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Thanks for your engaging explanations!

I think there is something not just precise: the Boltzman entropy kb\ln(W) is not equal to Shannon entropy which is instead the average entropy per particle. By the way, there is a simpler intuitive definition of Entropy in information theory, read the first 13 pages of the paper by R.V.L. Hartley "Transmission of Information" (1928), I think Shannon took the idea from it.

This was a superb presentation. I would like to know how to calculate the curvature of spacetime though. How does parallel transporting vectors on a curved triangle reveal the amount of curvature?

A demoness infested an Earthling with a mission to divert scientific progress - Empty/No-ether

cool

This is why, imho a cardioid best describes the overall curvature of the universe. There seem to be limits, deep voids and event horizons. The point tangent to circular orbit, and the node where the tangent is 90° to circular, radial to origin.

Why did you stop uploading? Your videos are very good.

Great vid. Thanks for uploading!

worth rewatching

Great video!! I'm currently doing a directed reading program at my university on QFT and never really understood the real intuition behind a vertex Feynman diagram and how it relates to the evolution of coupled fields. I'd love to watch more content on QFT if you ever decide to pursue that

5:49 this is breaks my flat and linear brain - how can you translate a vector in parallel way in a space where you have ether no parallel lines at all or infinite sets of them? The parallel translation of a vector should be undefined there, but you are trying to define something through it. How is that suppose to work?!

a nice intuitive explanation, I love the context it gives for Noether's theorem. Emmy N is my hero.

Dude why are gems like you still hidden,at least the algorithm revealed you to me today.

Channel is so underrated it’s insane

Ditch the sound effects.

this was awesome, fist time understood the meaning of lagrangian clearly enough to speak about it somewhere, awesome work brother

thank you sooo much 🤩🤩🤩

Just found this channel and it’s actually insane can’t beleive you don’t have so many more subscribers

Lil bro forgot the formula

Informative lesson. ❤ And I'm stealing your teddy bear.😆 📲

There is no Lagrangean mechanics. This is just a different formalism or approach to mechanics. Using Lagrangean is a convenient way to study physics just like the Hamiltonian. Newtonian mechanics offers the same physics.

I just found your channel, I can't believe how amazing it is for every physics liver 💞😭😭😭

I would just say, man you explained it extremely extremely well. Keep up the good work. Normally every RUclips video explaining concepts would leave somethings vague and it's hard to grasp the concept of it.

pleasee pleasee make moree videoss!! ❤

background music makes it completely unwatchable. decide if you want to educate or have a disco show.

You could totally make a video just about thermodynamics because after studying it I've found that most popular understandings are like slightly wrong in a way that critically skews perception. To give some examples: The first law is often said to be "energy can neither be created nor destroyed only transformed" this is not wrong but it's basically the same idea as conservation of energy which is just a basic physics thing not really a thermodynamics thing. The formulation I prefer is "the internal energy of a system is equal to the heat added to it plus the work performed on it" or U=Q+W, I prefer this formulation because it actually makes a statement about work and its relationship to heat and it clarifies the concept of internal energy as distinct from just heat. All of this is way more useful when doing thermodynamics. The second law has a similar problem, the most popular formulation is "the entropy of the universe tends towards a maximum" or something similar like that but this formulation kinda says nothing, like what is entropy? (I know wrong video to say that) and why does it increase? Another much better formulation is "It is impossible to realize a reversible cyclic process where work is performed by extracting heat from a single reservoir that remains at the same temperature", this of course sounds like nonsense but if you understand the Carnot cycle it basically boils down to saying "no engine can be more efficient than the equivalent reversible Carnot engine" and that of course means that a heat engine must deliver some amount of waste heat to the cold reservoir. Another formulation that is also somewhat common and in my opinion pretty good is "heat cannot flow from a cold body to a hot body without work being performed", you can see how this is equivalent to the other one I liked if you just perform a thought experiment where you have a Carnot engine and then some magical substance that can transfer heat from a cold body to a hot body. In that case what you end up with is the cold reservoir remaining at the same temperature while all of the heat energy of the hot reservoir gets turned into work. Other than that actually putting the Carnot cycle in it's proper historical context is really interesting, like Carnot was trying to improve steam engines and if you just take the conclusions of the Carnot cycle you can explain basically all the technological developments of the steam engine. Firetubes in boilers are a way to raise the temperature of the hot reservoir, compound expansion engines are a way to let the steam undergo adiabatic expansion for as long as possible and thus get as close to its condensation temperature as possible, and the limiting case of an extremely high number of pistons is basically just a steam turbine, which is why they're so efficient. Some early steam engines had their pistons contained inside the boiler but this obviously means that there is direct contact between the hot and cold reservoirs and thus it made the engine less efficient, even though it seems like a smart way to provide insulation. Superheated steam is another effort to make the engines as reversible as possible, since the Carnot engine assumes an ideal working gas and wet steam is very much not an ideal gas (which follows intuitively from the kinetic theory of heat) however by superheating the steam it does start to act more like an ideal gas. Maybe I'm just saying all of this because I just wrote about it but I think it could make for a good video, if I at some point have time myself I'd probably give it a shot.

Slight correction, Carnot did not have the concept of entropy since he believed in the Caloric theory of heat. Therefore in his original description of the Carnot cycle the engine takes out as much heat, Q, from the hot reservoir as it returns to the cold reservoir. So he didn't believe that a heat engine does work by extracting heat from a heat difference, and the concept of efficiency, how much work the engine can extract from the heat, did not exist in his conception. Though he did sorta prefigure the idea of the 2. law off thermodynamics with his proof that no heat engine can be more efficient than the equivalent Carnot engine, but since he didn't conceive of heat as energy he also didn't think that the heat the engine delivered to the cold reservoir was lost energy. The version of the Carnot cycle you have up, and the formula for the Carnot efficiency were conceived by Clausius in order to rectify Carnot with the modern molecular theory of heat, who also coined the term entropy and the most common formulation of the laws of thermodynamics. So he probably deserves a lot of the credit. Though one thing that's sorta neat is that Carnot described a heat engine as "something that interrupts the free fall of heat", which is very close to a more modern understanding of heat "falling" from a state of low entropy to a state of high entropy and heat engines accelerate that fall by extracting work from the heat difference.

This was a really insightful video! Thank you! Also, if it isn't too personal, where is your accent from ? It sound's American but with a British 'A'? It sounds really cool.

Is this weird that I'm a fan of quantum mechanics more than the classical mechanics ? Bruh I ended up hating classical actually. My physics teacher 🫠 well kinda brainwashed my intuition and fundamentals. Successfully wasted my 11th grade! Yay! 😭

Wow! This video has helped me massively. Your presentation style is so engaging. Thank you so much!!

superb video. got me hooked after only few seconds. subs and like

Thanks happy bear creature.

Your math warning was 4 minutes and 17 seconds too late into the video

19:30 So gravity is an "unremoval fictitious force". Nice! 🙂

NOW DO THE TWIN PARADOX.

This channel is disgustingly underrated.

Gauges having symmetries sound like groups. Gauges describe the interactions using something that looks like a generating function at 11:10. Groups have associated generating functions by Molien’s theorem.

loved it

Wick’s rotation connects entropy to quantum mechanics by way of statistical mechanics. The prime number theorem can defined using the offset integral Li(x) = ∫ li(z) dz. Notably, the Li(x) bounded between 0 and 1 = -ln 2 like the information content defined at 7:45 and like how probability (and information) where defined as S = k_B ln W at 9:22. Also, Chebyshev’s functions for prime numbers are similarly defined to that of Shannon’s entropy at 8:38. This suggests the primes follow some entropy law and randomness. Thermodynamics and the dissipation it entails through entropy have solutions that are described using Gaussians and Fourier series. These solutions generalizes to harmonic analysis, automorphic functions, and automorphic forms such as modular forms and provides a mathematical basis to do entropy.

Take the KE and subtract it from the potential energy means your equation is backwards in your example.

5:30 this doesn't make sense. The particle will only ever go to one place, but this lets you make it go anywhere.

Great video! Only thing that I noticed is that sometimes you wrote Albelian not Abelian

Great video. May I ask what your background in Physics is? I find your videos to be very good at illustrating bigger concepts in general, you should make more

hoe can you multiply two 1,2, etc, column VECTORS, You CANNOT! NO CAN DO need to get the transport of the first one.

Translations and rotations are BOTH SPATIAL

I specifically was searching for a SoME video on this, only to find this was the second result when I searched #SoME2 ! This is a fantastic explanation

Penrose is a lunatic, and doesn’t use any “science” or logic for any of his crazy nonsensical “theories” including that the universe came from multiple infinite timeless explosions that don’t correspond to physics or reality. These men… these cowards… these liars like Richard Hawkins, Sam Harris, Lawrence Kraws, and Shane Carol are committing blasphemy in its truest form. None of their methods have been replicated in a lab or demonstrated to be true. These are put forth hypothetical “models” that end up being closer to wild science fiction imagination than anything resembling actual truth or fact.