Sabine: As usual, I had to watch this video four times before having even the vaguest idea what you were talking about. Not to worry; my degree is in Economics, so we're not expected to understand anything. Understand or not, I enjoy your videos immensely Thank you for the countless hours you put in for us dummies.
@@SabineHossenfelder Can you please do a video reviewing Sara Imari Walker's book "Life As No One Knows It: The Physics of Life's Emergence"? The book makes a lot of bold claims.
They made us learn tensors in our mechanical engineering curriculum as undergraduates, mostly so we could make sense of material stresses and strains in both solid and fluid mechanics. My physics undergraduate buddies were impressed I was conversant with the incantations for these arcane objects. Determining failure modes for structures often means "take the trace of this tensor and see if it's greater than something" or "take the largest principal component while holding a candle and chanting Timoshenko's name backwards!"
It's said that if you stand in front of a mirror at midnight by candlelight and chant "Ambitwistor" three times, the ghost of John VonNeumann will appear and solve a maths problem for you.
It's rare to introduce where all this math is used and useful in engineering. Many equations are buried in computer aided drawing systems just waiting for a user to hit a go button. Next time you drive over a bridge you may want to thank a mouse click?
No surprise here. This reminded me of the theory of everything that Feynman jokingly proposed. Let us add the left sides minus right sides of all physical equations. The sum will be zero. We give a fancy symbol to the sum, for example 💢. Then, we get 💢= 0, an equation that includes all known physics, but... adds nothing new 😂
Feynman had a good sense of humour! But as a pedant I must add, such equation would be wrong :P The reason is A + B = 0 has more solutions than A = 0 and B = 0. If we don't observe those this "generalisation" is broken.
"What I cannot create, I do not understand." -Feynman Maybe a clueless master student can build a "useless machine", the "simplest robot" (a pendulum) and teach it how to "learn how to learn" about physics, by warping the state space to experience "Fuzzy" reasoning, while "standing on the shoulders of giants", and so, maybe then, a "theory of everything" is achieved, via humility and error 🔥🎩+💦=⛄Frosty, though it will probably talk to itself in Chinglish, or some 👽 alien language. Hopefully it's goal will be to teach us the "theory of everything" beyond just a mere answer of "42" 🎩🤠
@@Tablis0i don't know Feynmans joke, but I guess he was clever enough to add the norms of those differences (or some other related quantities like the squares of norms). Since norms are always nonnegative real numbers, their sum is zero if and only if each one is zero.
I didn't mention this in the video, but the authors have previously written several other papers on the topic. Once you get the first paper published, the later ones are easier. Actually the new paper is pretty much incomprehensible on its own and that probably helped getting it published.
@@SabineHossenfelder It might be interesting to feed it to one of the new AI models that can do math well to see how well it does in picking the paper apart.
Yay! Tensors introduced to a broader audience! I learned them in university, and at first, they looked scary. Instead of a scalar, you had to work with a matrix, but a couple of years later, I recognised the beauty of defining a real-life object using a matrix and a set of rules attached to it. Gradients, rotors, operators, different multiplications and differential equations in a unified notation format! They are not easy, but they can describe the uneven transparency of a chunk of a mineral, rotation of an object with no circular symmetry, and a lot of curved, deformed, uneven real-life stuff. Very useful mathematical construct!
Something to note here: Not all tensors are matrices! While you can express a second degree tensor as a matrix you most definitetly know at least one other tensor that is in the simplest form a third degree. The levi-civita tensor ε_ijk. Using permutations you can actually generalize the concept of that tensor into even higher dimensions. It gets a bit more complicated but it is very useful while working with 4-objects in relativity.
@@derdotte Indeed, but as an AI programmer I know you can express any tensor as a multidimensional array. A matrix is a 2d array. You can express a vector as a simplified matrix with just one row or one column. In fact the dot product, cross product, scalar multiplication, and vector addition/subtraction can all be expressed as operations on a matrix.
Well, the unification of vector calculus is much more nicely done through differential forms than through tensors! At least you avoid the horrible "debauche of indeces", as rightly pointed out by the great mathematician Elie Cartan 😁
I LOVE YOUR STYLE, @Sabine! I would love to have teachers and tutors with this both rebel spirit and strong commitment with solid science back in my student days!
I'm pretty sure I didn't understand much of that but I have found a new reason to watch Sabine's videos: there will come a day when she sets papers on fire but will have forgotten to turn the smoke detector/fire suppression system off first.
@@SabineHossenfelder Well the world is clearly going up in smoke so 'when in Rome' as they say lol. If only RUclips enforced transcripts you could have battle after battle with your detractors!
That was a really nice conceptual explanation of why tensors are important! Also, Feynman hated that conference and, at one point, shouted “NO!” loudly three times at a fellow physicist. He told his wife never let him go to a GR conference again.
I’m trying to watch this, but I cannot get my head around tensor math. Differential equations is about the boundary for my understanding of math. Beyond that, it’s as if I’m a dog and you are talking me, “Yap yap yap Steve. Woof woof yap, Steve. Yip woof yap, Steve.” You’re talking to me (I hear my name….) but I have no idea what the hell you want!
@@stevenslater2669 Try the paper NASA/TM-2002-211716 "An Introduction to Tensors for Students of Physics and Engineering" by Joseph C. Kolecki (2002), which is accessible online.
@@stevenslater2669 are you, by any chance, referencing the Far Side comic that compares what the dog's master says to what the dog hears? You made your point well in any case!
Wow. That was the best 5 minute introduction to tensors and GR I've ever seen. What's next quaternions?? I'd be careful about pissing off Alena, though! That geometric mu nu stuff is something I had hoped to understand someday, but none of the texts I have from my failed undergraduate 50 years ago cover it. Same with anything on Riemann. I'm thinking of buying Susskind's theoretical minimum series of books to see if those can help.
Do the texts you've studied include Misner Thorne & Wheeler's Gravitation? They provide quite a lot of introductory material bringing these ideas to those new to all that stuff. Published something like 50 years ago, quite popular, but probably superseded at this time by other books and videos. Woefully old when it comes to gravitation waves - please ignore that chapter! But the math of tensors, metrics, curvature is still good. What books have you found most useful?
Thanks Sabine once again! nice that you explained so nicely. Although, I am only a PhD in medical imaging so I do not know much about tensors. I remember that while dealing with vectors, to develop the algorithm I was working with, I wanted to study tensor. Because vectors are also one type of tensor. But I could not find enough time to do so. Maybe, this video again motivates me to go back to studying tensors. :)
Sabine, I believe I can learn physics by hosmosis by watching your videos. While I don't learn, I can offer some compliments: congratulations, your image today is much better than when you published your first videos.
Now I have a dream, to get a paper burned by SABINE, I will make a theory of everything that at least is worth of your time burning it. Would you give tips of how to reach that point??
Once AI agents start filtering out and ripping up junk papers from the publication record, sabino will be shown to be the absolute sweetheart that she is by comparison
I wonder if you realize your significance. Confidence in science has been shaken. Your work publicly deflates Science-the-Industry and Science-the-Brand back down to a discipline--the simple and ruthless application of the Scientific Method. From my perspective, universities and companies have a conflict of interest resulting in overly-optimistic reports of theories and breakthroughs. I don't have the skills to judge the veracity of peer-reviewed publications. But I know that a paper that *you* find plausible, even in part, is worth reading. I suspect this might make you unpopular in physics social circles. I imagine hopeful young physicists approaching you with their new giant red balloon, and you're ready with the needle. Keep it up! You're appreciated.
Not really. Science has always had charlatans and bad scientists. That's why things need to be peer reviewed and can be changed whenever new evidence is found.
Well, I wish I could say I fully understand what shed said. But even so, it's so nice to see her show her intelligence and confidence in those videos. An idea for you: bring one of those authors to debate about the paper subject and see what comes from it.
I had to laugh out loud when you wrote "BS!" on the paper, because that was EXACTLY what I was thinking in that moment. EDIT: I certainly do not want to start any theories, not even hypotheses. I merely scratch the surface and my knowledge is thinner than a razor.
I love this video, and I'm following with great interest. As Sabine notes, if you learn only one thing then learn about the metric tensor at 4:39, from which the Riemann tensors and scalar are based. Einstein said they were like beautiful carved marble, while the stress-energy tensor T is made out of wood, as it depends on what kind of matter-energy one is talking about.
I watch, and really want to understand, but after watching Sabine explain or debunk these papers, I just go back to my colouring book, and I will still watch tomorrow too
Hi Sabine, thanks for triggering flashbacks to my college days in math trying to visualize tensors. They all were fingers showing the right hand rule flying about. The best part was the transformation of the paper into fumes and ash, which I will now think of as the Sabine transformation.
Most of us have learned about solving multi-variable simultaneous equations, even large sets using matrices. Imagine having to solve 10's of thousands ( or even more ) equations simultaneously, to describe the flow of time and matter. This tensor research is attempting to do that. I applaud their effort to move the math forward. This is what Phd's should be doing, the hard stuff.
Oh god, Tensors... Makes me remember my second year at uni and a dread memory of the day I realised that there was a lot of maths that wasn't just tricky, but really very very tricky. I remember a lecturer, my mental image is that he was at least 120 and had one of those beards only 120 year old men can grow, talking about Dirac for at least an hour before he eventually got back onto the maths he was supposed to be helping us with. His descriptions of Dirac as some sort of mentally gifted maniac (maniacally gifted that is, not that he was a murderer or something), do give me a fond memory of how much the profs used to worship their heroes. Its a nice idea that there are still (or were 20 years ago when I was trudging to 3hr lectures written mostly in greek) some people who idolize genuinely clever people, and not just investment capitalists who self-proclaim themselves to be clever.
If a light bulb is the sun a stress map could be a tensor. A stress map represents how forces distribute across different dimensions, much like how tensors describe complex relationships in multiple dimensions.
What a nice opportinuty to recall and thank once again two great titans - G. Ricci-Curbastro and his apprentice T. Levi-Civita, the fathers of tensor analysis. Their gift to humanity is truly priceless! 🥰
I just ordered Existential Physics. I am really excited. Stoked, one may say. Thank you for all of the information and entertainment through the years, Bee. This goon can't get enough.
I was going to organise a gofundme page in order to fund the purchase of a new chair. The damage to the chair looks permanently distracting. I never got round to it because something distracted me and when I refocused, it seemed a bad idea. Loved the video.
Understanding Tensors, Covariant Derivatives or Differential Forms and other Concepts like Topologie is the Key to understanding Physics. I always view my hard earned Ability to work with Tensors as the greatest tool of all I learned in Math in my whole Life.
02:20 _There are a lot of maths things which are not tensors._ However, scalars and vectors don't belong to this category because they are tensors of 0th and 1st stufe, respectively.
That's right. But mathematically nothing is preventing you from, say, combining 4 scalars to a thing with an index which would then not be a vector, if you see what I mean?
new rule, all papers a a new "theory of everything" have to be peer reviewed by Sabine herself before they can claim it truly is a theory of everything
18 минут назад
I like introducing tensor via categorical thinking. Like if you have a bunch of fruits, you can split them into apples, oranges, bananas, etc.. but you can always split further by arbitrary categories, like color, sweetness, size (in discrete sizes first). Though it is not a linear algebra object, you can still do a lot of operations on it, and it is very handy when discussing quantum computing.
Your presentations are always fascinating and instructive. They are, however, very often 2 or 3 light years over my head. I was always interested in physics (Newtonian) but decided to study chemistry instead. Occasionally, some of what you are discussing manages to penetrate into my consciousness but I still fall back on good old chemistry - a reaction either does or doesn’t. It is not dependent upon the spin of the solution . . . . Or does it? Damn! Thank you for what you do. If my physics teachers had been up to your level I most likely would have changed my focus.
I too was fascinated when I first learned about tensors in physics. I sensed that there was an important solution to the universe there. That's exactly why I attempted to take a tensor analysis course. My enthusiasm faded quickly. I still feel something about tensors. They are cool.
Ugh, I hate that sort of thing! You probably got stuck in the mud dealing with definitions, proofs, details of transformation formulas, and zero or very little intuitive applications. Tensors are beautiful mathematical concepts once you get past the math!
Funny how I used my torch too, and got it all the way through it in 1 viewing. So, aren't these tensor connections just 'filter transforms' coupled serially and also in parallel. Just like a modern control system that runs your furnace... ???
Long time fan!!! Obviously your delivery is always priceless. Though I’ve never been a good student of math in my younger years, starting in my 30’s, I’ve become fascinated with physics. At 52, do you feel Brilliant would help, not just in understanding what has been done, but to also explore new ideas? Thank you!!
Brilliant is a good study buddy, or reference guide to what you're studying. It reinforces what you're already learning. On its own though, it's not as effective. At least in my experience.
The formula you show fits well with a holistic approach to gravitation, where gravitation is seen as an emergent phenomenon deeply interconnected with other aspects of the universe, such as quantum fields, holography, and specific structural interactions. It could be used in a theoretical framework that does not limit gravitation to mass and energy, but also addresses other emergent aspects of the physical world and its dynamics. However, many terms are still missing on the right-hand side... Question: If the rest of the paper is lit again🔥 with the same lighter, is it the same flame🔥? Or not! 😉
I'm not a physicist, but a fiction writer, and some of this goes over my head, but thank you for the "Gee-mew-new" I appreciate that. I promise I will use it only to express something overheard to denote someone else is smarter than others, not as any BS thing I make up from thin air to explain my hand of the author needs. 😉
That's why I'm writing my state representative concerning building codes -- to demand that from now on all houses and buildings be made of quaternions!
Tried banging my head on a wall, still don't understand what a tensor is. Will leave the physics review/critiques to others. Thank you for what you do.
I had my own fun theory when I was studying science. I tried to explain faster than light information exchange of entangled particles. I had to solve the distance problem. So I proposed, that instead of 3 dimensions of space and 1 dimension of time we had 3 dimensions of time and one dimension of distance. So, reality looks and acts exactly the same under such system, with the only difference in it continuously creating parallel dimensions along 3 axis. We have 3 sets of probabilities crossing through eachother. A series of parallel futures and pasts passing through now. We are the moment between possibilities that surround every particles well... like the wave function. My system is functionally the same as the system where there are 3 dimensions of space and 1 dimension of time, but just like time can be collapsed by the speed of the observer, I was trying to turn distance into a collapsible parameter that then could nullify distance between objects. Entangled particles are the white holes people look for. They expect white holes to be massive, but they're tiny and right under our noses. They are aligned in pairs and the distance component between them is collapsed. They are anti-black holes existing at the opposite end of possible physical scale. Time is a vector and space is a quantity. Think about that. Same math. No paradoxes. Spacetime is already linked. Just think of it as Timespace instead, and how you can different things, if you combine space into 1d and make time 3d.
Always start with action (or Lagrangian density as told by Sabine). To have a physical theory we must start with a physical problem. That's the constraints a physicist abide by.
Thanks for this, I came across this paper in my feed and wondered what you thought about it. Also, why is a gravitational field NOT a function of angular momentum like electrical?
That's interesting. I've been exploring similar concepts in the context of extended Lagrangians, particularly those that incorporate higher-derivative terms or non-Riemannian geometry. My research has focused on understanding how such modifications can affect the dynamics of spacetime and potentially provide a framework for unifying gravity with other fundamental forces. While I appreciate the attempt to explain dark energy and quantum physics through the 'Alena Tensor,' I remain cautious. Many theories have come and gone, promising to be the 'Theory of Everything,' yet ultimately failing to deliver on their promises. My experience has taught me to be skeptical of such claims, especially without rigorous mathematical backing and testable predictions. I'm particularly interested in seeing the explicit form of the Lagrangian that incorporates this 'Alena Tensor.' How does it modify the Einstein-Hilbert action, and what new degrees of freedom does it introduce? Does it address the long-standing problem of renormalizing gravity, or does it simply shift the problem to a different sector? And, of course, the most crucial question: does it offer a natural and compelling explanation for the observed value of the cosmological constant, or does it merely introduce new parameters that need to be fine-tuned? Until I see a concrete mathematical formulation and a detailed analysis of its implications, I remain unconvinced. However, I'm always open to new ideas and perspectives, and I'm eager to learn more about this 'Alena Tensor' and its potential contributions to our understanding of the universe.
Even better and far more elegant than Alena tensors are Bivectors as developed from abstract Clifford algebra by Hestenes into "Geometric Algebra" specifically to unify maths for physical applications.
For a quick crude intuitive notion of what tensors are, imagine you have a small stretchy object, maybe foam rubber, gelatin, or a patch of bubbles floating on water. Pull on it in some direction and it moves that way. That's a vector. Now pull on one end and pull the opposite way at the other end. If your pulls are outward, away from the center of the object, that's a tensor, a symmetric one. The stress tensor in mechanical engineering is just like this. OTOH if you're pulling up, let's say we're pulling north, on the east side of the object, and pulling south on the west side, the object will rotate. That's an anti-symmetric tensor. As a practical mathematical concept, it's a rotation matrix. In relativity, a "boost" - to make something move faster or slower or go sideways - is the same thing as rotation but "space-time" rather than "space-space" like a rotation. That's hard to explain further in a youtube comment. The capital 'F' you see in that paper Sabine shows is the electromagnetic tensor, which combines rotations (for magnetic fields) and boosts (for electric fields) into one 4 dimensional antisymmetric tensor. Now imagine having a rod or cylinder of some material, like a can of soup or wood dowel or an common everyday battery (AA or D size, whatever) Twist one end. A twist is basically a rotation, which we already established is an anti-symmetric tensor made of two vectors. We need a third vector to say where we're applying this twist. Balance it out by twisting the opposite end in the opposite direction. We just made a rank-three tensor, anti-symmetric. There are more examples I could give, but I'd be writing an article suitable for Medium or Substack, too large to fit in RUclips comments, and I'd want to make illustrations. Someday...
![Felix "Unfair" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/Oswujxm2Ag0/mqdefault.jpg)
Sabine: As usual, I had to watch this video four times before having even the vaguest idea what you were talking about. Not to worry; my degree is in Economics, so we're not expected to understand anything. Understand or not, I enjoy your videos immensely Thank you for the countless hours you put in for us dummies.
Happy you like it!
@@SabineHossenfelder Can you please do a video reviewing Sara Imari Walker's book "Life As No One Knows It: The Physics of Life's Emergence"? The book makes a lot of bold claims.
It’s been up for 18 minutes, and it’s 11 minutes long. Nice job with the time travel. 🎉
@@jrector666or perhaps it first came out to members.
@@SabineHossenfelderSABINE SHUT UP !!!!
They made us learn tensors in our mechanical engineering curriculum as undergraduates, mostly so we could make sense of material stresses and strains in both solid and fluid mechanics. My physics undergraduate buddies were impressed I was conversant with the incantations for these arcane objects. Determining failure modes for structures often means "take the trace of this tensor and see if it's greater than something" or "take the largest principal component while holding a candle and chanting Timoshenko's name backwards!"
It's said that if you stand in front of a mirror at midnight by candlelight and chant "Ambitwistor" three times, the ghost of John VonNeumann will appear and solve a maths problem for you.
I feel like tensors are pretty simple overall. Am I alone in that?
It's rare to introduce where all this math is used and useful in engineering. Many equations are buried in computer aided drawing systems just waiting for a user to hit a go button.
Next time you drive over a bridge you may want to thank a mouse click?
@@SolidSiren "overall" is fascinatingly ambiguous phrasing.
@@SolidSiren3D tensors are a doddle.
No surprise here. This reminded me of the theory of everything that Feynman jokingly proposed. Let us add the left sides minus right sides of all physical equations. The sum will be zero. We give a fancy symbol to the sum, for example 💢. Then, we get 💢= 0, an equation that includes all known physics, but... adds nothing new 😂
Feynman had a good sense of humour! But as a pedant I must add, such equation would be wrong :P The reason is A + B = 0 has more solutions than A = 0 and B = 0. If we don't observe those this "generalisation" is broken.
@@Tablis0 Try again. If A=B and C=D, then A-B + C-D=0 is always correct.
"What I cannot create, I do not understand." -Feynman
Maybe a clueless master student can build a "useless machine", the "simplest robot" (a pendulum) and teach it how to "learn how to learn" about physics, by warping the state space to experience "Fuzzy" reasoning, while "standing on the shoulders of giants", and so, maybe then, a "theory of everything" is achieved, via humility and error 🔥🎩+💦=⛄Frosty, though it will probably talk to itself in Chinglish, or some 👽 alien language. Hopefully it's goal will be to teach us the "theory of everything" beyond just a mere answer of "42" 🎩🤠
@@cheshirecat111 yes, but the logical inverse of that is not true. A-B + C-D=0 does not imply A=B and C=D
@@Tablis0i don't know Feynmans joke, but I guess he was clever enough to add the norms of those differences (or some other related quantities like the squares of norms). Since norms are always nonnegative real numbers, their sum is zero if and only if each one is zero.
Thanks!
Thanks, happy you like it!
Thank you🔥🐝
Thanks, happy you like it!
I am surprised that the paper passed peer review but didn’t stand a chance against the “Pen Of Doom” :-)
I didn't mention this in the video, but the authors have previously written several other papers on the topic. Once you get the first paper published, the later ones are easier. Actually the new paper is pretty much incomprehensible on its own and that probably helped getting it published.
@@SabineHossenfelder It might be interesting to feed it to one of the new AI models that can do math well to see how well it does in picking the paper apart.
@ I did with O1 and the article in Physica Scripta, it found multiple inconsistencies, also offered some good ideas how to fix them
@@ivaylovasilev2688
Curious, have you tried the communist one?
Just meme'ing but also, I could see it be better at this kind of stuff.
Yay! Tensors introduced to a broader audience!
I learned them in university, and at first, they looked scary. Instead of a scalar, you had to work with a matrix, but a couple of years later, I recognised the beauty of defining a real-life object using a matrix and a set of rules attached to it. Gradients, rotors, operators, different multiplications and differential equations in a unified notation format! They are not easy, but they can describe the uneven transparency of a chunk of a mineral, rotation of an object with no circular symmetry, and a lot of curved, deformed, uneven real-life stuff. Very useful mathematical construct!
Indeed, it's interesting that curvature naturally pops up in certain materials.
Something to note here: Not all tensors are matrices! While you can express a second degree tensor as a matrix you most definitetly know at least one other tensor that is in the simplest form a third degree. The levi-civita tensor ε_ijk. Using permutations you can actually generalize the concept of that tensor into even higher dimensions. It gets a bit more complicated but it is very useful while working with 4-objects in relativity.
@@derdotte Indeed, but as an AI programmer I know you can express any tensor as a multidimensional array. A matrix is a 2d array. You can express a vector as a simplified matrix with just one row or one column. In fact the dot product, cross product, scalar multiplication, and vector addition/subtraction can all be expressed as operations on a matrix.
Well, the unification of vector calculus is much more nicely done through differential forms than through tensors!
At least you avoid the horrible "debauche of indeces", as rightly pointed out by the great mathematician Elie Cartan 😁
Werent tensors introduced to broad audience when nvidia made RTX cards? I wouldnt call some old woman video "introducing to broader audience" lmao
I LOVE YOUR STYLE, @Sabine! I would love to have teachers and tutors with this both rebel spirit and strong commitment with solid science back in my student days!
"So much about being nice" XD I love it.
But reassurance about the impending revolution. Or resolution. Nice enough…
One day you will find a theory of everything paper that actually works. I'm here for it.
I am keeping an eye out for it!
@@SabineHossenfelder Just make sure you don't burn it 🤣
I'm pretty sure I didn't understand much of that but I have found a new reason to watch Sabine's videos: there will come a day when she sets papers on fire but will have forgotten to turn the smoke detector/fire suppression system off first.
A bit feeble - not so ? Sabine is quite serious about her work and why would she destroy is? Nihilist ?
I think that's a 200euro fine for the HRT to turn up and turn off the fire alarms...
I just watch this channel to keep myself humble. Fantastic work as usual, I assume.
You have a unique capability - You're a stand-up comedienne who can perform sitting down.
Sabine and the lighter approach
😂 now considering an entire series called "the lighter side of physics"
@@SabineHossenfelder Well the world is clearly going up in smoke so 'when in Rome' as they say lol. If only RUclips enforced transcripts you could have battle after battle with your detractors!
@SabineHoss😂enfelder
@@SabineHossenfelder mmm, i could really need that hehe, i have a lot of gaps to fill in and wiki can be a bit dry on the humor side a veces jiji ❤🔥
Lighter side of physics - rotflol. But I'm also German so my word play comprehension is likely on a similar level as Dr. Sabine's is.
That was a really nice conceptual explanation of why tensors are important!
Also, Feynman hated that conference and, at one point, shouted “NO!” loudly three times at a fellow physicist. He told his wife never let him go to a GR conference again.
I have a lot of understanding for that...
I’m trying to watch this, but I cannot get my head around tensor math. Differential equations is about the boundary for my understanding of math. Beyond that, it’s as if I’m a dog and you are talking me, “Yap yap yap Steve. Woof woof yap, Steve. Yip woof yap, Steve.” You’re talking to me (I hear my name….) but I have no idea what the hell you want!
@@stevenslater2669 Try the paper NASA/TM-2002-211716 "An Introduction to Tensors for Students
of Physics and Engineering" by Joseph C. Kolecki (2002), which is accessible online.
@@stevenslater2669 are you, by any chance, referencing the Far Side comic that compares what the dog's master says to what the dog hears? You made your point well in any case!
@@TerryBollinger😂
Every fundamental physicist, before going to bed, check inside the cupboard to make sure that Sabine is not there
The ending made me laugh out loud. The face. The tone of the voice. And then there was the burning.....
I didn't understand a word You said. I really enjoyed lighting up the papers. Thank You!
I'm actually surprised how well the camera captured this. I might burn some more things...
@@SabineHossenfelder 😂
@
😂😂😂😂😂@@SabineHossenfelder
We’re happy to contribute to your delinquency… 🤣😂🤣
Wow. That was the best 5 minute introduction to tensors and GR I've ever seen. What's next quaternions?? I'd be careful about pissing off Alena, though!
That geometric mu nu stuff is something I had hoped to understand someday, but none of the texts I have from my failed undergraduate 50 years ago cover it. Same with anything on Riemann. I'm thinking of buying Susskind's theoretical minimum series of books to see if those can help.
Do the texts you've studied include Misner Thorne & Wheeler's Gravitation? They provide quite a lot of introductory material bringing these ideas to those new to all that stuff. Published something like 50 years ago, quite popular, but probably superseded at this time by other books and videos. Woefully old when it comes to gravitation waves - please ignore that chapter! But the math of tensors, metrics, curvature is still good.
What books have you found most useful?
Thanks Sabine once again! nice that you explained so nicely. Although, I am only a PhD in medical imaging so I do not know much about tensors. I remember that while dealing with vectors, to develop the algorithm I was working with, I wanted to study tensor. Because vectors are also one type of tensor. But I could not find enough time to do so. Maybe, this video again motivates me to go back to studying tensors. :)
Sabine's smirk when she sets the paper on fire at the end had me completely cracking up 🤣
Sabine, I believe I can learn physics by hosmosis by watching your videos. While I don't learn, I can offer some compliments: congratulations, your image today is much better than when you published your first videos.
Finally I understand tensors better intuitively, thank you!
Now I have a dream, to get a paper burned by SABINE, I will make a theory of everything that at least is worth of your time burning it. Would you give tips of how to reach that point??
i didnt know sabine burning a paper would tickle me so, but it does! excellent video
This is good science communication.
Once AI agents start filtering out and ripping up junk papers from the publication record, sabino will be shown to be the absolute sweetheart that she is by comparison
The hilarity of your honesty of not having ANY sense of electromagnetic constant...
Priceless honesty.
You should work on that.
I wonder if you realize your significance. Confidence in science has been shaken. Your work publicly deflates Science-the-Industry and Science-the-Brand back down to a discipline--the simple and ruthless application of the Scientific Method. From my perspective, universities and companies have a conflict of interest resulting in overly-optimistic reports of theories and breakthroughs. I don't have the skills to judge the veracity of peer-reviewed publications. But I know that a paper that *you* find plausible, even in part, is worth reading. I suspect this might make you unpopular in physics social circles. I imagine hopeful young physicists approaching you with their new giant red balloon, and you're ready with the needle. Keep it up! You're appreciated.
Not really. Science has always had charlatans and bad scientists. That's why things need to be peer reviewed and can be changed whenever new evidence is found.
Well, I wish I could say I fully understand what shed said. But even so, it's so nice to see her show her intelligence and confidence in those videos.
An idea for you: bring one of those authors to debate about the paper subject and see what comes from it.
Talking about the function of tensors in physics was incredibly insightful, you did a great job with this review!
This is one of your best videos in a while. No flashy stuff. And no talking down. Just straightforward. I like it better.
I had to laugh out loud when you wrote "BS!" on the paper, because that was EXACTLY what I was thinking in that moment. EDIT: I certainly do not want to start any theories, not even hypotheses. I merely scratch the surface and my knowledge is thinner than a razor.
After watching this 5x, I formed the view that Sabine fully understands what she talking about...
😂Every of her vids makes a tiny little bit smarter though.
A neat 'new' way to present the videos we all love. Love it! :)
I love this video, and I'm following with great interest. As Sabine notes, if you learn only one thing then learn about the metric tensor at 4:39, from which the Riemann tensors and scalar are based. Einstein said they were like beautiful carved marble, while the stress-energy tensor T is made out of wood, as it depends on what kind of matter-energy one is talking about.
Speaking of “brilliant” , careful observers will have noticed another German humour Easter Egg in here - “… because physicists ran out of coffee “.
More paper review videos please! It's actually super helpful for me being in grad school.
A wonderfully dry dismemberment of this paper. Sabine is brilliant, and it is a joy to listen to her.
I watch, and really want to understand, but after watching Sabine explain or debunk these papers, I just go back to my colouring book, and I will still watch tomorrow too
Lighting the paper on fire was somewhat redundant, since Sabine had already burned the theory to the ground, lol
I really admire your intelligence, passion and devotion. Thanks for being you Sabine. Glad your microphone is'nt hiding your pretty face.
Thanks. So badly needed! Keep up the awesome work!
😅 love your content and your sense of humor 💖
I need that on a T-shirt.. "Always Start with the Lagrangian"
The smirk while setting the paper on fire 👍 ....
Hi Sabine, thanks for triggering flashbacks to my college days in math trying to visualize tensors. They all were fingers showing the right hand rule flying about.
The best part was the transformation of the paper into fumes and ash, which I will now think of as the Sabine transformation.
Not gonna lie, that look of genuine enjoyment as you lit the paper on fire scared me a little.
Most of us have learned about solving multi-variable simultaneous equations, even large sets using matrices. Imagine having to solve 10's of thousands ( or even more ) equations simultaneously, to describe the flow of time and matter. This tensor research is attempting to do that. I applaud their effort to move the math forward. This is what Phd's should be doing, the hard stuff.
Oh god, Tensors... Makes me remember my second year at uni and a dread memory of the day I realised that there was a lot of maths that wasn't just tricky, but really very very tricky. I remember a lecturer, my mental image is that he was at least 120 and had one of those beards only 120 year old men can grow, talking about Dirac for at least an hour before he eventually got back onto the maths he was supposed to be helping us with. His descriptions of Dirac as some sort of mentally gifted maniac (maniacally gifted that is, not that he was a murderer or something), do give me a fond memory of how much the profs used to worship their heroes. Its a nice idea that there are still (or were 20 years ago when I was trudging to 3hr lectures written mostly in greek) some people who idolize genuinely clever people, and not just investment capitalists who self-proclaim themselves to be clever.
I am so glad youl talk about things like this.
Too many questions in my head now, but at least this episode made some sense of older questions thank you
If a light bulb is the sun a stress map could be a tensor. A stress map represents how forces distribute across different dimensions, much like how tensors describe complex relationships in multiple dimensions.
That look on her face when she lit the paper on fire... LOL 🤣
Thanks Sabine,
Giving insights into physics based on a bs paper is what i like the most on this channel.
Turning slop into gems!
Sabine has this talent.
What a nice opportinuty to recall and thank once again two great titans - G. Ricci-Curbastro and his apprentice T. Levi-Civita, the fathers of tensor analysis. Their gift to humanity is truly priceless! 🥰
New career goal: have a "theory" paper torched on youtube by Sabine.
I just ordered Existential Physics. I am really excited. Stoked, one may say.
Thank you for all of the information and entertainment through the years, Bee. This goon can't get enough.
Pyromaniac Sabine!!! I'm loving it LOL
5:26
🧐Gmunu?
Gmunu,too?🤨
😎GMUNU😎
I was going to organise a gofundme page in order to fund the purchase of a new chair. The damage to the chair looks permanently distracting.
I never got round to it because something distracted me and when I refocused, it seemed a bad idea.
Loved the video.
now i can’t unsee it
'Never start at the level of equations of motion. Always start with the Lagrangian equations.'
Absolutely right!
Now THAT is a thumbnail!❤❤❤
My first thought!
Understanding Tensors, Covariant Derivatives or Differential Forms and other Concepts like Topologie is the Key to understanding Physics. I always view my hard earned Ability to work with Tensors as the greatest tool of all I learned in Math in my whole Life.
02:20
_There are a lot of maths things which are not tensors._
However, scalars and vectors don't belong to this category because they are tensors of 0th and 1st stufe, respectively.
That's right. But mathematically nothing is preventing you from, say, combining 4 scalars to a thing with an index which would then not be a vector, if you see what I mean?
Thought about Tensors some time ago. Found out my understanding on the concept was wrong
That thumbnail is 🔥🔥🔥🔥🔥
You are a force of nature Sabine. :) Keep up the good work!
Im just glad the field is still active.
new rule, all papers a a new "theory of everything" have to be peer reviewed by Sabine herself before they can claim it truly is a theory of everything
I like introducing tensor via categorical thinking. Like if you have a bunch of fruits, you can split them into apples, oranges, bananas, etc.. but you can always split further by arbitrary categories, like color, sweetness, size (in discrete sizes first). Though it is not a linear algebra object, you can still do a lot of operations on it, and it is very handy when discussing quantum computing.
this video inspired me to get one of those torches.
I gotta get me one of those mini-torches!
Your presentations are always fascinating and instructive. They are, however, very often 2 or 3 light years over my head. I was always interested in physics (Newtonian) but decided to study chemistry instead. Occasionally, some of what you are discussing manages to penetrate into my consciousness but I still fall back on good old chemistry - a reaction either does or doesn’t. It is not dependent upon the spin of the solution . . . . Or does it? Damn!
Thank you for what you do. If my physics teachers had been up to your level I most likely would have changed my focus.
1:19 brutal and I love it 😂
I too was fascinated when I first learned about tensors in physics. I sensed that there was an important solution to the universe there. That's exactly why I attempted to take a tensor analysis course.
My enthusiasm faded quickly. I still feel something about tensors. They are cool.
Ugh, I hate that sort of thing! You probably got stuck in the mud dealing with definitions, proofs, details of transformation formulas, and zero or very little intuitive applications. Tensors are beautiful mathematical concepts once you get past the math!
Love the thumbnail. Dramatic 🔥😮
Funny how I used my torch too, and got it all the way through it in 1 viewing. So, aren't these tensor connections just 'filter transforms' coupled serially and also in parallel. Just like a modern control system that runs your furnace... ???
Long time fan!!! Obviously your delivery is always priceless.
Though I’ve never been a good student of math in my younger years, starting in my 30’s, I’ve become fascinated with physics. At 52, do you feel Brilliant would help, not just in understanding what has been done, but to also explore new ideas?
Thank you!!
Brilliant is a good study buddy, or reference guide to what you're studying. It reinforces what you're already learning. On its own though, it's not as effective. At least in my experience.
@ thanks for the heads up. No escaping the grind I suppose haha
The formula you show fits well with a holistic approach to gravitation, where gravitation is seen as an emergent phenomenon deeply interconnected with other aspects of the universe, such as quantum fields, holography, and specific structural interactions. It could be used in a theoretical framework that does not limit gravitation to mass and energy, but also addresses other emergent aspects of the physical world and its dynamics. However, many terms are still missing on the right-hand side... Question: If the rest of the paper is lit again🔥 with the same lighter, is it the same flame🔥? Or not! 😉
I'm not a physicist, but a fiction writer, and some of this goes over my head, but thank you for the "Gee-mew-new" I appreciate that. I promise I will use it only to express something overheard to denote someone else is smarter than others, not as any BS thing I make up from thin air to explain my hand of the author needs. 😉
My neck became a bit tensor while watching this. Thanks.
Sure I did not understand much, but fun to watch. Thanks
Next video: How to keep heating costs low -> burn nonsense papers.🤪
You should make a series: the weekly theory of everything bullshittery
From the video I learned that tensors are not fire resistant
That's why I'm writing my state representative concerning building codes -- to demand that from now on all houses and buildings be made of quaternions!
Very interesting indeed, Sabine! Thanks! 😊
Stay safe there with your family! 🖖😊
i definitely watched this with my head hitting the wall
Thank you, your explanation was actually very useful.
Tried banging my head on a wall, still don't understand what a tensor is. Will leave the physics review/critiques to others.
Thank you for what you do.
I had my own fun theory when I was studying science. I tried to explain faster than light information exchange of entangled particles. I had to solve the distance problem. So I proposed, that instead of 3 dimensions of space and 1 dimension of time we had 3 dimensions of time and one dimension of distance. So, reality looks and acts exactly the same under such system, with the only difference in it continuously creating parallel dimensions along 3 axis. We have 3 sets of probabilities crossing through eachother. A series of parallel futures and pasts passing through now. We are the moment between possibilities that surround every particles well... like the wave function. My system is functionally the same as the system where there are 3 dimensions of space and 1 dimension of time, but just like time can be collapsed by the speed of the observer, I was trying to turn distance into a collapsible parameter that then could nullify distance between objects. Entangled particles are the white holes people look for. They expect white holes to be massive, but they're tiny and right under our noses. They are aligned in pairs and the distance component between them is collapsed. They are anti-black holes existing at the opposite end of possible physical scale. Time is a vector and space is a quantity. Think about that. Same math. No paradoxes. Spacetime is already linked. Just think of it as Timespace instead, and how you can different things, if you combine space into 1d and make time 3d.
I am fascinated by your zest for your trade, Sabine! Setting the BS to fire was very satisfying... Thank you!
Always start with action (or Lagrangian density as told by Sabine). To have a physical theory we must start with a physical problem. That's the constraints a physicist abide by.
Thanks for this, I came across this paper in my feed and wondered what you thought about it. Also, why is a gravitational field NOT a function of angular momentum like electrical?
That's interesting. I've been exploring similar concepts in the context of extended Lagrangians, particularly those that incorporate higher-derivative terms or non-Riemannian geometry. My research has focused on understanding how such modifications can affect the dynamics of spacetime and potentially provide a framework for unifying gravity with other fundamental forces.
While I appreciate the attempt to explain dark energy and quantum physics through the 'Alena Tensor,' I remain cautious. Many theories have come and gone, promising to be the 'Theory of Everything,' yet ultimately failing to deliver on their promises. My experience has taught me to be skeptical of such claims, especially without rigorous mathematical backing and testable predictions.
I'm particularly interested in seeing the explicit form of the Lagrangian that incorporates this 'Alena Tensor.' How does it modify the Einstein-Hilbert action, and what new degrees of freedom does it introduce? Does it address the long-standing problem of renormalizing gravity, or does it simply shift the problem to a different sector? And, of course, the most crucial question: does it offer a natural and compelling explanation for the observed value of the cosmological constant, or does it merely introduce new parameters that need to be fine-tuned?
Until I see a concrete mathematical formulation and a detailed analysis of its implications, I remain unconvinced. However, I'm always open to new ideas and perspectives, and I'm eager to learn more about this 'Alena Tensor' and its potential contributions to our understanding of the universe.
5:53 what about the Alena Smart speaker from Jeff Bozos😂
Love your clip ending and your new hair style!
Even better and far more elegant than Alena tensors are Bivectors as developed from abstract Clifford algebra by Hestenes into "Geometric Algebra" specifically to unify maths for physical applications.
For a quick crude intuitive notion of what tensors are, imagine you have a small stretchy object, maybe foam rubber, gelatin, or a patch of bubbles floating on water.
Pull on it in some direction and it moves that way. That's a vector.
Now pull on one end and pull the opposite way at the other end. If your pulls are outward, away from the center of the object, that's a tensor, a symmetric one. The stress tensor in mechanical engineering is just like this.
OTOH if you're pulling up, let's say we're pulling north, on the east side of the object, and pulling south on the west side, the object will rotate. That's an anti-symmetric tensor. As a practical mathematical concept, it's a rotation matrix.
In relativity, a "boost" - to make something move faster or slower or go sideways - is the same thing as rotation but "space-time" rather than "space-space" like a rotation. That's hard to explain further in a youtube comment. The capital 'F' you see in that paper Sabine shows is the electromagnetic tensor, which combines rotations (for magnetic fields) and boosts (for electric fields) into one 4 dimensional antisymmetric tensor.
Now imagine having a rod or cylinder of some material, like a can of soup or wood dowel or an common everyday battery (AA or D size, whatever) Twist one end. A twist is basically a rotation, which we already established is an anti-symmetric tensor made of two vectors. We need a third vector to say where we're applying this twist. Balance it out by twisting the opposite end in the opposite direction. We just made a rank-three tensor, anti-symmetric.
There are more examples I could give, but I'd be writing an article suitable for Medium or Substack, too large to fit in RUclips comments, and I'd want to make illustrations. Someday...
i love your symbolism in this video! great work as always Sabine