Negative Temperatures are HOT - Sixty Symbols
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- เผยแพร่เมื่อ 11 มี.ค. 2013
- Temperatures below absolute zero are HOTTER than those above, explains Professor Philip Moriarty. More Daisy pics: periodicvideos.tumblr.com/post...
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First I didn't understand anything. Then I thought I understood something. Then I realized I understand even less. Negative learning.
+apinakapinastorba And being negatively learned, knowledge will flow from you to positively learned individuals.
+apinakapinastorba But the absolute value of learning can still improve right
knowledge cannot be created or destroyed only change form from false to true to quantum
+Anthony Pedraza but it can be lost
+apinakapinastorba Its how it is supposed to be. Its learning how complicated something is.
Professor Moriarty is definitely in a high energy state.
Mattias Sollerman Was about to make this comment hahaha
420 high level
im literally crying.
Moriarty. an excellent example of how even the brightest minds can be susceptible to deceit. this is the guy sargon of akkad lambasted for his support of SJW
Haha get a grip
it's easy... take 1 degree,... add to that 2 degrees, the 3, then 4, then 5... keep adding heat to the infinity and then you get -1/12 degrees!!!
Felix Rojas its a troll but to answer you... the wavelength of whatever astronomically high energy rays coming from that object would be smaller than planks distance which means its smaller than space itself... i dont think the concept of temperature still holds up till this stage
Is this a reference to riemann ?
Felix Rojas okay this is epic
You can't do it sequentially like that. The heat death of the universe will happen before you're done.
Use a super task. Wait 1 minute, and increase the temperature by 1. Then, after half a minute, increase by 2. After a quarter, increase by 3. After an eighth, increase by 4. Then by 5 after a sixteenth, and so on. After 2 minutes, you completed all of the steps to create negative temperature
What I've learned is that physicists can never put books on the lower shelves of their bookshelves because they need to keep some free to visualize energy levels.
Or, find a way to differentiate high-energy books from low-energy ones.
This guy is my absolute favorite
Pun intended?
Positively!
I thought there was something of value around here, but I needed a sign.
Alyosha Romanov what?
Positive or negative?
didnt understand a thing , but loved the energy of the professor lol .
same here!
I love how engaged in teaching he is, i wish all teachers and tutors were like this!
Atabey Ayata I am thinking the same thing time and time again when watching him explaing everything. It must be a real delight to be taught by someone like him.
Atabey Ayata I am thinking the same thing time and time again when watching him explaing everything. It must be a real delight to be taught by someone like him.
To everyone posting their weird analogies to try to explain negative temperatures: Stop. This is a purely quantum effect and has no classical analogue.
Heres the best description I can give: (as a note, I am a masters engineering physics student to give a little credibility):
Temperature, for most people, is defined by the kinetic energy of a system. That works because thats the most apparent macroscopic factor. But on a quantum scale, we define temperature more fundamentally - as a function of entropy. Effectively, as you add energy to a system, the entropy of the system increases, and thus its temperature goes up.
Now, a 'Negative Temperature' would be if you added energy, but the entropy DECREASED. This never happens in classical physics. To do this, you would need a system that has a /bounded/ maximum energy. Aka there is a cap to the amount of entropy it can have. So what kind of system has this?
Picture a bunch of particles with nuclear spins which can only be in an up or down state. With no magnetic field on them, both states are the same energy and so there is a 50/50 that a particle is up or down and so this is a maximum entropy state. However, apply a magnetic field, and suddenly one of the states (ie up) is now higher energy. Now, as we pump in more energy, the particles which used to be spin down take it and become spin up, moving the system away from the initial 50/50, and therefore decreasing the entropy. Thus, this system has a negative temperature since as energy is added, entropy decreases. If we put this system in contact with another system, energy will flow to the new system to try and get these particles out of the high-energy state.
Very nice explanation.
Nyx72 So it can't work like the usual definition of "negative," where if you increase the quantity it moves toward zero, because you're adding energy and the temperature is becoming more negative (as opposed to heating it and it's coming back toward absolute zero). I might prefer to call it "super positive" even though some of its properties are opposite of those of typical positive temperatures.
Cooper Gates In a sense, yes. Negative temperatures are 'hotter' than positive ones
Nyx72 So it's any sort of an inversion, where the majority of the molecules or electrons are in the higher energy state? Or not that broad?
Cooper Gates Its any situation where inputting energy decreases entropy.
That can include states where the majority of molecules are high in energy IF AND ONLY IF this energy state is LOWER in entropy than a lower energy state. But in general, no, not that broad.
Please tell me this man is a teacher.
In a way, he is. :-)
He's a professor of physics at the University of Nottingham. So yep, he is
6:35 "Got an equation and a graph, I'm very proud! Whether it makes the final cu-"
Oh Brady.. :P
I'll have what he's having.
Coffee, lots of it
I'm starting to notice that quite a few physicists have the same level of enthusiasm. As a group, its more than I've seen in any other field. Somebody should do a study to find out if/why this is true and apply it to a business model. Lol
+Tyler Harris it's the coffee
+Tyler Harris An incredible passion for what you love and a job that fulfills your life?
+Alex Serrano exactly
Trying to explain physics without mathematics is like trying to do masonry without chisels.
This poor man is clawing and ripping on the marble.
+Taxtro I think that is going to be one of my favorite quotes.
Thank you for making my day :)
@Gumbo Clay his problem is that they are very restricted on how much math they can use in the videos
@Gumbo Clay Clearly the same problem as Moriarty had at the end when the analogy broke down.
Everyone is missing the most important thing here, which is that HIS NAME IS PROFESSOR MORIARTY.
Yes, I noticed that. Thanks, Sherlock. (no pun intended)
No shit Sherlock...
His parents are massive StarTrek TNG fans.
@@fillemptytummy so was sir arthur conan doyle
Literally no one missed this
I love his reaction when Brady told him to imitate particles with negative temperature.
Been watching these for couple days now. I don't get how Nottingham has managed to get some of the most charismatic physicists ever to stay working there.
Shout out to Professor Copeland and Moriarty for being awesome.
"whether it makes the final cu-"
X3 you are so mean. you should let professors do more equations, or maybe do a variation of the same video with more complex explanations.
nvm, invalid due to timeframe. this is a lot older than i thought it was. =P
They have an extra channel for more detailed explanations. There the profs sometimes even get to write equations :D I thin it's called Nottingham science or something like that...
Wulframm Rolf in fact the equation made a great job of making me understand the model
I laughed at that mark. Lol
I would really love to see a version of this that _does_ explain it in terms of entropy.
***** No, that absolutely did the trick refreshing my memory of thermodynamics. You put a lot more energy and time in this than I ever asked for, thanks! If this was Reddit I'd give you gold.
So it seems like it is simply another feature of the nature of integrated infinities tending towards weird numbers?
@Cedric Wehrum you know I used to watch sixtysymbols‘ videos and other ones like these back in like 6th grade or so (I’m in year 12 of Highschool rn) and I couldn’t understand a thing. My interest in these topics however hasn’t faded one bit and reading your explanation of the statistical interpretation of entropy (something that I’m just beginning to grasp as of right now) really made me feel like I’ve come a long way. thank you I guess for motivating me even further 😄
I want a follow-up with imaginary temperatures.
Reminds me of e^πi=-1
And then 3D temperatures
complex temperatures?
I love your work, Brady. All of your videos are interesting and educating while reaching most of the masses - I hope!
Phils reaction is priceless, always makes me laugh. Keep up the questions Brady.
I love how frustrated the Prof gets XD 'Show me what happens when that's a negative temperature' ' NGHH YOU CAN'T DO IT.'
that's how he got bald
There is nothing sexier in this world of an attractive witty man who can talk about things my brain could never even try to think to elaborate and has such a cute dog too. Fact.
It's just that he's so passionate about it. The passion he has for it is really quite attractive.
It seems to me (no expertise on this subject) that the system/equation of "negative temperature" might as well not be called that, it might be more accurate to call it anti-temperature. It's a system that's structured opposite to our basic understanding of temperature.
No, it isn't. Temperature is not, strictly speaking, the amount of 'jiggling' of particles. If you want the proper physics definition, Temperature is a slope. A positive temperature occurs when increase in energy increases entropy (technically, the rate of change of energy with respect to change in entropy). A negative temperature (as in lasers or magnetic spins) occurs when increase in energy causes a decrease in entropy. It isn't so much that the 'basic understanding' of temperature is only applicable to positive temperatures, but rather, the visual explanation that temperature is the amount of random motion is only factually correct for systems with positive temperatures.
I think the problem is in reusing everyday vocabulary for something very different. Like spins, like colors, like orbitals.
Yes, that is basically correct if im understanding this correctly (the first part only.) It is the inverse of the arrangement of particles that we call positive temperature.
This reminds me of learning how space becomes timelike in a black hole or about past and future light cones on a spacetime diagram.
I cannot believe this video is 8 years old! It's been so pivotal in how I understand temperatures.
It's rare to see a professor so passionate about his field. If all teachers were like this, it would make education much more interesting. Most of the time, teachers drone on like they wish they were somewhere else, especially in lower level courses. In the few cases where I have had professors who are that passionate, it made the subject matter infinitely more enjoyable. Their passion sparked my interest in the subject matter at hand.
This video is an example of how hard it can be to explain some concepts in physics without going to the maths and equations, etc. Makes me feel like cracking open my old physics books and getting back into it. Great job though explaining something that's so hard to visualize. You guys are awesome!
13:06, this is where the analogy breaks down, the right explanation from a professor to a layman. It's worthwhile to watch 60 symbols. Thanks Prof. Moriarty and Brady.
Hope TH-cam lives for 1000 years so that this gold can be seen by people in future, like I saw it after 10 years
It seems like if you can understand this video, you don't need to watch this video; confusing stuff! :)
Roli Rivelino I’m a physics undergraduate student and I didn’t know about this. I understood what he was saying, but if you don’t, that’s perfectly fine.
i am a highschool student if you are not getting this it is probably due to the equation you need to get the essence of the math first
pariot 456 shutup
A combination of videos usually explains it, each one has gaps. Another explains "infinite limit of temperature where the distributions of energy states are equal" low temperatures are unequal as all in low energy state. High ones spread to all energy states. Negative ones are unequal in HIGH energy states.
I believe then this is perhaps how temperature is defined as a distribution curve, and not just 'how much heat energy' because these circumstances of sticking in higher states are "quantum weirdness" or such like, never formed the distribution/entropy definition, like feeding the max amnt of energy usually causes 'maxing out' at this equal distributions (low P: low probability in equation btw), and the only way to achieve beyond equal, as in more higher states than lower states is through some "quantum loophole" for want of better term.
I want to know more about Professor Moriarty's dog
I've watched the intro to this so many times! It's gold!
I appreciate all of the videos you folks post, making more of an aware individual everyday.
When anyone talks about the absolute zero they always talk about Kelvin. Poor Rankine is always forgotten...
I didn't understand a word of this. After about 6 minutes it was like I was just watching Telemundo.
it seems like the deeper I look into physics, the more it looks like programming.
Very excited to get a reply! I'm a comp. scientist and my fiancee a chemist, and it was a pleasure to show her this video. I'm getting her hooked on all of the science-y youtube channels (this, #phile, etc). As an American, she finds your accent charming.
Videos like this one give me a healthy dose of the other sciences, and your efforts to enlighten the masses are so greatly appreciated. You and Brady really nail a thought-provoking balance of facts vs entertainment. Keep up the good work!
If I were the physicist, I would have opened up the bag and made a huge ball pit mess when he asked to demonstrate negative temperature.
"I got an equation and a graph! I'm very happy. Whether it makes the final cu- ..."
0:28
This is just so pure everytime, I could watch that 100 times in a row
if you shoot a very powerful laser to a metal plate, the temperature of the plate will increase, whether the temperature of the plate is close to absolute zero or glowing red-hot.
"Do photons have negative temperatures?"
Please tell me that is NOT a Les Paul propped precariously against the cabinet behind you. Lucky to be in one piece with all the energetic particles, professors and unruly dachshunds flying about.
A white (Buckethead special, I'm guessing) Les Paul and also a dreadnaught right next to it. Both guitars would be worth 3000$ in total
Mathematics on many things goes beyond reality. Mathematics have little to no bounds is all, so just because you can express or "prove" something mathematically, it doesn't guarantee that the real world will agree.
So he tried to use maths to prove something that can't happen?
@@fillemptytummy wow this was a while ago. I had to watch the video all over again. To answer your question, yes and no. Different things can happen in quantum physics. The rules change, and progress in figuring out what those rules actually are is ongoing (with great success) . So in terms of standard physics, yes, math can produce what the real world cannot, BUT that kind of ends when you get down to the quantum level, because different rules. So in it's SIMPLEST form, to make for a shorter response, the most fundamental level of traditional physics (sub atomic particles) are the net result of a different set of rules (quantum). So when you actually manage to force a limitation of the real world in its laws of physics, a different set of rules is in play, and we can't interact with that in a traditional "physical" sense.
This is one of my favorite videos in the entire series. I actually have it bookmarked separately because i've watched it so many times. Every time i do, i end up thinking about the implications in a different way.Prof. Moriarty's explanation not only gives you a working idea of the theory, with an equation to boot, but also provides multiple ways of visualize the subject. Good job on working in several offensive terms while also bashing a nationality! A valuable addition to this site, no doubt
I remember when I first watched this 4 years ago, being confused. But now, re-watching it, I think I understand it (a bit) more! At least, the equation and the explanation of the equation make much more sense. Yay for a growing understanding of the universe! :D
Teachers should be like this, shaking a bag of balls and telling you that dachshunds are disobedient little ones.
It's important to say that, in statistical mechanics, temperature is NOT defined as the mean kinetic energy of a system. It's defined in terms of the change in entropy with energy. Like this:
T^-1 = ∂S/∂E
Sometimes this definition falls within our normal understanding of temperature, sometimes it doesn't.
If, in the case presented in the video, there was only one particle it's temperature would be 1 over 0 because entropy is always 0, regardless of which level the particle is on.
I’m reading same article and thank for making it easier to understand I wish u were my professors
I keep coming to this video just for the clip at the beginning and Prof. Moriarty flipping right out.
Also for the mindbending concept of negative temperatures, which at some point in the video does click in one's head correctly.
EDIT: Wow, I just saw a comment I left a year prior to this, saying basically the same thing.
Wait his name is actually professor Moriarty? AWESOME
Sometimes I want to watch these videos, then I remember I'm not smart enough...
perhaps time to get to the kitchen?
I really appreciate the fact that this guy tore his entire office apart to explain this concept.
i dint understand shit, but his enthusiasm and passion for physics is what pulled me through to watching the whole video :)
I'm no less confused.
Now I'm more confused.
Very interesting.
So going off the ball metaphor, if I understand at least part of this video correctly, a negative temperature would be pinching off the top of the bag, turning it upside down, then quickly releasing the pinch?
No, as he says the analogy simply doesn't work for negative temperature.
That doesn't have anything to do with it
Oh well, thanks to you both for the clarification. I'll be honest, I forgot I asked this question until you both replied. Well, all metaphors break down at some point, and I guess we've found that point.
This is an awesome channel! I know you try to avoid mathematical formulas but I think that they can be very useful. This video is a great example.
Love your teaching style. Subscribed
but with negative temperatures that equation becomes non normalizable, thus non physical..?... or thats why you need an upper limit so that you can normalize it?
Has temperature got a limit or is it 'infinite'?
மிக நன்று, மிக்க நன்றி! Superb explanation... Thank you....
This is one the best sixty symbols - love the passion
this must be what my dog feels like when I talk him ...
Math and science are awesome, i like to share that fact often
Very nice. Very informative. Thank you!
I'm dozing off in front of the screen with my homework out in front of me, and suddenly I hear "Balls". Just that word with quite a bit of emphasis haha.
actually, if you put something to absolute zero, it is still moving due the the Heisenberg uncertainty principal which states that the closer you measure something then that measurement will affect molecules around it. so by measuring to see if all motion has stopped you have inadvertantly created motion. an example of this would be when you are trying to observe an electron, but to observe it you need light, or photons, and the photons would hit the electrons, skewing you observation. so if an atom has a defined position, it cannot have a defined momentum, so therefore your statement about no motion is FALSE.
***** isnt that the same thing i wrote?
Okay I understand.
You state hasn't invalidate anything. Your statement merely shows why we can't get something to absolute zero. There's no way to remove the consequences of the actions you use to lower the temperature. IF something was at absolute zero, it would not be moving. It's just impossible to actually create that state.
*****
The answer lies with your confusion on how to visualize the topic as shown by this: "Electrons cannot reflect light." No one states that they reflect light, it's that they absorb photons. This gives them energy, thus putting it in what is often referred to as an "excited state" when the electron has moved up an 'orbital' (for the sake of simplicity you can simply picture this as Earth sundenly switching to Mars's orbit around the sun, but know that that is not accurate, it's just a metaphor of sorts) however the electron is in a more stable state in the lowest available energy level, so it releases a photon and drops down to the original level. This is why the sky is blue, as the amount of energy released in the photon determines it's wavelength and frequency it will have, thus the oxygen releases blue light when energized by the sun.
As you see, this much different from what you thought of it. You're right as there are many characteristics of the electron to try and study it, however you have to do something to it to observe these characteristics. Information doesn't just randomly transfer from something to else ware. Each method interacts with the electron (or whatever else on this scale) thus altering it. When can learn one piece of date at the cost of another (for example it's position or its direction but not both).
The reason the OP mentioned photons the the only way to detect the movement of something is hit it with a photon and analyze the released photons. Basically it was specific to his example.
it was really just a rough comparison trying to explain that in the process of observing something, you affect how it will act.
So in essence they didn't go THROUGH zero Kelvin... They hopped over it?
If I understand correctly, negative temperatures are hotter than positive ones, because if you put a negative temp' object next to a positive temp. object, heat will flow from the negative temp to the positive temp. It has to be this way from the second law of thermodynamics.
Essentially they went through infinity rather than through 0.
I think I see what you're getting at.
TheAllBlackMan no
Wow, 0 is apparently even scarier than infinity!
Zacchon they're two sides of the same coin, if T is 0 in the equation he showed you'd be dividing by 0 and going to infinity. A negative temperature on the other hand can be handled.
Love that frustration, I get like that right before I start to understand lessons.
Just found your channel. Awesome explanation of negative temperatures. Subscribed! ❤👍
Welcome aboard - thanks.
Never draw a graph without labelling the axes.
But he did label the axes
-1/12 all over again. Infinite numbers really tend to be negative, huh?
Marcus Liebenthal Yeh, look at 1/x graph from right to left.
I really only got this when I was learning about lasers later. Look into Population inversion for optical pumping or laser pumping. That kinda helps.
I'm re-visiting this video after having watched it in March, and on second look, a possibility has occurred to me: perhaps our mathematical understanding of temperature is backwards. If something that has "negative" temperature can always transfer heat into something with a "positive" temperature, then that means the negative temperature object has more energy. It wouldn't be the first time conventional thinking has got something arse-backwards. Look at electricity: you have "conventional current", where electricity flows from positive to negative, which was decided entirely abitrarily, and you have the way things actually are, "electron flow", where electrons move from a negatively charged body to a positively charged body.
It could also be that what we've thought of as a one-dimensional concept for so long isn't actually one dimensional.
Temperature thing just goes back to the Theory of Relativity, mostly. It's a matter of where the observer that determines the values and associations.
Kory Steele this is very intresting. could you explain the idea a bit or give me one or two links? thank you
It's not backwards, and negative temperature systems don't necessarily have more energy. Here's the math:
Temperature is defined in the following way: dS/dE = 1/T, where dS is the differential in entropy, and dE the differential in energy.
Consider a heat-exchange process between a system with negative temperature, T-, and a system with positive temperature, T+. The change in entropy for this process is:
(Delta)S = (dS+/dE)(dE) + (dS-/dE)(-dE)
The dE outside of the derivatives is the amount of heat exchanged. There is a minus sign in front of the dE in the second term because heat differentials for the two systems must have opposite sign - in one system heat is added, in the other heat is taken away.
Now, substitute the the derivatives in the above equation using the definition of temperature:
(Delta)S = (1/T+)(dE) + (1/T-)(- dE) = dE[(1/T+) - (1/T-)]
In any process, entropy must increase or stay the same (i.e., (Delta)S >= 0). Since [(1/T+) - (1/T-)] is a positive number minus a negative number, this factor is always positive, no matter the magnitudes of the two temperatures. This means that dE must also be positive in order for the expression on the right hand side to be positive. Based on the sign convention I used above, dE can be interpreted as "heat added to the positive-temperature system." Since this dE is always positive for arbitrary T+ and T-, heat always flows from a negative-temperature system to a positive-temperature system, regardless of the magnitudes of the temperatures involved.
You're forgetting the key element of what he was saying. Distribution of Energy in a given area.
Really nice to see other open minded people on our planet : ) somehow it seems im surrounded by them 24/ 7
wait he's called moriarty? he certainly is clever enough
This was higly interesting..
Higgley interesting lmfao
Jarmo187 highly*
I often come back to this video just to replay the first 34 seconds. I love Prof Moriarty.
I can't believe he slipped a equation and a graph in, this is actually an amazing explanation on pressure and distributions when discussing gasses.
Shouldn't this be considered "Inverse" and not "Negative" temperature?
That is basically the same.
They are, but I feel that "Inverse" is less confusing and misleading than "Negative".
Inverse means 1/x not -x so no
Would time stop at absolute 0?
No, why would you think that?
bdbdbd why wouldn't it? isn't time responsible for all motion?
No? If time stops, all motion stops as well, but if motion stops at some place, time doesn't stop right? Motion is local and time very general.
bdbdbd no you're wrong motion can't stop that means absolute zero which isn't possible? why does multiple clocks have anything to do with this?
Which scale are we talking about? Quantum or Relativity?
i love his reaction to the question in the beginning.
"IT CANT HAPPEN!"
Thanks for explaining this
3ed time i have watched this, finally get it!!
Matt Dolloff No you don't.
A famous physicist once said something along the lines of: "if you think you understand quantum mechanics, you don't understand quantum mechanics." And this is a top tier physicist saying this; who are you?
Max J lifting videos So if you think you don't understand it then you do understand it? .... ;)
Cooper Gates Makes me think of the Dunning-Kruger Effect.
+Cooper Gates I just think I don't not understand it. Perhaps a double negative helps here :)
It's ironic that he said that his head hurts when he contemplates entropy, because too much entropy for the brain to handle is the cause of headaches.
Ummm... No. Just no.
How does entropy cause headaches? Or are you talking through your hat?
+Eric Haag (Physics) Deepak Chopra, is that you?
I absolutely love this guy. He's so passionate. :D
I think a lot of confusion could've been avoided if nobody had mentioned temperature in relation to this, and just left it in the rabbithole of quantum-mechanics, where it belongs.
Can you guys start doing videos that use math??
Love from India sir..
I still amazed by this concept.
I watching all of your videos in a row.
Wish I could join you too..
Thank you for the kind words about our paper!
Temperature is defined as how hot something is. Once again we have scientists trying to change how things are defined to make life easier on themselves. What we have here isn't negative temperature, what we have is a positive temperature that has an inverted energy density function or however you want to say it. Something with negative temperature would have to be able to absorb energy from any system, including those at absolute zero. What they have effectively described in this video is infinite temperature.
Why isn't this comment rated higher? This video is complete BS and this comment completely embodies why.
Matthew Brown That's because this comment is incredibly ignorant, and the video is broadly correct.
Did you even watch the video? 7:50 the Boltzmann factor describes the population distribution of the particles. At positive temperatures, more particles populate the lowest energy states, and exponentially less particles populate higher energies. But at a "negative" temperature, exponentially more particles possess higher energies, a phenomenon called "population inversion". Look at the equation again and you will see why
RipleySawzen It's scientists understanding things better than you.
jimsir812 OR our understanding is flawed. An inversion of the energy distribution doesn't mean the temperature is negative. 0K is an absence of heat energy. We haven't been able to observe 0K (and thus haven't obtained 0K) because of this. How then can you say that negative temperatures have even MORE energy? How can you say that a negative temperature is hotter than a positive one? Heat energy flows from high to low, this is something we know. Heat flows from so-called "negative temperatures" to positive ones. I'm less inclined to think that our understanding of heat transfer is flawed and more inclined to think the math/understanding of the "negative absolute temperature" scale is wrong.
I see this as being another case where theoretical physicists are believing that maths is the real world, rather than an esoteric concept we have invented in an effort to describe and understand the real world. Just as conventional physics math falls apart with the very small requiring quantum mechanics I think going below 0 Kelvin is a similar case
Fantastic stuff there!
i love these science educational networks because some are super high quality with formal experiments and complex animation, and then there's two blokes in a tiny room with some chairs, some books and a dog blanket
That is some brilliant editing at 6:39
Awesome and I thought it was a great and simple to follow explanation
I understood this!!! - I'm amazed that I did!!! thank you!
This video and the One about Touching atoms are my favorites
I wish there were more equations and graphs in these videos....or maybe a follow up on the Nottingham physics channel
Do you explain like this in class as well? Your students would be really fortunate for having a teacher who simplifies things so nicely (as well throws in a couple of funny remarks here and there :-) )!
Such passion
The idea comes from the 1st law, dU = TdS - it all boils down to the shape of S(U), and u can see how the 'upper bound' thingy comes about if you think, for a 2-level system, in terms of _how many distinct states_ (AKA entropy) can you get by distributing particles along these two levels (S is a symmetric function of U!). Now, if u want to think in terms of the Boltzmann kernel, I think it's more useful to think that it's the distribution that defines what T is, not the other way around: if u _make_ a system in which the probability of the higher levels being occupied is bigger, than when u fit this into the 'Boltzmann scheme' using a fitting parameter T, this parameter will be negative :)
These graphs look amazing for being hand drawn.