pulsar distance: one weird trick
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- เผยแพร่เมื่อ 20 พ.ค. 2024
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4-22. A pulsar emits a broad spectrum of electromagnetic radiation, which is detected with a receiver tuned to the neighborhood of f=80 MHz. Because of the dispersion in group velocity caused by the interstellar plasma, the observed frequency during each pulse drifts at a rate given by df/dt = -5 MHz/sec.
(a) If the interstellar magnetic field is negligible and w^2 much bigger than wp^2, show that :
df/dt ~ -c/x (f^3/fp^2)
where fp is the plasma frequency and x is the distance of the pulsar.
(b) If the average electron density in space is 0.2 cm^-3, how far away is the pulsar? (1 parsec =3x10^18 cm.)
Link to another coffee and the problem: • can we space elevator?... - วิทยาศาสตร์และเทคโนโลยี
horrified as a mathematician watching a physicist write 200/3 as 70
Physicists committing math crimes, mathematicians being horrified; a cycle as reliable as a pulsar
Since 200/pi = 60 we can conclude that after taking the average 200/3=70 . No problem here.
technically speaking mathematicians also have to round down 200/3 to some number of decimals. They cannot show infinite number of digits.
as long as the approximation is smaller than your margin of error you've got nothing to worry about :^)
...70 +/- 70
checks out👍
Coffee and the problem is great except I'm much better at coffee than I am even understanding the problem
16:09 still trying to understand the algebra lol
@@user-vn8pw4yf3hIt's a partial derivative as denoted by the curvy d symbol. Idk why it is the partial derivative, but it's still functioning like a regular derivative w.r.t time in this case.
It's like watching a piano recital of Chopin pieces. I am not musical and cannot understand how the arcane notation of music can be turned into audible form so (seemingly) effortlessly, yet I see (and hear) that it can be and I can appreciate the result.
A banger of an idea, except I don't drink coffee and don't understand how I'm even supposed to approach the problem 😂
This is why I majored in history rather than physics. Historians generally don't need to know math. What do they need to know about? Clothmaking. A good working knowledge of clothmaking is essential to being a historian.
24:09 As a retired academic I'm thinking "this guy was teaching this stuff!".
Nice work identifying this as Prof Longhurst's book. You're right about the (mostly obsolete) books we hold on to. I guess when I go someone will just send mine for shredding, with no idea who all those famous (to me) authors are.
Sigh.
Feeling mortal today, I spread my Mum's ashes yesterday.
Sorry to hear about your mum.
@@archivethearchives Thankyou.
Will your library to Dr. Collier?
@@AnnoyingNewsletters Hi Don, now that IS an amusing thought! I think the freight cost from the other side of the world would be prohibitive. Regards, Andy
PS I liked your username.
HOT and JIGGLING ions near your location!
🥵🥵🥵
😂
BOOM! 😂
I love ion on ion action.
The Hoax Hotel
Oh shit, I have time to watch this before my menial retail job!!!
Good to know there are others.
@@jordancate5401 Is it good? Is it good for us to know there are others suffering like we do?
My man......hehe.
my weekly shot of advanced physics from my personal dealer
❤️ you!
I loved this as I was making breakfast and drinking coffee! Thanks for sharing your book and its cool history.
Same
O dear I hope this is ironic as I've abandoned STEM for creative writing and almost every young writer wants you to know that their protagonist uses a dealer.
Hey, this is tangentially related to my day job!! Precise GPS algorithms also rely on figuring out how much the signals are delayed while traveling through the ionosphere. We're kind of working the problem the other way around, and use several approximations but it's very cool to see the same basic problem from a different point of view.
BTW the use of ancient mellenial memes? *chef's kiss*
Angela "It's a really easy problem, we don't need the solution", me completely lost nodding "uh huh".
I watched to the end so my Int stat has increased.
Not unless you solved the problems underway.
That last part about Glen's notes is so touching. It's super cool to get the thoughts of someone who was teaching the class on the textbook being used to teach it!
I absolutely love those old textbooks too. Which reminds me, speaking of old books, I have a collection (well parts of it) of the "Most important books of the Western World" and it has several books in one. Like one has Faraday, Lavoisier and.. Pascal? I think. Anyways... I was reading part of the Faraday section and HOLY HELL. I mean, I know Faraday is one of the most famous experimental physicists of all time (if not THE most famous), but you can immediately tell why when you read his papers. Like, I won't even type an example because it would be 3 pages of how he setup the experiment and tried pretty much every single iteration of the different ways it could be performed and made notes of all of it. Even if it amounted to nothing. Dude was a machine.
It's even more impressive when you remember his only training was reading books between him binding books
I have the same book! It's Fourier, not Pascal. Which makes it foundational for pretty much all of modern engineering and science one way or another between the three of them.
What a wonderful way to start the day. Thank you Dr Collier. Your videos have been one of the valuable bright spots in the difficult world we live in, and I am very grateful for the time and effort you put in to making them. What a gem, to have randomly recieved Dr Longhurst's annotated copy of that text book.
Elegantly put, fellow spacetime traveler!
Did you know of him/her before?
I loved you doing the solution as I drank my coffee. Plasmas are also very important in down to earth applications like semiconductor manufacturing. Keep up the good work.
What pulsars actually provide is the "dispersion measure" - DM - the mean plasma density times the distance. If you look at pulsars or FRBs (fast radio bursts) _out_ of the galactic plane, it does seem that mean densities are pretty constant, so you can divide by that to get distances. But, for pulsars and FRBs _in_ the galactic plane, that is clearly not true at any distance. One person's noise is another person's signal, and those DMs are used to determine variations in the plasma content of the galactic plane.
Vastly underrated comment
I really get a kick out of the fact that you have the exact same molecular cell biology textbook in your bookshelf that I have. I think it's even the same edition. That was my favorite class in college.
Your videos are great, thanks.
Great that you got the old press, the 2010 version has some pretty annoying typos and printing errors.
I LOVE this! Also, the fact that you got a copy of the book with annotations from someone who taught the class is SUPER cool 😎
The music in your videos is always great. The aesthetics this episode were extra awesome. And don't worry, your hair looks great, keep doing what you're doing.
I tried to solve the problem before you did, but I'm bad at math, so my answer was "European honey badger." I'm not sure which step I got wrong but I noticed it by the time you got to the Taylor series.
I did the coffee part successfully. Hopefully that's half of my grade.
Your production values are getting pretty great........the steaming-coffee outro is lovely. Thanks
The lighting is also much better in this video, probably because she's near a window and it's daytime.😊
I’m not a scientist or mathematician or anything.
I have degrees and background in writing and audio/visual communication….
If I weren’t poor, and I had some pull somewhere… I’d send recruiters after you nonstop to teach any subject.
You’re such a fun and effective communicator.
It's pretty straightforward to calculate the 1/f^2 term from first principles when the plasma is neutral. The positive ions have a much larger mass than the electrons so to first order a passing E&M wave does not move them compared to the motion of the electrons. So, a passing E&M wave moves the electrons off of their default position, and the charge of the stationary positive ions provides a restoring force. So, you have a second order harmonic oscillator with the plasma frequency (f_p) being the resonant frequency, and so the response to a wave at frequency f goes as (f_p/f)^2 - as long as f >> f_p.
Oh, hey, Marshall. Have your people briefed you yet on phased-array antenna techniques using non-planar arrays?
@@sciptickAll VLBI is in practice done with non-planar arrays.
70 parsecs, (+/- 70 parsecs)! I literally laughed out loud!
Well I can believe the +70 parsecs but I don't believe the -70 parsecs. The idea that the uncertainty is symmetric around the answer is usually not true for large uncertainties. More often you find plus or minus a factor 2, thus +100%, -50% which is symmetric on a log scale.
Being a bit of a bibliophile, my immediate thought when you showed us Introduction to Plasma Physics was:
"That cover is too large and the corners are too sharp! The cloth will be worn through at those corners in no time, and at the top of the spine shortly after..! At least the seams on the spine are oversize, so if it's been collected in small lemmae, the pages won't be falling out after two read-throughs..." 😉
Closer inspection showed me to not be wrong: The corners are showing pronounced wear, the lower front one has taken the book-version of breaking a toe by opening a door in to your bare foot...
Ech. Pulling myself together to actually watch the video, now 😅
Ohhh! As a real beginner at stitching and binding, thanks for the mini tutorial!
My profesor in EE would say old textbooks had so much condensed information that to unpackage it all it would have to be 1000 pages. I do wish they would combine the digestive ease of information and older textbook graphics and questions.
Love your videos! Thank you!!
Your current lighting setup is really aesthetically pleasing. Love the glasses shadows, especially works well with dark hair and eyes and other shadows.
Sorry if that's weird I just found it really striking.
Thise glasses shadows do have an interesting gothic effect, now that you mentioned it. I highly doubt thats what the doctor was aiming for, but its fine.
COFFEE AND A PROBLEM, this is so good, you are so good, I am beside myself, Dr Collier, Angela, you are gift to the world at large and to my continuing education. This is EXACTLY what I want to do on a Sunday morning! I have my notebook out and everything!
Thanks, Collier. Very well presented, informative, clear.
Tbh, makes me feel better about every time I'm doing my homework for math methods and DE. I like to see not everyone is perfect and thanks. I feel better about looking down the concept of going into grad school and feeling uncertain
Awesome that book went to you! You have just shared it with the world. What a great outcome!
Thank you for working through this problem Professor Collier! Can't wait for the next lecture 🤓
thank you for stepping through the equations and showing your work. its very helpful
I was initially skeptical of this video, but your monologue on the aesthetic appeal of a textbook on the intro kept me hooked. Instantly set the mood.
damn how do you manage to consistently make vids on topics relevant to me specifically at the moment. i've just started a course on em waves in plasma at uni, it's a little different, we're mainly talking about the earth's ionosphere instead of pulsars and such, but still it's great to get a different, less formal view on the problem. love your output, keep it up!
I regret that I have but one like to give for this video. Headed to Patreon now to see what videos I've missed. Please keep doing your thing here on youtube.
24:50 aww your tribute to the dead teacher here is beautiful, cool edition of that book that you have
As a freshman studying physics and nuclear engineering your videos are so enjoyable and make me look forward to what's to come on my journey. I also just think you're an amazing and funny creator and love all of your videos. Thank you so much!!!
That textbook story was so cool. What a find! That's like ending up with a certified Picasso that you bought at garage sale. So fucking rad!
I love watching Angela work through reason and using generality. This demonstrates to all of us that there is "specifically" this trick, and of tricks there are many that give us the same general answers. It demonstrates that there are so many ways to skin a cat, as I assume Schrodenger would be agreeable with the skinning of cats. To arrive at where we are at in the universe, and at the same time arrive at being closer to understanding "fusion" with plasma is poetic and demonstratable.. We use the gigantic to study the insanely small, and the ways of thought bring us useful answers to apply to the real world around us. Relativity is about being relative, it's amazing we can include an absolute in the equation. Gr8! Peace ☮💜
I LOVE these segments. I had no idea you did this. Keep it up. Thank you. And yes, when I got my EE degree, I was equally frustrated that all we did was math and the math was for the math. Often times you didn't need to know the subject, just how to crank out partial derivatives.
thanks for showing us the most* beautiful textbook, and great find. Unbelievably, you are teaching and writing the book to us as a perfect steward also. Thanks for buying and transcribing.
Your lighting and audio are so much better!
I just sat down with a coffee and this is a very welcome coincidence.
Also the part in your hair kinda looks like the bottom part of pulsar graph you showed if its rotated 90° clockwise, very on topic!
That was the exact text book used in my plasma physics class back in 1978! I attended the University of New Mexico In Albuquerque where Sandia National Labs resides. I was an undergrad student, the only one in the class, competing with many grad students who worked at either Sandia NL or the Air Force Weapons at Kirtland AFB. Huge amounts of research in nuclear weapons effects and inertial confinement at these facilities. And when Reagan became President the money flowed. While attend UNM and afterward I spent 15 years doing EMP and ionizing radiation effect studies of defense systems both in theory and testing. Exciting research about a not so nice issue.
This brought back a lot of memories! And, I agree, Chen created an excellent textbook.
Please keep up the good work.
Illinois EnergyProf (Prof David Ruzic U of Illinois) has a great video on inertial confinement from about 4 years ago called "Inertial Confinement's Progress". He has a bunch of good videos on fission and nuclear reactors.
Fusion, as you know, is the energy source of the future - and always will be :-)
You had me in the first half, ngl
Getting super duper excited about how the Faraday effect could significantly affect photons' polarisation over stellar distances, before slightly abashedly looking into the camera and wondering if anybody at all would find that just as exciting an example. I can barely wrap my head around the physics and oh god my brain is struggling to grasp back any knowledge of college calculus left but your energy sure did still punch through the screen at me. Thanks for the videos. 🥰
edit: no, I didn't take any notice of the top of your head until I had to pause to check out what this new grey box was informing me. I was actually checking to make sure I understood the algebra workings out correctly
One minor addition. Plasma is super important for a lot of industrial proceses and it has room to enter into so many more. For example plasma is esential in producing microelectronics and all sorts of surface coatings and other material proceses. So there is a lot of interest in it even when you take space or fusion out of the equation.
It is only fir graduate engineer that learn plasma. The question: how to realize plasma? Concerns engineer. Physycist stays at the general principle of physic. Fluid dynamic or heat transfer are much more well manage by engineer than physicist. E.g pitot probe for conpressible fluid like the air and for viscous fluid have the same shaoe? No. Even if in pitot theory the viscosity doesn t appear clearly
Angela is brilliant and fun. Coffee never tasted so good.
I watched this a few weeks ago. Today at work I was randomly looking at some books that our former library discarded (ya know everything is on line). My good luck, I found a copy of this book, the condition is not as good as the one Dr. C has but good enough for government work!
Always looking forward to your videos, great stuff.
Beautiful books definitely spark joy in me. A favorite author of mine recently released some gorgeous editions of his most famous novel. I wanted to cry, they were so lovely. The departed professor's annotations really do make that beauty a treasure.
Good stuff, Doc.
Sunday morning, fresh sheets, cold drink, a cool, gentle breeze, and physics. Perfection.
Lucky you, we're having torrential rains here at the Mediterranean ⛈️
SUNNY IN THE HOT TUB IN PALM SPRINGS 🙃
Angela. I am a physics major. This is amazing. I will watch these.
That was lovely, what a wonderful find, old books are the best! Great channel
this video was a journey of self discovery. thank you so much.
I watched this, instead of 3 seperate other youtube videos that came up on my feed; in the 25 minutes free before work. This was Much more interesting and thought provoking.
Nice to know I’m not the only one who remembers angular freq backwards sometimes.
my favourite "one weird trick for distance" is to use super-distant lensed events - different paths arrive at different times. if you can find events separated by 30 years, then you have a difference in distance traveled by 30 light years. if you can use the difference in brightness, or redshift on the two paths to get an absolute measure of distance , not just a relative one that a single redshift measurement would do - "Strongly lensed supernovae as a self-sufficient probe of the distance duality relation"
I was going to dispute the ability to measure distance accurately this way due to disproven assumptions of "average plasma" , but you got me with the 70 parsecs plus or minus 70 parsecs.
I love this woman.
So smart and lovely.
This was a really fun watch, i do struggle with the part about finding which equations to use for solving it
The book cover kind of reminds me of my 1st edition of the Silmarillion which is also from the 70's love it so cool
I share your emotions about second-hand science books. We stand on other's shoulders. I always hope there is a name of the previous owner in there. My bookcase is a sanctuary for (affordable) old science books.
Dame Jocelyn (no) Bell
she don't give a hell
she found what she found - you can't get around it
no matter who got the Nobel for it
Working on plasma physics homework as I watch this. That first edition of Chen is certainly more aesthetically pleasing than the third edition I own.
The maths in this one were way over my head, Dr Collier, but keep it up. You're incredibly listenable regardless
In half a year's time you have become my favorite science communicator. You have the knack
15:25 "part b is just plug and chug." lol, I haven't heard that phrase in 20 years. What a trip!
Do I spend all my time doing (undergrad) research thinking about pulsars? Yes. Am I delighted in having Dr Collier explain them to me? Also yes.
Seeing you without glasses weirds me out. Its like seeing your teacher outside of school as a child.
That is a gorgeous textbook.
I had to listen in after seeing the video's clickbaity thumbnail. I heard it in my head with Angela's wry wit and irony, and I adore it. 😂❤
3:24 holy shit the texture of that paper it's gorgeous like yeah the stuff you pointed out with the cover and diagrams are great but wow!! the paper!!!
What I’ve learned from your videos is that in ten years, we’re having another physics revolution. No matter where we are in time: in ten years, it’s coming, babe.
It’s amazing how much an object mean when you know it’s history. Your attachment to this book, its provenance, is the hallmark of a true nerd. Love it.
Making Physics fun, even if I do not understand it.
Looking forward to the next vlog, Please.
One of my favorite text books I have ever used. I have the 1984 edition. The cover is similar but blue
I always go into your videos with the best intentions…I dropped out of school for a reason
Excellent video.
I like this kind of video a lot!
My father (a math professor) had that same edition of Numerical Recipes I see on the bookshelf.
Honestly…this is some of the best deadpan humour on all of the internet 😂
Fun fact, Chen's book is based on the notes from John Dawson. The same diagrams and figures are in the notes, but just hand drawn by Dawson.
I love your videos.
"Astrologist hate her even more"
Imagine you're a pulsar.
I'M A PULSAR WOO WOO WOO WOO
I have like zero background in plasma physics, so I was scratching my head on how to get started with this one. I wrote down Maxwell's equations and tried to derive a dispersion relation, but gave up lol. Then you pulled out the dispersion relation from your memory like a badass. I love this series!
Side note: do you have any other good textbook recommendations for self-guided learning in plasma physics? Is Chen plenty to get started?
"We don't really deal with plasma much on earth."
Styropyro: "heck"
in 1976 the US Energy R&D Administration projected how long fusion power would take to develop at various different funding levels. With "maximum effective effort" aka blank check funding, they believed we'd have a working fusion reactor by 1990. With various later projected dates based on lower funding levels. They called the 1976 level of funding "fusion never". The actual funding for fusion power since then has been below the "fusion never" line.
I found the solution on page 459 of the 3rd edition... It converts the distance of x = 1.9x10^18 meters to 63 parsec. Great video, I learned a lot..
I am going through an estate-level amount of math books from a math professor.
He also had some physics books. The books that I’m finding are mostly First or even Pre-First Editions, given out to people at conferences in the 1960s. Completely bonkers.
This is the best thing you have ever posted. Short form is welcome.
But aren't the pulsars' beams interpreted, these days, as precessing, or wobbling, rather than rotating like a lighthouse? Also, I just found out (sue me!) that the temperature required to significantly ionize hydrogen and helium is order(s) of magnitude higher than the black-body temperature of (almost?) any star. Doesn't that mean the light from regular stars is not coming from plasma? Is it only the trace-minority fraction of lower-ionization-energy "metals" that are ionized? (I read somewhere that a 10^-4 concentration of ions still exhibits plasma-dynamic phenomena. Is there enough? Does that even matter, here?) Finally, doesn't blackbody radiation imply emission from condensed matter, i.e. solid, liquid, or supercritical? What is the condensed matter in a star?
"Also, I just found out (sue me!) that the temperature required to significantly ionize hydrogen and helium is order(s) of magnitude higher than the black-body temperature of (almost?) any star. Doesn't that mean the light from regular stars is not coming from plasma?"
Plasma is defined as a quasi-neutral mass of collectively behaving ions - note that there is nothing about temperature in this definition! The interstellar space is filled with tons of hydrogen and helium plasma, and it's at near absolute zero!
It's true that heating up gas to insane temperatures is the easiest way to make it on earth, but it's far from the only one. All you need is for the rate at which ions are formed to be higher than the rate at which they reform into atoms, which is necessitated by the insane amounts of energy gained from the fusion in the star and the extreme pressures surrounding them.
In the interstellar space it's due to the low density of vacuum, which in simplified terms leads to the ions taking extremely long to find a partner to recombine with (longer than it takes for radiation travelling through space to make more ions, despite how rare that is).
So yes, the light absolutely can (and does) come from the plasma!
Keep it up girl 👌
Thanks!
Cool video and book. Speaking of beryllium, some of the oldest stars in the Milky Way, in NGC 6397, date back to 13,537,200,537 +- 969 years ago (Galaxy Quest, 1998, historical document). Amazing, considering that observing the spectral lines for beryllium required a space-based observational platform.
If the older book is still relevant it costs less. Money saved allows us to have large personal libraries.
And, thanks for telling me that most matter is plasma. I did not realize it.
You are worth your weight in gold.
Yay plasma physics!
Quiz-time: was the note you mentioned for the derivation of ion-acoustic waves?
In our university book-store they had two variants of Chen, one expensive with proper vector-graphics figures, and one cheap where the figures were clearly scanned into some bit-mapped format (one could easily count the pixels) - just as a warning for someone thinking they're about to make a good deal on a cheap book...
Water can also act very interestingly under turbulent flow. Do a Navier Stokes video next Angela, or a series of them. Water, plasma, coffee, all related.
Watch cream disperse into coffee.
Oh look, you found my subfield!
It's sort of weird that the textbook put this in terms of df/dt ~ f^3, rather than dt/df ~ f^-3, or rather Δt(f) ~ f^-2, which is how I'm used to thinking about it. I mean, I guess df/dt is the actual slope of the "line" seen in that plot from Jodrell Bank (which is one of the most common ways people tend to plot these things). But I'd argue that df/dt is kind of the "wrong" thing to look at (even though mathematically it's all equivalent): it suggests that t should be thought of as the independent variable, when really f is the independent variable.
That is a pretty text book, but does it come with an informational CD-ROM?
not in 1976. 1996 maybe, 2006 yep for sure