What is the Chandrasekhar limit for White Dwarf Stars?

This video provides a simplified step by step derivation of the Chandrasekhar limit for White Dwarf stars. After briefly discussing the history of white dwarf stars, an overview of electron degeneracy pressure is provided. Using a combination of quantum mechanics and Einstein's theory of special relativity, the Chandrasekhar mass is derived. The video ends with a discussion of the conflict between Chandrasekhar and Eddington.
References:
Gravity from the ground up - Schutz
The Quantum Universe - Cox and Forshaw
Black Holes and Time Warps - Kip Thorne
Introduction to Quantum Mechanics - Griffiths and Schroeter
Introduction to Quantum Mechanics - Phillips
Astrophysics in a Nutshell - Maoz
The Planck Mass and the Chandrasekhar limit - Garfinkle
Chandrasekhar vs Eddington - an unanticipated confrontation (pubs.aip.org/physicstoday/art...)
Chandrasekhar limit: an elementary approach based on classical physics and quantum theory - Pinochet and Van Sint Jan (iopscience.iop.org/article/10...)
The Physics of electron degenerate matter in white dwarf stars - Ganapathy (scholarworks.wmich.edu/cgi/vi...)
scholar.harvard.edu/files/sch...
www.astro.princeton.edu/~burr...
scholarworks.wmich.edu/cgi/vi...
The Chandrasekhar Limit - A simplified approach (iopscience.iop.org/article/10...)
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iopscience.iop.org/article/10...

[@PhysicsExplainedVideos]

There is a small typo at 08:20, Heisenberg's uncertainty principle should be written as (delta x)(delta p) ≥ h-bar/2 without the pi! Sorry about that, let me know if you spot any others.

[@electronichaircut8801]

I discovered your channel about a a year ago. Can you please make a video about atomic orbitals?

[@PhysicsExplainedVideos]

@@var67 thanks for letting me know! Hopefully it doesn't cause any confusion

[@DrDeuteron]

1:16 drawing a line down (up) ward towards (away from) the horizon in the northern (southern) hemisphere.

[@justanotherguy469]

Bless you. You explain the subject matter so well. Are you a professor, because you teach this and make it easy to understand? Your love and dedication to the education of others, is beautiful.

[@neil2444]

Thank you for not dumbing down your content! People afraid of equations can just cover their eyes. :)

[@d2factotum]

Regarding Eddington's opposition to this, I can't help but remember the Arthur C. Clarke quote: "If an elderly but distinguished scientist says something is possible, he is almost certainly right. If he says that it is impossible, he is very probably wrong."

[@bobhope7958]

After deriving the electron degeneracy equation: “the fact that density changes throughout the radius of the star is rather complex and beyond the scope of this video.” Not sure I should have laughed so hard at that line.

[@jerkfudgewater147]

It seems fairly obvious that the stuff at the center would be more compressed than the stuff at the surface 28:23

[@Kanitoxx]

It's indeed seriusly complex, in my early years of University i tried to independently derive the expresion to do this in solid matter (planetary sized iron balls) and then switched to degenerate gas, and it's still a little more complex than the detivation of the electron degeneracy equation.

[@PolarisNC001]

Indeed. I was assigned an analysis of this kind of density as part of a computational physics class as an undergraduate. As I recall, the equations were essentially impossible to resolve algebraically, and had to be approached via successive approximations. It was interesting to program, even if I barely understood the physics involved.

[@tippyc2]

Not only complex, but it doesnt really contribute to understanding the core lesson. First, we'd have to express density as a function of "r" before we integrate, which needs to account for compressibility, mass, temperature, temperature gradient, etc. Getting that one right in an object that we can only look at and theorize about is probably worthy of a PHD on its own. Of course we also get stuck in a catch-22 because mass is the unknown we're trying to solve for, but mass is now a constant in the analysis. So we cant just write one nice neat expression that simplifies elegantly and looks good in a youtube vid. Instead, we have a big messy expression that we have to iterate until we converge on an answer.

[@nigeldepledge3790]

I think laughter at this point can be described only as maniacal . . .

[@polyreza]

The way you explain tough scientific concepts is incredible. As far as I know, you are the only channel that provides mathematics of such theories in detail. Awesome. Keep it up

[@PhysicsExplainedVideos]

I really appreciate the positive feedback, it means a lot!

[@JC-zw9vs]

Maybe at one time there were 10^57 physicists doing this stuff, but they reached a critical limit, so they all collapsed to form the one that now posts as Physics Explained!

[@MaryAnnNytowl]

There are a few others. There's even one that's been doing something like a primer for trigonometry, along with the other science/debunking stuff he does. His channel is called ResearchFlatMoon. I know, silly name, but it does get one noticed. 😄

[@mihailmilev9909]

@@JC-zw9vs lol

[@mihailmilev9909]

@@MaryAnnNytowl tysm!

[@HectaSpyrit]

I will never get tired of Physics Explained videos

[@sirbarringtonwomblembe4098]

Me neither. Right - that's me off to bed now.

[@sphakamisozondi]

When the scientific world needed him... He returns!

[@MoxlyMakesGames]

Man, what a coincidence! I was just looking through your channel wondering why you haven't uploaded in a while, then suddenly you dropped this gem! Thanks for all the good work, man.

[@omnipotent1992]

I too thought of this. I think we're brothers now

[@boggless2771]

I have a professor named Chandrasekhar and he said he is not related to this dude. Then KZbin recommends this video to me. Tbf I like physics, but the coincidence is too high for me to believe KZbin isn't listening through my phone.

[@nookleer]

Hmm. Now im wondering. I literally looked up the Chandreskar limit last night..

[@joelpenaflor314]

@@boggless2771 i looked this up at work but didn't get to watch until it recommended on my phone a couple days later 🧐

[@supreetsahu1964]

What a great video! Also special thanks for featuring an Indian scientist. Most of us are unaware of the actual contribution of Indians to Science. It is either underappreciated by most people or grossly overestimated by nationalists.

[@DrDeuteron]

BEC? (e.g. not a fermion but a _________?), e+e- --> e+e- ? inelastic scattering of light, the partition function of a plasma, CXO, ...I'm not feeling your post whatsoever.

[@supreetsahu1964]

@@DrDeuteron you understood my post but you are deliberately acting dumb. I am aware of the work of ramanujan, jc bose, sn bose, cv raman, s chandrashekhar. But most people are not aware of India's contribution to science. And jingoists in India say that all modern science was already written in the religious texts, which is completely wrong

[@DrDeuteron]

@@supreetsahu1964 "understanding it" and "feeling it" mean two totally different things.

[@utkarshrastogi2482]

@supreetsahu1964 inferiority complex se bhare hue ho tum. Internet se bahar niklo aur duniya ghoomo.

[@tarangsrivastava3638]

In some universe, Chandra might have continued his work. A big WHAT IF to thought about. Thank you so much for this video

[@PhysicsExplainedVideos]

My pleasure :-)

[@jasperism27]

Imagine the immense progress in astrophysics if Chandrasekhar wasn't harassed into a 25 year break.

[@Euquila]

by, surprise surprise, rich established men who show cowardice in the face of diversity

[@MOllySixxxCA]

There’s no doubt in my mind he would have contributed more. However, let’s not dismiss the work he did after this limit and the fact he didn’t just stay still. Stellar structures, hydrodynamic and hydro magnetic stability, radiative transfer, and number of others I can’t think of at the moment. He was a once in a generation pioneer.

[@Rudra_om]

they are still doing this

[@taufiqutomo]

Even though your videos are usually 30-60 minutes, I play them at least twice. Once to sleep, and once more to try to understand its contents.

[@ruinenlust_]

Glad to see I'm not the only one that falls asleep to science videos!

[@polyreza]

Kinda ASMR😁

[@justanotherguy469]

I as well! Something about his cadence, and the visual absorption of the nomenclature, especially the sinewyness of the definite integral, combines to give me nocturnal bliss...oh my.

[@MaryAnnNytowl]

If anyone is interested in microbes, there's a great channel to do the same with (watch to sleep, then watch to learn), called Into the Microcosmos. Great voice, really neat microbes, and great visuals, too!

[@stephuf6915]

Fantastic ! I could not do it again on my own, but you succeeded in bringing me so far ! I would not have imagined before that I could more or less understand this. Thank you !

[@yvongaltier258]

" That is Sirius " Nobody said drawing a line was funny.

[@STriderFIN77]

lol :)

[@6612770]

And you can completely forget about "Shirley" too...

[@sirbarringtonwomblembe4098]

John McEnroe certainly knew his stars in 1981!

[@JC-zw9vs]

Simply astounding how much you can achieve using high school mathematics and some good approximations. I also like the way you explain the limitations of your approach and the effect that has on the prediction. Many many thanks for this!

[@starryfolks]

Brilliant. This kinda thing should be awarded.

[@justanotherguy469]

Instead, Cardi B. and Lizzo are winning Nobel prizes.

[@hacun3jr]

Why did he remove the schrodinger video?!?!

[@brianflaherty9054]

He’s back!

[@rallymax2]

Wow. Your most comprehensive wonderfully articulated subject yet. I wish I had received teaching like yours when I did my bachelor’s in physics. I feel I would have been a different person.

[@PhysicsExplainedVideos]

Glad it was helpful!

[@jannegrey593]

Fantastic video as usual. Shame about Chandrasekhar's work not being accepted initially (probably in some way because he was Indian - though we can see that Eddington was always scared of black holes). I hope next time we will see a video on Neutron Stars then ;) I'm joking of course - any in-depth video you make is going to be interesting and a nice surprise, but a welcome one.

[@UteChewb]

Thank you so much for this. Way back in prehistory when I was studying this stuff, I read Chandrasekhar's book on astrophysics. I remember thinking how elegant his theory was. Beautiful. But I have forgotten everything about it, so it is wonderful to see a gentle re-introduction.

[@aliexpress.official]

I want a "Theory of Everything" style movie based on Chandra since i nearly teared up here.

[@samw3086]

Great video as usual. Bringing everything down to calculus and well known physical laws which are understood by most engineers and students of science is welcome.

[@PhysicsExplainedVideos]

Thanks!

[@clavinrali9245]

Your Channel was what KZbin was missing. Thank you ! I've been searching for a channel that Explains and derive equations of amazing scientific principles !

[@franckmalers2299]

aaah, finally a new episode of my fav science channel

[@amaze2n]

You have one of the best physics channels on KZbin. Great work.

[@PhysicsExplainedVideos]

Thanks!

[@TheMixxon2]

I LOVE THIS SO MUCH I LOVE YOU SO MUCH, NEVER STOP DERIVING THESE BEAUTIFUL EQUATIONS !!!

[@Maxmaxmax63]

YES! A new video! I can’t tell you how much I enjoy these videos. I have many regrets of not studying math and physics in school (social work was a calling for me). Watching your videos scratches so much of an itch for me, its such a pleasure watching these. Thank you!

[@JosefHabdank]

Absolutely stunning video. Please continue in the same fashion to describe the forces preventing the neutron star from collapsing.

[@PhysicsExplainedVideos]

Thank you!

[@OsscarBones]

My bachelor is focused on quantum mechanics so there was no chance for me to work with general relativity, but I took an astrophysics course for extra credits and I absolutely loved it. I now greatly appreciate astronomy and cosmology, as it is the only field I have encountered so far where so many branches of physics are applied at the same time.

[@jannegrey593]

I was worried that something happened! So glad to see you active! I hope you're okay. I'm sure I will love the video!

[@simonhoracek8490]

What a great video! Our high-school physics teacher told us this quote from Eddington, but hearing about its consequence after understanding what exactly it referred to just hits different.

[@dogcarman]

48 minutes after pressing play and my brain is creaking and smoking. But I am happy. Thank you!

[@ProfessorBeautiful]

By coincidence (?) you end with the word "beautiful"; I was formulating a comment declaring the beauty of this video. The satisfaction to understand finally a bit about Chandrasekhar's result overwhelms me. The historical perspective adds so much. Thank you! And congratulations.

[@henryD9363]

Beautiful! This is such an excellent lecture. I followed almost all of it through with satisfying understanding of the physics and its math. (The busy details of algebra notwithstanding.) Your pace of explanation and amount of detail are balanced so very well. My goodness, I learned so much and in such a reasonable amount of time. I kind of want to say that I don't deserve to have this. Thank you

[@t-roy80]

maths & physics are hard... " so lets do that!" this channel is awesome!

[@Israel2.3.2]

Currently reading Chandrasekhar's Principia for the Common Reader. It's essentially an annotation that greatly clarifies and contextualizes the text. I tried reading the Principia last year but the content of Newton's propositions assume a 17th century geometric vocabulary. Chandrasekhar fills in these classical gaps and accelerates apprehension by using algebraic notation to describe proportions, easing the burden of seeing the mutual relations when keeping track of Newton's ratios of evanescent quantities.

[@nigeldepledge3790]

This is a brilliant piece of work, even though my classical mind had to run away weeping, eventually to sit gibbering in a corner.

[@DoctaOsiris]

Excellent episode as always! 😊 Glad to see you back! 🙃

[@PhysicsExplainedVideos]

Thanks!

[@bcaldwell50]

BRILLIANTLY ARTICULATED!!! 👍

[@sethconnor1018]

I just heard of this subject last week and I don't believe in coincidences concerning studies. Thank you for sharing

[@PhysicsExplainedVideos]

Glad it was helpful!

[@PiercingSight]

I haven't done any physics in years, but this was so incredibly easy to follow and made perfect sense, almost as if I could have derived it myself. Absolutely stunning work. Thanks for the video!

[@iwashere2365]

I know nothing about physics and barely passed in school. I have no idea what all the equations were but still watched the whole video. You kept it interesting.

[@uvofsam]

Next will be neutron stars, Neutron degeneracy pressure and TOV equations

[@EddieA907]

Thank you for bringing those dark issues of controversy to light. Your channel is great .

[@alienbroccoli8296]

I really thought you dropped the channel. Thanks for not doing so. I love your videos

[@kruksog]

I knew nothing of Bessel, but actually have a book on Bessel functions. Cool to hear a bit about him.

[@haneen3731]

Awesome content, keep up the great work!

[@PhysicsExplainedVideos]

Thanks, will do!

[@satyamkumarmall8600]

Thanks for the quick explanation , I was watching Oppenheimer and the point came up of a dying star which lead me to this . It was very tragic that Chandrashekhar had to go through this .

[@steveboigon5478]

i have enjoyed all your videos! You do an excellent job! You have not posted anything new in over 5 months...Please don't give up on this series...I love them!

[@davidripley2916]

Isn't the Chandra x- ray observatory named with a tip of the hat to this genius?

[@MsAlfred1996]

This channel is SO GOOD THE BEST OF THE BEST IN KZbin

[@hygri]

Wow, I've just discovered your channel and you're superb! I never had a solid grounding in mathematics, though being a chemist I'm conceptually and functionally familiar with the principals - and you explain it so clearly and concisely I actually managed to follow along with the derivation! Ace!! Thank you so much. Fully, fully subscribed :)

[@thorntontarr2894]

What a fabulous presentation about the history of science and human personality. Of course, the 'simplified' argument creates many questions (for another video) but given Chandrasekhar's ocean journey where it is said he completed this analysis, the fact that he could arrive at such a "simplified' model combining so much complex physics is truly remarkable. So, is the model presented here that of Chandrasekhar ? I have always wondered why it as almost 50 years later that Chandrasekhar was awarded the Nobel Prize; now I know.

[@thomaslawrence2210]

Another powerful video on a very complex subject. Your use of simplified anslysis is remarkable and very enlighting. Keep it up.

[@friedlotto]

You sir, do the channel name justice. The appalling level of science illiteracy these days is not being helped by “the blind leading the blind” in terms of science reporting in the media. Nothing wrong with simplifying advanced concepts to make them digestible by amateurs. But this should only ever be attempted by those who are fluent in the subject.

[@vldptz]

im of the humans and arts area, dont understand a thing about mathematics but i really admire your videos! They have mathematical explanations about the topics youre approaching, thing that usually a lot of astronomy channels (for example) barely bring up. It makes all your videos scientifically concise, explaining the conclusions scientists had through their calculus... things makes more sense. Keep making amazing content! :)

[@oatmilk9918]

13:30 my understanding of physics is a little above a-level, but to me this sounds related to to E = mc^2, whereby the electron gained 'mass' equivalent to the increase in energy it would have otherwise received.

[@atharvshendage4705]

great detailed video, I knew this limit existed but never took an effort to understand how it was derived, thanks for the explanation, really feels great to see the physics and maths behind it. I'll never look at this limit like any other space fact, but a theory that's really, really true, and someone was able to see the death of the star, setting here on earth, using a pen and paper.

[@koenth2359]

Great stuff! A wonderfully well made video, especially for those who are not afraid of an equation or two. Subscribed to your channel. Cant wait to watch the follow up about the maximum mass of neutron stars.

[@truephilosophy2055]

Your videos are awesome. Clear and well spoken and provide enough for someone to follow along, if they do the work. Thanks for what your doing! It would be great if you might do a video on the gluon, like the associated equations used to include it in the standard model. Let me know if you would like to collaborate, I have some theories.

[@JagdishCVyas]

Very crisp and simply brillient exposition. Thank you.

[@PhysicsExplainedVideos]

Thank you too!

[@ethandolin290]

yet another masterpiece. well done.

[@dcterr1]

Excellent and very understandable derivation of the Chandrasekhar limit for white dwarfs!

[@robertmcknightmusic]

nice to see another upload from you!

[@ChaineYTXF]

Extraordinary work. Both Chandrasekar's ... and yours! I watched and let you perform the calculations and develop the intuitions. I will come bqck to do them myself. Neat video.

[@meetthakor4019]

Great work sir, please continue this channel. Also explain more in quantum mechanics and modern physics. 🙏🙏🙏

[@PhysicsExplainedVideos]

Thanks!

[@jean-baptistedherbecourt3878]

Liked how it all starts with looking at the brightest star in the night sky

[@edcoad4930]

Welcome back and as always a glorious, wonderfully paced and informative video on something I knew very little about! Surely this is the starting point of quantum gravity. I do have 1 question; why integrate over discrete values of n to get energy? I refer to the UV catastrophe video which demonstrates this difference between continuous and discrete energy states. Is this because n is so large it can approximated to 1/n -> 0?

[@gato_omega]

I literally have the same question posted a few seconds ago.

[@srinivasatr1395]

I have been waiting for your video on Quantum Mechanics, particularly on Schrödinger equation...

[@parikshitkulkarni3551]

10 minutes in and it's already going above my head

[@elmirelmir842]

What an analysis! Mind blowing!

[@PhysicsExplainedVideos]

Cheers!

[@pdxholmes]

Nice morning surprise! A new Physics Explained video.

[@OSAMAMAful]

Wow man, your explanation is better than a movie!!! Thank you!!!

[@thedragonslyr1]

What a great video, I always feel like I better understand the universe after these. If you are taking suggestions on future videos, I have one. Vacuum decay. I understand that it's unlikely to happen, but I find the concept fascinating, and everything I find online is either too simple, or too complex But regardless, I look forward to your next video

[@MoeNinjaCat]

The equations are kinda over my head but I really enjoy the explanations

[@narfwhals7843]

I love it when you say "ghastly expression"

[@djm.4807]

Just yesterday i wondered if/when you will be back with another video! =D

[@DrDress]

Yeeeey. New physics explained video!

[@JordanWeitz]

I was so confused when he kept saying "sphere" instead of "ball" or "interior of a sphere." Sphere is the locus of points on the boundary: the solutions to *equality* of x^2+y^2+z^2 = r^2. The author refers to this as "spherical shell."

[@KarelduPrie]

you’re back! finally :)

[@BlackeyeVuk]

31:58 Always love to hear whenever you had opportunity to smack on spaghetti monster equation as ghastly.

[@WilliamDye-willdye]

Thank you for including the math!

[@justanotherguy469]

The way he explains it, you can see the math at work. I can not read music, but this must be what a musician feels when he looks at the compositions of great classical composers and can actually hear the music in his head.

[@tim40gabby25]

@@justanotherguy469 spot on.

[@avihayasraf2404]

"this ghastly expression" you've shown ghastlier P:

[@puffthemagiclepton7534]

Ha! I had this problem on my Astrophysics final in undergrad. Thanks for the 'membries!

[@anasroumeih3605]

the king is back

[@MrYukon2010]

What a great way of honouring Chandrasekhar. And again, your way of deriving how to calculate his limit is brilliant because of it's simplicity. I hope there are a lot more video's of you to come in the future.

[@BM-jy6cb]

Firstly, this is superbly presented. The pace of narration and animations are spot on. Second, I can't help feeling there was an element of ego and arrogance in Eddington's objection. Having been in the position of a hailed astronomer seems to have given him the impression that he could discount a theory simply because science at the time could not explain the implications. History is littered with such arrogant assumptions. (I am of course using the words 'arrogance' and 'ego' here in their impassionate sense, and not as a personal slur).

[@TheReptileDragons]

Could you do a video involving the math of quantum field theory? I'm having trouble learning it because I cant find any videos with any sort of rigor. Like how can we calculate the motion of two electrons exchanging a photon? Also a random question: if maxwells equations are the wavefunction for a photon, then photons do not have probabilistic motion?

[@narfwhals7843]

Viascience has many great videos and his ongoing QFT series goes into a lot of mathematical detail. The latest 3 videos are on interacting fields kzbin.info/aero/PLsp_BbZBIk_6_5pi9tHHmoVJzjqpfBkgJ I hope @Physics Explained doesn't mine me linking another channel but I think what you're asking for is a bit out of his scope. Or maybe it's not and he'll make a great video about it.

[@iwashere2365]

I have no idea what you asked... but sounds interesting

[@farhadmodaresi4182]

great work, missed your videos

[@PhysicsExplainedVideos]

Hey, thanks!

[@daveanderson718]

I noticed that you take care to included mathematical derivations in most all of your presentations and that is important to what you want to communicate. Good news and bad news; first the bad news: it has been 30+ years since I last had a differential equation, let alone a complex algebra course, and as reality would have it, I couldn't figure one out today if my life depended upon it. The good news is that your presentations are dummied down enough that I can follow the math you provide........but barely, lol! BTW, you explain things much better than my university professors did. Thanks.

[@andredavis4657]

Brilliant presentation

[@PhysicsExplainedVideos]

Glad you liked it

[@akshayambekar4266]

Thanks for the video.. I respect such people who immersed themselves to find the nature of reality. 😭😭😭🙏🙏🙏

[@Cole-ni8ib]

I appreciate the graph and the constants A and B

[@ZbyszekJot]

Well, this is one really Sirius topic! I understand 5% of it tops, but still fascinating :)

[@MiticaF]

I can’t help but wonder, who the Chandrasekhar’s of today are, and what might be their faith in today’s world? Will we ever know of their discoveries? Brilliant video, Thank you!!!

[@reintsh]

Very good video! This is physics!

[@AndersWelander]

So what happens when the gravitational force is too large for electron degeneracy is that electrons and protons form neutrons. We will need to look at the wave function for that. Funny how the electron resists this marriage with a proton so much. They should be attracted to each other but the electron finds the proton too fat and heavy. Muons on the other hand are more willing to mate since they are pretty heavy too. Just as tips for new topics, I would love to see videos about: neutron stars black holes muon-catalyzed fusion spin-polarized enhancement of fusion. My field is magnetized fusion plasma, focusing on making the magnetic field nice for fusion. So that field I would probably already know but all the rest you show here is useful for me. It helps improve my understanding of some things I may have missed and teaches me some new things and I get reminded of many things I once learned. And it is just a pleasure to watch your videos. Maybe you don't have time to make lots of these but the ones you have made will likely be valuable for decades for many people.

[@Jagzeplin]

god damn i shouldve stayed in school. not one part of that math was understandable to my tiny brain. comforting to know there are people smart enough to be in this video's target audience

[@dragoda]

Your story telling skills are Godlike.. You should make documentaries for bbc earth or netflix.

[@jrr7031]

Ha ha ha!! While i might not get the math, because I havent studied it....i DO get the relationship and understand the fundamental constants (Planck, cosmological constant, etc) this is a super simplification of a very complex topic. Thats so cool i understand it. Great explanation!