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. :)

[@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 . . .

[@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."

[@sphakamisozondi]

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

[@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!

[@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

[@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 🧐

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I will never get tired of Physics Explained videos

[@sirbarringtonwomblembe4098]

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

[@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.

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@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 :-)

[@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 !

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

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lol :)

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

[@sirbarringtonwomblembe4098]

John McEnroe certainly knew his stars in 1981!

[@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!

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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!

[@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.

[@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!

[@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.

[@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 !

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Brilliant. This kinda thing should be awarded.

[@justanotherguy469]

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

[@aliexpress.official]

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

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He’s back!

[@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!

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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!

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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!

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

[@PhysicsExplainedVideos]

Thanks!

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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!

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

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Why did he remove the schrodinger video?!?!

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aaah, finally a new episode of my fav science channel

[@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.

[@JosefHabdank]

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

[@PhysicsExplainedVideos]

Thank you!

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

[@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

[@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.

[@dogcarman]

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

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BRILLIANTLY ARTICULATED!!! 👍

[@alienbroccoli8296]

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

[@DoctaOsiris]

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

[@PhysicsExplainedVideos]

Thanks!

[@EddieA907]

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

[@davidripley2916]

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

[@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.

[@haneen3731]

Awesome content, keep up the great work!

[@PhysicsExplainedVideos]

Thanks, will do!

[@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!

[@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.

[@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.

[@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.

[@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!

[@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.

[@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!

[@thomaslawrence2210]

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

[@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 :)

[@kruksog]

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

[@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

[@robertmcknightmusic]

nice to see another upload from you!

[@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.

[@djm.4807]

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

[@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.

[@ethandolin290]

yet another masterpiece. well done.

[@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! :)

[@pdxholmes]

Nice morning surprise! A new Physics Explained video.

[@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.

[@KarelduPrie]

you’re back! finally :)

[@DrDress]

Yeeeey. New physics explained video!

[@avihayasraf2404]

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

[@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 .

[@JagdishCVyas]

Very crisp and simply brillient exposition. Thank you.

[@PhysicsExplainedVideos]

Thank you too!

[@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.

[@srinivasatr1395]

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

[@dcterr1]

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

[@supreetsahu1964]

Bro, please shill your patreon at the end. A lot of people might not know you have a patreon

[@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.

[@OSAMAMAful]

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

[@elmirelmir842]

What an analysis! Mind blowing!

[@PhysicsExplainedVideos]

Cheers!

[@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.

[@meetthakor4019]

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

[@PhysicsExplainedVideos]

Thanks!

[@soulesswanderer2452]

great just waiting for this amazing post

[@reintsh]

Very good video! This is physics!

[@jean-baptistedherbecourt3878]

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

[@anasroumeih3605]

the king is back

[@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."

[@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

[@farhadmodaresi4182]

great work, missed your videos

[@PhysicsExplainedVideos]

Hey, thanks!

[@GoodMan-rq6no]

Finally quality KZbin content

[@puffthemagiclepton7534]

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

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Fantastic. Keep up the great job

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New video yes!!!

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I always wait for your videos

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The best youtuber top 10 I would have said it's you (his remains my opinion)

[@akshayambekar4266]

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

[@ZbyszekJot]

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

[@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).

[@BlackeyeVuk]

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

[@vinayakumarbvk]

Very nice presentation, once again.

[@PhysicsExplainedVideos]

Thanks!

[@wdavis6814]

Another fantastic video!

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@LaserGuidedLoogie]

Awesome! Thanks for this, subbed!

[@PhysicsExplainedVideos]

Thanks for the sub!

[@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.

[@narfwhals7843]

I love it when you say "ghastly expression"

[@Fpires92]

MORE VIDEOOOOOOS PLEEEEEEEEEEASSSSSSSSE

[@PhysicsExplainedVideos]

More to come!