@@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
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!
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
@@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.
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 :)
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.
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.
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
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.
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.
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.
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.
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
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.
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?)
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.
@@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
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.
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. >:(
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."
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.
I am taking undergrad Electronics engineering and though Ohm's law is popular, it does not necessarily having anything astounding in it. So I'd give it C or D as well.
The problem is that everybody commenting on Ohm's law here reveal a lack of proper education in electrodynamics. Ohm's law is NOT R = U / I. That is only a special case which is obtained by integrating the differential form of the principle. J = k E is Ohm's law and there are some interesting insights to that. But despite not being that old I feel like I'm a boomer when I see how shallow people study stuff in college and university these days. Or maybe I just went to a really good university where the professors were no superficial retards.
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.
EE here, I disagree with the EE above saying that they took ohms law D-tier personally... However Maxwell's equations on the other hand, that was a hit
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!
Maybe a little unfair on Navier Stokes. It can be made relativistic (even can be formulated in GR) and is particularly applicable for modelling the insides of stars in GR (which let's you compute conditions for star collapse etc)
I can't imagine what if Aristotle, Euclid, Archimedes come back to life and observe how far we went into the field of physics, especially into classical and quantum cosmology. They will certainly freak out!!!
@@vinvic1578 That would be mind blowing, especially for aristotle Euclid and other greeks that they barely knew the shape of the Earth, and now we know the shape of the universe (barely, too ;)).
@@mohannadislaieh3009 The fact that the tools are that precise is amazing, but rarely are further precise measurements that exciting. Being able to figure out that the Earth must be spherical from basic observations is an amazing thing to do, but getting a slightly more precise answer for its size and exact geometry is boring.
@@mikhailmikhailov8781 I would mostly agree. Indeed, observing peripheral phenomena with almost zero knowledge, at the very begining of science, must have been quite advanced at the time said. However, the notion that it was advance must suggest that science is getting harder and harder, a function of time. This also assures that we now know, know a lot!
Ranking some of the most important ones missing: Friedmann equations as a special case of the Einstein field equations definitely get an A tier from me. Callan-Symanzik equation also gets easy A tier. Wheeler-DeWitt equation gets B tier for ruining my life in grad school, but deep down it's still a cool equation. Fermi's golden rule B tier as well. Weisszäcker empirical formula D tier, it hurts my eyes only seeing it and it isn't even analytical. Same thing for Weisskopf-Wigner formula. Gibbons-Hawking thermal spectrum S tier because of course. Hellmann-Feynman theorem and Ehrenfest theorem A tier. Ideal gas equation B tier because it stops being useful once you get to grad school level statistical mechanics.
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!
"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
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
