a word lol
And Paul Gerber published E=mc^2 15 years before Olinto De Pretto and 17 before Onestone.
But SR and GR are both ad hoc anyway.... both have been debunked already but the mathemagicians and cult of newton can't handle it lol
Acceleration is a GUESSTIMATE and Descartes Momentum is better than it.
Newton did a goodjob on Mass but Universal Gravitation and overreliance on the Mean Value Theorem meant it was always doomed to fail lol
How about Sophus Lies not so abstract math after all?
I really appreciate you bringing up Einstein’s contemporaries that aren’t household names but we’re an integral part of Einstein’s work.
Thanks! There were others as well who I didn't mention, for simplicity's sake. A few other mathematicians who helped Einstein with the math are mentioned by others in the comments.
One more person who I didn't fit into the video (again, for time/simplicity reasons) was Michele Besso. This was Einstein's close friend during his time working at the patent office. In Einstein's paper on Special Relativity, the only person he thanks is Besso, with whom he took many long walks where they talked through the ideas together.
@skippy6086That was General Mayhem. 😋
Wow Ben! This must've been a huge undertaking. Amazing video, full of wonderful visual explanations and put together extremely well. Great music choices, great story. Love the addition of the interview with Professor Alex K! You should be very proud of this.
Thank you Joel! I learned a lot making this and I'm proud of the result. I definitely appreciated your notes at the end on some of the finer adjustments too.
"This was when Einstein came upon what he later called the happiest thought of his life. He imagined a painter falling from the side of a building-"
This made me laugh
I’m glad it made you laugh! I think it’s funny too. There were a few variations of this story that floated around in the press at the time (eg did he actually SEE a painter falling, or did he just imagine it?), but the basic idea of Einstein envisioning a thought experiment similar to this is pretty solidly in the typical telling of the story at this point. It’s possible though that Einstein was having a bit of a laugh to some degree at the expense of the reporter - don’t forget that he WAS more than just a little bit of a troublemaker…
@@bensyversen LIAR, Read Einstein's own book on relativity instead of getting your science not from DUD like Laurence kraus or the nutter neil tyson de grasse.
One of the greatest achievements of this short video is it allows me to see all these great historical figures in the overall context. We all know Riemann hypothesis, the Hilbert list of problems etc. But now I can directly connect all these geniuses and see them in the great spacetime of the cosmos.
Thank you, I’m so glad that you enjoyed It and got this out of it!
There have been many good videos on Einstein, but this is probably the best
Amazing that Hilbert deferred to Einstein, whereas Poincaré did not
@@robertunderwood1011 Thank you, that is very kind. The story itself is amazing and I was just doing my best to do it justice!
I‘m so glad TH-cam recommended this incredible quality video after two months
Thank you!
Besides Minkowski and Grossman, Einstein also received help from Constantine Caratheodory, a Greek Mathematician considered one of the best of the 20th century. Caratheodory researched and wrote his PhD under the supervision of Minkowski at the University of Gottingen.
Wow I will look him up, thank you. I knew that Einstein consulted with other mathematicians as well, but I didn't encounter their specific stories in most of the sources that I consulted.
Dirac needed the help of Weyl and Oppenheimer for his famous Dirac equation.
Leibniz published calculus before Newton did. And consulted the works of Fermat and Descartes before publishing the error-riddled masterpiece Principia Mathematica.
There is no such thing as a "lone" genius.
Einstein's "problems" in mathematics didn't stop him from predicting stimulated and spontaneous emission; nor entanglement; nor Bose-Einstein Condensates; etc.
And in your video, you make a glaring omission: the REASON Einstein BEAT Hilbert to the final field equations of General Relativity is precisely because Einstein understood the necessity of a coordinate system that was generally covariant - Hilbert did NOT grasp this until it was too late (even though as the premier mathematician of his day, he should have known this).
The video does a great job of humanizing Einstein, foibles and all, while treating the other characters with a deference that they don't deserve. Michelle Besso deserves a bit of a shout out for helping Einstein as well.
For instance, you make no mention of the fact that it was Einstein's openeness to share his ideas with Hilbert after Hilbert invited Einstein to Gottingen to give lectures on relativity theory that LED to Hilbert trying to "nostrify" Einstein's work. You also don't make it entirely clear that it was more likely than not that Hilbert had copied ideas from Einstein from reading a preprint of his November 1914 paper.
You'd think Hilbert, not Schwardschild, would have come up with the first exact solutions to GR. And you'd think Grossman, as the professional mathematician, would have identified general covariance as a necessary framing for making use of a coordinate system, but they did not.
You should also do a deep dive on how Heisenberg needed Max Borns MATH and how Born, not Heisenberg, but matrix mechanics into quantum theory.
Also do a deep dive on how Einstein got about 33% of the way to what is now known as The Schrodinger Equation, and that without Einsteins direct help, Schrodinger likely never gets to discover the very thing he's most famous for (as Schrodinger always acknowledged).
Or how Max Born credited Einstein with the idea of probability waves.
It's become en vogue to declare all the "help" Einstein got as a way to humanize him. However, the opposite is also true. Einstein GAVE a lot of help to scientists who took his ideas without attribution and he often gets overlooked for ideas he came up with.
De Broglie is a great example. He took Einsteins equations in his 1906 - 1909 papers on quantization of energy and applied them to a gas of electrons, rather than photons as Einstein had done, and got matter waves.
Or how Einstein predicted the boson (which really should be called an Einsteinion) after Schrodinger completely misunderstood Bose's paper so thoroughly, Einstein had to write a letter to Schrodinger showing an example of the new quantum statistics (e.g. 1/3 instead of 1/2).
@@feynmanschwingere_mc2270 Hi, thank you for watching my little video and for taking the time to write this very thoughtful comment. You are certainly right on these points about the people and information that I left out of my video. In fact, I very much wanted to include something about Besso, AND more detail about Einstein and Hilbert's relationship. However, this video's runtime of 30 minutes very much pushed me to my limit as a fledgling video creator, so I had to cut fairly ruthlessly, keeping the total number of historical "characters" introduced in my narrative at 6 (Einstein, Minkowski, Grossmann, Riemann, Hilbert, Eddington) and leaving out any detail that would provide more refinement to other people involved besides Einstein. (As far as the discussion of WHY Einstein beat Hilbert, it is a fascinating detail but I thought that it could be a little bit too "in the weeds" for a general audience).
Do you have any favorite books or resources that you would recommend to viewers who are interested in learning more about these figures and the relationships that you describe?
@@feynmanschwingere_mc2270Poincaré contributed to SR by suggesting that the physics should be the same for all observers, regardless of the reference frame. When discussing GR and SR, people always omit his name. Remember, this is the backbone of RT, as it uses coordinate and Lorentz transformations to preserve Poincaré's "principle."
@@feynmanschwingere_mc2270so, in the details, is the Devil or God there?
This is awesome. Your visuals compliments the concept and you explain it well. Not too easy, but not too dense either.
Thank you!
@@bensyversen you set a high bar too early. no pressure 😉 your style is really good. It’s “accessible” but not condescendingly “dumbed down” like I’ve seen. It’s a tough concept at once but you break it into pieces that explain it in chunks.
@@nadionmediagroup Haha, yes I've thought about that. :-0
This one took me four months to make if you include the time spent figuring out the concept/framing of the story. Now it's time for a few shorter, more concise videos I think!
@@bensyversenyeah, I could tell. I just watched your archimedes video and clicked on this one and had to check that I was on the same channel cuz the lengths were so different
@@nathan9901 Yeah. Seems like people are voting with their eyeballs and telling me that shorter is better, at least for now. Gonna stick with shorter and more concise videos for the next few.
Stunning video! Always fun to learn about the history of physics. Especially with a production value like this. Impressive work
Thank you very much!
This is the most informative piece I have ever seen about AE. I was amazed to learn of his initial disdain of higher level math and of his intuitive use of the axiomatic method. Congratulations to Ben and the team for creating this gem!
Thank you very much!
Omg! This adds such a depth to the development of Einstein’s theories that I have never seen. I love this addition of seeing what he saw as a child, that lead him to develop theories and then having others expand upon those theories and leading him to appreciate math he had previously found unhelpful. It really digs into the importance of how we educate our youth. Something I am passionate about. I hated math. Same situation you mention in this video, how am I ever going to use this complex math in my life? What is the point on learning this? Later in life I grew to appreciate that same math when I grew fascinated by naked eye Astronomy. First looking at stars. Constellations. And eventually planets. And I wanted to know how we figured it out. Thousands of years ago. Without calculators or computers. Just smart people seeing a problem, and the math couldn’t explain discrepancies with a theory and observations. This was such a treat finding this video! Thank you for making it and sharing it! Brilliant!
Thank you so much for this extremely kind comment! I'm really glad to hear that the big themes that I was thinking about while making this video resonated so well with you!
This was incredible! Thanks!
Thank you very much!
This is criminally under viewed! What a great piece about one of the most important moments in the history of science and math!
Thank you for your kind words!
@@bensyversen - Keep at it!
good things are always under appreciate. ❤
I'm not a scientist. I have only a layman's grasp of the basics of all of this. But I too was baffled by the mysterious merging of Einstein's theory and the miraculous math that supports it. How on earth did this 'just happen'? This video really sheds light on the whole thing. Thanks Ben and Alex.
Thank you!
I remember reading about the history of mathematics and Archimedes use of infinitesimals. It gave me a much better understanding of calculus.
Overall, The video quality was great and the information presented is a brief summary of the history of physics and maths and how the latter provides the foundation for the former. I thank you and Mr Alex for separating some time from your busy schedules to make this well-produced and informative video. I hope to see more such collaborative videos by you.
You deserve more attention than youtube has allocated for you.
Alex Kontorovich's role in this video was similar to Minkowski's role in Einsteins work. I am proud of him for advocating Mathematics in such a happy and exciteful way.
Thank you very much! The math world is lucky to have as excellent a communicator as Alex Kontorovich around, and I was thrilled by his participation here.
I can't believe this only has 4k views right now! Bpund for millions! Amazing production and storytelling.
Thank you. Fingers crossed!
I remember a moment during a tutoring session nearly a decade ago when you gave me the best explanation of the number "e" - and years later, when teaching logs and "e", I still attempt to replicate your demonstration of a random accountant trying to continually compound interest with an obsolete gear/lever machine until his arm nearly fell off (of course, I add my own dramatic flair)! Anyway, fast forward to this week, when one of my more curious students came to me asking me a LOT about "e" and its discovery and significance and oh so much more. Naturally - pun intended - I thought of your work, and that this might be an interesting topic for a future undertaking of yours!
Good idea Laurie!
I'd love some good "e" video
@@mescwb Good call. I've got something planned for the fall that I think will fit the bill.
I’ve seen hundreds of videos about Einstein and relativity. This is top 3 for me. Glad I found it
Thank you for the wonderful comment! I’m glad you enjoyed it!
@@bensyversenI’m coming back a day later because I vaguely remember when I was dozing off to dream land last night that there was some other recommended channel in the video you said to check out but can’t seem to find it.
@@mcnugget9999 oh, the channel Float Head Physics (linked in the description) has some very good videos going into more detail on things like special relativity, exploring it in a way that I think can help people understand the intuition behind the ideas.
@@bensyversen thank you!!
One of the best video I ever watched on this weird website... Great work guys!!! Thanks for making such a great video...
Thank you for watching and I'm glad that you enjoyed it! I'm looking forward to making more.
30:07 bro went "my pain is greater than yours" 💀
yeah and nowadays we have emo pfps in youtube posting youtube shorts about pain lmao goobers
Love how everything comes together in the end and things work out
Thanks for watching!
This was so great!!! Our history of innovation is just thrilling. I loved seeing the ways people worked together to do something no one ever thought possible!
I’m glad you enjoyed it and thank you for watching!
I love the way this explains everything without explaining anything!
Well, you can't explain everything...or maybe anything?!?
@@bensyversen 🙂
Levi-Civita gave Einstein the tools he needed to flesh out general relativity with tensor calculus.
One of the best video on this topic, and also in general. Hope to see much more from you
Thank you!
I wish there was a channel highlighting the great math and science races of history like Hillbert and Einstein... great video
That is a fun idea! Some day I hope to do a video about the Newton/Leibniz dispute over the creation of calculus.
28:46 even more ironic and interesting is that the brilliant Bernhard Riemann while a student at university was assigned in a sense a doctorate thesis research topic to formulate a generalized geometry that would extend beyond classic Euclidean "flat" geometry. Riemann as this young student was not particularly happy or interested to be working on this topic of research but ventured forward none the less thus developing this new field of mathematics known today as Riemannian geometry.
Wow that is very interesting!
I hadn't thought of it quite like that. Gravity is a function of distance, but distance isn't fixed... love it. Thank you.
Thanks for watching!
You deserve way more subscribers! This video put together so many loose ends flopping around in my head, so many pieces now fitting together, the space time interval, and general relativity, it's all starting to make sense! Keep up the stellar work, please!
Thank you so much!!
HOW DOES THIS GUY HAVE ONLY 13K SUBS????? I EXPECTED AT LEAST 300K..... CRIMINALLY UNDERRATED
I need to make more videos first! The next one is long delayed but I’m excited for it…it will be good when finished.
You earned a subscriber with this one! Really well put together!
Thank you!
Bro this video was so good
Thank you!
Great work! 🤞👍Hope your channel grows!
Thank you!
@@bensyversenas a hobby, we kind of gave up of gave up on shortening the proof of Fermat’s last theorem.
The CDC 6600 counter-example won’t likely work for the Collatz Conjecture, and I’m glad I wasn’t a maths major.
Keep showing the world such fundamental break downs of the scientific stories making up our world today. Awesome work Ben ! Really places many scientific aspects together in a coherent framing as allowing far more people to efficaciously apperceive & cognitively grasp. Such important information.
Thank you very much!
how is this channel so small? the quality of this video is amazing!
Thank you!
This is an excellent presentation. Kudos and thanks!!
Thanks!
One of the best Einstein videos I've seen! Amazing!
Thank you!
By far and away the best explanation of the space-time concept I have ever seen!
That is very kind of you, thank you!
(Personally, I think that there are definitely better, more complete explanations of space-time out there than mine, but I'm very happy to hear that you found it helpful!)
Excellent Video! This is a Netflix worthy documentary! One small note - I think it would be better if u included the Michelson-Morley experiment on how the speed of light is constant in all reference frames to explain how Einstein got his postulate for special relativity
Thank you for your very kind comment!
As far as the Michelson-Morley experiment, this was one of the juicy historical tidbits that I came across in researching this video that I had to leave out for time purposes: It’s actually unclear whether Einstein was familiar with the Michelson-Morley experiment at the time that he wrote his 1905 paper (the physics taught at Zurich Polytechnic at the time that he attended was somewhat dated, and when he worked at the patent office he had a hard time keeping up with the latest research because the library was closed by the time he got off of work).
Einstein himself said different, slightly conflicting things over the years: physics.stackexchange.com/questions/89375/did-einstein-know-about-the-michelson-morley-experiment/89379#89379
There are two reasons why I love this historical tidbit so much:
1) It reminds us that history is messier than just connecting the dots chronologically. Human elements played a role back then, just like they do in our own lives.
2) Like so many of us, Einstein was once a 20-something with a day job and a dream (and a pregnant girlfriend, but that's a whole other story that I also had to leave out of the video...), and sometimes his day job got in the way of his dream.
@@bensyversen In my opinion there is no proof in the Michelson-Morley experiment or for that matter any other experiments that I have seen that the speed of light is constant in all reference frames. In every one I have seen it is the "Two way" speed that is measured as far as I can see.
It is my opinion that the speed of light is probably constant but from a constant stand still meaning that any moving observer should see the speed being slower (red shifted) if you are moving away from it's origin and faster if you move towards it's origin.
The time dilation is correct I believe. That has to do with time keeping that on the very small scale (in the atoms) must have to do with the electro magnetic propagation speed.
Time itself is a different story i believe. I believe it only exist right now. Time gone only exist as a memory and the future is yet to come but that is philosophy.
That any body's time moving at any speed should go slower than my time if I am the observer I believe is wrong. If not then a light beam emitted from my point of view should move away from me with the speed of light even though I might be moving nearly as fast in the same direction.
@@leonhardtkristensen4093 And so it does! (c + (2/3)c) / (1 + c * (2/3)c /c^2) = (5/3)c / (5/3) = c.
This video presents the common narrative used by most pop-sci stories about (what was eventually named) Special Relativity which leaves out a lot of important details about the theory itself, and the context Einstein was working in as he developed it... _and the actual problem Einstein was trying to solve_ You highlighted that in the introduction of Einstein's paper on the "Electrodynamics of Moving Bodies" but didn't explain what problem Einstein was referring to. It's actually a very important detail for understanding Special Relativity.
I'm actually falling asleep at the moment and can't focus on writing this comment right now. To summarize what I was going to say in a lot of words, what someone really needs to understand is:
• Inertia (yep, Newton's first law of motion, and Galilean Relativity)
• Classical electromagnetism (Maxwell's equations and the Lorentz force)
Special Relativity is a direct logical consequence of this.
Furthermore, nobody was surprised by Einstein's 1905 papers on electrodynamics. Lorentz, Fitzgerald, Larmor, Poincaré, et al. had already figured out the same thing over the previous 20 years (in a tremendously convoluted roundabout way). The reason why Einstein didn't explain anything like why the speed of light is constant for all observers, _is because everyone already knew that_ ! Maxwell figured that out in the 1860's (arguably the experimental measurements going back to Rolmer in the 1700's also indicate a constant propigation velocity for light).
The controversy over Special Relativity at the time it was published was about whether or not it was actually a new idea. There were at least four other theories of relativity by other people at the time. Most people credited Poincaré until Poincaré said that Einstein's theory was completely unrelated to his theory of relativity.
I've actually read Poincaré's papers, and it's stunning, because it's what gets used to explain Einstein's Special Relativity in pop-sci videos about Einstein... which brings me back to my original thesis...
The stories you hear, outside of an actual physics class, in the popular media _is the old Lorentz-Larmor luminiferous aether theory_ with the word "luminiferous aether" crossed out. That's why everyone who hears these stories thinks: "Why isn't there an aether? It sounds like there should be an aether." The source of pop-sci explanations of Special Relativity are _other_ pop-sci explanations of Special Relativity, and not modern physics textbooks. So these pop-sci stories haven't been corrected since the 1920's.
I have a lot to say about how badly Relativity gets presented, but I'm currently falling asleep right now, so I'll have to write it later.
HI thank you for writing. You’re right that there are a lot of details left out. That’s by design - this video is intended as more of an overview/starting point than any kind of definitive word, especially as it relates to the details of what’s known as special relativity. The broad outline and conclusions about originality that I convey are mostly based on the Walter Isaacson biography(certainly you’d probably categorize that as pop sci), but I’ve also listed in the description a number of other resources that I consulted, esp with regards to things like Minkowski’s work.
I invite you to write again with more detail on your perspective, and I would ask that you also point the audience towards reputable resources where they can learn more if they are interested. Thanks again!
Leaving this here to get notified when an update comment is posted
@kingZ3ro I haven't forgotten about this; I have just been very busy with other stuff and not... you know, writing stuff in TH-cam comments.
Most of the explanation is about _inertia_ specifically _how_ it works. Inertia is fundamental to the very core of Einstein's Relativity. Also, electricity and magnetism. Special Relativity *_unifies_* electricity and magnetism into _electromagnetism_ (This *is* the actual reason Einstein created "Special Relativity" as it's now called.)
@@juliavixen176 Understandable, people have stuff to do
But about the unification of electricity and magnetism, I'm probably missing something here, but wasn't the whole point of Maxwell's laws to prove that electricity and magnetism were two sides of the same coin?
If so what was then the need for special relativity to unify them?
Sorry if this sounds like a dumb question.
@kingZ3ro There's a "problem" with Maxwell's Equations. There's nowhere to stick a velocity term... You know how a moving electric current creates a magnetic field, and a moving magnetic field creates electric current? How does the magnet know it's moving? Moving _with respect to... what_ ?
If Alice and Bob are looking at some electrically charged whatevers, and Alice stands "at rest" on the surface of the Earth, while Bob rolls by in a tain car in a straight line at constant velocity. Bob has two electrically charged balls sitting on a table, at rest, inside the train. From Bob's point of view, the electric charges are _not_ moving, and so there's no magnetic field. Alice watches the train with Bob and his electric charges moving in a straight line at constant velocity. From Alice's point of view, the electric charges _are_ moving... so Alice will see a magnetic field... right?
So, is there a magnetic field or not? Who is correct?
Anyway, the solution is to invent Special Relativity.
By using animation, right brained ppl like me can finally understand mathematics.
I feel like I'm really learning for the first time in my 57 years.
Thanks for your effort to educate the masses who want to learn.
You’re welcome. I’m glad you enjoyed It and found it valuable!
excellent video... explanation... personal anecdotes making it seem I was there... well done!
Thanks!
This is a fantastic documentary. Really well done.
Thank you!
Hilbert Space and other math concepts --> String Theory --> Modelling problems from other domains
This video is underrated, soon this channel will average 10x the amount of views per video
Thank you!
Great work. It’s easy to get blindsided by Einstein’s unfathomable genius and forever that he was standing on the shoulder of giants and collaborating with other masterminds to put together the puzzle of space time
A different but very relevant perspective on how Einstein arrived at his general theory of relativity. Very well made documentary 👌
Thank you!
This was lovely to watch; I am shocked to find out that Einstein wasn’t a mathematician. It’s so much more accurate to call him a logician with a focus in theoretical physics.
I’m glad you enjoyed it!
To be clear, he was an excellent mathematician by the standards of most of us “regular people”, but for general relativity he definitely needed to call in help. There were other mathematicians he consulted too besides Grossmann but I left them out for simplicity’s sake.
@@bensyversen oh absolutely, I love math and I couldn’t imagine wrangling Riemann’s stuff.
But for some reason I always thought of Einstein as this math-focused genius, where his Theory of Relativity came from investigating math and seeing how it bumped up into physics and the cosmos.
It’s super interesting to see that it was the other way around. Obviously the math is very advanced and complex and necessary, but the math theory was developed separately, and the implementation of the math came from the physics.
And all of that was building not just on knowledge of physics, but overwhelmingly on a foundation of logististical prowess.
Obviously Einstein was brilliant, and his knowledge of Physics and Math was incredible. But this is the first I’ve heard of him as a logician and I absolutely love knowing that about him.
@@titaniadioxide6133 I love it too!
Very good production. Melvyn Bragg in his BBC Radio 4 'In Our Time' repeatedly marvels at how abstract maths or things done just because someone thought about doing it often turn out to be part of or essential too later developments in science and / or technology.
Yes indeed. Thank you for watching!
this is so well made!
Thank you!
This video is really cool!
Thanks!
Ben you are killing it with those two videos please don’t stop uploading.
Thank you very much! Looking forward to making more. I’ve got something shorter and fun in the works as well as something else that’s more ambitious.
Ben, this was a very enlightening and enjoyable treatment of Einstein. Keep up the good work. By the way, the music was just fine for me. It added to the excitement of the presentation to me. Especially when watching it later in the evening.
Thank you very much! And thank you for the comment about the music. I’m glad you enjoyed it. I definitely plan to continue including music in my videos, though I’ve identified some ways that I can improve my skills to make it more effective going forward.
@@bensyversen The stuff is interesting enough without music. But if you "must" have it, keep it on very low level, barely audible. It will still have some effect subconsciously!
@@user-gr5tx6rd4h Thanks for watching! Yes, I'm working on improving my sound design choices and execution for the next one.
Well deserved sub. Great material, groundbreaking for my understandanding of Einsteins ideas
I’m so glad to hear it! Thank you for watching
That was very well done! Thank you
Thanks for watching!
Amazing video bro. Congrats.!!
Thank you!
Really excellent video!! I remembered an anecdote about Einstein"s trip to Italy. Back from there he was asked by a Journalist what he had enjoyed best of it, at which he answered: "Maccaroni and Tulio Levi Civita" who was one of th few mathmen that mastered the absolute differential. calculus or diferential Geometry without which you can't figure GeneralRelativity. Regards!
Thank you very much for watching! That's a great anecdote.
enjoyed the video very much! 😌
Thanks!
Very well done!
Thank you!
Love hearing the shotout for floatheadphysics!
He’s so great!
Amazing video, thanks so much. Really interesting and nicely put together. I subbed.
Thank you!
I can see a new Veritasium. Brilliant documentary man! Keep it up.
Thank you very much!
Love your work! You’re awesome!!!
Thank you!
Speaking of math coming before physics, David Hilbert is the same Hilbert who created "Hilbert spaces", essentially the general abstraction of dimensional space, with possibly infinite dimensions, that lies at the heart of the math of Quantum physics.
Absolutely amazing video 🎉🎉🎉
Thank you!
Great content. I hope you stay motivated making these videos
Thank you!
Getting ready to start my phy 405 hw this just motivated tf out of me thank you
That’s awesome! And good luck with the hw!
I always struggled with math in high school but at 23 watching this video this made perfect sense to me?
That’s great!
Thank you for posting the correct (to the best of our knowledge) Pythagoras story.
Very well researched and presented in an interesting manner . Kudos !
Thank you!
FANTASTIC !!! What a great presentation.
Thank you!
Very nice, lucid explanation. I wish I’d had you as a teacher. 😊
Thank you! And thanks for watching!
Good video and clear explanation!
Will try to find out more explanations & understanding of the Theory of Relativity in your other videos, hopefully!
Pls cut down the voume of the background music at the beginning.
It was hard to concentrate, so as to hear the voiceover.
Thank you!
Yes I am aware of the music issue. I can’t make changes after upload to this one but I’m working to improve my sound design for my upcoming videos.
Ahh, this whole narrative is so well-crafted! You really had me at the edge of my seat by the end there... brilliant storytelling on display here 👏
Thank you so much!
That's a really cool new proof of the Pythagorean theorem.
That was wonderful. Thanks.
Thanks!
Einstein is my mathematical hero. He knew things ordinary people cant phathom.
Amazing video! A great channel is in the making!
Thank you so much!
That was a great video, I'll check out your other ones. Thanks.
Thanks for watching!
Dirac needed the help of Weyl and Oppenheimer for his famous Dirac equation.
Leibniz published calculus before Newton did. And consulted the works of Fermat and Descartes before publishing the error-riddled masterpiece Principia Mathematica.
There is no such thing as a "lone" genius.
Einstein's "problems" in mathematics didn't stop him from predicting stimulated and spontaneous emission; nor entanglement; nor Bose-Einstein Condensates; etc.
And in your video, you make a glaring omission: the REASON Einstein BEAT Hilbert to the final field equations of General Relativity is precisely because Einstein understood the necessity of a coordinate system that was generally covariant - Hilbert did NOT grasp this until it was too late (even though as the premier mathematician of his day, he should have known this).
The video does a great job of humanizing Einstein, foibles and all, while treating the other characters with a deference that they don't deserve. Michelle Besso deserves a bit of a shout out for helping Einstein as well.
For instance, you make no mention of the fact that it was Einstein's openeness to share his ideas with Hilbert after Hilbert invited Einstein to Gottingen to give lectures on relativity theory that LED to Hilbert trying to "nostrify" Einstein's work. You also don't make it entirely clear that it was more likely than not that Hilbert had copied ideas from Einstein from reading a preprint of his November 1914 paper.
You'd think Hilbert, not Schwardschild, would have come up with the first exact solutions to GR. And you'd think Grossman, as the professional mathematician, would have identified general covariance as a necessary framing for making use of a coordinate system, but they did not.
You should also do a deep dive on how Heisenberg needed Max Borns MATH and how Born, not Heisenberg, but matrix mechanics into quantum theory.
Also do a deep dive on how Einstein got about 33% of the way to what is now known as The Schrodinger Equation, and that without Einsteins direct help, Schrodinger likely never gets to discover the very thing he's most famous for (as Schrodinger always acknowledged).
Or how Max Born credited Einstein with the idea of probability waves.
It's become en vogue to declare all the "help" Einstein got as a way to humanize him. However, the opposite is also true. Einstein GAVE a lot of help to scientists who took his ideas without attribution and he often gets overlooked for ideas he came up with.
De Broglie is a great example. He took Einsteins equations in his 1906 - 1909 papers on quantization of energy and applied them to a gas of electrons, rather than photons as Einstein had done, and got matter waves.
Or how Einstein predicted the boson (which really should be called an Einsteinion) after Schrodinger completely misunderstood Bose's paper so thoroughly, Einstein had to write a letter to Schrodinger showing an example of the new quantum statistics (e.g. 1/3 instead of 1/2).
Hi, thank you for watching my little video and for taking the time to write this very thoughtful comment. You are certainly right on these points about the people and information that I left out of my video. In fact, I very much wanted to include something about Besso, AND more detail about Einstein and Hilbert's relationship. However, this video's runtime of 30 minutes very much pushed me to my limit as a fledgling video creator, so I had to cut fairly ruthlessly, keeping the total number of historical "characters" introduced in my narrative at 6 (Einstein, Minkowski, Grossmann, Riemann, Hilbert, Eddington) and leaving out any detail that would provide more refinement to other people involved besides Einstein. (As far as the discussion of WHY Einstein beat Hilbert, it is a fascinating detail but I thought that it could be a little bit too "in the weeds" for a general audience).
Do you have any favorite books or resources that you would recommend to viewers who are interested in learning more about these figures and the relationships that you describe?
Without Einstein's equivalence principle Hilbert would never have thought of GR.
Wonderfull! Thank you! I especially liked the "wink" toward Platonism at the end. :-)
Thank you for watching. I’m glad you enjoyed it!
Einstein's Pythagorean Theorem uses scale-symmetry, and that's what gave him relativistic intuition. Wish I could show him my d=(c-b)/a base scale. Maybe he could've used it for simpler gravity math. Thanks for the insight that a cone is Thales Theorem with infinitely sized radii.
I love this Ben! Congrats on a fantastic production!!
Thanks Morgan! Hope all's well with you these days!
@29:40
The TL:DR is.. Nothing, I ramble aimlessly.
I love the point being made here, about the mathematicians coming up with their crazy stuff, no one paying much mind to it, for decades, until one day someone realizes it's exactly what is needed to explain something else.
I like learning about how "we" know what we know (yes, "we" is doing a _lot_ of lifting here), and how the kernel of an idea can be picked up, put down, and eventually end up sidelined, possibly for years, before finding its way to someone who is at the right place, and time, to be able to recognize it is a missing piece of a breakthrough puzzle.
It happens a lot, and it's nuts how often someone has come up with something that didn't find a practical use in their niche area of expertise, but turned out to be in some way central to the progress of another, sometimes long after the original author/ creator has shuffled off this mortal coil.
I read a few of the speeches/ talks, articles and interviews that Einstein did, and something he made a point to discuss, more than once, was the importance learning the history of, and reading good works in the philosophy of science. It seems like it should be a no brainer, really, but some really nerdy people are bizarrely blinkered. Einstein seemed to consider this knowledge to be key to future progress.
I personally think that the "shut up and calculate" contingent of modern physics, those who have been vocal about their disdain for the notion of philosophy having merit, at all, are possibly some of the most confused people on the planet, right now.
It is hilarious to hear several someones who aren't even a little bit your practical, hands on, experiment devising/ conducting type of physicist, snarking that philosophy is garbage because you can't further the fields of physics, by (paraphrasing), sitting in a chair thinking really hard about things.
Like, uh, projection, maybe? Or, seriously confused about the fundamental nature of what it is that they're doing when they're trying to solve problems by sitting on their arse, thinking really hard about things?
I know ostensibly the idea is that their work will lead to something that a testable hypothesis can be created from, that will have practical use, progress the field and what have you, but until that time, they're just engaging in using very, very advanced math to represent the values of processes and physical constants, involved in very complex ways, which are derived using the axioms of mathematics, an understanding of the nature of the interactions, and by thinking really hard about it all...
It's really complicated, logically rigorous and robust, very niche, tunnel visioned philosophy, really.
Point is, Einstein was obviously correct to point out how important it is to learn and understand how progress and breakthroughs happen. If you pay attention to history, there is a predictable pattern of breakthrough - Flurry of progress and understanding - over confidence in some newly created concepts/ notions (s) that emerge, - hubris - academics chasing their own tails while inexplicably doubling down on defending a very obviously incompatible idea /or three - Philosophically inclined contributors begin to converge on concepts that lead directly to the next paradigm shifting breakthrough - Flurry of progress.... and on it goes.
We need a few more academics with outlooks like our happy math genius here, embracing the philosophical and using it as the invaluable tool it has been, I think there is a shift already happening, away from the philosophically phobic view, which fills this rambling moron's heart with joy -
why i didn't discover this cannel earlier? This videos are pure gold ty
Thanks!
Nah this video was beautiful from start to end
Ben your content is addictive keep going 😍😍
Thank you! I’m working on more!
This is an awesome video. Very inspirational, in fact.
Glad you enjoyed it!
@@bensyversen The Pythagorean space-time interval was fascinating. Consider me a very uneducated enthusiast, so I likely get quite a bit wrong.
This past week I got interested in Heron's Formula for the area of a triangle and found the sum of 4-d cubes subtracted from the sum of 4-d prisms.
x^2+y^2+z^2 - (ct)^2 reminded me of that sum of volumes minus other related volumes.
My flawed intuition would suggest adding, not subtracting, that fourth element in the space-time interval.
Wonderful food for thought. I have much to learn.
@@johnnyragadoo2414 Yes, I agree that the space time equation feels a bit counter intuitive.
Here's a video that does a good job around 5:40 of visually explaining the fundamental invariance that it preserves, when they represent it by areas of the figures being shown being preserved as the shape is stretched. Subtracting the (ct)^2 term is what leads to the hyperbolas you see: th-cam.com/video/uVxL8Q4bpqc/w-d-xo.html
@@bensyversen Fascinating. Thank you for that reference!
Great video, honestly i wanted it to be even more longer.
Thank you! No question that I had to leave out a lot to get it to 30 minutes
I gave this a thumbs up primarily because of the mathematician's statement at the end that mathematics approximates the universe, it doesn't govern it. I really detest the phrase "governing equations". Equations don't govern anything. They describe, and usually only approximately. Kudos.
Thank you, and thank you for watching!
Now the next step is figuring out how general relativity and quantum mechanics fits together and once again time is the key. General relativity and quantum mechanics will never be combined until we realize that each individual observer is observing them both at different moments in time. Because causality has a speed limit (c) every point in space where one observes it from will be the closest to the present moment. When one looks out into the universe they see the past which is made of particles (GR). When one tries to measure the position of a particle they are observing smaller distances and getting closer to the present moment (QM). The wave property of particles appears when we start trying to predict the future of that particle. A particle that has not had an interaction exists in a future state. It is a probability wave because the future is probabilistic. Wave function collapse is what we perceive as the present moment and is what divides the past from the future. GR is making measurements in the observed past and therefore, predictable. It can predict the future but only from information collected from the past. QM is attempting to make measurements of the unobserved future and therefore, unpredictable. Only once a particle interacts with the present moment does it become predictable. This is an observational interpretation of the mathematics we currently use based on the limited perspective we have with the experiments we choose to observe the universe with.
Great youtuber. Thank you.
Thank you!
Nice 🙂 documentaric information 👍.
Thanks!
Great music in the foreground.
Haha yes I’ve heard feedback that the music was too loud. My bad. I will definitely be sharing my mix with a few unbiased sets of ears before I publish the next one.
@@bensyversen Thank you !
One more thing which could be mentioned (but not essential in an overview) is that Rieman tensor was not suitable for solving the problem. This requested to switch to Ricci tensor (Rieman's is a matrix of matrices, while Ricci's is a matrix of scalars, to simplify a bit) while subtracting 1/2 of the Ricci scalar (the trace of the tensor) including the metrics (g(μ)(ν)). To do this he had to ask for the help of Tullio Levi Civita, who would teach Einstein this kind of math. Einstein had really to delve in complex mathematics to solve his problem!
Thank you! Yes the story is more complex than the format of this video really allows room for. In addition to Tullio Levi Civita, other commenters have also highlighted Constantine Caratheodory's contribution to Einstein's understanding of the mathematics involved.
Beautiful video
Thanks for watching!
I suggest on the history of mathematics you make one about Isaac Newton.
Newton is on my mind! 😀
I was reading about Eddington and his full story along with another guy who was on a similar mission and it was a huge accomplishment with many obstacles. According to the story I read Einstein even had time to make some type of correction to his prediction before the final results had been made.
I wish I could remember where I found it.
Yes there was a whole earlier expedition that I really wanted to include in the video but left out due to time and relevance. Basically, there was a solar eclipse happening in 1914 in the Crimean peninsula, which was a part of Russia at that time. Einstein found a young German astronomer named Erwin Freundlich and helped arrange the funds to set up the expedition (I think he even paid some out of pocket). Freundlich and team arrived in the Crimea several weeks before, and then World War I broke out. Since Germany and Russia were now enemies, the team was arrested and their equipment confiscated. (They were eventually sent home)
This was all lucky for Einstein though, because his prediction at that point was wrong. It was basically in line with the prediction that would have come from treating light as a particle with mass using the Newtonian model.
I read about this in the Walter Isaacson biography of Einstein, but here is a more detailed article on the topic: www.machinedesign.com/automation-iiot/article/21835940/how-wwi-saved-einsteins-theory-of-relativity