Fermions Vs. Bosons Explained with Statistical Mechanics!
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- čas přidán 11. 06. 2024
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If I roll a pair of dice and you get to bet on one number, what do you choose? The smart choice is 7 because there are more ways for 2 dice to come up 7 than any other number. Well, it turns out that you can apply the same logic to predicting the behavior of the universe. Let’s see how some of our most powerful tools in physics are really a game of cosmic craps.
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Hey Space Timers! It's nice to be releasing episodes again. If you're looking for comment responses for the last six episodes, check out Matt's comment response here: czcams.com/video/HmOQrEdhsuI/video.html
🙌
Olá, eu sou brasileiro e gosto muito dos seus vídeos e os vejo pelo tradutor automático, seria muito legal se tivessem legendas diretas em português ou espanhol. Agradecido pelos vídeos de ciência!
Do our bodies affect surrounding air pressure and temperature and electrons. So now come out brains don't have any affects on pressure or electron path ways based energy levels on space
But, IIRC, your time frame given for the 1/10^100 odds of any particular pattern occurring is non-sense, as it is just as likely to happen in the beginning, in the middle, or at the end. The ONLY time the end of the time frame applies is if you want to know how long it will take for ALL POSSIBILITIES to happen.
How many times do you have to shot the videos to get it all in one take? Just realized most the content on this channel is a single shot.
Cheers to the likely unsung heros of Space Time, the Graphics Artists. Great looking episode.
The video is pretty baller💀🤨
Yknow what I mean
Are you the artist?
@@markthebldr6834Oh no, that'd be rather gauche.
People comment something like this in every episode 😅 The only way they're "unsung" is that none of those comments have actual songs. And to be fair, there are no songs about Matt either.
@@dr.victorvs Thanks. Good to know.
I love the minigame at the end of every episode where you have to guess how they’re gonna tie in the words “space time”
And just like in every episode of Perry Mason, I never get it right!
I love how the intro to chapter one "Thermodynamics and Statistical Mechanics" of [1] reads
"Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hands. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics."
Truly the most hardcore intro to a graduate textbook ever.
[1]: David. L. Goodstein, "States of Matter" (New York: Dover, 1975)
😂😂🤣🤣😅😅😅.....🥲
I'm going to tell Papa Flammy about this intro, so he can post it as a meme.
Studying a difficult subject increases how much energy someone's brain uses, and thus increases entropy in their brain. So anyone who chooses to study Thermodynamics, chooses a subject that will probably lead to a shorter life.
@@FLPhotoCatcher That and being unjustly rejected by peers who should know better.
Thermodynamics is inherently depressing.
After all these years, I finally understand the difference between bosons and fermions. Videos like this make me wish I was 15 years younger and could study this in school again
Your hormones would distract you just as much the second time around.
Yeah the problem is using big words and math you can't easily digest when describing lots of science but we all have a different way of intuiting abstract information. It is why when you get an epiphany about new knowledge it feels so obvious and natural because you can relate it to a particular thing...the problem is there are many microstates of things for everyone so that the probability of them lining up is low but when you get it you finally really get it into a ''macrostate.''
This kind of video sparked my interests back into physics and mathematics after years out of school. I invested in getting the Feynman lectures out of regain of interest, and your videos continue to server as a motivational beacon as they help me visualize and think about lectures. Thank you for what you are doing, it really matters at least to me.
No you don't! Stop the lies! It's all secrets and lies!
Same here, minus the forking out for the lectures. I just keep watching channels like this, Fermi Lab and even ones like Cool Hard Logic, Martymer 81, Potholer 54, the Living Dinosaur & Thunderf00t (amongst many others!) who all started out introducing different types of science and maths to young Earth creationists and then moved on (or did more alongside) their areas of expertise. I'm not sure what CHL does but he knows a ton about maths & cosmology, but the rest in order cover physics, geology, biochemistry and any number of areas of expertise but essentially a nuclear chemist (I think that's his closest description). They can all talk about other subjects well but will always say that it's not their subject, or they don't talk about it in the first place. Unlike creationists and other fundies.
Matt inspired me so much that I’m back at university doing a BSc majoring in Maths and hoping to do a Masters in Astrophysics, I just turned 65 yo.
I'm currently reading the Feynman lectures and even as someone who somewhat studied physics they are a lot of fun.
Awwwww
Wow. Fermions and Bosons make a lot more sense now. This was really helpful. I'll have to watch this again, I think there's a few more details to pick up.
I like bewbs
My favorite lesson from stat mech is that it is possible, though extremely unlikely, for all the oxygen in the room to be in the corner and you suffocate.
You better hope you can hold your breath for long enough.
why has it never happened ever then?
@@kennythelenny6819 Because the probability of it is so insanely low that we may just assume that on practice it's 0.
Liechtenstein and San Marino are microstates, whereas Canada is a macrostate.
There's also some degenerate matter, a.k.a. ruSSia.
Canaduh is a colony built on stolen land.
@@winstonknowitall4181, North Korea, Eritrea etc.
@@winstonknowitall4181 Profile pic checks out, isn't "degenerate" an insult Nazis use anyway?
@@nektariosorfanoudakis2270 I have no idea what insults ruZZian Nazis use, sorry.
Here is first paragraph from the book "States of matter" by Goodstein.
1.1 INTRODUCTION: THERMODYNAMICS AND STATISTICAL MECHANICS OF THE PERFECT GAS
Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics.
I love how the next paragraph starts as "Perhaps it is wise to approach the subject cautiously."
One of the greatest physics memes of all time.
This got me to read Boltzmann & Ehrenfest's wikipedias. I have whiplash from reading Ehrenfest's ending
I’m a mechanical engineering graduate and was told to take Stat Mech by my advisor since I was going to work in molecular dynamics. As the only mechanical engineer in a physics class of 40 students, I single-handedly brought the class average down by a full grade 😂
So to you my dear reader I say this:
Have faith in yourself, you got this 💪🏻😂
Good work!
@@wjrasmussen666 thanks I guess 😂
I wonder how you did that! If the other 39 scored a top score of say 10/10 and you scored the lowest possible score of 1/10, then you could only bring the class average down by .225
@@danielsocher3763 let’s just say the abysmal performance was spread across the entire semester
@@danielsocher3763 The flaw in your analysis is due to using traditional math instead of quantum math. Grade distribution is influenced by spooky action at a distance.
Statistical mechanics was one of the five most difficult classes I took when I was in undergrad. But I'm so grateful I studied it.
It's cool to see it applied to astrophysics!!
What were the other four hardest classes, tho?!
What were the other four hardest classes, tho?!
@@butthole9843 the others were fluid mechanics, thermodynamics, crystallography, and mass transfer. Bane of my goddamn existence.
Dang, I also did not know some of this before and also hated Stat Mech and Thermo. Did not mind fluid mech, but don't think I did much with crystallography.
@@me0101001000 Mass transfer is some sort of separate field of study? I've heard of the others talked about, but not that one.
We do these kind of Macrostate/Microstate calculations all day with colors. You can perceive orange as the pure wavelength or as a combination of red and green light.
I happened to just complete my graduate-level statistical mechanics course this semester. This video being released the day after my final exam is a traumatic coincidence. Lol
"Bouncy death storm" pleased me more than I can say.
Wow this was amazing; I took an intro stat mech/thermodynamics course about 3yr ago and remembered being confused on the distinction between macrostate & microstate.
You and the Spacetime team did a phenomenal job in explaining this and also key fundamentals of particle statistics.
Awesome video! This is one of my favorites (partially biased as a stat mech enjoyer)
Dr. Matt O’Dowd, thank you for this exceptionally clear and well-done video on the deep importance of statistics to fundamental physics.
I've always loved this subject because it makes quantum physics seem so simple, the fact that a simple mathematical law is behind so many observations. Essentially everything follows from "the most likely outcome is the outcome you will observe"
Why do you think this
It's exactly the other way though.
Statistical mechanics has given us the most intriguing explanation for entropy
It's been more than a decade since I was in school (chem eng with some grad CFD), and this gave me some flashbacks of deriving the Navier-Stokes equation and the accuracy of the continuum assumption. My wife got a chuckle overhearing me blurt out, "WHAT ABOUT REAL ATTRACTIONS AND REAL VOLUME?" and "FUGACITY" as I watched this.
But an actual question. Heisenberg was quoted as saying, "When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first." I was wondering if you'd considered a video on turbulence, though I could see how it might be a little outside the normal scope. (Which is technically a statement, grammatically.)
Anyway, thanks for the great content!
Funny how just yesterday I was taking an exam in Statistical Mechanics, partition functions are so fun to calculate in most ensembles minus the microcanonical.
I did mine a week before. It was in fact a wild ride. The last homework assignment was pretty rough, having to derive density of states functions for Maxwell, Bose, and Fermi.
I always come up snake eyes somehow anyway.
* kicks the dirt *
Suskind has a great stat mec course in Stanford open courses. The field is known as a favorite past time of great theoretical physicists, simple but unpredictable and amazing results from rather simple mathematics. It’s amazing that the field of statistics itself is only a couple hundred years old. It’s not intuitive, and it’s complexity and nuance is an surprise for most students. Lots of fun for life time learners.
This is your best video to date. Excellent explanation of the difference between Fermion and Boson particles
"Cosmic Craps" is a really mean thing to call the universe PBS
I'm suddenly seized by the _linguistic_ aspect of this discussion. A “seven” is the most likely outcome of “rolling two dice” merely because of an arbitrary cultural convention of naming the state by adding all the upward-facing pips. If we bet on odd/even, or the difference between the red die and the blue die, or how nearly the edges of the dice aligned north-south, we'd see different results with different distributions. This doesn't have any obvious profound implications for traditional applications like air pressure in a room (except possibly near edges?), but once we start looking at problems involving classification-? Then again, it could be argued that's what's happening in the Fermi-Dirac case: we've changed the underlying algebra.
Yes! Isn’t this the case with all discussions of “entropy?” We impose an anthropic bias to select an arbitrary arrangement that we call “order,” and then note that the system tends to not produce our “unlikely” patterned state.
Thank you for making statistical mechanics approachable to anyone with a rudimentary understanding of statistical mathematics.
I like how statistically, over enough period of time, any configuration of space possible should be able to simply come into existence randomly. And how mathematically this also is the same amount of time that it takes for everything in the universe to disappear.
Not true ya doper
Yeah all microstates are equally likely, so at the end of the universe huge cores of remnant stars will eventually randomly end up in the microstate where enough matter is pack together to spontaneously collapse into a blackhole, which will then evaporate away
Not true. Just because something is infinite, doesn't mean it contains all possibilities. While this statement could be true for simple things like discussed in the video, extending this out to the universe is not true
@@rb1471 Not true either.
There is a very low probability that an identical clone of you will appear in your room. Very unlikely, but not impossible.
This video was more informative than an entire university module
"The balls are small enough that they never actually hit each other." Animation shows the red ball bouncing off at several other balls. :P
You guys should do more videos on this topic! Really interesting!
Yeah! Good to see new content. Haven't a bloody clue but still fascinating stuff.
Stat mech has always been my favorite topic. Had the most fun with this compared to almost any other class in college.
Emergent properties are truly the most fascinating part of our Universe.
And they are everywhere; we saw yet another example recently with LLMs, which gives a hint that consciousness itself is also one of them.
Brain melted as always. Awesome. The more I watch the more I feel we are exactly the same as fish, in an ocean of space and could never comprehend or understand what’s above or below the water.
Excellent explanation
8:49 Settlers of Catan Shout Out!
Excellent video. Keep the hard work.
00:01 I pick 12, because it is the "upper limit" 🕶
1:00 11s ,,master thermodynamics, there is too many of them. What are we going to do?''
blows at them
When I took an advanced physics course (I forgot the formal name) in college and learned this. It really blew my mind about how much of physics is just statistics and how other phenomenon can be derived from such.
0:08 Oof, rolled a robber.
What's so fascinating about statistical mechanics for me is how purely mathematical arguments are able to give us deep insight into the fundamental laws of physics.
Apparently, it's also vice-versa: physics inspiring mathematics
@@samvv that's true, but unlike in other areas of physics, where we start with some physical assumptions or postulates (e.g. quantum mechanics), statistical mechanics seems to be a sequence of entirely mathematical arguments, which nonetheless predict reality (e.g. 2nd law of thermodynamics).
@@456dave7 Yeah that's true 😊
@@456dave7 But "math" is fruit of observing the world, like counting apples.
@@ThePowerLover That's a deep philosophical question right there.
man i love those episodes
Superb video, as always!
I love coming back to these videos when I'm feeling smart. I suddenly stop.
Thanks for the streams
It only took 8 minutes to get to Boltzman. I was waiting! I'm not holding my breath for a disembodied space brain to discover us on earth, but there's something comforting knowing that somewhere out there.... Hahaha. Love PBS Spacetime!
I used the Reif textbook for both my undergrad and graduate stat mech classes. Great textbook!
Aw man this was a good one. It scratched the itch
I have been waiting for this video for 3 weeks. Thanks so much for making fun and digestible videos PBSspacetime.
@ 2:15 "Bouncy Death Storm" best band name ever...
Thanks for this
Thanks!!
This is great!!
This was wonderful, thank you!
this episode is ballin'
I finally understand why "bosons" and "fermions" are named what they are.
I remember only one question from my statistical physics exam. It was "Ideal gas in gravitational field". I remember that deriving it was not easy. I got an approximated solution but still I got the best score in my class.
This is like the statistical groupings of Lego set distribution! ❤
I feel like that was one of the longest closing lines to lead up to "... spacetime". But well put, Matt, per usual.
Awesome. Didnt know about Fermi-Dirac statistics
"a bouncy death storm" don't threaten me with a good time, Dr. Matt.
Love how this video comes out a few days after I passed my statmech exam with exactly 1 point above passing grade :)
I'm gonna be frank and say that I'm WAY too hammered to understand any of this right now, but what I WILL say is that I enjoy this channel a ton.
Long time viewer, really appreciating your work. Thanks Matt and team!
Particles obeying the laws of Fermi-Dirac statistics are called fermions, but if the coin-flip had come up tails, we would call them diracions.
Dirac vs Bargmann-Wigner is still UNSOLVED ! so
Both Boltzmann and Ehrenfest discovered, possibly posthumously, the FIFTH law of thermodynamics: "Things get worse under pressure."
Great as always...
I have been avoiding getting into the math. this videoe convinced me i must dig into the statistical mechanics !
Oof, I've had a hobbyist's interest in physics since I was young and I'm just now picking up on fermions being named after Fermi.
Yes. Also the Higgs boson is named after Peter Higgs 😊
Missed these videos
It is videos like these that got me into astrophysics, I’m almost done with my undergraduate
I've always suspected that fermions matter.
Good dynamic on why bigger heavier elements do not stay together!
How fitting - tonight I'm wrapping up grading for graduate stat mech as my final TA duties of grad school! (I graduate officially tomorrow after defending about a month ago.)
Nice idea with the Balls
Wow! This is incredible! The end really changed everything for me
It's interesting that this episode comes out right after I watch all of Stephen Wolfram's interviews with Lex Fridman.
Wolfram's computational approach to physics got me into exactly the headspace for this episode to really hit home.
Cart before the horse maybe, but I love it when multiple angles of similar topics pop up in the same week.
Great episode! Keep up the good work!
“It’s all about counting”. That’s also what the Count said on the Muppet Show!
Shooting craps with the various particle states of matter in the universe lol. Thank you for the fun analogy and another interesting episode. I may need to listen to this one again though 😅.
God be with you out there everybody. ✝️ :)
This video really takes a different angle to explain things. Gonna have to rewatch a few times. Interesting way to categorize elementary particles.
Wonderful! 🎉
Great episode, Always worth watching PBS Space Time for sure.
Matt, you and the team are a light that, beyond shining brighter than than a kiloquásar, ignites something greater than organic life (for it prevents organic understanding from not expanding towards itself, even with unfortunate distractions such as `kiloquasar’ or the following:)
PBSST > photosynthesis
Photosynthesis just preceded PBSST.
Boson like every hand in blackjack and fermions are the lucky random strings you insert yourself into
@PBS Space Time
My proposition for a single unified theory is waiting on you Matt
Yeah I had to cover a chunk of this for my master’s thesis in catalysis. Between that and my undergrad in physical chemistry…
it sure paints a different lens to view astrophysics through. Entropy and Chaotic Determinism can bring you through some dark places.
Thanks !
One of the coolest things about statistical mechanics is that a lot of systems with chaotic microstates (chaotic systems) have macrostates which aren't chaotic. A lot of the study of chaotic systems is in finding well behaved macrostates (perhaps states which share a value of an invariant) which can then be predicted, modeled, and experimented upon.
Keeping this in mind is also important for your scientific literacy: one of the easiest ways to spot a quack talking about climate change for example is to see if they complain about "compounding errors" in climate change. The macrostates in climate study (the rolling average number of hurricanes in a sample of years for example) are actually fairly stable and have been predicted with increasing accuracy for the past 50 years. It's the weather (=microstates) that exhibit chaos, not climate!
In an alternate universe the Maxwell Boltzman distributions are called "Maxwell's Hierarchy of Speeds".
I'll see myself out...
One of the best videos ever. So much insight. And my intuition of entropy has further increased because of it❤
This might be one of the best episodes yet. Good stuff. Thanks
Love that explanation "because quantum mechanics".
Because magic/God/the laws of the universe/is the way of things...
Boltzmann was genius by coming up with statistical thermodynamicsm 😊😊
And so I finally understand why an *infinite* improbability generator is necessary. Time to fire up the kettle...
Are you guys making a video on ER=EPR and the recent results on that? That’s right up this channels alley
I was just thinking of this earlier.
Like how the qauntom realm directly effects atomic structures.
It’s also why I believe in the great cold crunch, when all the energy hidden behind the qauntom realm breaks free as atomic structures freeze to a point of crumbling.
And as we know energy can’t be destroyed only converted into something else, thus the energy release causes the universe to enter a new extremely hot and dense state, until the energy goes from plasmid to new universe falling into the great heat death and cold crunch. Infinitely.
This reminds me of a lecture with the great Hans-Uno Bengtsson, ~30 years ago. He asked: "Have you ever worried about taking a breath, while at the same time all air molecules happened to be going away from you so there was no air to breathe?", and then calculated the probability of that happening by throwing balls at us. 😋⚾
funny enough in Jeddah they play the same game but simulating high pressures instead :P
Splendid introductory description of one of the most complicated aspects in physics!
I loved statistical physics in university. Classical physics uses simple mathematics to explain so much of the world around us, and that aspect is what many physicist first fall in love with in physics. I felt statistical physics was a beautiful more modern extension of the idea of simple mathematics explaining the complex world around us, making so much more about the world simple and understandable. You take something so simple and ridiculous at first, like why would all of the complexities of matter be simplified down to a few random numbers? and then somehow end up deriving all of the states of matter and thermodynamics, it blew my mind. Then those principals can be applied to even more complex problems throughout physics, giving them simple to apply solutions, it is incredible what you can do with it.