An Introduction to Curvilinear Coordinates in Differential Geometry

Рет қаралды 35,268

Күн бұрын

The equations of General Relativity are written in the language of curvilinear coordinates, where mathematical objects like Basis Vectors, Metric Tensors, and Christoffel Symbols dominate the landscape. But where do these concepts come from and how can we connect them to our physical intuition? Join us to find out. Plus -- hotwheels! (Note: some familiarity with vector calculus is highly recommended.)
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Conceptualizing the Christoffel Symbols Video:
• Conceptualizing the Ch...
Metric Tensor Trilogy:
• The Metric Tensor
Contents:
00:00 - Intro
00:50 - What are Curvilinear Coordinates?
03:28 - Basis Vectors & Parametric Basis
08:00 - Coordinate Acceleration & Levi-Civita Condition
11:47 - The Christoffel Symbols
12:53 - Characterization of Arbitrary Coordinates
14:42 - Characterization of Polar Coordinates
19:12 - Geodesics
20:31 - Curved Surfaces

Пікірлер: 203

@sudokode 2 ай бұрын

Babe wake up. New Dialect just dropped

@shiftedprograms86 2 ай бұрын

I never slept.

@justanotherguy469 2 ай бұрын

At what speed? 9.8 m/s^2?

@rebase 2 ай бұрын

It didn't "drop". It merely followed a spacetime geodesic.

@sudokode 2 ай бұрын

@@justanotherguy469 c 👀

@Voshchronos 2 ай бұрын

@@rebase nice 👌

@stephanieparker1250 2 ай бұрын

This channel is criminally underrated. 😫

@001firebrand 2 ай бұрын

Cause knowlegde is power. In our case, knowledge of tensor algebra, tensor calculus and differential geometry is absolute power 😎

@jiiiiiiiiiiiiiiiiiii Ай бұрын

I'm confused, shouldn’t it be relative power?

@neil1629 2 ай бұрын

I'm confused, I was told that Differential Geometry was really hard, but this is unbelievably clear. Thank you.

@dialectphilosophy 2 ай бұрын

😂

@DanielKRui 2 ай бұрын

These videos are the new standard for differential/Riemannian geometry education (just as 3b1b's linear algebra videos were instantly the new standard for linear algebra education). I am grateful to live at during a time in which they exist.

@juliavixen176 2 ай бұрын

Eigenchris also has a very good series of videos on differential geometry. (search for "Eigenchris")

@damienthorne861 2 ай бұрын

Absolutely correct. 3b1b actually helped me to understand linear algebra. And these dialect videos are amazingly helpful for me to conceptualize on an intuitive level. I've got to get there first before I can go to the abstract

@nickcunningham6344 Ай бұрын

3b1b's series is the only reason I was able to pass linear algebra. I'm grateful as well.

@lupen8095 2 ай бұрын

Oh this is exactly what I needed in my study of differential geometry!

@Rendertk1 2 ай бұрын

Completely agreed! There were so many times where I just felt like I was doing the maths and didn't really get it. This made everything so much clearer to me.

@g4_61 2 ай бұрын

I am a novice in multivariable calculus, but I find these animations beautiful and intuitive. You have your own distinctive style of animation and explication, masterfully juxtaposed, and I implore you to hold fast to it. Thank you and keep up the great work!

@dialectphilosophy 2 ай бұрын

Thank you for watching and we appreciate your kind encouragement!

@anandbavkar8572 2 ай бұрын

Dialect consistently amazes me with their mind-blowing content. Animations are top-notch and even provide insightful revelations on how to approach thinking about these matters. I am eagerly anticipating their next videos. Thank you so much!

@GaryPansey 2 ай бұрын

Thanks for a masterpiece of video graphics. The visualization and utilization of the driftwood flow gradient is very original and useful.

@crawkn 2 ай бұрын

This is brilliantly illustrated and explained. I would recommend opening with a more directly stated context for how it relates to the arc of the long-term narrative, a simplified summary of the main conclusions, and a brief preview of the next step in our quest. It is very evident to some, while predictably opaque to others.

@davidmexicotte9862 Ай бұрын

This is the best explanation of this I have ever seen. Great job.

@black_crest 2 ай бұрын

If this becomes a series by DIALECT. It will be my dream come true.

@mobilephil244 20 күн бұрын

This material and presentation are simply ground-breaking, astonishing.

@dimitrisnatsios8409 2 ай бұрын

New dialect video day is always a good day.

@CthulhuW8ingInTheDeep 2 ай бұрын

I've never seen such a clear explanation of this. This is so well put together and crystal clear. Can't express it enough. Job well done!!!

@dialectphilosophy 2 ай бұрын

Thank you for watching!

@astronomy-channel Ай бұрын

This is the single best video I’ve ever seen summarizing Reimannian , geometry, and general relativity. Absolutely brilliant. Bravo bravo!!

@001firebrand 2 ай бұрын

Outstanding! ❤ Yet we still wait for the lesson how to deduce Riemann-Christoffel curvature tensor with metric tensor for an arbitrary manifold ✊

@dialectphilosophy 2 ай бұрын

It's a few videos in the series down the line, but not too far off!

@001firebrand 2 ай бұрын

@@dialectphilosophy If you refer to the lesson when Christoffel symbols are evaluated I remember it very well, but in that lesson we never mentioned Riemann-Christoffel curvature tensor and its properties. You promised to talk about it much more then 👍

@robertwilsoniii2048 2 ай бұрын

You use determinants. You can convert the paramentric vector space to the curvilinear one by using determinants as a linear transformation.

@robertwilsoniii2048 2 ай бұрын

The parametric space can be represented as the column space of a Jacobian matrix (of coordinate derivatives). Each coordinate derivative is the eigenvalue of the Jacobian matrix. Because of this, you can take the determinant to explain a chain of linear transformations to apply to the columns of the matrix, thus specifying how to transform into the curvilinear coordinates. This can be done in any number of dimensions, including greater than 3. 😜🔥 This is called a differential-form, and that's how you do it. Essentially, the differential form becomes a change of basis matrix that converts back and forth between the parametric space and curvilinear space. An arbitrary manifold's surface will be specified by curvilinear coordinates. This allows you to convert back and forth between euclidean flat coordinates and the native local area of the manifold in question, in order to study an analyze the manifold. Now, in terms of physics, I think the error screwing us up on a theory of everything all this time is a universal false assumption that space is continuous. Discretize space, aka finite difference methods, and that is a big step in the right direction in my opinion. But anyways. The real bizarre thing is that the human brain thinks in terms of euclidean spaces when there is no empirical basis for perpendicularity in the real world -- it is just a figment of our imagination.

@se7964 2 ай бұрын

I think Dialect means he’s planning on making the video in the future, as in a few videos down the line from now. Riemannian curvature requires a few more pieces of understanding but at this point you really aren’t far off

@Person-ef4xj Ай бұрын

I love how in your videos you explain what the symbols used in GR mean in a way that I can understand. Your videos are like a Rosetta Stone for understanding the language of GR.

@claudiocasellato 2 ай бұрын

Thank you for breaking it down so clearly! And the animations are just 🔥

@sriramfavouritesongs32 2 ай бұрын

A beautifully thought out and illustrated video. Great for beginners to differential geometry before they jump into relativity! Really well done and thank you for your efforts 🙏

@TheSkaBouncer Ай бұрын

Very, very stoked to see where the next videos in this set go

@hazimahmed8713 2 ай бұрын

Amazing! Well explained!! Even after 8 mins into the video.

@WIDSTIGETHEVLOGGER 2 ай бұрын

Even though I don't have time to watch this video for a while, I felt like I had to put it on in the background for the algorithms sake. Your videos are a gift to mankind and you deserve a lot more views, thank you sir.

@lucasf.v.n.4197 2 ай бұрын

boy, oh boy; I see a new dialect video, I simply watch it right away ❤;

@Leo-if5tn Ай бұрын

The QUALITY 🤩

@Saki630 2 ай бұрын

great channel damn very good animations and explanation that easily covers topics that rich kids pay $120k per year to achieve at 'college'.

@martijn130370 Ай бұрын

great graphics and explanations, thanks!

@Shubhendu-ik6lj 27 күн бұрын

Great for providing such a quality content video with this level of clarity and imagination building 🎩

@WSFeuer 2 ай бұрын

This is just top-notch, amazing content!

@peterhall6656 2 ай бұрын

You did a really good job on this topic.

@timurtihonov2859 Ай бұрын

Why is this so good? How long does it take to make a video with all these awesome animations? The last one wasn’t even that long ago!

@mighty8357 2 ай бұрын

Top notch animations!!

@SchmittsPeter 2 ай бұрын

A finally the next episode in this story. It feels like it has been an eternity.

@patrickpaterson4442 2 ай бұрын

Wow! What a fantastic visualization

@wahoobear6588 8 күн бұрын

The present animation is very clear. I like it 😊

@ced1401 2 ай бұрын

Fantastic as always.

@alanthayer8797 2 ай бұрын

Thanks fa Visuals visuals visualization !

@flamingowrangler 2 ай бұрын

your voice is hypnotizing

@whig01 11 күн бұрын

Curvilinear Algebra, you've fixed everything.

@ryansamuel8835 2 ай бұрын

When production is this good, math videos become the most interesting entertainment option in 2024.

@matthewhall6288 2 ай бұрын

Thank you!

@mcdaddy000 Ай бұрын

Why the fuck didn't I get recommended this or notified? I've been so excited for a new video of yours. I'm subscribed and have watched everyone single one of your videos. Fuck youtube.

@irtizahussain5001 Ай бұрын

Absolute Banger!!!

@MissPiggyM976 2 ай бұрын

Great video!

@realcygnus 2 ай бұрын

Superb !

@astronomy-channel 2 ай бұрын

Totally excellent!

@justaguy3518 2 ай бұрын

new video, yay!

@-_Nuke_- 2 ай бұрын

Just like every time, my day is made when I see a new Dialect upload! I don't really have anything to note about this video because its already a masterpiece! I can't wait for more! My only question is going to be about the nature of General Relativity... I am starting to get the feeling that there is a misconception about General Relativity and Newtonian Gravity... Many people seem to believe that Newton had no idea what Gravity is and where it comes from and that somehow Einstein with General Relativity gives us an intuitive explanation to not just how gravity behaves, but also what it is and where it is coming from... So I am starting to believe that that is sadly not the case. Sadly, Einstein still had no idea what Gravity is and where it is coming from either; After all, a curved spacetime isn't any less magical than a gravitational field... The big change from Newton to Einstein is that now we know that the Universe has a speed limit! The speed of light, therefore Gravity needs to respect that law. Thus we need to update Newtonian Gravity with General Relativity, to see how Gravity behaves in a Universe with an actual speed limit; But neither theory actually makes anyone more intuitive to where Gravity is coming from... So for certain, General Relativity has been falsely "advertised" it seems by science communicators - as this theory that puts Newton into shame, explaining how Gravity isn't a force but the outcome of acceleration and all that jazz... But in reality all we have, is just a mathematical model, where its manifolds can be subjects to higher dimensions and non Euclidean surfaces... Ok - its just mathematics, we can do whatever we want with them because they are in just in our brains... But does this General Relativity give us any real intuition about the nature of Gravity and its real origins? Maybe not; Gravity is a fundamental force... We have no real explanation to how ANY other fundamental force works either... Electromagnetism? You mean this magical EM field that permeates all of space? I hope that Im wrong. I hope that General Relativity really does give an intuitive explanation to Gravity, in a way that we can understand it in an amazing AHA moment, and we are just too uneducated to do that now; Hence we are watching videos like these... But I don't really believe that anymore... I think that its just all mathematics and just like mathematics, everything is permitted; But if we say that "spacetime is Mikowskian therefore this and that", that sentence is still no less magical than a "gravitational field"... Anyway, I hope Im wrong! Ill be watching these videos to find out :)

@AshrafElDroubi 2 ай бұрын

Just awesome!

@ibrahiymmuhammad4773 2 ай бұрын

My brain tells me I understand my lexicon invites disparaging criticism

@SrChengLX 14 күн бұрын

brp why teachers dont make slides like this much easier to understand rather than just showing bunch of formulas

@excentrisitet7922 Ай бұрын

I have a degree that is analogous to European PhD in physics. Particularly in experimental physics. Yet this topic has always been over my head. I can grasp the basic concepts yet complete mastering is out of reach... I always feel like a main character from "flowers for Algernon" novel. No matter how hard I try I just can't fully conceive such complicated things. My cudos to people who can though! They make our world a better place.

@Grateful92 2 ай бұрын

I thank KZfaq for recommending me this video

@ignazratski-ratski9760 2 ай бұрын

Thanks!

@dialectphilosophy 2 ай бұрын

Thank you so much for your support!

@I-M-2. 2 ай бұрын

Beautiful ❤

@robertrusiecki9033 2 ай бұрын

Great explanation! The only thing I'm missing is an explanation in terms of geometric algebra and the external product. This is important because geomathematic algebra is widely used in computer graphics and there is a lack of materials translating (or including) relativism into the language of external algebra.

@dialectphilosophy 2 ай бұрын

We don't know much about exterior algebra, unfortunately, though we understand it ties closely to this sort of subject.

@Mr_Happy_Face 2 ай бұрын

At 7:34 shouldn't the law of cosines be c.c = a.a + b.b - 2a.b? (as opposed to + 2a.b)

@toddpedlar5431 5 күн бұрын

Nice video... though I have to say "curvy-linear" catches me every time :)

@tulliolevicivita4443 Ай бұрын

Great video. Are you preparing a curvature tensor video??

@dialectphilosophy 29 күн бұрын

Yes. It may still be some ways down the line however -- we apologize, as we wish we could work faster, but there's a lot on our plates!

@PerpetualScience 2 ай бұрын

I'm currently looking into evolving spacetime entirely with tetrads(basis vectors), so I can't use the metric tensor nor the Minkowski metric. I'd be interested in a way to get the Christoffel symbols entirely from the basis vectors without having to embed my manifold in a higher dimensional space. I'm currently looking into Teleparallel gravity, or the tetrad formalism of GR. I look forward to your future videos on this!

@dialectphilosophy 2 ай бұрын

Sounds like you're a bit ahead of us! We know Einstein was looking into similar subjects in his latter years (though if we recall correctly he was also suggesting the use of antisymmetric metric tensors as well) so it'll definitely something we'll be looking into down the line.

@PerpetualScience 2 ай бұрын

@@dialectphilosophy I look forward to it! The reason I'm dropping metric tensors altogether is because I've deemed them unnecessary and problematic. In GR, the determinant of the fully covariant metric tensor pops up a lot. However, the determinant is only a defined operation for mixed-index rank-2 tensors. If you convert the metric tensor to one of those, the determinant is always 1. When we normally take the determinant of the metric tensor, we mistreat the fully covariant tensor as a mixed index tensor. This is a gibberish operation though! Not allowed! This is why I've deemed it somewhat problematic. This issue can be avoided though if you avoid ever taking the determinant of the metric tensor. What the metric tensor is supposed to do is define distances in spacetime. Lets say you have a given vacuum solution for a topological soliton of spacetime. Lets say this topological soliton is a particle, say a hydrogen atom. Vacuum GR is a scale invariant theory though, so we can scale this solution up and down however much we like. This means we can have an asymptotically Minkowski space where copies of these particles of different sizes coexist with each other. In real life though, all particles of the same type are the same size. You could make two rulers with atoms of different sizes and measure the same length and get two different values. The metric tensor had one job, and it has failed. This is why I've fired the metric tensor. A consequence is that nonmetricity is an undefinable concept in this new formalism I'm working on.

@dialectphilosophy 2 ай бұрын

@@PerpetualScienceThat sounds very interesting. Again you’re talking a bit over our heads here, but definitely feel free to contact us via our email and send any of your work you’ve done on the subject.

@PerpetualScience 2 ай бұрын

@@dialectphilosophy Well it's still very much a work in progress, so nothing's published yet. I'll probably just keep on polishing it. It might end up as part of my PhD dissertation.

@codetoil 2 ай бұрын

Take a peek at the Tetradic Palatini Action and the Spin Connection...

@malikamulla2899 2 ай бұрын

Will you do a video on covariant and contravarient components?

@dialectphilosophy 2 ай бұрын

Yes. We'll probably be doing a series on tensors down the line, and that will be a crucial component.

@Time-cc2qb 8 сағат бұрын

wow so much clear now

@al7aroDos Ай бұрын

Hey friend! Could you share which technology (software) you use to create those math-related graphics like formulas, surfaces, etc.?

@dialectphilosophy Ай бұрын

We'll be putting those up on our Patreon soon!

@svendkorsgaard9599 2 ай бұрын

Hey man, amazing video as always! May i ask, how do you do the animation? Do you use 3D software such as blender or unreal?

@dialectphilosophy 2 ай бұрын

It's a combination of programs, but this one was mostly made with blender. Just don't give our secret away 👀 🙃

@svendkorsgaard9599 2 ай бұрын

@@dialectphilosophy Ah thanks dude! Dont worry, our secret is safe! Just a quick question: in blender do you animate everything manually or do you use scripting to get the shapes right? I want to try doing some similar animations myself in the future :)

@FunkyDexter 2 ай бұрын

So basically the levi civita connection is the derivative of the wedge product?

@super-cylinder Ай бұрын

sire, What software hath thy used to make Thee Animations?

@RobertFuszenecker Ай бұрын

Hi, I hope you are well these days. I have been thinking for a while how the world could look like in a spacetime with positive curvature. It's clear that the space have a finite size (without any borders or special points in it), but should it be true for time, as well? How could work causality in this world? Should the wavelength of a particle in harmony with the finite amount of space/time? Thanks in advance! Robert Fuszenecker

@seditt5146 Ай бұрын

If electromagnetism was actually warping of spacetime in this wave like curvilinear space, would we be able to actually detect this as our matter would be warped with the waves? Basically asking if there was a way to detect if EM radiation could even be experimentally shown to be a high frequency gravitational wave. Due to it warping matter we likely would only see it acting on one axis at a time.

@Amipotsophspond 2 ай бұрын

if you are still also having trouble wrapping your mind around Curvilinear Coordinates look at a Topographic map and pretend their is no Z up and Z down, like maybe you are building a flat foundation on a steep curvy hill and you want to know exactly how to make the foundation 10 meters by 10 meters.

@2712animefreak 2 ай бұрын

In polar coordinates, what happens at the origin?

@Person-ef4xj 15 күн бұрын

I think the description you gave for how something needs to accelerate in the parametric space in order to travel in a straight line in the Cartesian space might be incomplete. I tried simulating motion in polar coordinates and checking whether it would correspond to a straight line in Cartesian coordinates and found that if I simply took the opposite of the sum of the christoffel symbols with the upper index that refers to the same coordinate I’m using the object still accelerates in Cartesian coordinates. If I first multiply each christoffel symbol by the components of the velocity that correspond to its lower indices and then add up their opposites I do get a straight line in Cartesian coordinates.

@dialectphilosophy 13 күн бұрын

Hmm... in the first example, where the Christoffel components are simply summed, the parametric velocity components are both equal to one. Before the ending however, we mention that for parametric velocities not equal to one, you have to scale the Christoffel components by the respective velocity component. Did you perhaps miss that part of the video, or are you saying that you did something differently than us?

@Person-ef4xj 12 күн бұрын

@@dialectphilosophy Well the example given makes it look like you first sum the opposites of the Christoffel symbols and then multiply them by the velocity component corresponding to their upper index. I found that I seem to need to instead multiply the opposites Christoffel symbols by the velocity components corresponding to their lower indices first and then sum them together.

@user-my4vb8pd4v 2 ай бұрын

Which software use for this video graphics?

@moussaadem7933 2 ай бұрын

i would assume mostly programming geogebra

@APaleDot 2 ай бұрын

There is no way that is geogebra. Looks like Blender to me.

@xaniarzaer 2 ай бұрын

❤

@rupertchappelle5303 29 күн бұрын

Spacetime curvature is the crack of science.

@Oylesinebiri58 2 ай бұрын

👍

@vaioslaschos 2 ай бұрын

Maybe you should make also videos of how you make these videos :-)

@dialectphilosophy 2 ай бұрын

We wish we had the time too 😂 We are going to try to start uploading some behind-the-scenes stuff on our Patreon soon

@Zero_Contradictions Ай бұрын

The Discord Invite link doesn't work :(

@dialectphilosophy Ай бұрын

Thanks for letting us know! We're not sure why it stopped working, but we've since updated it so maybe try again!

@Zero_Contradictions Ай бұрын

@@dialectphilosophy Thank you!

@user-vy9eh6zf7x 2 ай бұрын

best best best best best best best best best best best best best best

@twetch373 2 ай бұрын

Good morning

@Waferdicing 2 ай бұрын

⤴️

@leshommesdupilly 2 ай бұрын

Fun fact: Einstein invented this type of geometry because one day he was so drunk he couldn't draw a simple square but wouldn't admit it

@HaramGuys Ай бұрын

Much further back in history, Gauss

@leshommesdupilly 2 ай бұрын

all these squares make a circle all these squares make a circle all these squares make a circle all these squares make a circle all these squares make a circle

@DanielKRui 2 ай бұрын

@10:20 I don't see the intuition behind why this should be true. I have two cars moving in the "horizontal" green directions, and I take the difference in their velocities to get a vector (V1 let's call it since I don't want to type out the full name). I do the same thing for 2 cars moving the "vertical" purple directions, to get a difference of velocity vector V2. I don't have any "feel" for why these vectors V1,V2 should be exactly equal.

@dialectphilosophy 2 ай бұрын

It's a tricky point. The first thing that's necessary to clarify is that the condition is only infinitesimal; so if you are looking at too large a region it will not hold. But in the infinitesimal space, essentially, if one coordinate basis vector expands or contracts along its own direction, then the other coordinate basis vector must rotate and pick up a component in the direction of that expansion/contraction in order to compensate for this. Indeed we'd recommend watching our "conceptualizing the christoffel symbols" video; around the half-way mark we do an infinitesimal walk-through of the Levi-Civita condition and it becomes a lot clearer there. We didn't want to go into the infinitesimal picture here in this video, but without presenting it the Levi-Civita condition is almost impossible to grasp intuitively.

@jamesmorgan9502 2 ай бұрын

holy shit.... :O

@damienthorne861 2 ай бұрын

Is it wrong to be addicted to dialect? 😁

@AdRock 2 ай бұрын

Who is dialect?

@cunjoz 2 ай бұрын

curvy linear

@snappycattimesten 2 ай бұрын

My cat’s breath smells like cat food.

@EpoxyCircus 2 ай бұрын

As does…

@justanotherguy469 2 ай бұрын

I love that smell. Oh, his ;little breath. 🥰

@kered13 Ай бұрын

Polar Bear lost his job to Hot Wheels!

@dialectphilosophy Ай бұрын

He required a lot of computational time and effort 😂 However he will be back... at some point!

@robertwilsoniii2048 2 ай бұрын

Personally, I don't believe in the existence of perpendicularity.

@mikkel715 2 ай бұрын

The very question is: How does this reconcile with the "Matrix Theory"?

@dialectphilosophy 2 ай бұрын

It was actually the study of General Relativity, with its emphasis on coordinative maps and metrics, that first led us to the idea of Matrix Theory. So yes, they will be reconciled soon...

@thetelescreen372 2 ай бұрын

half convinced that the whole "special relativity doesnt yey have a physically meaningful interpretation" thing is just an excuse to teach general relativity

@SixTimesNine 2 ай бұрын

Sure beats blackboard and chalk

@kevinbush4300 2 ай бұрын

in-fin-i-TES-uh-muhl

@tedsheridan8725 2 ай бұрын

"Curvy-linear" lol. Great video though!

@axle.student 21 күн бұрын

Good video, but I really think this is the wrong geometry for relativity or space-time. I think wrong geometry may be the flaw in SR.

@dialectphilosophy 21 күн бұрын

We don't actually disagree with you there; what we've learned is that these "alternate" geometries are actually just descriptive conventions; two geometries can in fact describe the same theory. We tackle the geometric conventionalism of SR in our video "The Loophole"; we have yet to seriously treat on it in GR, but we are headed definitely headed there.

@axle.student 21 күн бұрын

@@dialectphilosophy Thanks for the reply. Much appreciated, and I am looking forward to what perspectives you present (for write or wrong). "There is nothing either good or bad but thinking makes it so" - Shakespeare > I have been working over a number of fundamental geometries that Einstein could have had in his mind, before it was possibly re-interpreted or misinterpreted by his mathematician colleagues. Each geometry "appears" to go some way toward describing the concept of "combined" space-time in SR, but fail at the extremes or have quirks. In any functional geometry (in my mind visuals) that describes relativity with combined space-time (distance-time m/s) I cannot find any natural x,y,z(3D) x,y,z+t(4D) and even a xt,yt,zt appear to break spacetime into space AND time. I can create the 2 spherical histograms of any point observer for past photons in m/s along the radius lines in my mind which is more complex than it first appears, but in both cases I think anything other than radial coordinates (ones using 2D polar surfaces) seams to break the mathematical description back into space and time separately. > So, we have 2 possibly functional distance-time m/s radial (spherical like) geometries that the mind can grasp visually and conceptually (when it learns how to) and any attempt to describe it in our 2D, 3D paper breaks it. And the math based geometry appears to recreate space-time in mans image and breaks it too lol It really is difficult to translate into human language outside of the mind :) > Good luck with your quest and take care. If I see you down the rabbit hole I'll give you a hello :) Thank you for your videos and perspectives. > P.S. Not an indentured physicist. I lean heavily upon philosophy and cognitive psychology in an attempt to describe the human reality and then step beyond to the external reality (what physics looks for). Kind of lift the veil of the human condition to see outside in a more real raw way.

@aaaaaaaaaaaa9023 2 ай бұрын

Fam, you need to spice up your titles and thumbnails. 😭

@j.r.8176 Ай бұрын

Unbelievable! Shocking breakthrough proves spacetime can be curvier than Stacy's Mom! You won't believe what happened next..

@LazyRare 2 ай бұрын

@anglaislangletaire2098 2 ай бұрын

Thank you .I need to repeat the videos because it contains very important ideas related to GR theory.

@moussaadem7933 2 ай бұрын

@@anglaislangletaire2098 OP just said hi..

@JuBerryLive 2 ай бұрын

I want to hear a debate between the creator of this channel and a mainstream physisist. The subject: Does the ether exist?

@juliavixen176 2 ай бұрын

There's nothing to debate, there are several experimental measurements that when combined together will give you the Lorentz transformation, and _only_ the Lorentz transformation. That's a requirement for any luminiferous aether theory... and for special relativity... and any theory using the Lorentz transformation is going to make the exact same predictions.

@bologna470708 2 ай бұрын

Aether is the source field where 1) Force and Motion 2) Inertia and Acceleration 3) Capacitance (Permeability) and Resistance (Permittivity) >>>> into >>>> Magnetism, Electricity, Di-electricity and Gravity >>>> manifesting into >>> Mass, Matter and Energy.

@JuBerryLive 2 ай бұрын

@@juliavixen176 I mean, the author of this channel tries very hard to re-introduce the idea of an ether... and most physisist believes it doesnt exist and has been disproven. So I think there is indeed something to debate lol.

@PerpetualScience 2 ай бұрын

Physicist here, although not exactly mainstream. Dialect's matrix theory is just GR but with a definite correct coordinate system which an observer can never determine. This naturally gives the exact same predictions as GR, and isn't really even a different theory. We have coordinate systems for black holes(Gullstrand-Painlevé raindrop coordinates) where the speed of light in the radial direction varies depending on whether it's ingoing or outgoing. This can be interpreted as spacetime flowing into the black hole, reaching light speed at the event horizon. Dialect hasn't done anything particularly innovative or controversial here, although it does go against the spirit of GR in some admittedly unmeaningful respects. Any debate on the matter would be purely on the philosophy of science, as the theory has no meaningful differences.

@JuBerryLive 2 ай бұрын

@@PerpetualScience ok ok. So you are saying that his interpretation doesn't give rise to new predictions or anything like that? It's just a different interpretation of the framework that produces exactly the same results as GR? What's the goal then?