This thermal motion is essentially random, and the electrons constantly scatter off the nuclei every which way, so it cancels out and doesn't create a net current.

So, it's less than the electrons gently move under the influence of an electric field, and more that it introduced a slight bias in the existing thermal motion.

E: To clarify in case it may have been unclear, this is unrelated to the speed of propagation of the electric field, which as the article says is the speed of light.

The mean distance they move in a copper wire between collisions is about 0.00000004 meters. At 100 km/s it would take 0.4 picoseconds to travel that distance.

https://en.wikipedia.org/wiki/Golgi_apparatus

Similarly, organelles group related process together. So for example DNA related proteins are in a nucleus not inefficiently bouncing off the cell wall.

Which helps explain why mitochondria were so beneficial. Keeping a bunch of related machinery all tightly clustered together it makes more efficient use of each individual protein and can quickly replace anything that gets damaged. ATP however can diffuse through the cell just fine because so many processes use it that extra copies isn’t a major issue.

And yet we know it’s mostly just empty space. I’m assuming it’s more because of the electromagnic force being particularly strong at those scales rather than a straight up “collision” right?

Atoms aren't really empty. They're electron clouds with an extremely dense core of protons and neutrons, but the electron clouds are what we care about.

To add a bit of a complication, if two particles that have mass, even one as tiny as the electron, come closer together than some minimum, general relativity predicts that they would collapse into a (really really tiny) black hole. Of course, we don't know how and if general relativity really works at this level, so the relevance of this is unclear.

You can even take it up a level and say that interaction events are the only things that really exist. That's more or less what Copenhagen QM boils down to. It is not at all a given that "particles" even exist between interactions.

Intuition insists that if something happens here and something apparently related happens over there and you can move here and there around to make a line or curve, then something physical is moving between here and there.

But actually - no. Not necessarily. All you have are ghost traces of an apparent chain of causality. And you can play with those traces experimentally to make them do incredibly weird shit in very surprising ways.

I'm so tired of this. If atoms are "empty space", then there's no such thing as non-empty space, which makes the concept meaningless. Electron clouds have all the properties we want from non-empty space, mainly excluding other objects made of non-empty space, so let's just admit that's what non-empty space is and move past this pseudo-profound silliness.

No, it does not. It illustrates that the portion of an atom that strongly scatters alpha particles occupies a small fraction of the atom's volume. Asserting that alpha particle scattering is the only correct definition of the threshold between emptiness and non-emptiness is an awfully strange position to take.

When interacting with other electrons at energy scales relevant to human life, i.e. maybe ten electron volts and down, an electron cloud is somewhere between solid (core electrons especially in heavy atoms) and squishy (valence electrons). Give a rock the ol' "I refute it thus!" and your toes will report that that rock's electrons are quite competently occupying their space.

Ask an alpha particle at nuclear energy scales a million times greater, and that electron cloud is like a swarm of gnats to a speeding car. The electrons only interact with the alpha electromagnetically, and it takes another object that interacts through the strong nuclear force to really bother a nucleus (most of the time).

Ask a neutrino, and it will tell you that all the nuclei in the Sun are but a wisp of fog.

This is a good example of how approximations valid in one regime fail in another but are not therefore useless. Rutherford's experiment reveals that there is more going on with matter than what can be probed by fingers and microscopes and chemical reactions, but it in no way invalidates those other observations.

https://www.youtube.com/watch?v=tMP5Pbx8I4s

And with this, there's no empty space in atoms, as the vacuum perturbations from each particle spread out to infinity, so inside the atom there's more energy in those perturbations than outside - the space is less empty inside than outside.

Either I'm going schizo or I should read some real books on the subject.

As I understand it, the idea in the video is that if vacuum can be seen as non-linear elastic medium, then with the right functions for elasticity and stress, you can create conditions where EM waves at high enough frequency will hit the "sweet spot", a local minimum, where the energy gets confined in space by those non-linear properties, and can't leave without supplying additional energy. And such confined energy seems to behave like you'd expect particles to.

Again, I am not a physicist, so I'm probably wrong in understanding what half of the words I used above mean. But I do understand the idea of multiple forces creating semi-stable states that are "energy traps". For instance, the balance between electric repulsion vs. attraction from strong nuclear force is what defines how tightly bound is the nucleus of any given atom (aka. the "nuclear binding energy"). The nucleus can't expand or split apart, nor can it contract, unless you supply additional energy. When you do - say, you hit a large atom with high-speed neutrons to break past strong force attraction, or smash two small nuclei together at high speeds to overcome electric repulsion, the other force takes over resulting in a rather spectacular release of energy[0] as matter finds new stable configuration.

So I feel the idea here is similar, but with stress and elasticity in place of strong and electric forces - if there's enough energy propagating through some space, the wave gets trapped in a spatially-confined region instead of dispersing into the medium.

--

[0] - https://www.marketbusinessnews.com/wp-content/uploads/2014/0...

That said, I don't remember the orders of magnitude here, the relevant question being how cold "room temperature" is with respect to the Fermi level -- a quick Google suggests quite cold, in which case the Fermi velocity should be a very good approximation.

In which case, it's interesting to realise that the motion of the electron gas comes mainly from Pauli exclusion rather than thermal noise! It's not a result I would have expected.

This is pedantic because there's practically no difference. But just to be pedantic, it's not the speed of light and I'd argue it's not usually even close to the speed of light. In communications we are talking about anywhere from 60% to 80% the speed of light through most mediums.

I was thinking of using a high-frequency trading example, but here's a case that's a bit more normal: stadium concert audio for a live band. Stadiums are big enough that you need to deal with latency issues for audio, because the back of the venue will get its audio a bit later than the front of the venue (assuming the sound is wired so the board is in the front of the floor and no adjustments are made). That is obviously disconcerting to the audience. Adjustments usually are made to handle this problem.

Then were somehow able to turn the light bulb on and apply a charge to the that rod at the same time. While also having a detector that can sense a photon and a change in electric field some equal distance away from the bulb and rod.

Then the photon (from the bulb) would reach our detector before the detection of the change in electric field (from the rod)?

Let's suppose the medium is just plain air, and not particularly humid.

Overall the picture is like this:

- massless particles like photons travel at speed c in empty space, in a straight line

- massive particles like electrons travel at a speed slightly less than c even in empty space, in a straight line

- inside a medium, any particle traveling in a straight line will quickly bounce off/be absorbed and re-emitted in a new direction because of some field given off by another particle; so, the average speed at which particles actually traverse through the material is lower than c. How low depends on properties of the medium, mainly how dense it is; for copper and most metals commonly used in electronics, this varies between 60-80% of c.

- When applying a potential difference to a metal wire, the electrons which normally are moving at speeds very close to c in the empty space between atoms in random directions (amounting to an overall speed of 0 along the wire) will start collectively moving in the direction of the potential difference (towards the positive node), at a very low average speed called "drift speed"; this is caused by their normally completely random bounces now being biased in the direction of the electric field;

- However, the current in the wire (the EM radiation) moves extremely fast along the wire, at the same speed that light moves (on average) through the wire. You can think of this as being caused by photons (since EM waves are photons) moving much more easily than electrons through the wire, simply because they don't have a charge of their own and so don't get caught so easily by other atoms as electrons do.

So you have 5 speeds relevant to this: the speed of light/photons/EM waves in vacuum (c), the speed of an electron in vacuum (very close to c), the average speed of all electrons in a metal wire without any electric potential (0), the average speed of all electrons in a metal wire with an electric potential (drift velocity, very small), and the speed of EM waves in a wire (60-80% of c in typical conductors).

Edit: one more note that complicates this picture, but the EM waves in a charged wire don't really move inside the wire, or not entirely - they move mostly around the wire - which means that their actual speed depends not (just) on the material from which the wire is made, but also the insulation outside the wire. That is, the EM field will propagate a different fraction of c for a copper wire than for an aluminum wire; but also for a copper wire wrapped in plastic versus one exposed directly in the air.

This brings me to a Veritasium video of a few years back that I didn't quite understand at the time. [1]

The claim being made was that if you connected a light bulb to a switch, with 300'000 km of wire left and right, and if the switch and the light bulb were 1 m away, the light would turn on in 1/c seconds.

But this would imply that the information travel is not along the wires, but straight from the switch to the light bulb?

[1] https://www.youtube.com/watch?v=bHIhgxav9LY

In theory the change in electric field will induce a small current in the other wire, and their magical science lamp turns on at any non-zero electricity. Whether the wires are connected or not at the far end doesn’t matter.

They never clarified how strong the other current would be.

Also, the phenomenon being discussed in the Veritasium video is slightly different, and that video sort of mixes up two things to make things more mysterious.

The simple explanation for what is going on in the video is that whenever you have a voltage change in a circuit, such as closing it with a switch, you get a tiny bit of radio waves being emitted radially outwards from that point out *.

In the Veritasium experiment, with a very precise measurement tool, they could detect the tiny radio pulse emitted by the switch at the moment it was closed, far before the main current reached the same point moving along the long wires.

The other thing he was mixing this up with is the Poynting vector, which is a mathematical object that represents the direction along which power (as in, worl, the thing you measure in Watts, not the actual current which you'd measure in Amperes) propagates in an electrical circuit. It's not clear at all that the Poyinting vector is a meaningful aspect of reality and not just some mathematical tool. It does happen to coincide with the direction that the radio waves propagate as described earlier, so some physicists do like to interpret it as a deeper, physically real, thing that is related, but you can just as easily ignore it.

Note that when I say that it's "not real", this is similar to how I would describe the Lagrangian and Hamiltonian of a classical mechanics system. It's an extremely useful mathematical tool and it predicts the behavior of the system perfectly well, and is mathematically equivalent to Newton's laws of motion. But while the laws of motion describe real direct aspects of reality, such as objects having mass and momentum, the Lagrangian doesn't really represent an actual thing in physical reality.

The above comes with a gigantic caveat: in QM, the Lagrangian and Hamiltonian correspond to the wave function, which is, to the best of our current understanding, the real underlying thing behind reality, with particles and waves and things localized being the artifical objects we introduce merely for convenience.

* This is normally completely negligible for DC current, but for AC current, where the current switches direction all the time, a relatively high amount of radio waves get generated radically put from the wires along their whole direction. This can lead to problems such as AC power lines causing significant radio interference. This is also normally described as "parasitic", since the power those waves carry is lost from the transmission line, which is designed to carry as much as possible of the power generated at the source towards the destination.

The complicating factor here is that when you have electricity flowing in a wire, the fields are generally mostly outside the conductor, not in it. That is, the signal propagation delay depends more in what you are using as an insulator around wire than the material of the wire. This has had practical consequences in the past; if you replace the insulating jacket of one wire in a twisted pair with a slightly different material, on long runs it will ruin your signal.

Is the only part that's not wrong in your post.

Photons only have one speed in empty space. They slow down when traveling through any medium other than vacuum.

> However, electrical conduction is the movement of electrons, not photons.

Electrons move because they influence each other through their fields, which are transmitted by photons. Electrical conduction happens at the speed of the fields, not at the speed of the electrons. When you push one more electron into one side of a conductor, an electron flows out the other side when the fields reach the other side, not when the electron does.

(As an analogy, consider a rubber hose full of steel balls. When you slowly push an additional ball in from one side, another ball starts to fall out of the other side as you push the first ball in, perceptually instantenously⁰, regardless of the speed you are pushing the new ball in.

(0): After a delay of (length of tube)/(speed of sound in steel)

It's only after the fields interact with electrical charges (atoms and their electrons for example) that a secondary field is induced as these charges begin to oscillate. This field will add over the original field, "shielding" an external observer from the original oscillation and apparently slowing down the propagation of electromagnetic waves.

There's a very good video by 3Blue1BRown that explains this kind of weird concept way better than I could: https://www.youtube.com/watch?v=KTzGBJPuJwM

no, not because it's every which way.

it doesn't create net current because if, randomly, net charge moves in some direction, the resultant electric field will put pressure on the random movement to bring it back to equilibrium, 0.

"Random Motion: Even without current, electrons are jiggling around at high speeds (~10⁶ m/s at room temperature) due to thermal energy. The electric field just adds a slight bias to this chaotic motion, resulting in the net drift."

- Sean M Carroll's work, in particular his Biggest Ideas in the Universe books: https://www.preposterousuniverse.com/biggestideas/

- Artur Ekert, basically the father of Quantum Cryptography has an amazing course for free on youtube: https://www.youtube.com/@ArturEkert . It's a very precise and understandable explanation of quantum computing, and some of the math that is involved with quantum mechanics.

- If you have hours to spare, watch Richard Behiel's videos on Youtube. He's like the 3Blue1Brown of Quantum Physics. His latest video on superconductivity and the Higgs Field is almost 5 hours long (!!!) https://youtu.be/DkH1citHtgs?si=-yQNYDu9TlTpE1A0 . It builds on his other videos, so I'd recommend starting at the beginning.

This doesn't happen with unpaired free electrons because their energy spectrum is pretty close to continuous.

Very not my field, but perhaps that's "all the paired electrons"? Brief ai-ing (do we have a verb yet?) suggests only some small fraction of conduction electrons form pairs, let alone all the rest.

What definitely affects resistance is the vibration of the nuclei lattice, in which thermal energy is also stored. This vibration makes the electrons more likely to scatter. This means even in a non-superconducting metal, resistivity drops as you get colder.

The special thing about superconductors is that there's a temperature where the resistivity suddenly drops to zero. (If you look up "superconductivity resistance against temperature", you'll see some graphs showing what I mean.)

I don't know exactly the details of why this happens, but it has something to do with Cooper pairs. Electrons in these states are also sensitive to being knocked out and bumped up to regular conducting states by thermal noise.

The idea of the book is that we spend lots of time teaching students various incorrect and inconsistent models for how electricity works, that also don’t optimally build intuition for working with the stuff.

The book’s remedy is to say “forget all that: here’s a wrong model that is good at building intuition for working with electricity, and if you’re not planning to go for a physics PhD, that’s much better for you than the other wrong models”

I don’t know enough about electricity to evaluate whether this was a good idea or well executed, but it’s an interesting approach.

https://goodreads.com/book/show/304551.There_Are_No_Electron...

I couldn't get through it. I got to just past the holes part.

It is written well, so might be worth a shot.

https://eukaryotewritesblog.com/2021/05/02/theres-no-such-th... crops up on HN periodically.

    “Trees” are not a coherent phylogenetic category. On the
    evolutionary tree of plants, trees are regularly
    interspersed with things that are absolutely, 100% not
    trees. This means that, for instance, either:

    - The common ancestor of a maple and a mulberry tree was
      not a tree.
    - The common ancestor of a stinging nettle and a
      strawberry plant was a tree.
    - And this is true for most trees or non-trees that you
      can think of.

Attitude I have about knowing stuff is asking if I can use it predicatively or for design. I feel that for most attempts at explaining how electricity actually works the answer is no. And the amount of torment I'd have to subject my brain to order to make that a yes is higher than I'd like.

Examiner: "What is electricity?"

Student: "Oh, I do know, I mean I used to know, but now I've forgotten."

Examiner: "How very unfortunate. In the whole of history only two people have known what electricity is - the Creator and yourself. And now one of the two has forgotten."

In that sense, we don't know what anything is. But we can still use it. And because everything we learn seems to become useful sooner or later, it doesn't pay to stop asking.

Our current BFF, ChatGPT, says the question is about "charge" in that we don't know why particles have a charge. So what is a "charge" and why? Gravity is also presented as a thing we don't fundamentally (ontologically) know about. Interesting!

And not disagreeing with the desire to keep asking, nor with the desire to find a final answer. The author of the article puts it fairly well:

We don’t have philosophically satisfying insights into the universe at subatomic scales...there’s no straightforward explanation of what a bound electron actually does: it’s not orbiting the nucleus or spinning around its own axis in any conventional sense. Most simply, it just exists as a particular distribution of an electrostatic field in space.

Every time I understood it less.

I even watched some videos where people interviewed physics professors, to explain what it really is, and the explanations only got more convoluted.

Seemingly not because those people were bad at explaining, but because if you want to explain it as correctly as possible, it just isn't intuitive at all.

https://www.youtube.com/watch?v=2AXv49dDQJw

Gravity is a thing, and we can feel it under us. But we can’t touch it, or see it.

Intuitively things that we can touch and see should be qualitatively different, but this intuition is wrong. Turns out it’s just big weak fields like gravity, and small strong fields like electromagnetism.

Sometimes, things are just hard to understand. Sooner or later students are going to have to face that, so why do we delay the inevitable?

Very few people need to know the subatomic behaviour of electromagnetic fields that make electricity work, but all of us need to know that it travels in wires and it can kill you.

I see this as well when it comes to teaching programming to freshman CS students. For some reason, we've strayed away from lower level languages like C and don't introduce the low level details until students are quite far into their curriculum. Abstracting away the details just muddies the waters in my opinion.

If you're trying to learn "class, method, extends, static, var/Integer/int, interface, abstract, virtual, different exceptions, recursion and loops, etc" having to also learn about memory is not helping and if you try to do basic pointers first it becomes kind of like spell chanting. You just start trying different combinations of * and & until it works. Partially because you're a bit overwhelmed and partially because it seems like useless knowledge.

The more I worked the more I started to appreciate subjects like operating systems, algorithms, etc but at the time of doing them they seemed too theoretical since they were way above my practical knowledge and useless to the projects I was doing. "Why would I need to know how to build a file system/compiler/etc? Why in the hell would I ever do that?"

The other aspect is that if you start with learning the theoretical side you end up worrying you won't be able to code by the end after a bit. For example you've been there for 2 semesters and while you can talk about low level subjects you've barely done a todo list/calculator/chess. If you start with the more high level things by the third semester you can definitely be working part time.

This is from the POV of doing CS to start working as a dev and not do academia.

But there is an accessible video that explains electricity pretty well. Veritasium - The Big Misconception About Electricity: https://www.youtube.com/watch?v=bHIhgxav9LY

There is one commonly used concept that requires understanding electricity correctly, and not just as a combination of waterhoses and gizmos. It's impedance, and it directly corresponds to the "controversial" experiment that Veritasium is proposing in his video. Impedance breaks the pipe-of-electrons analogy.

You would have to start with alternating current water, since "DC" water maps to DC, where impedance =resistance.

Once you've got alternating water, you can add inductance (inertia) and capacitance (rubber diaphragm tanks) and I think it all works out.

It's just that we don't have a good intuition for alternating water current so it's not a very useful analogy in that case.

One way to look at this is that there is no such thing as a hose for electricity. It cannot be confined to a conductor, even if it is also wrapped by an insulator. It is only mostly confined. And this is not some failure of materials engineering that we may overcome one day, this is just how this stuff works.

BTW, the answer in the video is 1/c seconds, i.e. one meter worth of speed of light. And the lightbulb will experience current determined by the impedance of the transmission line. Then the fields will do a full wraparound the ends, at which point the circuit will start stabilizing around the resistance of the load. It can take a few back-and-forth iterations to stabilize the current.

Sounds bizarre, right? That's why this is mostly ignored unless it can't be, for example in very fast circuits.

Sometimes its a whole lot easier to speak the truth than to speak in analogies.

We say B is electrised positively; A negatively: or rather B is electrised plus and A minus ... These terms we may use until your philosophers give us better.

Here A and B are Franklin's buddies, standing on insulating plates while one of them rubs a glass tube with a piece of, if I remember rightly (can't find the proper source), "buckskin". Then they reach out to join hands and a spark crosses the gap.

Problem is, it isn't even clear from the experiment which of A and B really was negatively charged, because it turns out the charge depends on the nature of the "buckskin" (or whatever term he used), and how hairy, furry, or possibly even leathery it was. The resulting charge could be positive or negative, depending. So he defined the terms, but didn't even clearly assign them to direction of electron flow.

Edit: the ambiguity is shown in this picture:

https://en.wikipedia.org/wiki/Triboelectric_effect#/media/Fi...

Here leather is above glass, and fur is below it. He was definitely rubbing glass with something like leather or fur, but the resulting charge depends on where in the series that thing was relative to glass.

You'd think we would understand the science of contact/static/tribo electricity by now... And yet this posted 1 day ago: "Static electricity depends on materials' contact history" https://phys.org/news/2025-02-static-electricity-materials-c...

  Historically, several studies have suggested that insulators could be ordered based on the sign of charge they exchange, from the most positive to the most negative. For instance, if glass charges positively to ceramic and ceramic does the same to wood, then glass (usually) charges positively to wood. Thus, glass, ceramic, and wood would form a so-called "triboelectric series."

  The problem with these triboelectric series, according to Waitukaitis, is that different researchers get different orderings, and sometimes even the same researcher does not get the same order twice when they redo their own experiment.

And https://en.wikipedia.org/wiki/Triboelectric_effect#Explanati...

  There are many cases where there are triangles: material A is positive when rubbed against B, B is positive when rubbed against C, and C is positive when rubbed against A, an issue mentioned by Shaw in 1914.[29] This cannot be explained by a linear series; cyclic series are inconsistent with the empirical triboelectric series.[75] Furthermore, there are many cases where charging occurs with contacts between two pieces of the same material.[76][77][47]

Uh, "tribbing" is a sexual act that women can do.

that's how i figured it out, but:

> 1965, "study of friction," from tribo-, a word-forming element in physics with the sense "friction," from Greek tribos "rubbing," from tribein "to rub, rub down, wear away" (from PIE root *tere- (1) "to rub, turn") + -logy. Related: Tribologist; tribological.

Edit: I think I found the author: https://en.wikipedia.org/wiki/Charles_Fran%C3%A7ois_de_Ciste...

His wikipedia page seems to confirm he discovered there are two kinds of electricity and named them "vitreous" and "resinous".

I can relate. This is just a quick hack to get to production, we can always rewrite it later!

Ben Franklin arbitrarily picked the positive anode as the starting point when coming up with the idea of electricity flowing, long before we had any understanding of atomic theory.

It wouldn’t make sense to just invert everything after we discovered that electrons are the actual fundamental charge carriers.

like scientists didn't realize electrons were flowing in the opposite direction, but engineers already had working electrical devices

You mean flow of charge.

My favourite thing about electricity is how the actual energy is transferred on the outside of the wires, in both the directions of positive and negative charge. Resistance is the portion of the energy that accidentally enters the wire. The energy flux inside the wires -- and on the surface of the wires -- is zero. Just outside their surface it is very high.

A capacitor wouldn't work if the energy came from its poles. No, the energy used to charge it enters from the side. This is so counter-intuitive!

That bullshit model about electricity flowing around the wires is good for generating Youtube engagement, but it doesn't represent the actual physics, makes things impossible to calculate, doesn't lead to any intuitive understanding, and makes things impossible to learn. Or, in other words, the model is bullshit.

DC current flows entirely in the wires (up to at least "parts per billion" precision), as does energy, because energy flows at the same place current flows. AC current leaks. Everybody knows that, how it leaks is well known, and there are plenty of resources to calculate almost everything around it.

I didn't even bother asking why he hadn't thought of just removing the wire altogether.

I started tutoring other kids in grade school and eventually got paid for it as a side gig later in life. If I ended up covering electronics and/or general electricity, I saw the same thing I saw as an undergrad taking EE courses: confusion. A lot of people found the situation counter-intuitive. It required extra mental labor for them. Hence, multiplied against millions of people, there's overall lost time.

And this isn't just in young people, either. Knew a guy who swore up and down that the "electron holes" really represent positrons.

Bad notation, weird syntax, poor choices in variable names, and so on, all of these are a collective drag which could be streamlined away.

Humans are more than capable of handling that minor conceptual change. Life routinely throws far more challenging changes to adopt to.

Nothing fundamentally changes because of Franklin's incorrect guess. The postit sticker goes "there " instead of "here" kind of a thing.

Certainly not as grandiose and melodramatic as putting humanity back by a decade.

> Electricity is of two kinds, positive and negative. The difference is, I presume, that one comes a little more expensive, but is more durable; the other is a cheaper thing, but the moths get into it.

And that's sort of all I need to know.

Best simple description of an electron I think I’ve heard yet. I wish we would drop all the dumb analogies. From a kid’s perspective (at least what I can recall from high school), these macroscopic analogies mislead you into thinking the laws of physics work differently than what humanity’s best models of physics actually predict.

For instance, I never liked the sense of “arbitrariness” I felt while learning about the periodic table in K-12 school. The diagonal rule. Hund’s rule. The exception to Hund’s rule. And so on. Don’t even get me started on organic chemistry. But if someone had told me “Forget about billiard balls and wave/particle duality. Our best models consists of solutions to simple and beautiful equations that are extremely difficult to solve”, then that would have made a lot more sense to me.

The author of the article describes the truth as “weird math”. I don’t think that’s necessarily the case. Unitarity is aesthetic—it just “feels right”. The correspondence of atomic orbitals to irreducible representations of symmetry groups is beautiful. Why don’t we teach that to kids? You don’t have to go into the mathematical details of group theory, but just let them know these odd shapes originate from symmetry constraints. Much better than my reaction to seeing an illustration of a d_z^2 orbital in high school. I remember thinking “What the heck is that? This subject makes no sense.”

I did a physics PhD. I still never got a really good answer to a question I asked in year-1 senior-school (11 years old, for non-Brits)… “What, exactly, is a positive charge ?” The waviness of the hands diminished over time, but it never really went away.

When you are in grade school science you are told that a car can just be modeled as a cube.

In high school you learn you can use 3 cubes.

In college you learn you can do with hundreds of cubes.

In post-doc you learn to do it billions of points with fractal levels of interaction.

When writing the text book for grade school after years in physics academia, you write:

"A car can be sufficiently modeled as a cube".

What's the next level where that breaks down?

°Though the Benjamin-Franklin-reversed-the-signs thing I learned about for the first time up-thread has me thoroughly confused. Positive charge means it... Has fewer?

Momentum and energy may feel more intuitive, but I'm not sure they really are, especially within QM.

I'm not sure if we have any deeper explanations than these symmetries.

Btw, questions formed like "What is X?" can have this kind of problem in any domain, especially if we expect some answer that is both intuitive and provides an essentialist explanation.

For instance "What is consciousness?". "What is intelligence?", "What is the meaning of life?"

What I've come to think, is that these questions come from the same type of mistake:

As any Physicist would know, the world as described by Physics and the world as we intuitively start to understand it as small children are quite different, especially at scales far removed from our senses (like in QM or Cosmology).

Humans simply doesn't have access to the full extent of reality, nor would our brains be able to do something useful with it if we had it, since we don't have anything near the processing power to comprehend it.

What we're always stuck in, is an inner world model that is some kind of rough representation of the outside world. Now let's assume the outside world actually EXISTS, even if we don't know all that much about it. Physics is just a hint of this mismatch. If we simply let go of the assumption that there is a close correspondence between our internal model of the world and the actual world, we no longer have an obligation to form strict correspondences between object within our internal simplified simulation and the outside world.

Now we're prepared for the next step: To understand that there probably is a REASON why we have this internal representation: It's there for evolutionary purposes. It helps us act in a world. Even for concepts that do not have a 1:1 correspondence with something in the Physical world, they may very well have correspondences to aspects of the world we're simply not able to comprehend otherwise. For instance, fully understanding what "consciousness" represents (how it emerges) may not even be possible without extreme amounts of computational power (the compute part may be irreducible).

Concepts like charge are similar, except that we DO (through some advanced math) have some kind of ability to build mental models that DO (perhaps) capture what gives rise to it in the Physical world.

But it still will not map onto our intuition in a way that give us the feeling of "understanding" what it "is". It kind of feels like "consciousness is an emergent property of sufficiently large scale computational system that build world models that include themselves". Still doesn't correspond to how we "feel" that consciousness "is".

But if we simply stop insisting on full correspondence between the intuitive representation of the world and the "real" (or rather, the one represented through accumulated scientific knowledge), but instead realize that the intuition MAY still be useful, we not only avoid stress related to the disconnect, we even allow ourselves to bring back concepts (like "free will") into our intuitive world model without worrying about whether it's "real".

This provides two benefits:

1) We are "allowed" to use concepts that we know are not 100% accurate representations, and even have good reason to believe they're fairly useful simplifications of aspects of the world that ARE real, but too complex for us to grasp (like QM charge for a 5-year-old).

2) As opposed to idealists (who think the inner word is primary), we don't fall into the trap of applying those concepts out of context. Many idealist philosophies and ideologies can fail catastrophically by treating such simplified ideas as fundamental axioms from which they can deduce all sorts of absurdities.

They're incredibly useful tools for thinking about things. You don't need or want QM to perform most reasoning tasks. Even MO is often overkill.

I agree though that we should lead with the truth - that these models you're being taught are useful abstractions but ultimately wrong. That each successive model brings with it more accuracy and nuance but is more difficult to comprehend.

A particular strength of that approach is that after making it to QM at the end it leaves you wondering what's next. It really drives home the point that the map is not the territory and that all we as humans can ever actually have is a succession of maps.

> Forget about billiard balls and wave/particle duality.

Actually that one is rather important. QM wave functions really do collapse. Things really do switch from behaving like a wave to behaving like a particle. This fact has significant effects on behavior.

> these odd shapes originate from symmetry constraints

Well they might fit those constraints, but can they really be said to originate from them? Is there actual cause and effect there? The answer to that would require understanding what gave rise to the phenomenon to begin with.

Electromagnetism is one of the four fundamental forces mediated by photons which are its basic quanta and is Bosonic field (spin 1) and therefore are neutral.

The interaction of these two fields is depicted via Feynman diagrams.

Macroscopically observed Electrostatic field of a charged capacitor, is mediated by the superposition of virtual zero frequency (ν = 0) photons, which are off-shell and non-radiative. Field’s energy arises from the cumulative effect of infinite virtual photon exchanges. Whether virtual photons are "real" is debatable and confuses those who prefer intuition to computation.

https://en.wikipedia.org/wiki/Virtual_particle

We'd also need to revamp some of the math, chemistry, and physics curricula to build on the quantum basis of things.

Few years later orbitals were introduced as, essentially, motion blurs formed by our little zippy guy. I approached our teacher and asked what if that 'motion blur' is all there is and that billiards ball electron is just a bed-time story. That's an adequate way to think he said. Electron mass gets more difficult to explain to school kids in this line of thinking.

Please stop teaching the history of what we used to think the atom looked like. We’ve reached the point where we spend 99% of the material teaching what we know the atom doesn’t look like and very little on what it does look like. Even this author offers a picture for what it doesn’t look like and nothing for what it does. Physicists should know the value of a good picture/mental model better than anyone else.

I challenge you to go on Wikipedia and find the article/space for the current understanding of the atom. Was that hard for you to find? Would a curious high schooler have enough information within that article/space to learn everything you now know (textbooks are too expensive and inaccessible for high schoolers to rely on, physics websites are hit/miss). Is this how you would prefer to have been taught?

That's how I finally understood that power is energy rate (Joules per unit time), current is charge rate (electrons per unit time), and voltage is energy per unit charge (Joules per electron). Voltage makes a lot more sense as the excitation of electrons; them wanting to jump gaps and go to a lower energy place feels more intuitive in that framing.

As a notable example, macroscopically electricity is totally symmetric - positive current flows the same as negative current does. There are components that exhibit asymmetric behavior but they can be arbitrarily oriented so it doesn't really matter.

But if your aim is to answer questions like "why do different colour LEDs need different resistors" or "what does it mean for something to be a semiconductor" pretty soon people will start talking about 'electrons' and 'holes' and 'band gaps' and 'depletion regions'.

Really there has been only limited success in discovering new semiconducting technologies motivated from first principles -- it's mostly intuition and dabbling and experimentation that has yielded the advancements. To some degree of course motivated by models of behavior, but it's very easy to ignore all the blind alleys that theory has led down.

Mostly you're better off understanding that semiconductors work by "magic" and knowing what the response curves look like (or building mental approximations and heuristics) and otherwise just treating things in terms of currents and voltages (and fields at the lower level as necessary).

Our analogies and intuitions are based off of our macroscopic experienced reality, this seems to be an entirely emergent phenomenon based on those strange behaviors described by quantum mechanics. If those insights ever do come, I don’t believe they’ll correspond to anything prewired into our brains or experienced in our lives, and will never be remotely satisfying.

I don't know why you'd assume that.

Euler's identity certainly doesn't correspond to anything prewired, and yet it's very satisfying.

The philosophical insights will be satisfying if they are simple and elegant. Our theory of biological evolution through natural selection isn't remotely prewired either, but that doesn't stop it from being one of the most philosophically satisfying theories we've come up with.

It's impossible for me to understate how awesome this is. And how hard it is for me to truly grok.

>It’s important to note that while the charge equalization process is fast, the drift of individual electrons is not. The field propagates at close to the speed of light in vacuum (circa 300,000 km/s); individual electrons in a copper wire typically slither at speeds measured in centimeters per hour or less. A crude analogy is the travel of sound waves in air: if you yell at someone, they will hear you long before any single air molecule makes it from here to there.

So basically electricity flows like a Newton's cradle. But this leaves one nagging question: what is the nature of the delay? This question also arises when considering the microscopic cause of index-of-refraction for light[1]. If you take a simple atom, like hydrogen, and shine a light on it of a particular frequency, I understand that the electron will jump to a higher energy energy level, and then fall back down. But what governs the delay between these jumps? And also, how is it that, in general, light will continue propagating in the same direction? That is, there seems to be some state-erasure or else the electron would have to "remember" more details about the photon that excited it. (And who knows? Maybe the electron does "remember" the incident photon through some sort of distortion of the quantum field which governs the electron's motion.) The same question applies to electron flow - what are the parameters that determine the speed of electricity in a conductor, and how does it work?

1. 3blue1brown recently did a great video describing how light "slowing down" can be explained by imagining that each layer of the material introduces its own phase shift to incoming light. Apparently this is an argument Feynman used in his Lectures. But Grant didn't explain the nature of the phase shift! https://www.youtube.com/watch?v=KTzGBJPuJwM

What governs the delay between one ball hitting the cradle and the opposite ball going up?

It's the electrical equivalent of the same thing. Specifically, electricity is delayed by the material absorbing it "elastically" for a short time before emitting it back. This is usually modeled as a capacitance and inductance on the medium.

> And also, how is it that, in general, light will continue propagating in the same direction?

It actually doesn't. It mostly follows the medium. That's why you can bend your wires and they keep working.

But if your question is why it doesn't go "backwards", they go, but there's an electrical potential there pushing your electrons on the other direction.

Sorry, its my fault for introducing light into a discussion about electric current. In fiber optics I believe they add "cladding" to achieve "total internal reflection" that somehow keeps the light going - not sure how it stays coherent though! And in electronics, I assume that the boundary of the conductor with non-conductor (e.g. air) provides a similar function. I've heard that conductors conduct almost entirely on their surface, another curious effect I'd like to undersatnd, and I'd also be curious if any applications use hollow tubes to conduct large currents and save on weight.

Electricity inside a conductor works more like a sound wave the article talks about than optical fiber. It's not coherent or directed, you have a high "pressure" on one end pushing the electrons, and they push each other forward as a consequence. There is no care about reflections (up until radio frequencies), it just moves into the direction of less "pressure" through the medium. (Even in RF, but on those the reflections cause noise.)

Optic fiber depend a lot on conservation of momentum. Electrical current has none of that. Even the reflections are caused by the "elastic absorption" of the medium, and don't behave like a collision.

> I've heard that conductors conduct almost entirely on their surface

That's not really right. Conductors conduct through all of their area, unless you have high frequencies. At high frequencies there is magnetic interaction between the electrons so they are pushed out of the conductor's center, but this is not a universal thing.

And then, in high frequencies you don't use hollow tubes. You use thin wires, insulated from each other, knitted in a way that every wire spends the same length on the middle of the bundle.

It would be worth mentioning why it happens as it's quite interesting.

From my understanding the quote is talking about electrostatic effects that occur when electrons move to fill a void/go away from a negatively charged area. Since the force that makes electrons repeal each other is very weak, I think it makes sense. But note that it mention "a single electron." Voltage deals with a difference in immense scales of electrons, so I assume the effect and speed would be different in practical cases.

So it gets tossed on the stack with all the other complex-and-unfalsifiable theories for which no evidence exists.

It might make for an amusing sci-fi plot though.

The obviousness or lack thereof is subjective, but the exclusivity is firmly established. The absolute indistinguishability of particles is deeply woven into quantum mechanics; you don't get a Pauli exclusion principle without it, for example. If the particles remembered their previous lives, and an electron that used to be tied to an iron nucleus weren't completely identical to one that used to be stuck to a carbon nucleus, all of quantum mechanics as we know it would be impossible.

Experimentally you'd be attempting to detect inexplicable single particle events above some level of rarity. You'd have access to only one side of the pair - you can't tell which one the other side is even if it's right in front of you (and it almost certainly isn't). So there's no discernible (to you) trigger for these events you're trying to detect. So you'd be trying to correlate frequency counts with bulk conditions as averaged across more or less the entire universe.

In the same vein as the God of the gaps the phenomenon could always be hiding below the noise floor.

Isn’t this a very good analogy? What’s so crude about it?