[steamer25]

Prior to computer-generated 3D animation, I can imagine it was very difficult to float and spin vector-arrows in mid-air with enough accuracy to show what goes on without having to resort to reams of explanatory paragraphs.

Eugene Khutoryansky is something of a lesser-known 3b1b that's more focused on physics than math. I found his animations very helpful for building intuition around Maxwell's equations:

https://www.youtube.com/watch?v=9Tm2c6NJH4Y

[s1artibartfast]

I wish most explanations wouldn't skip over the fact that field lines arent real, and just a tool to graphically depict what is going on. Statements like the following gets the causality entirely backwards.

>the strength of an electric field depends on the number of electric field lines.

[timeagain]

It’s like saying that rain falls where there are blue regions on the weather map :)

[psuedobrain]

I think the question of whether field lines are real is more of a philosophical (of physics) question so it usually falls outside the scope of introductory material on E&M. However, some texts like Purcell and Morin do kinda take a stance on whether fields are real: "since it works, it doesn’t make any difference."

[azalemeth]

Very much this. The (standard model's) "answer" is that the four vector potential probably is the "most real" and we're all just excitons along for the ride.

At some point the definitions become almost circular and opinions about what it fundamental have shifted a bit over the centuries. The cgs system of units -- which differs profoundly from SI in the treatment of electromagnetism -- was associated with those who viewed D and H rather than E and B the most fundamental. I'm quite happy with the level of theory used being appropriate to solve the problem at hand. There's always a bit of wiggle room around exactly what that problem is, however ;-)

[JohnFen]

So, a bit like how the conventional depiction of electric flow is in the opposite direction of the actual electron travel?

It doesn't matter in terms of the math (in the vast majority of situations), so while the conventional idea of electric flow is incorrect, we keep it anyway.

[s1artibartfast]

I think it is closer to the conventional view of current as the travel of electrons down a wire.

Current moves far faster than electrons. it is more similar to a wave in the ocean with the electrons being the water molecule.

As a result, and counterintuitively for most, the speed of electrons will give you a completely wrong answer for when a light will turn on after you flip a switch.

[Koshkin]

> Current moves far faster than electrons.

Current is the movement of charges. It cannot “move” faster than said charges. (Or, perhaps, you meant the electomotive force that makes the electrons move along the wire, then sure, that thing spreads pretty quickly.)

[s1artibartfast]

yes, the EM force, Field, or whatever it is called. I still struggle, mostly because I was taught a fundamentally flawed model for how electrical power is transmitted.

[nightlyherb]

Current is about the throughput of electrical charge at a specific point of an electrical circuit, while what you're describing seems to be about the latency or the speed of electricity.

[s1artibartfast]

it works for a physics test, but is also part of the problem, as it misleads and prevents conceptualization, even for simple problems.

[gosub100]

isn't that a special case of Plato's argument that "triangles aren't real. show me a perfect triangle...you can't, you can only show representations of a perfect triangle"

Your comment could be reduced to "lines arent real. show me a perfect line"

[rolph]

we can fix that.

the number of electric field lines, depends on the strength of an electric field. ,

[devmor]

Wow this video is actually great at imparting the concepts with animation.

It's a little distracting how it looks like an ad for an adult themed video game, but it's very well thought out.

[Terr_]

> It's a little distracting how it looks like an ad for an adult themed video game

Well-put: Does that demon-squid in the intro look like a Chihuly glass installation to anybody else?

Also I swear I've heard that song long ago on OCRemix.

[lumost]

I suspect something similar happens with manifolds for GR. Riemanian manifolds aren't a big deal when you contrast them to what happens inside of a DNN, but physical analogs for these structures start to break down.

e.g.

Imagine a 4-dimensional hyperbolic surface defined by the lightcone of a particular point in space-time, now imagine that this surface is stretched/compressed by the distortions of gravity. Now let's talk about equations which are only loosely tied to this surface.

vs.

Consider the metric tensor defined by this 4x4 matrix g_xz. Distance is computed as a^x b^z g_xz, now consider all possible walks from point a to c to b. Now let's show the relation between these walks and a quantity we'll call the stress-energy tensor which represents the energy/momentum density at any particular point in space, and it's flux towards any other direction in space.

The latter is a very algebraic description, which does not rely on the audience having to visualize the constructs involved. Practically, even if you get a feel for what a Riemanian manifold looks like in 4-dimensions - you'll struggle to visualize the Riemann tensor, or Christophel symbols.

[jereees]

This video is worth watching for the soundtrack alone. I came across Eugene’s channel before but somehow I missed this gem!

[Ringz]

> … for the soundtrack alone

Did I sense mild sarcasm here?