The Hidden Story Behind Maxwell’s Equations

[@quantverse1294]

As many of you have correctly pointed out(many thanks for that), several embarassing typos have crept into the video. Here are some of the corrections: a. At 5:00, the clockwise curl should be negative, while the counterclockwise curl positive. b. At 10:00, "magnetic" should be "electric". c. At 10:21, displacement current (D) should be replaced with current density (J). d. In the displayed Maxwell equations, the propotional sign should have been replaced with the full equation. e. At 6:27, Laplace should be replaced by Lagrange. We would also like to add some remarks: a. Many animations, especially about divergences and flux, are borrowed from 3blue1brown channel. We have credited them in description but we should have also done in the video. We apologize for that, and make sure to correct it in coming videos. b. We do have a section regarding Oliver Heaviside's contribution at 14:08. Unfortunately, we are still not convinced that Maxwell equations should be renamed "Maxwell-Heaviside" equations. But, we will do more research, and maybe even change our mind:)

[@backstrapped]

@@quantverse1294 We’re only human at the end of the day. Thanks for clearing that up - had spotted a few of these myself.

[@ntesla66]

Disregard Heaviside's contribution at your peril. Heaviside and Gibb's formulation of Vector Analysis would not have had so great an impact had W.K. Clifford not shuffled off the mortal coil...

[@eldersprig]

now do it as geometric algebra

[@RGD2k]

I favour calling the common dimensionless forms Maxwell-Heaviside, not to honour Heaviside, but rather because I consider them a diluted, rather than enhanced form. I hold Maxwell's original equations to be 'great guns' as he put it himself. More correct. The trouble is that the partial time derivative isn't the same as the total time derivative: Unless everything is motionless, and then you can make that identification. This leads to some confusion: Faraday's and Ampere's both correctly use the total time derivative, so Heavisides' form are really only good for substantially motionless things like electromagnetic oscillations shared between antenna and waveguides (so long as those aren't vibrating substantially themselves at similar wavelength: I hear the MEMS guys have it tough!) For electric motors and actuators, we (meaning, engineers who design these actual things) avoid them because they're not helpful. Ditto for 'high brightness' particle accelerators, where the approximation 'that nothing is moving' becomes increasingly invalid. Same was found to apply too for high current electron tubes. Heaviside's doesn't work where 'the moving stuff' itself affects the field. You have to correct for that and it generally rapidly becomes a mess, a game of numerical approximation, and flipping back and forth between pretending everything is motionless, so as to calculate the fields, then calculating the forces from the fields, then flipping back to Newton's equations of motion, and pretending there no fields whilst things are allowed to move just a little bit, then repeating ad-nauseum. But Heaviside's are great for designing (some) antenna. Here's my idea: I've recently come to the point of view that charge is probably fundamentally a trivector quantity, and so in 3d space it necessarily is constrained to take on only two possible polarities, which sum over volumes in an opposing sense, and for this sum to at least appear to be conserved. Consider the bivector case in a 2d space: coins on a table, either heads up or tails up. Flatland people would regard these coins as coming in two distinct 'flavours', the number of each of which they would find to be conserved: because they can't flip them. They can tell that they have these two different and clearly opposite polarities, and that these act as opposites when summed, but not much else. They cannot lift the edge of a coin, because to them 'up' doesn't exist. It's right-angles to every direction of space they know about. Addition of sufficient energy to our charges in 3d space to 'unfreeze' another spatial degree of freedom could cause it to behave like something that can suddenly take on three angles: Much like the bivector 'coin' on a desk can be only heads up or tails up, but when flipping through three d space, can take two additional angles of orientation (in this case, the coin is representing a bivector quantity, so doesn't get a third angle in 3d: bivectors have area and orientation, but no information about the shape of that area, so they can't carry any information about their particular angle around their axis of orientation, only about which way that axis faces). This idea implies that at a high enough energy density, good old fashioned electrical charge conservation might goes out the window if at these higher energies there is an additional degree of freedom which allows for these 'coins' to 'flip'. If they later 'settle down' into 3d space again, you may potentially end up with charge non-conservation, and during the collision at high energies, charge starting to behave like a quaternion (with three continuously varying, angles) rather than just a positive-or-negative one-quanta thing as usual. The reason I favour this interpretation is that it makes better sense of why Gauss' law, why divergence, and why charges come in two distinct 'flavours', as well as why those charges might seem to be very much conserved. Whilst also suggesting why high energy particle physicists had to invent a whole new theory called 'Colour charge' to explain what they found when they started smashing things together at ever-higher energies. (We do use a 3-space to represent colour: RGB values on a computer screen, and this is a lot like three separate angles in a four-space: quaternions, which are just a special case of more general Geometric Algebra). Quarks might just be some relative orientations of the things in the protons/neutrons when they cool off and 'fall flat' in 3d space again. The things happening during the collisions would be like a coin balanced momentarily on its edge, but not stable there. What would the flatlanders think to see a coin bouncing and flipping across their space? Perhaps this explains how neutrinos appear to us? In addition to bouncing through hyperspace, they could certainly also be rotating (rolling) as they go, such that their 'charge' appears to cycle. It's an interesting idea, I think, but probably wrong: Charge conservation really does seem to hold through high energy stuff. So perhaps charges are more like some kind of vortex-tubes extending into hyperspace only to bend over and have a low-mass 'tail' touching the 3-space brane somewhere elsewhere? The orientation of the rotation then gives us 'charge'. It being a vortex then guarentees total charge conservation: If one flips, a positive charge becomes a negative charge, but a corresponding negative charge becomes a positive charge at the same time, balancing it out and maintaining the conservation overall.

[@itzakehrenberg3449]

6:27 It was Lagrange, not Laplace, who first wrote Gauss' Law.

[@douglasstrother6584]

The collaboration between Faraday and Maxwell is sorely under-appreciated, both great men and great friends.

[@douglasstrother6584]

"Faraday, Maxwell & the Electromagnetic Field: How Two Men Revolutionized Physics" by Nancy Forbes & Basil Mahon is a great read.

[@susilgunaratne4267]

For all that greatness of Maxwell's equations & subsequent applications in modern physics & success of it we shouldn't forget the Faraday's introduction of great abstract concept, the "FIELD". In 19th century a completey novel thing. It's the start of all that.

[@douglasstrother6584]

"The Forgotten Genius of Oliver Heaviside: A Maverick of Electrical Science" ~ Basil Mahon is a great read.

[@YTEdy]

I think Maxwell initially published 15 equations. Heaviside was the one who reduced it to 4, now called "Maxwell's equations". I think that's true. Some people call them the Maxwell-Heaviside equations.

[@douglasstrother6584]

@@YTEdy Both Heaviside and Gibbs were big proponents of Vector Analysis.

[@maxheadrom3088]

When a journalist asked Eisntein about Newton's phrase "on the shoulder of giants" and if Newton was his giant the German physicist replied "no ... Maxwell is my giant" (paraphrased). Kudos for mentioning Oliver Heavside who, alongside Charles "Proteus" Steinmentz form the greatest Electric Engineers in history. What's surprising about Heavside is ... he wasn't an engineer - he didn't even have a bachelor degree in anything. A great math tinkerer he found (but did not prove) the Laplace transform for the step and impulse functions. It was the Nabla operator (the upside down triangle) another of Heavside's inventions - the one that made it possible to get the 20 equations and turn them into only four.

[@susilgunaratne4267]

Of course, Heavside was a original & out of the box thinker, his lack of academic qualifications had been a help for him to think that way.

[@krzysztofciuba271]

@@susilgunaratne4267 Yes, Now I see. From his X'=X x (gamma factor = now Lorentz), to calculate the Field in a moving system, one gets... (A.Einstein) relativity relations for distance and time!

[@danielturgeman8220]

its ridiculous to call Einstein 'the "German" physicst'. He had to flee Germany because he was a Jew. They wanted him dead. So its really not appropriate to title Einstein "German". Germany should receive no prestige for the Jewish scientists they wanted to exterminate at that dark hour.

[@JimTempleman]

I knew Faraday liked to draw pictures, but I hadn't learned about Maxwell's models. Thanks for that wonderful lesson, filling in the details & pointing out how long it took to be appreciated!

[@arjunsinha4015]

Maxwell equations always fascinates me because just imagine I am watching this video right now just because of this equation

[@quantverse1294]

Glad to hear it :) Maxwell is indeed underrated.

[@davidcabreramartinez4892]

Not really

[@frankdimeglio8216]

​@@quantverse1294The following solves what is the coronal heating “problem”. The following explains the fourth dimension AND the motionS of WHAT IS the Moon. Gravity/acceleration involves what is balanced inertia (or inertial resistance) consistent with the fourth dimension, TIME, time dilation, AND the equations F=ma AND E=MC², AS SPACE is (CLEARLY) electromagnetic/gravitational ON/IN BALANCE. In fact, WHAT IS E=MC² is taken directly from F=ma; AS TIME dilation is ELECTROMAGNETIC/GRAVITATIONAL ON/IN BALANCE. This explains the supergiant stars AND neutron stars. The stars AND PLANETS are POINTS in the night sky. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. The fourth dimension is consistent with F=ma, WHAT IS E=MC², TIME, AND TIME dilation. INDEED. I have CLEARLY solved WHAT IS the coronal heating “problem” !! WHAT IS E=MC² is consistent with complete combustion. I have CLEARLY proven WHAT IS the fourth dimension !!!! Two AND three dimensional SPACE are BALANCED in accordance WITH WHAT IS THE FOURTH DIMENSION !!!! (INDEED, consider WHAT IS THE EYE !!!! Great.) Now, generally consider what is sphericity !!!! Great. (Also consider what is a galaxy.) Magnificent !!!! Gravity/acceleration involves what is balanced inertia (or inertial resistance), AS the rotation of WHAT IS the Moon matches the revolution; AS WHAT IS E=MC² is taken directly from F=MA CONSISTENT WITH WHAT IS THE FOURTH DIMENSION; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE !!!! Absolutely fabulous. By Frank Martin DiMeglio

[@mikeottersole]

No. You are watching this because Maxwell, along with lots of other smart people, figured out how to use electricity. Which we still do not understand.

[@berniv7375]

@@quantverse1294 Totally agree. Maxwell was a giant in mathematics.

[@FabioLima-pc2dk]

At 5:00, there is an error: clockwise curl is negative.

[@bowlineobama]

I noticed that too.

[@joem8496]

Several errors throughout

[@vynderma]

I was just going to say that.

[@bledlbledlbledl]

There are also places where the narrator says "electric" where the text-label says "magnetic"

[@joem8496]

@bledlbledlbledl yeah it's all mixed up but still a really cool video

[@FranzBiscuit]

Excellent video. I had no idea just how brilliant really Maxwell was in developing his theory of electromagnetism. (Such a humble man, too!)

[@douglasstrother6584]

"When we turn our attention to the general case of electrodynamics ... our first impression is surprise at the enormous complexity of the problems to be solved.", Max Planck (1932), quoted at the opening of Chapter 15 "General Electromagnetic Fields" in Andrew Zangwill's "Modern Electrodynamics".

[@danielb028]

At 10:21 when you mention the displacement current, I think you are mixing up the displacement current (which is the "change" of D) and the electric current density J. There is also some mixed terms in the text in this minute.

[@VanWarren]

it was Heaviside that cleaned up Maxwell’s equation into their modern form. They were a mess before.

[@JimTempleman]

Clearly they had to be made heavier on one side.

[@KarlWork-n3i]

True - the vector calculus was not developed enough. Cross and Dot Product were separated and Convergence was given a minus sign and became Divergence.

[@MichaelKatzmann]

Heaviside dropped the potentials (deeming them redundant) and used (what is now the familiar) vector notation. He was criticized for using this vector notation rather than Hamiltonian quaternions (which now are seldom used). Curiously enough potentials had to be brought back for quantum electrodynamics (QED).

[@mntlblok]

@@MichaelKatzmann Somebody finally mentioned quaternions. Not that I understand *any* of this stuff. 🙂 "Kathy Loves Physics" is great for getting the history. Had read before that Maxwell had approached it from fluid-like waves, but had no idea that it was anything like this ball bearings stuff. Amazing.

[@EfficientEnergyTransformations]

Having read Maxwell's original papers, I can say that the equations ( 20 of them ) were not mess, but very consistent, and very detailed, representation of the properties of the electric and magnetic fields world, but using quaternions. It is true that they are not easy to read in its original form, and this is why, till the advent of Heaviside's rewriting, very few physicists understood what Maxwell theorized. Oliver Heavisde (a self-thought telegrapher) vision and understanding of Maxwell original equations, made him to rewrite them in the form we know today, for the sake of abstracting the detailed complexity and unveiling the picture they represent as the dynamics of the fields.

[@cweaver4080]

Maxwell is reputed to have used a silver hammer as an integral part of his experimental apparatus. Whenever another physicist disagreed with him or pointed out a problem with his maths, he would creep up from behind and...

[@backstrapped]

Great video. Always good to be reminded of Maxwell’s contribution. Hertz should receive just as much credit. He also discovered the Photoelectric Effect.

[@danblanks3190]

Excellent summary. Maxwell was amazing, a man decades ahead of his time. But let's not forget the man who first thought up the concept of fields, Michael Faraday. His genius wasn't in mathematics but rather in an instinct about how the universe works that was downright supernatural. Fortunately, Faraday lived long enough to see Maxwell vindicate his field approach to electromagnetism.

[@zachboschbird]

such a comprehensive video now i understand the equations even more

[@-danR]

I just wish there were an actual narrator though, and not TTS.

​@@-danRThe narration seems pretty ok to me. If it's TTS, it's quite good.

[@inflivia]

To be clear, Maxwell did not know the currently accepted velocity for the speed of light. He knew it was on the order of 3x10^8 m/s, but that's it. The only way to make Maxwell's equations output an accurate numerical value for c is to use measured values for permittivity or permeability. There are no closed form mathematical expressions for c, permittivity or permeability.

[@tomaslysonek2239]

Nice video! You should really credit the visuals by 3b1b right on the screen though, as an act of media honesty.

[@F.E.Terman]

So happy you mention Heavyside! By the way, around the 14 minute mark, the curl equations: both the narrative and the graphics are wrong, mixing up terms, but in different ways. 😮

[@martincohen8991]

Around 10:00 there are two places where magnetic should be electric.

[@bowlineobama]

I noticed that too.

[@JeffMTX]

Yep

[@irinamonich1895]

The analogy between the electromagnetic field and fluid is fascinating, even if the parallel turned out not to be exact.

[@sameranbanerjee1997]

One of the best coverings of EM Theory on KZbin! Amazing! ❤

[@martinsanchez-hw4fi]

5:05 the counterclockwise ones are shown as positive, contrary to what you said

I think the animation is right.

[@SampleroftheMultiverse]

A mentor of mine compare my quantum model to Maxwells mechanical model. Your video is the first one that I have seen that goes into detail about the beginnings of his work. Hope you don’t mind if I post my model link in my next comment. Hopefully I can post my supporters essay in another comment also.

Ha, I don't think your mentor meant that as a compliment?

[@SampleroftheMultiverse]

All models are wrong but some are useful.

[@maxheadrom3088]

Excellent concise video, Mr. verse! 11 out of 10! Great explanations about curl and divergent, btw!

[@OzGoober]

Excellent video. The ability to look over a lifetime of work and see how Maxwell at his end, could be so doubtful, is a beautiful tragedy of human genius.

[@philoso377]

Page 10:00 displacement current is a precursor for, 1. For electric charge to be stored in an ambient vacuum-space and 2. can also polarize the vacuum-space by an alternating polarity charge by an antenna.

[@philoso377]

This presentation is the best of its kind I have encountered. Thank you.

[@lazaraza]

The most astonishingly crystal clear explanation to the EM phenomena I've seen, thank you! Essentially, there can be no static sources of •B.

[@pompeymonkey3271]

Thank you for taking me through some of the thought processes that Maxwell probably took. I remember a lecture about his work, as a physics undergraduate, being so impressed that I just had to put my hand up and say "He was a clever bastard, wasn't he?". The professor did not disagree. :)

[@niko5514]

This is the best video to the Maxwell equations I have ever watched. Great job!

[@BreakingphysicsbeyondtheSMOPP]

Thanks this makes so much sense. It corresponds with the Theory of Everything which proposes that indeed the vortex model is correct but not arrived at by Maxwell's equations it was developed completely independently of any current models yet it concurs and unifies GR QM and Maxwell's Equations, that these vortexes move through an aether inside an extremely elastic network of pipes. The momentum twists the fabric creating what we detect as particles. Maybe you can appreciate that mathematicians are being irrationally harsh in their dismissal of it because all the detail in mathematics have not been finalised. Given it is only 5 years old and proposed by an interpreter, an interpreter who looked at the current data and said almost all current interpretations are wrong. It unifies GR, QM and Maxwell's Equations into one logical framework model. If you have colleagues currently involved in research please pass them the simple experiments. Here is one in this 1 minute video. With lots more experiments to build on this if it works. There's a lot of people talking about physics beyond the standard model but only testing within the standard model and very hostile to models outside the standard model, hostility which makes no sense so here's a very very simple test for physics beyond the standard model the ToE is linked kzbin.info4KH2_c94syk?si=TdnnrkzPgu4Zzq1A l

[@michaelabramowitz5264]

If only my physics education had been as clear as this. Intuitive understanding at long last. Thank you.

[@dcorgard]

I believe Wilhelm Weber had figured out the speed of light being connected to EM before Maxwell, I think it was in 1851. At least he showed 1/sqrt(mu_0 * epsilon_0) = c. There are supposedly some experiments that are to be going on soon to see if Weber's EM equations are the actualy equations, with Maxwell's being a specific subset. If this is the case, it opens up a LOT of strange possibilities. (See Dr. Assis from Brasil)

[@mattlast4093]

that picture of Faraday in a Christmas lecture.........wow

[@HenryJames-q6t]

Really good explanation of the historical significance of Maxwell.

[@clemensvorbauer1183]

thank you for this great video! Just a little remark: maxwell actually didn‘t have the mathematical means of vector calculus at his time, so he neber wrote his equations in this form as you state at the beginning…

[@elyepes19]

Thank you! Great vid, notice that you miswrote at @9:59 "The curl of the magnetic field (E) is proportional (to) the change in the magnetic field (B)" it should be instead "The curl of the Magnetic Field (B) is proportional to the change in the Electric Field (E)"

[@quantverse1294]

Yes, you are right. Sorry for the typo.

[@ND-im1wn]

Bravo, you did a tremendous job at presenting these concepts and you clearly did a lot of research beforehand. Thanks for this very interesting video!

[@michaelblankenau6598]

Very informative and well presented.

[@iangreenhoe6611]

What’s even cooler is that these equations can be turned into a single equation via STA (a type of geometric algebra).

[@kyoteecasey]

Great video. 😊. The slide explaining how his works is the master prototype for modern theories would be good at the start of the video maybe idk

[@michaeljames5936]

Very informative. Thank you.

[@hariharansankaran9012]

Superb video. Provided the missing parts.

[@denniswilson631]

0:05 - Actually, that was Heavyside.

[@kricketflyd111]

Absolutely beautiful ❤

[@frogandspanner]

11:30 JCM had hitherto built on intuitions - which are the foundations of the invention of hypotheses. He reached the point when these intellectual crutches were no longer required, then moved to the abstract domain. That is the scientific process.

[@EfficientEnergyTransformations]

The EM wave as generallyrepresented @13:30 is incorrect. The highest rate of change for the E field dE/dt is when the wave move from 0 to any value (an infinite rate of change) and this should create the biggest magnitude of curl(B). On the opposite side, the lowest dE/dt is when the electric wave is in (around) its highest point, and at that pint the curl(B) should be the smallest. Of course, the EM wave would require quite some change in the wave presentation dynamics like expanding and contracting swirls sharing common axis, for that to be the correct 3D wave representation.

[@kiranadhikari4192]

Kelvin's knot theory looks lkke string theory.

[@JimTempleman]

An irony in many ways.

[@johnc3403]

@@JimTempleman knot!

[@heroicboy3668]

Exactly

[@joem8496]

It's knot string theory

[@jimfarmer2499]

And now, gentlemen, having completely elucidated the nature of the fundamental energies of electricity and magnetism, let us turn our attention to another fundamental energy: Chi. The effects of Chi are physical and detectable, as for example by before-and-after X-ray images of bone structure and by ultrasound images of tumors being treated by practitioners of Energy Medicine, which involves the control of Chi flow by intention. Yes, it is real, and it's effects can sometimes be felt as well as observed.

[@SamMackrill]

Great video. A couple of minor errors in there where you confuse Electric/Magnetic e.g. 10:07

[@foxtrot8244]

Nice Explanation , BTW at 10:09 there is a mistake in the line. Curl of Mag. Field is proportional to Change in electric Filed, Correct if Possible.

[@philoso377]

Page 0.15 depicts radiating electric field out of a mathematic model have misrepresented Maxwell’s ideas. If the highlighted sphere represents an origin point charge of fixed polarity, there will be diverged e-field in all 3D space above and below the origin of x,y,z planes, and not as presented in 1.5D with alternating polarity with 50% vectors eliminated ahead of the displacement. If the sphere is positive charge it’s displacement in space cannot induce polarity change, and only magnitude change.

[@saultube44]

Maxwell was actually Max-Well: Maximum Wellness for Humanity. Thanks Sire

[@bjw0007]

Small correction - a clockwise rotation is negative, counterclockwise is positive per the right hand rule

[@dougr.2398]

Maxwell did not use curl or divergence. Those concepts were developed later, however Maxwell had all the components of them identical to the expanded and detailed equations

[@trevorbates8972]

I think you will find, at the end of the day, that the higgs-field is a fixed, imploding force, derived from solar blobs (stars) of swirling and crashing plasma hurtling through a high-speed universe. The slightest hint of exposure of such a hole will have plasma snatched into that higgs as neutrons. A subsequent pulse would pull more plasma as secondary atomic particles, and a third pulse electrons...all configuring themselves, according to the pulling and pushing forces emanating from the now, bunged up higgs.

[@Pedritox0953]

Great video! Peace out

[@Herzeleydt_Diesentrueb]

0:00 This form of the equations were brought by Oliver Heaviside.

[@jespervalgreen6461]

That's very nice. Thank you. Laplace's name is La-place, not lap-lacen; and on the whole I think it is just a good idea to learn the names, and how to say them, of the people you're going to mention. But very nice video.

[@filippomagaraci5802]

@5 min clockwise and counterclockwise in the speech are swapped compared to the animation. Which one is correct? By looking at the hands of a clock, clockwise means a circular motion that moves a vector aligned to the Y axis (upward) toward X axis (rightwards)

[@dcorgard]

Come on! Inaccurate information right off the bat! Those 4 equations are due to Oliver Heaviside, who took Maxwell's original 20 equations and reformed them into the vector notation in which we are now familiar. But you do mention this later, however I think it would have had a bigger impact if stated immediately.

[@RockBrentwood]

Actually, it was Maxwell who combined his equations into vector form - in his treatise. Heaviside produced equations more similar to those seen in the 20th century, but not equivalent, either (neither Maxwell's nor Heaviside's are equivalent to 20th century form). Moreover, Maxwell's equations *explicitly* involved the scalar and vector potential, which Heaviside (wrongly) took out and ignored, and Heaviside's involved non-zero magnetic current and charge densities (which is why he couldn't have the vector or scalar potentials). So, it's actually Maxwell's which are closer to "modern" form, while Heaviside's represented a step backwards.

[@eldunari6676]

I thought the thumbnail was a ball bearing for a second, before I read the title

[@anthonyconnelly7220]

Nice 3blue1brown animations

[@retrothink]

Thank you very much.

[@msf60khz]

Really enjoyed the video. Did Maxwell know how to create an EM wave - what is the thinking on this please? I realise Hertz did it experimentally, but I think Rutherford was first to suggest that an accelerating charge is required.

[@JeffJohnson-gq1yl]

Errors expressing Ampere's law @ ~10:00

[@user990077]

at 10:03 the diagram has E and B in the wrong spots and the sentence is wrong. It should say "The curl of the magnetic field (B) is proportional to the change of electric field (E) which is how he says it despite what the graphic says.

[@Darthvanger]

There's nothing weird in Maxwell's model: electrons spin in the atoms, thus every atom is a tiny magnet. This is the classical explanation, isn't it?

[@raycar1165]

I had high hopes for this video… Unless I missed it there was no mention of quaternions or æther. Seems this is the commonly accepted version of history not the hidden story. Much ❤ Love 🌏🌎🌍☯️⚡️ Terra 🌞 Pax

[@icebluscorpion]

Heavyside butchered Maxwells equation from 20 to 4 equation. No wonder that many people can't explain certain phenomena xD

[@PrashantNanda]

It's fine where you observed in latent, examples like vaccum and climate but what about express. Example like liquid and crystals. ?????????

[@KarlWork-n3i]

NOT TRUE. Maxwell had about 20 equations written using quarternions Read the brilliant book "The Maxwellions" They were eventually condensed into those four equations by Oliver Heaviside

[@ryan-cole]

The twenty equations are actually when expressed in component form, these reduce to eight equations in quaternion form. But yeah, Heaviside introduced the four Maxwell equations we know today.

[@杵渕亮子]

James Clerk Maxwells vector differential equations are comming from great Ghost and are wonderfool locking aut !...

[@billdoodson4232]

The text on screen at 10:00 is wrong, compared to the audible explanation.

[@norbertdapunt5092]

Awesome.

[@ralphmay3284]

Small mistake, at 5:05 you mention how the curl is positive if clockwise and negative if counter-clockwise. It's backwards funnily enough. My intuition for remembering this is an ever increasing angle goes in a counterclockwise rotation, therefore it's positive.

[@ralphmay3284]

Your animations are correct though, so no biggie

[@ralphmay3284]

and then at 10:10 I don't even know where to start... Electric field is E and magnetic field is B, I guess solves all the naming errors

[@Zbezt]

He woulda discovered more through octogons just saying it explains spin up and down

[@rclrd1]

I think you meant octonions?

[@Zbezt]

@rclrd1 ehhh potatoe potat-o a simple try angle works wonders if you get it just right

[@frankdimeglio8216]

What is E=MC2 is taken directly from F=ma consistent with what is the fourth dimension, as the stars AND PLANETS are POINTS in the night sky. Consider TIME AND time dilation ON BALANCE. By Frank Martin DiMeglio

[@dilippunekar6022]

🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉

[@fredbloke3218]

Like Newton and Darwin's concepts Maxwell's seem so obvious you wonder why they were not developed centuries earlier.

[@AndroidGbot]

Anyone else look at that second Divergence pic after the sink example, and 🤔 think "Why that looks like a visual description of universe expanding forever, and black holes in a way" or was that just me

[@victorfinberg8595]

impressive

[@RuslanKhamidoullin]

Великолепно!

[@drancerd]

That's not Maxwell real equations.

[@user990077]

Diagram is messed up at 10:21 also.

[@DCDLX]

Aha… did I spot a 3blue1brown animation here 0:16 ?

[@FriendlyCynic]

Wait, isn't QED and therefore EM an emergent property of QCD?

[@chrismaxwell9318]

why the advert to join church on a video about physics lol

[@PrashantKumar-r6k]

Bhola = Shankar= shiva = Mahadev= Rudra= each word has set meaning.Bhola for example is SIMPLE.DRESS LIKE PRIMITIVE HUMAN

[@MikeWiest]

Wow, that atomic vortex idea from Kelvin is pretty darn close to the spin 1/2 electron and the other irreducible representations of the Lorentz group that are the elementary particles!

[@pandzban4533]

Yeah, but nobody to this very day is able to explain why two permanent magnets attract or repeal each other. We are still within a realm of invisible fields and forces. Pure magic.

[@jenko701]

Heaviside formed the shape we know now .

[@mygreneyhyportnex4182]

1Darwin=0.01Maxell or 100Darwin=1Maxwell, in fact almost 100Anything < 1Maxwell

[@asjordan0yt]

10:02 - the graphics do not match the narration and further on, too.

[@tharunragumar4850]

thank u

[@EnergyTRE]

Nikola Tesla greatest achievement. Proving a magnet field is moving. You forgot to mention the Æther the known force that shapes existence. All those named you mentioned were not atomists.

[@jaybingham3711]

1:08 "This is how electric current was discovered." Um....no. Not true whatsoever. I believe you intended to say 'Galvani discovered electric current...was involved in the firing of muscles.'

[@RobertLeitz]

Look at "The Rainbow" as "A Gentle Pendulum Clock"... Green Arrow In Or Down.. Orange Arrow Up Or Out.... "Yellow Is The Tick".... SpaceX Launch Speeds Up The Pendulum.... "Squeezes The Rainbow Together"... Green Goes "In" The Engine.. You Can Only See Orange "Out".. Take Care...Bye... "Mechanically"..??... Green = BTDC...Yellow = TDC..Orange = ATDC.. The Rainbow Fires On All 3... But when you "Speed Up The Fire Engine"..??.. You can only see it firing on 2..Yellow/Orange.... That's why you won't see Green...??... In a "Fast High Energy Release"..... Take Care...Bye...

[@JrgenMonkerud-go5lg]

No, we don't take for granted that electric and magnetic fields can't be reduced to something else, thats all on you man. Why would you assume that? There is no good reason other than difficulty to assume such a thing..