The Meaning of the Metric Tensor

Поделиться
HTML-код
  • Опубликовано: 31 май 2024
  • In the follow-up to our prior video, Demystifying the Metric Tensor, we continue to explore the physical and conceptual intuition behind the complex mathematical object known as The Metric Tensor, whose crucial role in the General Relativity, requisite to understanding the theory, tends to be easily obscured by abstract ideas and mathematics.
    Support us on Patreon! / dialect_philosophy
    Contents:
    00:00 - Introduction
    00:54 - Spacetime Cartography
    02:30 - Maps / Coordinate Systems
    04:00 - Bar Scales / Metrics
    06:03 - Spacetime Distance
    07:30 - Topological Transformations
    08:39 - The 2D Metric
    13:58 - The 3D Metric
    18:39 - Conclusion
  • НаукаНаука

Комментарии • 396

  • @MrAguc01
    @MrAguc01 Год назад +86

    This is a fantastic video, with well explained concepts and perfectly illustrated! I have a PhD in Physics and a master in Mathematics but despite all this, I have never seen the tensors concept so well explained. Other videos are always focused in the matematical operations and interpretations but here you can see the how it relates to real world. You make it so simple in this video that I will recommend this to my students!
    Your series are a very welcome addition to explain the beuty of Physics and Math!
    Please keep the excellent work and I will keep helping you as well.Thanks!

    • @dialectphilosophy
      @dialectphilosophy  Год назад +15

      Thank you so much for your support! Feedback like yours definitely keeps us motivated, and your generosity is equally appreciated. Hopefully it will help your students wrap their head around the physics a little more easily. More is coming, so stay tuned!

    • @stevecrothers6585
      @stevecrothers6585 7 месяцев назад

      :-: Crothers, S.J. Proof that Einstein’s field equations are invalid: Exposition of the unimodular defect, Physics Essays, Volume 34: Pages 420-428, 2021. Received: July 8, 2021; Accepted: August 14, 2021; Published Online: September 17, 2021:
      vixra.org/pdf/2206.0082v1.pdf
      Abstract:
      Albert Einstein first presented his gravitational field equations in unimodular coordinates. In these coordinates, the field equations can be written explicitly in terms of the Einstein pseudotensor for the energy-momentum of the gravitational field. Since this pseudotensor produces, by contraction, a first-order intrinsic differential invariant, it violates the rules of pure mathematics. This is sufficient to prove that Einstein's unimodular field equations are invalid. Since the unimodular form must hold in the General Theory of Relativity, it follows that the latter is also unsound, lacking a proper mathematical foundation.
      www.physicsessays.org/browse-journal-2/product/1896-2-stephen-j-crothers-proof-that-einstein-s-field-equations.html
      Stephen J. Crothers: The General Theory of Relativity: Its Faulty Mathematical Foundations
      ruclips.net/video/0CSL702JSdY/видео.html

  • @alemorita92
    @alemorita92 2 года назад +106

    I did my undergraduate research and master’s on GR. Had I seen a video with this quality back then, I wonder how much faster I would have grasped concepts in GR. Fantastic video, explanatio, and animations!

    • @HarpSeal
      @HarpSeal Год назад +1

      Is this channel accurate on gr?

    • @jaimemat3
      @jaimemat3 10 месяцев назад +1

      De eso se trata, de acelerar la curva de aprendizaje en modo autodidacta, buscando el mensaje que calce con nuestro mood del momento.

    • @pushpendrayadav7069
      @pushpendrayadav7069 8 месяцев назад

      Where are you from?

    • @stevecrothers6585
      @stevecrothers6585 7 месяцев назад

      :: Crothers, S.J. Proof that Einstein’s field equations are invalid: Exposition of the unimodular defect, Physics Essays, Volume 34: Pages 420-428, 2021. Received: July 8, 2021; Accepted: August 14, 2021; Published Online: September 17, 2021:
      vixra.org/pdf/2206.0082v1.pdf
      Abstract:
      Albert Einstein first presented his gravitational field equations in unimodular coordinates. In these coordinates, the field equations can be written explicitly in terms of the Einstein pseudotensor for the energy-momentum of the gravitational field. Since this pseudotensor produces, by contraction, a first-order intrinsic differential invariant, it violates the rules of pure mathematics. This is sufficient to prove that Einstein's unimodular field equations are invalid. Since the unimodular form must hold in the General Theory of Relativity, it follows that the latter is also unsound, lacking a proper mathematical foundation.
      www.physicsessays.org/browse-journal-2/product/1896-2-stephen-j-crothers-proof-that-einstein-s-field-equations.html
      Stephen J. Crothers: The General Theory of Relativity: Its Faulty Mathematical Foundations
      ruclips.net/video/0CSL702JSdY/видео.html

    • @Blake_47
      @Blake_47 5 месяцев назад

      Hey I'm an undergraduate physics student and I've some questions

  • @jrv634
    @jrv634 2 года назад +214

    Wow! I rarely write any comments in RUclips but I must say the level of detail and simplicity with which you describe these concepts is astounding. Hope you get millions of subscribers soon, not only you deserve it but they would hugely benefit from this content.

    • @TheMemesofDestruction
      @TheMemesofDestruction 2 года назад +2

      ^ This :-)

    • @ihatethesensors
      @ihatethesensors 2 года назад +7

      I completely agree and I can't wait for the next one. The graphics were amazing! A difficult subject described simply - it's beautiful.

    • @-danR
      @-danR 2 года назад +5

      Dialect has suddenly become not only the most illuminating school of introductory SR and GR, but a model _master-class_ on _how to explain SR and GR_ . And I speak as one who has watched dozens of youTube channels on the topic and 100's of hours, and many years. It is in danger of rendering channels like eigenchris, The Science Asylum, SciencClic, Eugene Khutoryansky practically marginalized, if not irrelevant. They had better stand up and take notice: This is how you actually explain things.
      If I have any objection at all, it's that the (excellent) ambient music could be reduced to, say, 2/3's volume.

    • @TheMemesofDestruction
      @TheMemesofDestruction 2 года назад +1

      @@-danR We’re all entangled. But yes this Channel’s communicated knowledge per minute value is extremely high! ^.^

    • @squarerootof2
      @squarerootof2 Год назад

      Maybe if he introduced some cute cats mixed with some really stupid pranks and some tik-tok style hoes, he would reach a million subs...

  • @eigenchris
    @eigenchris 2 года назад +21

    Another great video on the metric. I've been through pages Schutz and MTW, desperately trying to understand things. It really helps to have a video like this to consult first.

    • @stevecrothers6585
      @stevecrothers6585 7 месяцев назад

      Crothers, S.J. Proof that Einstein’s field equations are invalid: Exposition of the unimodular defect, Physics Essays, Volume 34: Pages 420-428, 2021. Received: July 8, 2021; Accepted: August 14, 2021; Published Online: September 17, 2021:
      vixra.org/pdf/2206.0082v1.pdf
      Abstract:
      Albert Einstein first presented his gravitational field equations in unimodular coordinates. In these coordinates, the field equations can be written explicitly in terms of the Einstein pseudotensor for the energy-momentum of the gravitational field. Since this pseudotensor produces, by contraction, a first-order intrinsic differential invariant, it violates the rules of pure mathematics. This is sufficient to prove that Einstein's unimodular field equations are invalid. Since the unimodular form must hold in the General Theory of Relativity, it follows that the latter is also unsound, lacking a proper mathematical foundation.
      www.physicsessays.org/browse-journal-2/product/1896-2-stephen-j-crothers-proof-that-einstein-s-field-equations.html
      Stephen J. Crothers: The General Theory of Relativity: Its Faulty Mathematical Foundations
      ruclips.net/video/0CSL702JSdY/видео.html

  • @worldwithinadream
    @worldwithinadream 2 года назад +36

    I have bachelor degree in physics and I find this metric intuition as clear as it could be. Better than in any book I read.

  • @chyldstudios
    @chyldstudios 2 года назад +53

    I'm astonished at the level of detail in this video. Well done!

  • @nemvus_
    @nemvus_ 2 года назад +102

    The amount of this video that is 3D animated is impressive. I imagine it takes a lot of clever work to get the 3D shapes to behave that way in the video. Excellent quality content. Needs more views.

  • @jmchez
    @jmchez 2 года назад +46

    When Professor Goodstein of Caltech got a grant to film his lectures and use the latest 3d animation back in 1983, he created one of the greatest teaching tools in physics still fantastically useful to this day, "The mechanical World and Beyond". I've been wondering for a while how much better the animations could be done with today's technology. Frankly, not that much better. but your videos do fill in the gaps in some areas and are a worthy successor to Goodstein.

  • @stevewhitt9109
    @stevewhitt9109 2 года назад +19

    This was amazing. After years I finally get the intuition.

  • @mikegale9757
    @mikegale9757 2 года назад +17

    Beyond brilliant. You really got it down to the brass tacks. Testify!

  • @agrajyadav2951
    @agrajyadav2951 Месяц назад +1

    bhai kya gajab video banaya maja aa gayi, pasta khate khate dekha, metric tensor bhi samajh gaye aur swad bhi samjho double ho gaya, mauj kara di matlab. Adbhut bro keep it up!

  • @nosnibor800
    @nosnibor800 2 года назад +13

    Thanks that was well described - my God the amount of work you put into the graphics. The 4th dimension adds time. Then we need to understand how mass causes tensor to change. Thanks

  • @HassaanFareed
    @HassaanFareed Год назад +4

    How can someone be so perfect in explaining such a difficult concept. Your order of explaining things is perfect for the proper understanding. And I can understand how much difficult it is to produce animations of this quality. Keep making such an amazing content for us ❤️

  • @JoEbY-X
    @JoEbY-X 2 года назад +8

    I have a degree in mathematics and studied some physics but never formally studied relativity, but decided to learn it myself. After finally thinking I had a grasp of special relativity, I tried to tackle general relativity but never quite got a grasp of what a metric tensor is the few times I tried. Your video is the most amazingly intuitive treatment I could possible imagine. I get it now! Thank you!
    Also, I conceptualize special relativity just as you did at 6:16 with a light clock measuring time perpendicular to the velocity. But I never quite understood why the spacetime interval involves subtraction instead of addition. I can easily perceive time dilation and length contraction with a Minkowski diagram, but the image at 6:16 and your description of the spacetime interval as simply being the static proper time FINALLY made it click!

    • @dialectphilosophy
      @dialectphilosophy  2 года назад +4

      Thanks for watching! We put that visual of the light clock in exactly for that reason, so we're glad to hear it clicked for you!

    • @abnereliberganzahernandez6337
      @abnereliberganzahernandez6337 Год назад

      Man so you are mathmatican AND didnt had a course con diferencial geometry?
      Imean I am computer scientist AND love math.
      But It Is interesting to see that no body fully understands everything

    • @stevecrothers6585
      @stevecrothers6585 7 месяцев назад

      >>

  • @elindauer
    @elindauer 8 месяцев назад +1

    The visualizations in these videos are amazing. The whole series is beautifully instructive. Great work.

  • @flmbray
    @flmbray 2 года назад +2

    What an amazingly simple and straightforward explanation. Although I not a physicist, I do watch a lot of these types of videos, and I've seen explanations of the metric tensor before. But this is the first (and only) one that really made it clear. The analogy to old maps and how they depict a curved space in a stretched fashion for our benefit was absolutely perfect. It all feels so natural now that I'm sure I will retain this new knowledge. Thanks! You earned a subscribe from me!

  • @mickwilson99
    @mickwilson99 11 месяцев назад

    Bloody good start. One of my favourite analogues for tensors is playing games like Railway Life. The further you in the cab are from "events" (e.g. your destination at your scheduled arrival time) then shorter are your "kilometers" and the faster your "hours" pass. A great way for short-cutting the boredom of being stuck in proper-time-and-distance for a 500km run across Germany to France

  • @erikquintanilla7705
    @erikquintanilla7705 2 года назад +8

    Amazing content. Love the clarity

  • @nooneinparticular3370
    @nooneinparticular3370 2 года назад +5

    I watched the video and I honestly don't understand how such a small channel can manage to have such amazing animations, great job!
    Anyways, as a mathematician with physicist friends, in my experience what happens is that they don't have the mathematics physically and historically motivated, and so they're just left confused by it all, and it's only in hindsight that they realize what all those maths were saying physically, so this channel is certainly plugging quite a glaring hole in that regard!
    As it regards to tensors in particular, the issue I see is that the average physicist will ask you "How should I interpret _a_ tensor?", but the problem is that there is, to my knowledge, no good explanation or physical motivator for _all_ tensors that would allow physicist to go "Ooh, okay!"; you essentially need to go type by type, and then explain what the whole dropping and raising indices magic is.
    So far as I know (Gravitation is on the mail and I'll start getting serious with GR once it arrives), the only books that give a decent explanation and motivation for such geometrical concepts are (an honourable mention might be Jürgen Josts edition of Riemann's "On the Hypothesis Which Lie at the Bases of Geometry", which is a short and sweet book) Lee's "Introduction to Smooth Manifolds" and "Introduction to Riemannian Manifolds"; the latter even has the occasional detail about pseudo-Riemannian/Lorentzian manifolds.
    Which segways into my last point: I know it's hard, but I really hope you guys make justice to the distinction between regular old Riemannian manifolds (which are very intuitive) and the Lorentzian spacetimes one deals with in GR (which are completely alien to the uninitiated), and in particular explain at length how the mathematicallty seemingly innocuous condition of changing the signature of the metric tensor so as to ensure everyone measures _c_ to be the same everywhere has in fact huge mathematical (and therefore physical) consequences.

    • @dialectphilosophy
      @dialectphilosophy  2 года назад +3

      Thanks for watching! The interpretation of what a tensor "is" was something that frustrated us for the longest time, and we couldn't get good answers on it. The discussion of what defines a tensor in the abstract, general sense is something we dropped from these videos altogether, because we finally realized it just wasn't necessary. What a tensor is or isn't in terms of physical meaningfulness varies depending on context. And yeah, the Lorentzian vs. Riemannian signature was a little too much to squeeze into this video. More forthcoming!

    • @HesderOleh
      @HesderOleh 2 года назад +2

      This comment got me thinking that some of the math youtube channels should organize to make explainer videos for math wikipedia pages. Wikipedia pages are really great in most of the sciences, having both high level explanations along with some easier to understand explanations, but most of the math wikipedia pages just assume you know everything about the concept and are just wanting to look up some small detail of definition.

    • @nooneinparticular3370
      @nooneinparticular3370 2 года назад +1

      @@HesderOleh I know exactly what you mean, as I've found myself with the same problem too many times. I think the worst ones were either the page for "Spinors" or the one about the "Clebsch-Gordan coefficients"; the ones about the mathematics behind physics are the worst offenders in my experience.

  • @stevenschilizzi4104
    @stevenschilizzi4104 2 года назад +1

    Fantastic presentation. I’m eager to see the sequel. Thanks for putting all this together for us.

  • @alamagordoingordo3047
    @alamagordoingordo3047 2 года назад +2

    Great clarity. I can't wait for the next episode. Thank you!

  • @nicolaecoman7188
    @nicolaecoman7188 2 года назад +3

    Incredible animations and explanations. keep up the good work!

  • @SuperMenders
    @SuperMenders Год назад

    Wow the best Introduction to Differential Geometry, i have ever seen!

  • @Maderum
    @Maderum Год назад

    Wow! The animations and simplicity of explanations on this video blew my mind! Well done sir, well done.

  • @MictheEagle
    @MictheEagle Год назад

    Pure Gold! This is the school we all needed. Bravo! Keep it coming, and Thank you.

  • @jack.d7873
    @jack.d7873 2 года назад +1

    Newly discovered your channel Dialect. And as someone who's familiar with Special Relativity wanting to understand General Relativity, your visual presentation along side clear, slowed foundational GR language is absolutely brilliant.
    I feel it in your video's, your goal and target audience is too teach this subject to people who have zero knowledge of GR. And as someone who feels like your target audience, I must say again, the ways you teach are mindbogglingly sensational!
    I'll give you a donation for your service to humanity. You've earned it.

  • @manymany1191
    @manymany1191 Год назад

    I really like the pauses in narration at the right spots to give me a moment to think through what's just being said.

  • @png7
    @png7 2 года назад +1

    These video came out just before I needed them, They are very detailed and explain a lot with out be confusing.

  • @casaroli
    @casaroli Год назад

    Thank you for finally making this intuitive.
    No textbook I’ve ever read has been capable remotely achieving this.

  • @roberthayter157
    @roberthayter157 Месяц назад

    Absolutely stunning graphics. Brilliant explanations.

  • @bofink5377
    @bofink5377 2 года назад +1

    Thank You for the very clearly and straight forward explained Metrics and mapping. This clears many problems for me, trying to really understand the General Relativity and Gravitation in a more visual way, than just the plain raw mathematics.

  • @justynpryce
    @justynpryce 2 года назад

    Really happy to see this upload I appreciate you guys doing this!!

  • @yashasvikatara1244
    @yashasvikatara1244 2 месяца назад

    I cannot put it in words how amazed I am that you made such an intricate concept so easy to understand. I'm really greatful, thanks a lot ❤

  • @cesarjom
    @cesarjom 2 года назад +1

    Very well explained and demonstrated with visualizations!

  • @oblivitus.
    @oblivitus. Год назад

    You deserve a ton of veiws! Brilliant quality!

  • @sonysantos
    @sonysantos Год назад

    Your videos are very good, both in content and visual effects. You deserve more subscribers!

  • @snakecsmaker
    @snakecsmaker 5 дней назад

    I gave up science 8 years back. But this video made some dying neurons fired again. It feels always great! Thank you!

  • @deltalima6703
    @deltalima6703 Год назад

    This better not be clickbait. Could not resist the title

  • @jeanklein2198
    @jeanklein2198 Год назад

    May I share my praise to whoever scripted and executed this wonderful video. Excellent quality content

  • @brianyeh2695
    @brianyeh2695 4 месяца назад

    The effort required for this video is beyond words...
    Keep going man. I truly admire your great explanation. Other videos just focus on the math operations rather than giving intuitions for what they are doing. For example, you explain the shrinking of areas near the north and south pole by playing around the transformation matrix and squeezing the element in the animation at the same time! That's extremely helpful to understand!

  • @AlokKumar-ym8bl
    @AlokKumar-ym8bl 7 месяцев назад +1

    🎉 excellent information..thank you sir for making this highly informative article about space and time.

  • @jialixx
    @jialixx 2 года назад +1

    This is amazing! Can't wait for your next video. Thank you for sharing.

  • @jewulo
    @jewulo 2 года назад +1

    Hello Dialect. Awesome work. Simply brilliant. Thank you very much for this.

  • @tanyachou4474
    @tanyachou4474 Год назад

    One of the most underrated channel on RUclips! Thank you !

  • @umeshchandramakwana806
    @umeshchandramakwana806 Год назад

    Awesome !
    Really a great clarity in explaining the complex concepts! 👍👍👍

  • @jimlbeaver
    @jimlbeaver 2 года назад +1

    Outstanding…thanks for the patient and diligent explanation

  • @cesararf
    @cesararf 10 месяцев назад

    Amazing explanation. Until now I didn't understand anything on metric tensors although I had heard of them. You deserve a massive thumbs up. 🎉

  • @zerozzable
    @zerozzable 2 года назад +2

    Your videos are beyond brilliant. Keep it up.

  • @beln33
    @beln33 Год назад +1

    excellent job, Dialect. I highly recommend watching this video after the one titled "Demystifying the metric tensor in GR". After watching both (and taking some notes), the importance of the metric tensor should be obvious to anyone interested in GR and cosmology. I'm looking forward to watch "part 3" with will go about the 10 component tensor for curved spacetime.

  • @a.andacaydn9736
    @a.andacaydn9736 2 года назад +4

    Another amazing video! I cannot thank you enough

  • @1three7
    @1three7 2 года назад +4

    I love your videos so much. I'm not someone with enough math background to keep up with most physics stuff. But I also hate how unhelpful it is to just get over simplified analogies. It's hard to strike a balance of being clear to lay people but also being accurate and describing it with the underlying math in an intuitive way. Your channel is one that excels at that in my opinion. The animations really help keep things clear. Plus I love the music too! Thanks for putting the effort in on these. It's greatly appreciated!

    • @thorntontarr2894
      @thorntontarr2894 2 года назад

      Unlike you, I find the music annoying and distracting.

    • @DennisMHenderson
      @DennisMHenderson Год назад +1

      @@thorntontarr2894 I foun/d it, ‘Hard; 2bete [0ff] 2it-2nite

  • @matthewbusche4547
    @matthewbusche4547 2 года назад

    I've been looking for a simple explanation of GR tensors for years. This was fantastic. I too hardly ever write comments, and only hit the like button once or twice a year. Here I've done both. Thanks so much.

  • @Minstorm34
    @Minstorm34 2 года назад

    Insane quality from a

  • @SeaPpl
    @SeaPpl Год назад

    U shud deserve a noble prize for this explanation.

  • @TranquilSeaOfMath
    @TranquilSeaOfMath 11 месяцев назад

    Great presentation! Well animated and explained.

  • @v_wilson
    @v_wilson 7 месяцев назад +2

    Wow! Such a great animated video and explanation...🤩🤩🤩🤩❤❤

  • @williamolenchenko5772
    @williamolenchenko5772 Год назад

    Fantastic explanations and animations.

  • @cykkm
    @cykkm 2 года назад +5

    Dialect, you're a genius of a teacher!!! Holy Great Guacamole with vuvuzela on a Pogo stick, this is the most visual explanation of the metric tensor that I have ever seen! And I am not only a physicist by education; I had a full GR course with applied diffgeo in my grad school (following the MTW book) 25 years ago. The _abstraction_ of a tensor in my head has always been a row of columns of rows of columns of etc. (rows are covariant, living in a dual space, columns are your normal contravariant vectors); the metric you can slice either way. This is how it's easy to connect the tensor product with the normal linear algebra dot products, but that's only another, if a more familiar abstraction. Can you maybe eventually develop similarly simple visuals for tensor calculus? I'm not even working in physics any more, but I love GR so much for its concise elegance, but it's still a mathematical, not a visual elegance. But I'm ultimately a visual thinker, and I never looked at the spacetime like that!

    • @dialectphilosophy
      @dialectphilosophy  2 года назад +3

      Thanks for watching and we appreciate the compliments! In terms of how to define a tensor in the abstract and general sense, there seem to be a variety of ways to go about it and mostly they all confuse us 😂. When (and if) we understand the mathematics more fully, we may very well consider a series simply about tensor calculus in-itself. Of course, we tend to be more interested in the philosophy of mathematics, namely when its justified to apply certain calculuses, so you're more likely to see a series skewed towards that.

    • @-danR
      @-danR 2 года назад

      This _alone_ :
      0:35 - 0:38
      is one of the most expressive and illuminating 3 seconds in the entire history of GR pedagogy.
      And I speak as one who has watched 100's of hours of youTube explanatory videos on the subject. Now granted one would want some background material to understand what that elegant bit of choreography is describing. But one could dispense with those hundreds of other hours (scienceAsylum et al.) and replace them with the rest of Dialect's classes in Relativity, which are also master-classes in _how to explain Relativity_ .

  • @sinekonata
    @sinekonata Год назад

    Nah, thank you. So much. I can't believe we now get this much better of an idea just because someone on the internet decided to put big effort into visualising, explaining and then writing in video what he understands. We're pretty lucky. This kind of shit used to be only accessible if you had direct written correspondence with a physics master, waiting forever for his letter to come back or travelling to his university.

  • @Redant1Redant
    @Redant1Redant 2 года назад

    amazingly good explanation. I wish I had seen this 10 years ago. It would have clarified a lot. Thank you for this video.

  • @crabcrab2024
    @crabcrab2024 Год назад

    I am very impressed by your videos! Great Job of visualization and explanation. UR going to be a success.

  • @user-ph5in5fi1q
    @user-ph5in5fi1q 9 месяцев назад

    Just awesome. We lost the essence of physics behind those equations and maths. No one describes it visually like you did. Thanks a lot.

    • @stevecrothers6585
      @stevecrothers6585 7 месяцев назад

      ;;;;Crothers, S.J. Proof that Einstein’s field equations are invalid: Exposition of the unimodular defect, Physics Essays, Volume 34: Pages 420-428, 2021. Received: July 8, 2021; Accepted: August 14, 2021; Published Online: September 17, 2021:
      vixra.org/pdf/2206.0082v1.pdf
      Abstract:
      Albert Einstein first presented his gravitational field equations in unimodular coordinates. In these coordinates, the field equations can be written explicitly in terms of the Einstein pseudotensor for the energy-momentum of the gravitational field. Since this pseudotensor produces, by contraction, a first-order intrinsic differential invariant, it violates the rules of pure mathematics. This is sufficient to prove that Einstein's unimodular field equations are invalid. Since the unimodular form must hold in the General Theory of Relativity, it follows that the latter is also unsound, lacking a proper mathematical foundation.
      www.physicsessays.org/browse-journal-2/product/1896-2-stephen-j-crothers-proof-that-einstein-s-field-equations.html
      Stephen J. Crothers: The General Theory of Relativity: Its Faulty Mathematical Foundations
      ruclips.net/video/0CSL702JSdY/видео.html

  • @jzblue345
    @jzblue345 Год назад

    I'm so glad I found this channel.

  • @anandbavkar8572
    @anandbavkar8572 2 года назад

    Excellent Work!! I wouldn’t be surprised if this leads to true understanding. Thanks a lot for making these videos.

  • @tianchenzheng7464
    @tianchenzheng7464 2 года назад

    This is amazing, can't wait to see more of your videos

  • @massimoacerbis8138
    @massimoacerbis8138 2 года назад +1

    One of the best video on general relativity ever
    I have watched that many on the topics
    Highly recommended

  • @zacmilne9423
    @zacmilne9423 Год назад

    Such a well made and educational video. Subscribed!

  • @DickHoskins
    @DickHoskins Год назад

    Amazing video with respect to content and presentation. Graphics are superb and totally support the math. Thank you!

  • @Markoul11
    @Markoul11 2 года назад +1

    This video is a masterpiece! Bravo!!

  • @johnathos
    @johnathos 2 года назад +2

    Really wonderful! Please, keep going!!

  • @menglongyouk167
    @menglongyouk167 2 года назад +1

    Well-explained. Thank you.

  • @Ri-bc5ff
    @Ri-bc5ff 2 года назад +2

    Great job!
    Kindly make a video explaining concept of induced metric ,intrinsic and extrinsic metric

  • @Alpasonic
    @Alpasonic 2 года назад +1

    Thank you. It was extremely satisfying

  • @coolwinder
    @coolwinder 2 года назад

    First time i dvel into relativity, but just amazing!! You are amazing, thank you for this pace of work!

  • @aurelienyonrac
    @aurelienyonrac Год назад

    Each year is incomparable.
    Enjoy the present 🎁

  • @eduardogonzcerv4636
    @eduardogonzcerv4636 2 года назад +1

    Man, your animation is awesome!

  • @93katwal
    @93katwal Год назад

    thankyou for such a wonderful explanation

  • @muttleycrew
    @muttleycrew Год назад

    Excellent presentation. Thanks uploader.

  • @GrandMarshalGarithos
    @GrandMarshalGarithos 3 месяца назад +1

    Wow, this is superb. Thank you.

  • @abulkhondker3556
    @abulkhondker3556 2 года назад

    This is a superb video. The 3D animation is out of the world (pun intended). I cannot wait to watch more videos like this.

  • @geraltofrivia9424
    @geraltofrivia9424 Год назад

    Another masterpiece. Thank you very much for what you do.

  • @BravoZulu2023
    @BravoZulu2023 Год назад

    Excellent⋯get me to know and further understand more about metric tensor. THX.

  • @omsingharjit
    @omsingharjit Год назад

    This channel is going to hit Millions sooner

  • @hexeract9541
    @hexeract9541 2 года назад +2

    i literally have a project due on this in two days, thank you so much

  • @misnik1986
    @misnik1986 2 года назад

    I have just discovered your channel, this is an outstanding video, waiting for next

  • @tanvirfarhan5585
    @tanvirfarhan5585 2 года назад

    Besttt..!!!!!!! i really really love your contents, i appreciate your effort. You deserve a lot 🔥🔥

  • @Mouse-qm8wn
    @Mouse-qm8wn 3 месяца назад

    Master piece. Thank you so much. I finally get it 😉👍❤️

  • @lucasf.v.n.4197
    @lucasf.v.n.4197 Год назад +1

    Best explanation and animation

  • @EricKolotyluk
    @EricKolotyluk 2 года назад +2

    Wow, that was beautifully explained... thanks. Not that I grok it now, but I can certainly appreciate it better than before.

  • @winsomehax
    @winsomehax Год назад

    Yeah this is a great explanatory video. Really well done.

  • @sumanthakur1519
    @sumanthakur1519 Год назад +1

    Really such a good explanation hats off sir keep it up

  • @JeanSarfati
    @JeanSarfati Год назад

    Totally pedagogical. Bravo !

  • @twisted4872
    @twisted4872 Год назад

    Holy Higher dimensions . . .that was simply exquisite.

  • @BrendavonAhsen
    @BrendavonAhsen 2 года назад

    This is super good. You deserve more subs.

  • @inverse_of_zero
    @inverse_of_zero 2 года назад

    wow, this is an incredible video, with the concepts so well explained and illustrated! i have three mathematics degrees, with majors in physics and mathematics, and i have studied general relativity and differential geometry. but despite all this, i never fully grasped the concept of the metric tensor until you explained it so simply in this video. thank you! i will recommend this to my students; if only i had seen this when *I* was a student myself!

    • @dialectphilosophy
      @dialectphilosophy  2 года назад +1

      Thank you so much for your support! We're really glad the video helped and hopefully if you check back in a few months we'll be on to the connection coefficients and curvature tensor!

  • @GizmoMaltese
    @GizmoMaltese Год назад

    Best explanation of the metric tensor ever

  • @Burkard42
    @Burkard42 2 года назад

    Wonderful video. THANKS!

  • @MrStevieJStewart
    @MrStevieJStewart 2 года назад +1

    Dude that was amazing thank you!!!

  • @dfkjbdfondfngg
    @dfkjbdfondfngg 8 месяцев назад +1

    Awesome animations!

  • @stevedavey9435
    @stevedavey9435 Год назад

    THANK YOU SO MUCH FOR MAKING THIS VIDEO!!!!!!!!!!