Ranking Famous Physics Equations
ฝัง
- เผยแพร่เมื่อ 10 ก.ค. 2024
- Today I rank some physics equations you might have seen before, and have some fun talking about what they mean and where they pop up. The chancellor of physics DM'd me saying this is canon now.
Check out PhysicsOH's channel:
/ @physicsoh
and his twitch:
/ physicsoh
The tier list:
tiermaker.com/create/physics-... - บันเทิง
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Imagine working your whole entire life to find an equation just for some guy on youtube to put it on C tier
are you talking about Kepler's
@@itsmeagain1415 IMO Kepler's Laws themselves are not really used that much in general - but they are important mostly because they led Newton to his Gravitation formula
life is a cruel mistress
its a tier list. you cant put everything on S
Newton: *writes second law, fathering mechanics*
Andrew: "yeah, this one didn't age well for me"
Didn't he later decide it deserved more respect and put it in A tier?
@@asherkhan6023 maybe I'm a Newton fanboy but I wanted it in S ;_;
@@somethinglemon ANdrew's evaluation was absurdly anachronistic. It hurt my eyes to watch the whole video.
I haven't watched the whole video when I posted this comment. It got even worse.
all of mechanics can be derived from f=ma
"Navier Stokes... I'll put it B tier"
"Kepler's Laws... C tier"
Me, an Aerospace Engineer: "Am I a joke to you?"
Omg same here
Me, a chemical engineer: "Know your f*cking place, trash..."
Yes, you are a joke
Yeah true cuz it literally nerds too much of u sub to work out and that reduces my liking towards it.
@@colekinyon2267 Imagine unironically believing the "enGinEeR bAd" jokes
Nothing screams you're studying physics than having 4 tabs to physics stackexchange open lmao.
7 :')
This man really called the law of gravitation "cute"
I think in Griffith's E&M book, he used the word "cute" to describe examples a few times at least lmao.
Woudln't you?
@@XenOz3r0xT_88 love the way Griffiths writes lol
It is
For him and his langranians or w.e
It a seems so small and simple
It's a cute equation, what do you mean?
"Dont take it personally"
Alright
"Ohm's law is D tier"
I'm about to write an essay in the comments about this, and you cant stop me
This man knew he was gonna piss off thousands of people when he made this video
You're certainly resisting opposition to opinions😊
It would be nice to have some formulas from Optics. You know, to fill rank D a little bit more!
Lmao
what a savage
Yea let’s get some fresnel coefficients in there
😭
Snells law a tier though
Navier stokes b tier
Engineers : BLASPHEMY
*Sad supercomputer noises*
Last year, I had the Navier Stokes equation in my course, i had anxiety just by seeing the equation. Later when I finished solving it, i realised the elegance of the equation. One of the most beautiful equations in physics, hands down!
@@vladimirputin8495 i thought they were unsolvable?
My exact reaction when he put it in b tier 😔
@@schierke I assume he means solving special cases with some boundrary conditions that give weak solutions.
I'm gonna pretend this counts as studying for my QFT exam
It does
IT DOESN‘T
It totally does
Schrödinger's does(n't)
My essential piece is very elastic
"smart people" the further i get in physics the dumber i feel lol
True that except I learnt that at a young age we can still try to get to the point though don't give up
Sdunning, isn't it?
Paradoxically, that means you're learning!
@@justyourfriendlypebble8943 huh
Some people don't give a single fk about Physics, man.
My screen wants to thank you for ranking Noether’s theorem s-tier because otherwise I would have punched it quite hard.
lmao
What is this niche joke that I don’t understand?
@@zaraloves8420 Noether's Theorem is probably the single most beautiful result in all of physics. If we didn't have conservation laws, physics would be VERY different, and Emmy Noether formalized our understanding of conservation laws by relating it to an even more fundamental concept, differentiable symmetries.
@@azerack955 It popped up in a symplectic geometry course I was following. In there it's just a side remark as it follows super naturally from the theory. It was a big shame, I hoped it would be a highlight, something where everything just came together.
@@azerack955 Isn't it kind of obvious that a symmetry implies something is conserved? I guess formalizing that is pretty cool.
Pov: you are alone in your small apartment, rooting for famous physics equations to be ranked higher (or lower) on an arbitrary scale by a random -altough likable- dude on the internet you never met and who won't even hear or care for your opinion. Guess I'm living the dream
I must be in a simulation right now
The FBI wants to know your location.
Mannn
Why?
This man is very attractive and cute. AND he knows Physics 😍
“It’s fun to use gausses law because it’s kind of easy”
One of the great things about this channel is that it keeps my ego in check
Lol mines gone
Loooong ago gone
yeah it does!
I know it's an old comment, but it really is easy. If you have a spherically symmetric charge distribution and choose a spherical boundary, the closed surface integral over that boundary of E.dA becomes E*A or 4 pi r^2 E. From that, you can work out the electric field.
4 pi r^2 E = Q / epsilon_0 from Gauss' law
E = Q / (4 * pi * epsilon_0 * r^2) which is Coulomb's law
:)
You can only use gauss law in cases with cylindrical symmetrical spherical symmetry or uniform electric field
Well you could use it in other cases but you're not gonna get anywhere with it
My guy's complaining that a fluid dynamics equation isn't relativistic
*This post was made by classical gang
classic complaining
First time I saw the d’Alembert operator, I thought there’d been a problem when the book was printed and a little square got printed as a placeholder instead of some operator. Like when you get encoding problems.
Same! I thought they tried using an emoji or something
ཀཱ wow, that’s an interesting job
Andrew: it's 97 degrees
Me as a European: 👀👀👀
Lol I also thought he was boiling for a sec
Imagine not specificing the unit of measurement.
97 f is still hot
@@ngzbblax it's hot, but using an online convertor 97C° = 206.6F°
I don't think 97F° is quite on the same level
Me: a bit more than half pi
"Euler-Lagrange equation is essentially F = ma"
As a mathematician, this made me scream in variational principles.
He didn't say anything wrong, in classical mechanics the Euler-Lagrange equations give F = ma, although in quantum field theory it gives the particle wave function.
“Btw if it looks like I’m sweaty it’s just the sweat” is my favorite line of this whole video
She: "He's probably out there now thinking about other girls"
He:
Andrew: it’s 97 degrees
My Prof: Degrees of what? Oranges? Apples
Degrees of Freedom.
@@ausaramun lmaoo
@@ausaramun What in the System of bodies is that DOF?! Mental
but then what's the uncertainty
@@ausaramun omg im so dead
where my D=AB at?
How about 2 != 0?
Oh man this changes everything
I'm the 69th like :^)
What is this equation?
@@thephysicistcuber175 🙄
*Navier Stokes goes in B tier*
Mechanical Engineering/Pure Math Major: *Sad Noises*
Well, he is ranking important Physics equations, NOT maths!
@@sohangchopra6478 Fluid Mechanics is *PHYSICS* and it is *IMPORTANT*
You Physicists have abandoned us, we are *FAMILY*
F=ma was in B Tier until it was realized most of the modern world was built upon it
My school is teaching Ohm’s law now and I simply can’t stop laughing seeing it in D tier
I know, right? In high school, you solve a lot of problems using Ohm's Law. But later on-spoiler alert-you learn that it's applicable to only a small class of materials called Ohmic resistors-materials that obey Ohm's law. (Yeah, kinda circular definition.)
When AC and semiconductors get introduced, life becomes orders of magnitude more complex. Oh, how I long for the simpler days of V = IR!
@@nHans sounds like it comes straight out of The Devil's Dictionary, just like its definition of magnetism ;)
MAGNET, n. Something acted upon by magnetism.
MAGNETISM, n. Something acting upon a magnet.
The two definitions immediately foregoing are condensed from the
works of one thousand eminent scientists, who have illuminated the
subject with a great white light, to the inexpressible advancement of
human knowledge.
@@nHans Even if it gets a lot more complex and complicated, you still need Ohms law when working with AC or transistors... It's probably the most basic equation in electronical engineering
@@Eisommolos Not denying the importance, utility, or ubiquity of V=IR. But again: It's a property of a limited number of materials-an extremely useful property for us, no doubt. But it's not a universal law of nature. All the other equations on Andrew's list were laws of nature. To be sure, most of those were special cases. But they were not properties of specific materials.
I agree with you that in AC, you can continue using Ohm's Law with complex quantities.
And electronic circuits definitely contain lots of resistors-open up any electronic device and the PCB is chock full of them. And your mind immediately starts going BBROY...
However, I disagree with you regarding transistors (and other valves or semiconductor devices, including diodes). V=IR is useful only when R (or Z) is constant under operating conditions.
In fact, the whole point of electronics is in using components that don't have a constant R. You don't apply Ohm's Law to them. You use transistor parameters α and β, operating characteristics etc.
BTW, on the very first day of my college electronics course, the professor summarized the difference between electrical and electronics engineering in exactly that way: In electronics, we use many components that _don't_ follow Ohm's Law.
To be clear: Neither my professor nor I said that Ohm's Law is _never_ used in electronics-just that you can't apply it to every component. Electronics uses resistors, and resistors obey Ohm's Law. Period.
I tutor high school students in science, particularly for competitive college entrance exams. I can't help thinking how (relatively) easy their electrical circuits are, compared to what they'll be challenged with in future electrical and electronics courses!
However, even at the high school level, V=IR isn't enough to solve the problems they set for you. You also need P=VI, Kirchhoff's Laws etc. Unlike Ohm's Law, the latter two are universally true, and apply to all materials.
We are lucky that the metals Ohm studied obeyed Ohm's law. It makes it easy to study electricity and to design useful electrical circuits. *But it's not a universal law of nature.* There are materials that don't follow a linear V:I relationship. It's more difficult to build circuits with them, but not impossible. And like I said, we are doing it. That's why I'm not in the least annoyed when Andrew ranked Ohm's Law a "D."
@@nHans
I don't say that Ohms law is all powerful or something... It's a very simple and useful equation that is very important in electronics.
I know that you can't apply it to every component, but in almost every circuit are resistors and even the most basic transistor circuit needs resistors to adjust Voltage. So you still use Ohms Law
Navier-Stokes equation not being relativistic had me chuckle ngl
Me a musician who knows nothing about physics watching this:
Hmm yes V = I R really sucks. It sure does deserve D tier
Kepler at D tier. You can derive all of it from universal gravity
Everything in D tier. You can derive all of it from the lagrangian
This was such a fun video to watch. Please make more math-physics content with your commentary.
It took me quite a long time to really understand the significance of Kepler's laws but I feel like I'm appreciating them more and more the longer I do physics.
The first thing you have to appreciate is that they were all derived empirically by Kepler, simply by looking at tables of numbers. This was before any classical mechanics was formalised and arguably before experimental science became a major thing. Given that, it's really quite remarkable that all three laws have some profound meaning. Kepler must have had an incredible intuition.
The first law describes the orbits of planets in purely geometric terms. Historically, it was also important because competing models at the time modelled orbits as circular rather than eliptical, so this was a major discovery. It also somewhat anticipates energy methods in modern analytic mechanics, where people try to get information about a system from its integrals of motion, without having to solve the equations of motion exactly.
Regarding the second law, Feynman had a good comment. A lot of people (including me for a long time) think Kepler 2 is kind of trivial since it's easy to show from integrating the two-body problem. However, as Feynman pointed out, it's really just a statement of the conservation of angular momentum (which obviously did not exist as a concept at the time of Kepler), which is in fact much more general than Newton's laws of motion and gravitation.
The third law is perhaps the hardest to appreciate because it appears a bit arbitrary. The first time I understood its context was when I was reading Landau & Lifshitz vol. 1 in grad school. There they have a section on scaling and dimensionality and one of the examples is deriving Kepler's third law simply from seeing how the Lagrangian changes under rescaling. To emphasise this point, this is something you can do on the back of the envelope, without even writing down the equations of motion. The two ways of interpreting it then is, if you accept the inverse square law on theoretical considerations, then Kepler 3 drops out in a few lines. Alternatively, if you take Kepler 3 as an experimental observation, then it allows you to determine the power dependence of the law of gravitation. Again, to highlight Kepler's foresight, arguments from "power counting" in modern physics are usually the first thing you do when renormalising a field theory.
really profound stuff, thanks for the interesting read!
Ok, V = I R is bad but like that isn’t even true? Like it’s an edge case for a ohmic circuit. It doesn’t even require calculus.
more of an "Ohm's Rule" as my prof explained to me.
Yeah, it's a result from solid state physics that concentrates on a very specific usage regime of devices. These kinds of complicated systems are going to be nonlinear in nature, but Ohm's law can be applied very accurately for whatever conditions they are linear.
However, it's not just for resistors - a more general form much more widely used is V(w) = I(w) Z(w), as a frequency domain/phasor equation. This allows us to treat capacitors and inductors, whose behavior can be confusing and needs to be modeled by a diffeq, as ohmic (in sinusoidal steady state). In that way, Ohm's law creates a vital piece of the puzzle to solve more complicated circuits for much more interesting results than a high school resistor nest homework.
like, y do u say ‘like’ so much
Not to mention circuits suckkk
@@poge6192 yeah i personally find the equation for impedance in an AC-LRC circuit to be better than V=IR
I disagree with the ranking of F = ma (or F = dp/dt as Newton wrote it). While it could be considered "boring" in today's standards, this equation was a result of a huge leap in logic which may as well be the origin of physics as we know it. The equation encapsulates a basic but profound law of nature, such that even the most complicated quantum and relativistic equations can be reduced to it at certain limits.
Edit - found out you moved it up in the end, cheers!
Yeah, it looks really simple for us, but if I recall it correctly it was the first differential equation ever, and everyone can count for himself how many equations up there are NOT differential equations.
I think that this video might have focused a bit more on applications of the formulas. If it were influence/importance, then just about all of these would be S tier.
I would rank F=ma lower because a more general form would be F=dp/dt because that allows you to account for changing mass by using the product rule, for instance if rain is falling into an open carriage on a train.
@@maxdonaldson861 It doesn't. If you try to do that you would get an equation that isn't galilean invariant.
Me: *with only a high school physics background and is here for the vibes*
Andrew: next we have the euler-lagrange eq
Me: Ooo yes the best because drawing the L is fun.
Me too lmao
Man, and here I thought I would be able to relate, but I don't even know what it means
Most fun letter we've learned to draw is sigma :(
I don't even know why I'm here. I picked biology after catastrophically failing physics
I mean I'm going into my second year of physics at uni and I don't understand 50% of the stuff he's saying
Me: Ok so I just got through an extenuating exam session,I just want to relax for now
My brain: "EqUaTiOn TiEr LiSt"
"I haven't used [ohm's law]" - over a computer like a badass /j
Feels so nice to finally know all the most significant physics formulas.
Im glad you're uploading more often lately. Good job!
"Pushing aside their Arduino boards" hahaha
I cannot say I love your takes, but I appreciate you posting this lol
"If it looks like I'm sweaty, it's just the sweat."
This day just got so much better thanks to your new upload.
love the formulas video bro!
"Sorry Ohm's Law" in your wrap up at the end absolutely SENT me for some reason, don't know why I found it so funny
in fairness without ohms law literally all of experimental physics wouldn't be possible, that moment when u wanna do experimental physics but should've taken more engineering courses xd
Greatest tier list video in existence
I am so happy that relativistic energy is not just E=mc^2 in there. And I would add Boltzmann equation because its really important in statistics.
Yeah that would be a good one
"If it looks like I'm sweaty that's just the sweat"
*if it ain't broke don't fix it*
Always good to see some love for physicsoh! I think I mostly agree with this (except the standard model and Klein Gordon, those are both S-tier!). Though I don't think i personally would put the Euler-Lagrange equations that high, however I would keep the action at S tier. It's usually easier to vary the action directly; and the EL equations are really only a special case where the Lagrangian is first order and nothing too funny is happening with any boundaries. You can't even use EL with the Einstein Hilbert action, as the Lagrangian has second order derivatives with respect to the metric
There are higher order versions of the E.L.E's though, right? I think there's an exercise in goldstein where you have to derive the E.L.E's for a lagrangian that depends on second derivatives but I can't say for sure.
@@AndrewDotsonvideos you can, yeah. You end up with a series of higher derivatives, where in the derivation you have to do integration by parts an extra time for each higher derivative. But I'd argue this is often easier to vary to the action directly, with this generalised EL method you can end up needing to take some pretty unpleasant derivatives (for example, trying this with the Einstein Hilbert action would be horrendous. Which is why no textbook I've seen tries this).
This also doesn't deal with the possibility of strange stuff going on at the boundary. In GR this is even more complicated, as you need to add an extra Gibbons-Hawking-York term.
Yay! Another upload!!
Congrats with 200k subs
Glad the Uggos got some love *tears up* gives me hope.
You stabbed me in the heart with a dagger when you put F=ma in B tier then gave me a cupcake when you moved it up to A.
Zero curvature equation seems to be deep and elegant, containing Chern-Simons and also having intimate relation with integrability employing existence of infinite number of integrals of motion. Definitely would have included it.
All of y'all shitting on V=IR but that's deadass one of three equations I use in most of electronics engineering, it's technically ΔV but same thing
Same its s tier
What are the other two?
(I know Kirchhoff's Laws, complex values in AC circuits, capacitor's charge-to-voltage relation, transistor's α and β etc. Are you talking about any of those?)
Is V=IZ not just a more useful version?
@@nHans Ohms, Kirchhoff and Thevin/Norton is all you need mostly...
@@RedRacconKing And just but 1uF Caps everywhere.
We want justice for the Navier-Stokes equation.
No other equation can contain as beautiful (although numerical) solutions as NS.
No.
I don't know, the Einstein Field Equations have some pretty darn beautiful numerical solutions too.
Call me when someone solves its millennium problem
i love this video format
Couldv'e used boxes around your equations, but loved the concept and execution (and humility). Tibees sent me. Subbed. Thanks!!
-EM lagrangian
-QFT partition function
-Kramers-Kronig
-BE distribution.
I actually feel really sad about how the Navier-Stokes is written here, there are much more complete and elegant forms of it.
And yes, unsolveable analytically, but I just love the ingenuity of people when it comes to doing simplifications in order to get solutions which yield suprisingly accurate results. Working in fluid mechanics has an inherent feel of 'what are we missing, it all just feels as if it should work analytically' and NV is at the bottom of that.
Can't wait to study some relativistic flows, that's going to be some weird stuff.
Yeah I think I've come across prettier version in terms of what the fluid people call a material derivative I think.
@@AndrewDotsonvideos Not sure if the material derivative form refers to the same thing but one I particularly like from a theoretical point of view is the generalised vector form with the stress tensor and force acting on the fluid included.
That stress tensor is strongly related to solid mechanics and if you really wanted to torture yourself you could probably include some QM in the NV equation. Never gave it much thought or tried it though.
@@AndrewDotsonvideos yeah material derivatives are more cosmetic
But turbulence as a phenomenon is absolutely so interesting. Heisenberg's doctoral thesis was on it. It was verified later using DNS simulations in more recent times. His adviser was the Chad Herr Professor Sommerfeld of course
@@BamBoomBots the Boltzmann equation translates from statistical mechanics to Continuum, but it's strictly classical. Nothing quantum about FM unless you consider superfluid Helium
You should look up magnetohydrodynamics. It's pretty much coupling both the maxwells equation and navier stokes equation.
The video that we didn’t know we needed!
Where's pi=e=3 hmm?
I'm guessing, in the engineers' handbook of quick-and-dirty approximations?
Andrew boi we are gonna hit 200k subs !!🎊🎉🎆🎇
The feeling when I do understand words, but have no idea what he was talking about.....
But it was surely fascinating, i didn't get any of that, but keep doing what you do!
I'd say Newton's law is S tier given it's literally the first equation you really ever learn in any physics class, and the fact that you can use it for nearly 95% of IRL engineering - send people to fucking space with its consequences, makes it insane given it was postulated in the 1600s. That's crazy to me
I don't know what kind of trash school you went to but In Germany physics as its own standalone subject starts in 6th grade and you immediately start using equations since you learned a lot of basic maths betweenn 1st and 5th grade which is ready to be applied in 6th grade.
The video I didn't know I needed.
I really like that self-honesty at the beginning, cause it's true :-)
Almost at 200k? Lets goo!
I am studying electrical engineering , and my fav equation of all time is sin(arcsin(e^2)=((ln(e^g))^2)^(1/2)
calling Newton's equations "cute" lol, the power move
I have absolutely no clue about Physics but I still watched this all the way through. Very nice.
AYYY YOU’RE BACK
As an aerospace engineer, I totally understood when you put Bernoulli's equation quite low, as it doesn't work for incompressible fluids, but when you relegated the Navier-Stokes equations I was so pissed that I had to log in to write you an angry face. >:(
Noether's Theorem would be my first top tier pick as well. But I think it's even more than what you describe. Its semantic extent and conceptual importance is broader and more fundamental than what is captured in the equation for conserved currents. I thinks not even (primarily) a *physical* principle - it is a logical/philosophical principle, by introducing important precision into the very conceptual structure of and between the concepts of "symmetry", "continuity" and "invariance", the former of which is a "passive mode" of description - describes the properties from a static perspective (not necessarily merely static properties though). The latter is a fundamentally "active mode" of description - as "invariance" is always invariance *under* some process/transformation. Weyl was one of those who recognized this broader importance of Noether's work for questions of philosophy of science and ontology - and even tried to relate that insight to the layperson in a few popular science books - while being one of the last "universalists" in maths & physics (with maybe only von Neumann as a peer in this regard), himself advancing the state of the art in these matters.
In this regard, I think it's similar to the *general* "uncertainty principle" captured in fourier analysis, which also regards a "shift in pespective on the same thing", by translating between time and frequency domain - which is not actually mainly a fact about nature, but about our "frame of representation". If our "periodic table" for constructing/analyzing continuous signals are pure frequencies, their ideal nature includes extending infinitely in time and space. This entails - purely conceptually, you don't even need a physical context - that to represent continuous signals which are bounded in any way and thus non-pure, non-ideal, you get infinities - an infinite number of weighted contributions from the ideal, infinitely extending "elements". This in turn entails a general principle extending beyond the physical context - that the more finely you specify limits in either the frequency or time domain, the less "certain"/"specific" your value in the other is - there is a complementary relationship in specificity of determination. The wider the temporal boundaries are, the closer to "pure" we can get - with absolutely pure waves only being possible in the infinite limit. OTOH - the more narrow our temporal bounds are, the less selective/specific the distribution of frequencies with their weights.
This is why group-theory, and in general abstract/universal algebra, (higher) category theory etc are so useful - because they "extract" the most general principles which then apply to so many different situations.
bro i 100% agree with this list!!! Great job!
not putting Maxwell Equations in S tier feels almost illegal
Can be easily derived from Electromagnetic tensor in QED so not needed at all
My favorite quote: What's going on smart people?
The kind of video we didn't know we needed and also don't deserve
Ah....I'm currently feeling what you said about Schrödinger equation... Like it's really cool!
Living like the pilgrims. Bro.......newmexico with swamp coolers is awesome at 97 you can feel the dust stick to your ....everything.🤙 thanks for the video mane!
I love how ive been watching this channel for years when I dont even know what im looking at bc ive never taken calculus based physics or calculus lmfao
Missing the Clausius inequality which I would put as A tier
I am surprised Maxwell's equations aren't S tier. Griffiths would be disappointed.
Not angry. Just disappointed
I'm guessing, it might be because it's a classical theory and has been superseded by Quantum Mechanics. Andrew admitted quite plainly that he's biased towards anything "relativistically consistent or quantum mechanical in nature."
Cracked video
"if it looks like I'm sweaty, it's just the sweat."
siense
8:23
every high-school student ever: *looks at Andrew menacingly*
14:34 Correct me if I am wrong but the picture that is shown is Green's theorem, not the Divergence theorem right, cos the Divergence theorem is 3-dimensional.
5:07 that's S tier right there
I have no idea how I found this video, I barely know 5 or 6 of these equations and yet I watched the entire thing
This is the most random thing I have ever experinced , even more than my dreams. Still like it though
Well Andrew you could have uploaded this 1 week ago before my exams ended. Thanks a lot.
Also what has my youtube page come to. I'm convinced that being a physics student is just being in purgatory
Thanks for this idea, I know what I'm having my highschool students do tomorrow now
"F=ma yeah i never really used it"
Every jee aspirant ever:
My powersum formula for the any differential resolvent of any polynomial is not up there?
Every engineer watching this video: "After all the tools we built for you physicists, you disrespect us like that?"
Very interesting and worthwhile video. Good reasoning in your evaluation of these formulations of physics.
The pinacle of internet, a equations tierlist.
The "Master equation" has become my life. S tier for me
Why just listing these equations looks so hilarious
I messed with Kepler's law and simulated it in desmos and it was sick as hell and I was happy, then the third body came in.
The Kohn-Sham equation is a clear oversight imo
It’s basically just the Schrödinger equation though.
"IDGAF about Ohm's law" I love this vid so far. Pretty much the nerdiest discussions I've had with people. As someone now doing a master's in astronomy after finally giving up on elementary particle physics