What is the Chandrasekhar limit for White Dwarf Stars?
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- Опубліковано 25 сер 2021
- 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...
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.
I discovered your channel about a a year ago. Can you please make a video about atomic orbitals?
@@var67 thanks for letting me know! Hopefully it doesn't cause any confusion
1:16 drawing a line down (up) ward towards (away from) the horizon in the northern (southern) hemisphere.
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.
Thank you for not dumbing down your content! People afraid of equations can just cover their eyes. :)
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."
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.
It seems fairly obvious that the stuff at the center would be more compressed than the stuff at the surface
28:23
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.
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.
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.
I think laughter at this point can be described only as maniacal . . .
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
I really appreciate the positive feedback, it means a lot!
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!
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. 😄
@@JC-zw9vs lol
@@MaryAnnNytowl tysm!
Imagine the immense progress in astrophysics if Chandrasekhar wasn't harassed into a 25 year break.
by, surprise surprise, rich established men who show cowardice in the face of diversity
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.
they are still doing this
I will never get tired of Physics Explained videos
Me neither. Right - that's me off to bed now.
When the scientific world needed him... He returns!
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.
I too thought of this. I think we're brothers now
I have a professor named Chandrasekhar and he said he is not related to this dude. Then UA-cam recommends this video to me. Tbf I like physics, but the coincidence is too high for me to believe UA-cam isn't listening through my phone.
Hmm. Now im wondering. I literally looked up the Chandreskar limit last night..
@@boggless2771 i looked this up at work but didn't get to watch until it recommended on my phone a couple days later 🧐
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 !
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.
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.
@@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
@@supreetsahu1964 "understanding it" and "feeling it" mean two totally different things.
@supreetsahu1964 inferiority complex se bhare hue ho tum. Internet se bahar niklo aur duniya ghoomo.
In some universe, Chandra might have continued his work. A big WHAT IF to thought about.
Thank you so much for this video
My pleasure :-)
" That is Sirius "
Nobody said drawing a line was funny.
lol :)
And you can completely forget about "Shirley" too...
John McEnroe certainly knew his stars in 1981!
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.
Glad to see I'm not the only one that falls asleep to science videos!
Kinda ASMR😁
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.
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!
Why did he remove the schrodinger video?!?!
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!
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.
Brilliant. This kinda thing should be awarded.
Instead, Cardi B. and Lizzo are winning Nobel prizes.
Your Channel was what UA-cam was missing. Thank you ! I've been searching for a channel that Explains and derive equations of amazing scientific principles !
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.
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.
Glad it was helpful!
I want a "Theory of Everything" style movie based on Chandra since i nearly teared up here.
You have one of the best physics channels on UA-cam. Great work.
Thanks!
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.
Thanks!
He’s back!
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!
I LOVE THIS SO MUCH I LOVE YOU SO MUCH, NEVER STOP DERIVING THESE BEAUTIFUL EQUATIONS !!!
aaah, finally a new episode of my fav science channel
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!
Absolutely stunning video. Please continue in the same fashion to describe the forces preventing the neutron star from collapsing.
Thank you!
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.
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
maths & physics are hard... " so lets do that!"
this channel is awesome!
Excellent episode as always! 😊
Glad to see you back! 🙃
Thanks!
Next will be neutron stars, Neutron degeneracy pressure and TOV equations
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.
Thank you for bringing those dark issues of controversy to light. Your channel is great .
BRILLIANTLY ARTICULATED!!! 👍
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.
48 minutes after pressing play and my brain is creaking and smoking. But I am happy. Thank you!
I really thought you dropped the channel. Thanks for not doing so. I love your videos
Awesome content, keep up the great work!
Thanks, will do!
This is a brilliant piece of work, even though my classical mind had to run away weeping, eventually to sit gibbering in a corner.
This channel is SO GOOD
THE BEST OF THE BEST IN UA-cam
I just heard of this subject last week and I don't believe in coincidences concerning studies. Thank you for sharing
Glad it was helpful!
Isn't the Chandra x- ray observatory named with a tip of the hat to this genius?
I knew nothing of Bessel, but actually have a book on Bessel functions. Cool to hear a bit about him.
"this ghastly expression"
you've shown ghastlier P:
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.
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!
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.
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.
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.
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!
Another powerful video on a very complex subject. Your use of simplified anslysis is remarkable and very enlighting. Keep it up.
Nice morning surprise! A new Physics Explained video.
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 .
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 :)
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.
I have been waiting for your video on Quantum Mechanics, particularly on Schrödinger equation...
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.
you’re back! finally :)
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.
yet another masterpiece. well done.
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! :)
Very crisp and simply brillient exposition. Thank you.
Thank you too!
Liked how it all starts with looking at the brightest star in the night sky
Yeeeey. New physics explained video!
the king is back
What an analysis! Mind blowing!
Cheers!
Excellent and very understandable derivation of the Chandrasekhar limit for white dwarfs!
great work, missed your videos
Hey, thanks!
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?
I literally have the same question posted a few seconds ago.
Wow man, your explanation is better than a movie!!! Thank you!!!
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.
The equations are kinda over my head but I really enjoy the explanations
31:58
Always love to hear whenever you had opportunity to smack on spaghetti monster equation as ghastly.
Just yesterday i wondered if/when you will be back with another video! =D
Ha! I had this problem on my Astrophysics final in undergrad. Thanks for the 'membries!
Great work sir, please continue this channel. Also explain more in quantum mechanics and modern physics. 🙏🙏🙏
Thanks!
I love it when you say "ghastly expression"
nice to see another upload from you!
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.
Thank you for including the math!
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.
@@justanotherguy469 spot on.
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."
10 minutes in and it's already going above my head
Bro, please shill your patreon at the end. A lot of people might not know you have a patreon
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?
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 ua-cam.com/play/PLsp_BbZBIk_6_5pi9tHHmoVJzjqpfBkgJ.html
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.
I have no idea what you asked... but sounds interesting
Fantastic. Keep up the great job
Well, this is one really Sirius topic! I understand 5% of it tops, but still fascinating :)
Finally quality UA-cam content
great just waiting for this amazing post
Very good video! This is physics!
Brilliant presentation
Glad you liked it
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).
New video yes!!!
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
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.
I always wait for your videos
Very nice presentation, once again.
Thanks!
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!!!