Markus Deserno
@MarkusDeserno
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Theoretical and computational biophysicist @CarnegieMellon . Loves lipid membranes. (he/him) 🇩🇪🇺🇸
Pittsburgh, PA
Joined April 2020
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May I invite you to a fun thread about a delightful quirk of relativity theory? Starting with a simple fact about rotations, I’ll hope to give you some intuition about something that’s considered wildly counterintuitive: velocity addition. Intrigued? Buckle up!
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It’s been *forever* since my last Physics Twitter Thread 😳.
But today I ran into a beautiful artistic physics demo in my hometown that inspired me to write a few lines.
I’m sure you’ve all seen these massive floating granite balls. How do they work?
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New Physics 🧵! Ludwig Boltzmann was not just a father of Statistical Physics but also a master of Thermodynamics. That’s how he got his name on the Stefan-Boltzmann law. If you allow me, I would love to walk you through a magic moment in physics history. /1
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Here are 9 equations that make people go all “ooh” and “aah” because 111 is divisible by 3. 🙄
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So next time you see one of these floating granite ball fountains, you know how they work, and that it takes exceptionally little water pressure to lift the ball up!
And if you liked this thread—please retweet! Thank you! 🙏
13/13
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Why does increasing atmospheric CO₂ warm the planet?
The greenhouse effect, duh.
But do you know how that works? I can *almost* guarantee you that you don’t quite have the right picture in mind—in a way that actually matters.
Interested? Here’s a new physics thread!
1/29
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A lovely greeting to y'all! I have a new physics story I'd like to tell——about the relation between Statistical Physics and Quantum Mechanics! Or: why is Quantum Mechanics so in-your-face when it's cold, and why does it fade when you heat up?
Ready? Then buckle up!
1/28
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🧵 I was in the mood to write another thread on special relativity! Today I hope to introduce you to a very famous puzzle, known as the “pole-barn-paradox”, and its prescription strength version, the “stick-slit-paradox”. Intrigued? Buckle up!
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I've been grading my physics final exam, and I'm happy to report that student priorities haven't changed.
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@SneakerNerdJake
@Oliver_Stacks
Pennies are no longer made from pure copper, for that very reason.
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That is……surprisingly little! Water pressure in homes typically falls between 2 bar (pretty low) and 5 bar (a lot of oomph), so this massive granite sphere could be *easily* floated by the water pressure of your bathroom tap, even if you have pretty lousy water pressure.
7/13
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Heya, I’m dropping another relativity thread! This time I try to explain how Einstein’s two postulates, on which Special Relativity rests, spell doom for the notion of a universal time, and in particular the concept of simultaneity. Interested? Hop on board!
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Did you know that the famous Carnot efficiency of an ideal cyclic heat engine does not require this engine to run on a Carnot cycle? It holds for *any* reversible cyclic engine!
Curious to know why? Then buckle up for a short but fun thread!
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The movie above shows the “Kugelbrunnen” (“sphere fountain”—it sounds more charming in German!) at the Hugenottenplatz in my hometown
@erlangen_de
. Since about 1997 a granite sphere with a diameter of roughly one meter floats on a bed of water.
2/13
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Of course, there’s a reverse point of view: atmospheric pressure is surprisingly large! The pressure with which our atmosphere is crushing us is more than three times as big as the pressure with which this granite ball pushes on its support! Oof!
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Since pressure is force divided by area, all we need to do is divide the sphere’s weight by the area of the water bed it rest on. With a diameter of 0.94 m, it has an area of about 0.69 m², leading to a pressure of 21,000 N / 0.69 m² ~ 30,000 Pa ~ 0.3 bar.
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This is actually incredibly easy to check. Let’s start by figuring out some numbers. I tried my best to estimate the size of things, finding that the sphere has a diameter of D ~ 1.14 m, and it rests on a circular water bed of diameter d ~ 0.94 m.
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Clearly, it can’t actually be floating! Granite is denser than water, so it can’t buoy on top of it. But you can see water sputtering out at the bottom, since it is constantly being pumped under the sphere to push it up. That seems to require a lot of pushing—OR DOES IT?
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With a granite density of about 2.7 g/cm³ = 2700 kg/m³ we can easily calculate that the sphere has a mass of about 2.1 t. The associated weight of about 21,000 N is balanced by the water pressure from below. How much pressure would that be?
5/13
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So the equal weight water cylinder has a height of h ~ 2.7×1.1 m ~ 3 m. Conveniently remembering that 1 bar of pressure corresponds to a water depth of 10 m, we see—again—that the lift-off pressure is 0.3 bar. Voilà! 😁
12/13
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“The sun’s black body Planck spectrum peaks in the visible range.” Have you heard that before? Is it true? Want to follow me into a rabbit hole about densities and transformation laws? Then buckle up for another colorful physics/math thread!
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Let me also give you a slightly more elegant derivation of the same result, which doesn’t just juggle numbers. One which—if you’re willing to eyeball a few boring prefactors—will even give you the right order of magnitude immediately.
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Hello, my absolutely lovely membrane peeps! Would you maybe, pretty-please, let me proudly steer you to a MINI-REVIEW I recently wrote? It’s on asymmetric membranes in general, and differential stress in particular—subjects that I am massively interested in right now!
1/26
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The world of Statistical Physics has lost a giant: Kurt Binder has passed away this Tuesday. He was not only an outstanding scientist but also a wonderful human, full of heart and humor, who touched the lives of so many of us. He will be dearly missed. Rest in Peace!
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@MoneyTodayShow
@mattyglesias
The most powerful man in the world, with his own press department, gets thrown off a social media app after repeatedly violating their terns of service, and then whines about being censored…
Look, I’m no idiot. I know a bullshit argument when I see it.
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Let’s replace the sphere by a cylinder of the same volume, one which has the same support area—a circle of radius r. Equating volumes, (4/3)πR³ = πr²h, yields h = (4/3)×R×(R/r)². Since in our case R/r ~ 1.2, we get h ~ 1.9 R ~ 1.1 m.
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This cylinder, if made from granite, would exert the same pressure on the support as the sphere. If we instead make it from water, but want it to exert the same pressure, we need to make it 2.7 times higher, since granite’s density is 2.7 times that of water.
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Except, they are usually not called “hyperbolic rotations” by physicists. They are called “𝙇𝙤𝙧𝙚𝙣𝙩𝙯 𝙩𝙧𝙖𝙣𝙨𝙛𝙤𝙧𝙢𝙖𝙩𝙞𝙤𝙣𝙨”.
[END]
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When the Death Star destroyed Alderaan, would it have experienced a kick-back from its laser shot?
Absolutely!
Really? Light can cause a kick-back?
It sure can! If you wonder how much—buckle up for a new cute physics thread!
1/27
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(If you enjoyed this Tweetorial, please consider retweeting the first tweet at the top! I'd love to get more people excited about this ☺️ Thanks! 🙏)
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@mscots41
It’s the linguistic equivalent of this painting of a vase, which shows a bunch of dolphins.
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What we're looking at here very much reminds me of the phase transition in nematic liquid crystals. It LOOKS as if entropy goes down by shaking, but that's wrong: the nails can explore MORE phase space once they align. (Molecular) nematic ordering was first explained by Onsager.
This video is controversial but I’d like to explore its physics in this thread
As I see it the potential energy of the nails convert to kinetic energy so it transfers energy all through the box the entropy of the system is increased 1/🧵
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Wow. With just a single tweet,
@martinmbauer
brought out all the retired engineers with deep theories about light-quantum gravicentric black hole neutrino conscious protovariable simultaneous post-Einsteinian hyperdimensio quark string plonk crank poof zock quaffle sprock.
Velocity distribution of stars in a galaxy
Left : expected assuming only visible matter using GR/Newtons law
Right: observed
Something makes stars far from the centre move much faster then expected 🤔
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@SeamusBlackley
I really don't understand why this cannot be stopped. We do not have to kill innocent people. Nobody forces our hands. What is wrong here?
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@POTUS
Because that honor system works, right? Because anti-maskers have been so reasonable over the last year? Because I can tell vaccination status from the glimmer in their eyes?
I wonder whether you guys have thought this one through.
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@DrGuiton
I am so very sorry for you! This is painful. It is also borderline criminal negligence by the university, who apparently has no sense for how valuable these things are. If you express this in person years and lost grants, explain to your university that it cost you millions. 😢
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This weekend Justice Neil Gorsuch will speak at a Federalist Society’s event, which also features Ron DeSantis and Mike Pence. (No journalists allowed.) But it’s Biden who makes the Supreme Court political? Make it make sense.
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@keenanisalive
That’s because there’s a Jacobian in polar coordinates:
dA = r dr dφ ,
and that extra r messes with the density. But we can rewrite this:
dA = ½ d(r²) dφ .
The trick is hence to sample uniform in φ and uniform in u=r², such that r=√u. That’s exactly your algorithm.
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Well…
The fact that all these proteins are rendered in atomistic granularity, while the membranes are bland and insipid supporting actors, means that, from a purely professional point of view, I am obliged to be skeptical of this book’s vision of molecular cell biology.
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It speaks to the true power of thermodynamics that it lets us discover and explain laws of nature without knowing details of their underlying “microscopic realization”. We don’t always need to know what’s going on “deep down”! /31
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I’ve asked my students of Physics 3
@Physics_CMU
to create memes that reflect their first 2 weeks of learning Special Relativity—and oh boy am I impressed with their creativity and amazing sense of nerdy humor! Let me share some of their awesome creations with you!!!
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So far, the moral of our story is this: whether things look simple or not—intuitive or not—often depends on how you describe them. If you insist on the wrong mental framework, a simple fact might look needlessly opaque.
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@TimMarcin
A young couple posts a dance routine on TikTok, and the Twitter vultures congregate and compete over who can most creatively shit on them.
Seriously, you folks are awful. A perfect illustration why some corners of Twitter are just a burning hellscape of gratuitous hate.
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@ling_sprenger
Would it be weird to tell a painter you loved their painting? To tell a writer that you really enjoyed that book? A musician that that was a great performance? Who thinks scientists don’t also appreciate a heartfelt compliment? It’s OK. It’s normal. It’ll make them happy! Do it!
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@SneakerNerdJake
@Oliver_Stacks
Pennies made 1983 or later are made of 97.5% zinc and plated with a thin copper coating.
I recall this oddity because the "can't we make more money by melting copper pennies" strategy is a homework problem I often give to my gen-ed physics students 😉
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@WFKARS
Same with pears:
Too hard
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
Too hard.
You briefly step out of the room.
Mush.
Mush.
Mush.
Mush.
Mush.
Mush.
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@BJonani
@EricTopol
So what? What if a great protection doesn’t last forever? What if going to the dentist doesn’t mean you would never have to go again? What if taking a shower now still doesn’t protect you from getting dirty tomorrow? What if you still get hungry after eating?
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It always amazes me how much of a workout teaching is. After one hour in a well air conditioned room, I’m almost sweating and need a break. I move a lot, speak a lot, think a lot, …
But I still wonder: am I just getting old, or do others (maybe younger than me) feel the same? 🤔
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Modern Physics students tend to learn of this law as a simple corollary of Planck’s black body spectrum—how much power is emitted per unit area and PER WAVELENGTH, meaning, how much light do we get at different colors. /4
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Boltzmann used an exceedingly beautiful thermodynamic argument that did not require him to know quantum mechanics. Let me walk you through it now. Warning: some math and thermodynamics ahead, but I’ll try hard to make it palatable, promised!!! /7
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Hello my lovely Twitter peeps! If I may be so bold, let me point you to three lectures I have recently given on my research. I know, I know—tooting my own horn… But I think it’s a fairly decent intro to some of the work I do, so some of you might be curious?
(1/11)
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Woot! Our paper on cholesterol distribution in asymmetric membranes, spearheaded by Malavika Varma (not on Twitter 😭) is online in
@BiophysJ
!
Obviously, time for a Tweetorial!
Article Link (Free for 50 days!):
1/21
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@tommiedotjpg
Lest we forget: this dude also proudly presented a proof to the world that 1×1=2.
This is the proof to the World of Science and Mathematics that 1x1=2.
#mathematics
#worldofscience
@rollingstone
#proof
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@TamasGorbe
Yes! And the same is NOT true for the hyperbolic inverses arsinh(x) and arcosh(x), which instead correspond to AREAS—“area sinus hyperbolicus” etc. Which is why I have always hated Mathematica’s incorrect naming of these functions as “ArcSinh[x]”.
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@doctorow
@FerrisEmil
@fantagraphics
@MidsummerScream
@feliciaday
@RainaTelgemeie1
@ChuckTingle
I'm sorry. I'm SOOO sorry. Really. 😭😂😭😂
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In 1879, Josef Stefan experimentally showed that this radiant emittance is proportional to the fourth power of the temperature: j = σT⁴. The hotter a body is, the very much more energy it emits. /3
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So much for today. If you liked this thread and think it might be useful for others to learn about this topic, consider retweeting the first tweet. Thanks a lot for your interest! 🙏
29/29 and END
Why does increasing atmospheric CO₂ warm the planet?
The greenhouse effect, duh.
But do you know how that works? I can *almost* guarantee you that you don’t quite have the right picture in mind—in a way that actually matters.
Interested? Here’s a new physics thread!
1/29
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Let’s begin with the law itself, which says something about the light emitted by hot bodies—like glowing pokers or the sun. Specifically, let us look at the power (energy per time) such a body emits per unit area of its surface. That’s called the radiant emittance, j. /2
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First, the rotation is indeed not a rotation in 𝘴𝘱𝘢𝘤𝘦. It is a rotation in 𝘴𝘱𝘢𝘤𝘦𝘵𝘪𝘮𝘦! Relativity insists that changes between moving coordinate systems mix up space- and time-coordinates. That, indeed, is 𝘷𝘦𝘳𝘺 unexpected for our Galilean minds!
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In this notation, you might expect to find
β12 = β1 + β2
However, the 𝘢𝘤𝘵𝘶𝘢𝘭 answer is this:
β12 = [β1 + β2] / [1 + β1·β2]
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All you need to do is to integrate Planck’s formula over all wavelengths and, voilà, out pops the Stefan-Boltzmann law j = σT⁴. /5
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Here’s where it gets interesting, though. Planck derived his black body spectrum in 1900, and he needed to invent a key idea of quantum mechanics to do so: photons! But Boltzmann published his explanation in 1884—16 years earlier! How could he? /6
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@stianchrister
@CossackLaughing
@amalieskram
Precisely. They are pimping out female athletes for lecherous male audiences in pursuit of ratings and advertising revenues. These skimpy pants serve no athletic purpose whatsoever. It’s sickening to see this blatant sexism actually being defended in this thread.
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Until, one day, a particularly deep-thinking geometer, Al Unapietra, starts to think hard and deep about the true geometry of rotations, and he “re-discovers” the actual truth, and the more complicated formula. Everyone’s surprised. Most people are confused.
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🧵 It’s the weekend, and I haven’t yet unloaded all my opinions on relativity! Today I’d like to regale you with the sibling of all relativity puzzles: the twin paradox! As usual, my goal is not to derive any formulas, but to give you some intuition for what’s going on.
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Evidently, if 𝜙12=𝜙1+𝜙2, we also have
arctan(m12) = arctan(m1) + arctan(m2)
Moreover, exploiting the trigonometric identity
tan(x+y) = [tan(x) + tan(y)] / [1 – tan(x)·tan(y)]
this leads to
m12 = [m1 + m2] / [1 – m1·m2]
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OK, I’m done, and I’ll get off my soap box now! 😆
If you enjoyed this 🧵, consider retweeting the first tweet above. If I can somehow convince more people how beautiful thermodynamics is, that would make me very very happy!
/38 and END
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Now, hyperbolic rotation. This animation shows that, again, both axes tilt by the same amount, but in 𝘰𝘱𝘱𝘰𝘴𝘪𝘵𝘦 directions. Furthermore, the orbits are now hyperbolas, not circles.
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And second, I haven’t yet addressed that pesky minus sign difference between our “addition formulas”. It turns out that this is where it now matters. Our transformation is indeed not 𝘦𝘹𝘢𝘤𝘵𝘭𝘺 a rotation. Instead, it’s a so-called “hyperbolic rotation”.
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🎉 Happy birthday, Emmy Noether! Born on this day in 1882 in my home town Erlangen. One of the most influential mathematician and physicist of the 20th century.
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It is easy to see how they might develop some “intuition” for why this should be so. And how, as time passes, they would start to think of this formula not as an approximation but as the 𝘛𝘳𝘶𝘵𝘩, with a capital “T”. Habit is a powerful drug!
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It turns out that describing the motion of a “frame of reference” (e.g. a spaceship) by its speed is equivalent to describing the rotation of a line by its slope. It works, but it can get you in trouble, especially for large angles—or here: large speeds.
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Boltzmann started from three ideas: (1) thermal radiation as a thermodynamic system is “extensive”; (2) the pressure is ⅓ of the radiation’s energy density; and (3) the chemical potential vanishes. Uh oh. What does this even mean? /8
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📣 Big job announcement:
@CarnegieMellon
is searching for 3 (!) faculty in the areas of Cellular Biophysics and Quantitative Biology, a cluster hire to join
@Physics_CMU
,
@CMU_Bio
, and
@CMUCompBio
. Please spread the word!
Let me explain a a bit more:
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Incidentally, since angles add, both for rotations as well as for relativistic changes of reference frames, the angle 𝜙 also has a special name in relativity. It’s called “𝘳𝘢𝘱𝘪𝘥𝘪𝘵𝘺”. And as far as velocity addition is concerned, we can now see: rapidities add!
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The second idea quantifies the notion of “radiation pressure”: light can push you! Maxwell realized in 1874 that it follows from his equations, and Adolfo Bartoli gave a thermodynamic argument two years later—which Boltzmann had heard about. /10
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As a lipid geek, I have to share this interesting little thread about the lipid nanoparticles hosting the mRNA vaccines of Pfizer and Moderna. 😊
@moderna_tx
mRNA vaccine is finally arriving in Australia. It is very similar to the
@BioNTech_Group
/
@pfizer
#mRNA
The main difference is in the lipid nanoparticle (LNP) that deliver the mRNA. This is both in terms of the lipid chemistry and how the LNP's are formed 1/10
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@dynamicsymmetry
We Germans called it “vorauseilender Gehorsam.” A bit like “anticipatory obedience”, but more striving, eager, and willing.
Trust us, that didn’t work out well.
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For them, m12=m1+m2 always holds with excellent approximation. In fact, they might not be able to tell the difference, because it’s too small to measure. They might even start to think of this formula as being how rotations 𝘢𝘤𝘵𝘶𝘢𝘭𝘭𝘺 combine. You add slopes!
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I’ve never fully understood how Boltzmann exactly reasoned, but he must have intuited that the non-particleness of light means that μ must vanish. In modern parlance we would say “photon number isn’t conserved”. Maybe it was just a lucky guess? /12
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Permit me to conclude with a more “philosophical” outlook, but one that’s very dear to my heart. The fact that Boltzmann could derive this law, which has deep quantum mechanical roots, without knowing anything about quantum mechanics, is very profound. /30
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@allahpundit
This is what happens when unmoored opinions are considered just as legitimate in public discourse as verifiable facts and knowledge. But a disconnect from reality is ultimately dangerous, because reality doesn’t care about your opinion.
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At this point you might be asking, “Hello? Relativity? Didn’t you promise us a lesson in relativity?” Yes, I did. But I needed to 𝘱𝘳𝘦𝘱𝘢𝘳𝘦 you for it. That’s done now, and we’re ready for the harvest!
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The first idea simply says that the energy content of radiation scales with size. If you have two hot ovens of the same temperature, filled with thermal radiation, and the second one has twice the VOLUME of the first, then its radiation content also has twice the ENERGY. /9
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I am enormously proud that this has now been published in the American Journal of Physics:
Nothing in this paper requires math that wouldn't be available at the undergraduate physics level——say, in the junior year.
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That’s it for now! If you made it to the end: well done 🙌! And if you enjoyed this story, consider retweeting it. I love to see people engage with cool science and learn something deep while also having fun on social media. (Let’s have our cake and eat it!)
—THE END
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Does this remind you of something? Up to a + vs. – difference in the denominator (I’ll get back to that later!), this is basically the same as our fancy slope-addition formula! And the beautiful thing is: this is not a coincidence! Let me explain.
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📣 I’ve recently given a colloquium-style talk on membrane biophysics! Take a look if you're curious about lipid self-assembly, curvature elasticity, mediated interactions, fluctuations, Casimir forces, asymmetry, and differential stress:
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The third idea is the most elusive: the chemical potential μ essentially describes the thermodynamic cost of adding a particle to a system. But where are the particles in radiation? Boltzmann didn’t know anything about photons! /11
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In this small-angle-limit the slope-addition-formula simplifies tremendously: up to a tiny correction, m12=m1+m2. Slopes add! How nice! Of course, it’s just an approximation, but it surely makes life easier if we happen to be in a small angle regime.
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Is it, though? It’s only unintuitive if you insist on describing the rotation of lines by their slope m. But this is just not a very smart way of doing it if you want to add rotations! If you re-calibrate your thinking and return to the angle 𝜙, things greatly simplify!
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@equalityAlec
Can you maybe help me understand this: why does NYT regularly get away with this? Many of its readers truly care about objective journalism. They don’t like to be manipulated. And yet, here we are. What is the politics game here that I’m not understanding?
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You will of course not be surprised to learn that these hyperbolic rotations probably play a big role in relativity. And indeed, they do. An 𝘦𝘯𝘰𝘳𝘮𝘰𝘶𝘴𝘭𝘺 big role. In fact, all of physics nowadays must play nicely with these rotations.
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Great, welcome aboard! Let’s go! We shall begin by looking at a 2-dimensional rotation around the origin in the (x,y)-plane. We can quantify it by an angle 𝜙 and visualize it by a line through the origin that is rotated by that angle 𝜙.
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It is hard for me to adequately express how very beautiful I think this derivation is. Hendrik A. Lorentz called it a “a true pearl of physics” (“eine wahre Perle der Physik”). In fact, Lorentz was the first to add Boltzmann’s name to the Stefan-Boltzmann law. /29
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@jacasiegel
That is literally impossible: a professional reviewer is, BY DEFINITION, not a peer reviewer anymore. Which is why I am very much against this.
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