How Simple Math Led Einstein to Relativity
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- Опубликовано: 29 мар 2024
- Einstein turned the world on its head in November of 1919, when data collected during a solar eclipse matched the predictions of his Theory of General Relativity. But Einstein’s path to discovering his theory traces back much further, to when he was 12 years old and he first learned about an ancient mathematical method…
Special thank you to Professor @AlexKontorovichMath of Rutgers University and Museum of Mathematics (MoMath) for his help and participation.
Additional credits:
Giacomo Belletti - camera
Brandt Adams - newscaster voice
Kolja Gjoni - drum roll
Valentin Cazako - help with creating the “Pringle chip” model and 3D animations
Music from Epidemic Sound and Envato Elements.
Thank you to Joel Simser (@CreateSmarter) for valuable feedback on edits, and everybody else who gave me feedback and advice during this process.
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This video was originally inspired by a 2015 article by Steven Strogatz in The New Yorker Magazine about Einstein’s proof of the Pythagorean Theorem: www.newyorker.com/tech/annals...
“Einstein, His Life and Universe” by Walter Isaacson served as a primary source for the biographical details: amzn.to/3TxtJRS
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To learn more about Special Relativity and Minkowski space-time:
@Mahesh_Shenoy - The Triplet Paradox - • The complete intuitive...
'We all move at speed of light through spacetime'.. What does it really mean? - • 'We all move at speed ...
@MinutePhysics - SpaceTime Intervals: Not EVERYTHING is Relative | Special Relativity Ch. 7 - • Spacetime Intervals: N...
To learn more about General Relativity:
@veritasium - Why Gravity is NOT a Force - • How Gravity Actually W...
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*A Note about how I use AI generated images in my videos*
The emerging ability of artificial intelligence to generate compelling images from text prompts opens new possibilities for compelling storytelling. However, when mixed with real historical imagery, as is in my video, it has the potential to create confusion, or worse, if not handled properly.
I have set a few guidelines for my use of AI generated images in this video so that a viewer can easily understand which images are real photographs and which are synthetically generated:
ALL images that have been placed in a “frame” (eg a border that resembles an old photo print, etc) are REAL historical images.
ALL images that include Einstein's full face, as well as all World War I related images, are REAL historical images.
I have used Midjourney AI to create “stock” image elements including backgrounds, illustrations, and objects.
I have used Midjourney AI to create some images that are implied to be of Einstein. In these, Einstein’s face is FULLY OR PARTIALLY OBSCURED.
Please send me a message or drop a comment and I'll be happy to clarify any specific images.
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Items that Appear in the Video:
•“Notes for an Autobiography” by Albert Einstein - originally published in the Saturday Review of Literature, November 26, 1949
•Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise - Manfred Schroeder - amzn.to/3viq1n6
•Documents from Einstein’s Studies at the Zurich Polytechnical Institute - tinyurl.com/33ds27xa
•On the Electrodynamics of Moving Bodies - Albert Einstein - tinyurl.com/42hmyftj
•Space and Time: Minkowski’s Papers on Relativity - Hermann Minkowski - tinyurl.com/5n79k9ef
•An Introduction to Riemannian Geometry - tinyurl.com/yc5x2ac7
•The Collected Papers of Albert Einstein - einsteinpapers.press.princeto...
•A Peek Into Einstein’s Zurich Notebook - John D. Norton - tinyurl.com/4w2df5xt
•Hilbert Paper - tinyurl.com/3mdcercw
•Solar Eclipse Maps from 1911 - 1920 - tinyurl.com/3p8pmx8b
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Additional Sources:
•Relativity: The Special and General Theory - Albert Einstein - amzn.to/43xh4Tx
•Richard Feynman’s lecture on the Special Theory of Relativity - www.feynmanlectures.caltech.e...
•Hermann Minkowski’s Spacetime: The Theory That Einstein Overlooked - David D. Nolte - tinyurl.com/27aa9nw5
•How Einstein Lost His Bearings, and with them, General Relativity - Kevin Hartnett - tinyurl.com/3zv5awwk
•The 1919 Eclipse Results that verified General Relativity and their later detractors: a story retold - Gerard Gilmore and Gudrun Tausch-Pebody - tinyurl.com/54p2e4kt
•Marcel Grossman and his contribution to the General Theory of Relativity - T. Sauer - tinyurl.com/5ate8m6r
•Einstein’s Pathway to General Relativity - John D. Norton - tinyurl.com/3mjajz4c
Photos:
•Wikimedia Commons - commons.wikimedia.org/wiki/Ma...
•Leo Baeck Institute - tinyurl.com/f6vt5uhk
Note: Amazon links are affiliate links which help support the channel at no additional cost to you.
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!
This video twists a lot of things out of physics, truth and facts about Einstein. Axioms are entities accepted by humanity as evident truths. So, if I - by algebra - start shuffling the Pythagorean theorem by algebra rules and then begin working backwards by different algebra rules, I will come back to the point of my start. By multiplying a^2+b^2=c^2 by a constant and then during reversal and by using a different algebraic method I will come back to the original equation. So, the proof is circular here and really it does not prove anything besides the well established fact of Pythagorean theorem. It is not true that Einstein was the first to come up with the idea of relativity. Gauss, Bernhard Riemann, and Ernst Mach for general relativity. Subsequently, claims have been put forward about both theories, asserting that they were formulated, either wholly or in part, by others before Einstein who was not a mathematician but physicist. Einstein was bad at math. Grossman and his wife Mileva were doing math for Einstein.
The video makes a blunder at 18:31; the astronaut depicted is surrounded by gravity constantly for gravity is in Universe's space all over. It is because the gravity that the astronaut is in FREE FALL and not isolated from gravity. This is the cardinal mistake that physics students make in class thinking that a spaceman is floating because there is no gravity in his surrounding. THERE IS GRAVITY THERE but he is in precisely free fall because of gravity.
Einstein stole lost of ideas and works of other people. For example the Schwartzchild's metric tensors were incoroporated in GR by Einstein and Einstein worked on them but could not come up because tensor math is extremely difficult and Einstein was not a mathematician and the tensors are not his. Einstein never gave the definition of time. How can one work with time with no definition of it?
Also, space is not a flat sheet of cloth on which stars and planets are placed. Time can't have a direction as depicted on the space-time diagram because we are dealing with something substantial (space; we can measure it as a volume ) and an elusive entity (time) which can't be measured with a sentient device. Therefore, clocks have nothing to do with time for a clock does not feel time and moreover clocks have nothing to do with time as you try to measure time with a broken clock. Does a broken clock have anything to do with time? No, a broken clock or efficient clock have nothing to do with time not even atomic clocks.
Einstein did not come up with anything new and he did not come up with E=mc^. The equation of E=mc^2 DOES NOT belong to Einstein ! ! ! Before him there was Samuel Tolver Preston who developed the theory of relativity even before Einstein was born. Einstein is not the maker of E=mc^2. In Einstein's first paper about energy and mass, E=mc2 doesn't actually appear anywhere-he originally wrote the formula as m=L/c2. It was the Italian amateur physicist Olinto de Pretto who published E=mc^2 in 1903 and Einstein's Italian friend physicist Besso was given that equation by Olinto. Besso took that equation and gave it to Einstein. And Einstein plagiarized it changing the equation later on. Einstein was a plagiarist. Link:
ruclips.net/video/fsOba2upljw/видео.html
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.
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.
This video twists a lot of things out of physics, truth and facts about Einstein. Axioms are entities accepted by humanity as evident truths. So, if I - by algebra - start shuffling the Pythagorean theorem by algebra rules and then begin working backwards by different algebra rules, I will come back to the point of my start. By multiplying a^2+b^2=c^2 by a constant and then during reversal and by using a different algebraic method I will come back to the original equation. So, the proof is circular here and really it does not prove anything besides the well established fact of Pythagorean theorem. It is not true that Einstein was the first to come up with the idea of relativity. Gauss, Bernhard Riemann, and Ernst Mach for general relativity. Subsequently, claims have been put forward about both theories, asserting that they were formulated, either wholly or in part, by others before Einstein who was not a mathematician but physicist. Einstein was bad at math. Grossman and his wife Mileva were doing math for Einstein.
The video makes a blunder at 18:31; the astronaut depicted is surrounded by gravity constantly for gravity is in Universe's space all over. It is because the gravity that the astronaut is in FREE FALL and not isolated from gravity. This is the cardinal mistake that physics students make in class thinking that a spaceman is floating because there is no gravity in his surrounding. THERE IS GRAVITY THERE but he is in precisely free fall because of gravity.
Einstein stole lost of ideas and works of other people. For example the Schwartzchild's metric tensors were incoroporated in GR by Einstein and Einstein worked on them but could not come up because tensor math is extremely difficult and Einstein was not a mathematician and the tensors are not his. Einstein never gave the definition of time. How can one work with time with no definition of it?
Also, space is not a flat sheet of cloth on which stars and planets are placed. Time can't have a direction as depicted on the space-time diagram because we are dealing with something substantial (space; we can measure it as a volume ) and an elusive entity (time) which can't be measured with a sentient device. Therefore, clocks have nothing to do with time for a clock does not feel time and moreover clocks have nothing to do with time as you try to measure time with a broken clock. Does a broken clock have anything to do with time? No, a broken clock or efficient clock have nothing to do with time not even atomic clocks.
Einstein did not come up with anything new and he did not come up with E=mc^. The equation of E=mc^2 DOES NOT belong to Einstein ! ! ! Before him there was Samuel Tolver Preston who developed the theory of relativity even before Einstein was born. Einstein is not the maker of E=mc^2. In Einstein's first paper about energy and mass, E=mc2 doesn't actually appear anywhere-he originally wrote the formula as m=L/c2. It was the Italian amateur physicist Olinto de Pretto who published E=mc^2 in 1903 and Einstein's Italian friend physicist Besso was given that equation by Olinto. Besso took that equation and gave it to Einstein. And Einstein plagiarized it changing the equation later on. Einstein was a plagiarist. Link:
ruclips.net/video/fsOba2upljw/видео.html
@@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?
@@bensyversen What are these ''some other things'' I mention that you don't know how they relate to the video?
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.
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.
Huh. I thought General Relativity was a commander in the Napoleonic Wars. 🫤
@@skippy6086That was General Mayhem. 😋
"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.
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.
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
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?
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!
I‘m so glad RUclips recommended this incredible quality video after two months
Thank 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.
Thank you!
Stunning video! Always fun to learn about the history of physics. Especially with a production value like this. Impressive work
Thank you very much!
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.
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!
I remember reading about the history of mathematics and Archimedes use of infinitesimals. It gave me a much better understanding of calculus.
how is this channel so small? the quality of this video is amazing!
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.
One of the best video on this topic, and also in general. Hope to see much more from you
Thank you!
You earned a subscriber with this one! Really well put together!
Thank you!
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.
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!
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.
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.
Well deserved sub. Great material, groundbreaking for my understandanding of Einsteins ideas
I’m so glad to hear it! Thank you for watching
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!
Bro this video was so good
Thank you!
This is an excellent presentation. Kudos and thanks!!
Thanks!
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.
That was very well done! Thank you
Thanks for watching!
Hilbert Space and other math concepts --> String Theory --> Modelling problems from other domains
Very well researched and presented in an interesting manner . Kudos !
Thank you!
This is a fantastic documentary. Really well done.
Thank you!
Love hearing the shotout for floatheadphysics!
He’s so great!
I can't believe this only has 4k views right now! Bpund for millions! Amazing production and storytelling.
Thank you. Fingers crossed!
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 RUclips 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.
this is so well made!
Thank you!
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!
This was incredible! Thanks!
Thank you very much!
Wonderfull! Thank you! I especially liked the "wink" toward Platonism at the end. :-)
Thank you for watching. I’m glad you enjoyed it!
Very well done!
Thank you!
why i didn't discover this cannel earlier? This videos are pure gold ty
Thanks!
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!)
This video is really cool!
Thanks!
enjoyed the video very much! 😌
Thanks!
I can see a new Veritasium. Brilliant documentary man! Keep it up.
Thank you very much!
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.
I love this Ben! Congrats on a fantastic production!!
Thanks Morgan! Hope all's well with you these days!
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!
Amazing video! A great channel is in the making!
Thank you so much!
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!!
FANTASTIC !!! What a great presentation.
Thank you!
Great content. I hope you stay motivated making these videos
Thank you!
Very nice, lucid explanation. I wish I’d had you as a teacher. 😊
Thank you! And thanks for watching!
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: ruclips.net/video/uVxL8Q4bpqc/видео.html
@@bensyversen Fascinating. Thank you for that reference!
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.
A different but very relevant perspective on how Einstein arrived at his general theory of relativity. Very well made documentary 👌
Thank you!
This video is underrated, soon this channel will average 10x the amount of views per video
Thank you!
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!
Thank you for posting the correct (to the best of our knowledge) Pythagoras story.
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.
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.
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
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
as an undergrad physics student, it's nice hearing something about the actual people behind quantum mechanics' dear old Hilbert spaces, or Eddington's limit for the rate of black hole mass accretion. Nice video
p.s. please lend me your strength, I'm at my last exam and I can't take it anymore, I've pretty much wasted the last month
Thank you!
You can get through the last exam…it sounds like you’re really close!
Excellent Video!
Thank you very much!
Very inspiring!, very good!
Thank you!
Love this video!
Thank you!
@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 -
Great video, hope more people see this video
Thank you!
Amazing video!
Thank you!
BRAVO!!! Brilliant and beautiful!
Thank you!
Thanks Ben for this amazing video!!! Looking forward to more!
Thank you for watching! I’m looking forward to making more
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 love the way this explains everything without explaining anything!
Well, you can't explain everything...or maybe anything?!?
@@bensyversen 🙂
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
Outsanding work of art!❤
Thank you very much!
Nah this video was beautiful from start to end
Brilliant, thank you 😉
Did they ever consider that the Lorentz factors look surprisingly much like projections ("cosines") back and forth between the two systems, if we interpret them geometrically - so that is it's NOT the actual length of an object along its direction of motion that appears (!) to be contracted, but rather its projection (!) onto this dimension of space that shrinks more and more, as v goes towards, so that there really isn't any paradox - i.e.
the faster an object moves relative to an observer, the less it's present in this "length" dimension of the observer.
And in a similar way, but in the opposite direction for the time axis.
Have we simply been wrong all along in assuming a one (!) dimensional time, which can then be dilated or squeezed? - do these relativistic effects "really" stem from the observer and the object following different paths (directions) in a 2-dimensional complex time plan?
Hi, thank you for watching!
Yes, I am sure that Einstein, Minkowski, etc understood that the Lorentz transformations can be interpreted as "projections" of 4 dimensional space-time on 3 dimensional space, though I'm afraid I can't point you offhand to a specific document where they describe it that way.
I can say that there are a handful of good RUclips videos which use this approach to intuitively explaining Lorentz transformations. Here's one that helped me get a good handle on how to discuss this topic for this video: ruclips.net/video/TJmgKdc7H34/видео.html
Great presentation thankyou
I’m glad you enjoyed it!
This fucking awesome. Stick with it, you will grow quickly.
Ben your content is addictive keep going 😍😍
Thank you! I’m working on more!
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.
👍 Nice.
I suggest on the history of mathematics you make one about Isaac Newton.
Newton is on my mind! 😀
OMG!! What an incredible channel! I so much enjoyed this video. I consider myself very fortunate to have discovered this channel. I can't wait for your next video.
Thank you!
Regarding useless 19th C mathematics, that entire story would be replayed with the works of Sophus Lie, and the eponymous groups that are foundational in the standard model.
Levi-Civita gave Einstein the tools he needed to flesh out general relativity with tensor calculus.
With regards
Here's a case of Einstein being completely wrong:
"The observer performs experiments on his circular disc with clocks and measuring-rods. In doing so, it is his intention to arrive at exact definitions for the signification of time- and space-data with reference to the circular disc K', these definitions being based on his observations. What will be his experience in this enterprise? To start with, he places one of two identically constructed clocks at the center of the circular disc, and the other on the edge of the disc, so that they are at rest relative to it. We now ask ourselves whether both clocks go at the same rate from the standpoint of the non-rotating Galileian reference-body K. As judged from this body, the clock at the center of the disc has no velocity, whereas the clock at the edge of the disc is in motion relative to K in consequence of the rotation. According to a result obtained in Section XII, it follows that the latter clock goes at a rate permanently slower than that of the clock at the center of the circular disc, i.e. as observed from K.
It is obvious that the same effect would be noted by an observer whom we will imagine sitting alongside his clock at the center of the circular disc. Thus on our circular disc, or, to make the case more general, in every gravitational field, a clock will go more quickly or less quickly, according to the position in which the clock is situated (at rest). For this reason it is not possible to obtain a reasonable definition of time with the aid of clocks which are arranged at rest with respect to the body of reference. A similar difficulty presents itself when we attempt to apply our earlier definition of simultaneity in such a case, but I do not wish to go any farther into this question." (Einstein 1920)
Clocks at any two points on a rotating disc would always stay synchronized, because there is no relative velocity between them, exactly the same as if the disc were not rotating. If an outside observer saw a clock on the outer edge of the disc go out of sync with the one closer to the center, while they stayed in sync from each clock's viewpoint of the other, what would happen when the rotation stopped? The two clocks can't be synchronized and also desynchronized, it would have to be one or the other, and synchronized is the most logical, because otherwise observers with the clocks on the disc would see the clocks suddenly snap to a desynchronized state just because the rotation stopped. Since that wouldn't happen in the real world, we can conclude that the outside observer never did see the clocks desynchronized at any time, Einstein was just wrong.
I always loved doing thought experiments (mine are always blank)
That's some pretty advanced math he studied in high school.
For sure. There's a narrative that goes around that's not quite right, which says that Einstein wasn't a good math student. He mastered differential and integral calculus at 16, so he was definitely no slouch. But at the same time he was a bit of a troublemaker when it came to relationships with his teachers. And as I understand it, college was when he started to get lazy in math class because he didn't think it was important.
@@bensyversen The Einstein biography by Walter Isaacson gives an anecdote that when he was shown the fun fact that "The Genius Einstein failed maths in high school" (something like that), he chuckled and remarked that he had mastered calculus by the age of 15.
American math curriculum is way behind the curved and taught by NON MATHAMATICIANS . that is why is is so terrible .
@@georgesheffield1580The math curriculum in high schools in the United States is not uniform across the country - it differs from region to region, from state to state, from county to county, from school to school.
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!
Pythagoras isn’t just about geometry, it’s about any things that are unrelated, e.g. addition of uncorrelated errors, or how far a random walk takes you, or signal power and noise power, and so on …..
Good vid
Thank you!
Great.
Ben Syversen,
I would like you to accept a challenge in which I prove (using Occam's Razor) that Einstein was wrong about everything he said about Relativity, Time, and time Dilation.
You can count on me to provide an alternative representation (not using geodesics) that can reproduce all Einsteins' successes and succeed where he failed.
The Occam's Razor support comes from me providing a simpler model that doesn't require geodesics, metric, inflation, false vacuum decay, Higgs Mechanism for Inertial Mass Creation, Quantum Field Theory, Dark Matter, Dark Energy, Space Stretching.
You seem knowledgeable about Einstein's work and might still be capable of learning new tricks...:)
Marco Pereira
Length contraction is about the scale applied to space not the quantity of space (e.g. size). It is the mechanism for acceleration in a particle accelerator after the initial boost. The particle beam is because the time container is too small for the space contained.
Time scales space is a critical conclusion of Relativity. GR then applied that concept to show the mechanism for gravity.
Length contraction in Galilean Relativity was about change in position. It wasn’t about the size of a thing either. Common misconception leading to the erroneous concept of spaghettification…. But that’s a whole other story.
I would think that by 1905, Einstein would have heard of the Michaelson-Morley 1887 experiment.
The idea was that if light was a wave motion, it must be waves in something that filled space, the “luminiferous aether”.
Since the Earth presumably was moving through the aether, you should be able to measure the speed of light as different in different directions.
However, Michaelson & Morley did the experiment and could find absolutely no difference in speed for different directions and for different times of year. The speed of light seemed to be constant - which seemed nuts.
If Einstein had heard of these experiments, that would be the reason for his second postulate.
Yes. The answer to this question is a bit ambiguous though. Einstein didn't reference the experiment in his writings until 1907, and he said mixed things at different times in his life about whether or not he was aware of the experiment prior to his 1905 paper.
physics.stackexchange.com/questions/89375/did-einstein-know-about-the-michelson-morley-experiment
This might seem improbable in retrospect where the experiment is seen as such an important moment in the timeline of physics. But I'm not sure exactly how well-known and widely disseminated the M-M experiment would have been at that time: this was long before the internet after all. Also, Einstein's school did not emphasize the latest developments in physics so it is reasonable to think that he might have had some blind spots.
Einstein is my mathematical hero. He knew things ordinary people cant phathom.
More proof that the universe is well defined
17:35 This just popped into my head.
Could be meaningless.
Make of it what you will...
From a derivation of E=γm₀c²,
γ³m₀a(||) is used as the parallel component
(to velocity v) & γm₀a(⟂) is the perpendicular component, if I remember correctly.
For gravitational freefall, a=g & the perpendicular component is zero, so let's look
at the γ²m₀g part of F(||):
μ=GMm₀.
μγ²/R²
=μ(c²/(c²-v²))/R²
=μ(X²/t²((X/t)²-(x/T)²))/R²
=μ(1/(T² - (x/X)²t²))/(R/T)²
=μ(1/(T² - (x/X)²t²))/w²/4π², w=2πR/T
=μ(ω/w)²/((T/t)²- (x/X)²)), ω=2π/t.
For low velocities, m=m₀γ≈m₀, and the force in the v^ direction in this case is:
F(||)≈ GMm(ω/w)²/((T/t)²- (x/X)²))
So... c≡X/t and v≡x/T and I assume you're trying to... um... these are two different time coordinates? The "t" and "T" I mean, these should be the same since the velocities you use in that gamma factor are measured from _the same_ inertial reference frame. I think there's an algebra error because you go from c²/(c²-v²) to X²/t²((X/t)²-(x/T)²) but that should be (X²/t²)/((X/t)²-(x/T)²)
And why is there angular velocity?
But also... gravity is not a force in General Relativity. I'm not sure what you're trying to do.