This is extremely niche knowledge and there's a lot more stuff that should be explained first. I went to grade school in Virginia in the 90s and early 2000s. We were taught that the American Civil War was about states rights, and that it was the War of Northern Aggression. I'd much rather we focus broad educational efforts on making people understand their fellow humans and try to prevent repeating the atrocities of the past than get people to understand quantum flavordynamics or chromodynamics.

You are right - I spoke out of frustration. I understand that one of the greatest joys of pure science is being able to share it with the world. I’m sure the Physics community is just as frustrated at how difficult it is to spread this knowledge accurately to a broader audience.

Anything simpler necessarily sacrifices correctness. Metaphors are great, but it's clunky to explain when the metaphor stops working or becomes actively harmful to understanding. For example, adding a 4th neutrino that is otherwise identical to the other 3 would break the Standard Model would violate anomaly cancellation, making the model mathematically inconsistent. But explaining from scratch what an anomaly is or why they need to cancel would require a ton of vague, fragile metaphors layered on top of each other, at which point I'm not sure what value it would provide.

Imagine explaining how a CPU works on the silicon level to somebody from the 18th century. It's the same problem -- it's hard to say anything that isn't the length of a full textbook, or completely misleading, or bordering on woo. I've written and then thrown away a lot of attempted explanations because of this.

But not clarity.

This is the crux of the problem. Mathematicians, and by extension, theoretical physicists are under the impression that the most terse, most technical, most "correct" (by some abitrary definition!) definition is the only one that matters, and that nothing else should ever stain their lips.

Take a tour of any abstract mathematical topic on Wikipedia. It's a travesty.

Nothing at all can ever be understood from those pages by even an extremely intelligent person who doesn't already know the topic.

Do you see the issue? You have to already understand to gain understanding... err... of a thing you don't understand, hence the need for a Wikipedia page. If you understood it, then as a "quick reminder reference" the Wikipedia page might be useful, but then the audience is a few hundred people.

There is absolutely no difference between this idiotic behaviour of mathematicians, and the insistence of English priests in the middle ages of sticking to Latin for theology. NONE.

If you argue this point, first explain to me why physics is done with Greek letters.

I bet whatever you say will be indistinguishable from the arguments made by those priests.

> Imagine explaining how a CPU works on the silicon level to somebody from the 18th century

I could do this, no problem. It would take about 20-30 hours of talking and something to scribble on, but I could do it.

I would use analogies with things they already understand, such as the hydraulic control lines of steam-powered machinery, and explain that electronic transistors (called 'valves' back in the day!) are just like the hydraulically or pneumatically controlled valves they use every day in industry. Just more of them, faster, and smaller.

See, it's not that hard.

> I've written and then thrown away a lot of attempted explanations because of this.

Try using geometric algebra instead of the mishmash that is vector algebra. Try avoiding complex numbers. Try to avoid Greek letters. Try to avoid mixing ten branches of mathematics just to shave off a few letters in an equation somewhere. Try using an analogy with things the audience might already be familiar with.

Try harder.

> I would use analogies with things they already understand, such as the hydraulic control lines of steam-powered machinery

How many people from the 18th century knew how those worked? You would be talking to an elite engineer. And even then you would first have to explain to them how you can represent numbers and numerical operations with those valves. I am pretty sure that if you take a today's elite engineer and take the time to explain him the basics correctly, he would be able to understand theoretical physics. That's what's happening in universities every day.

> If you argue this point, first explain to me why physics is done with Greek letters.

There are probably some historical reasons for that, but today it's just because you are quickly running out of latin letters in complex equations, at least that's my opinion :)

If you haven't read Eistein's "Relativity : the Special and General Theory", I strongly recommend you do.

It's a book aimed at laypeople, that requires only a basic (1st undergrad semester) understanding of calculus and vectors (not vector calculus, not linear algebra, just vectors). Yet, it's precise and correct, sacrificing conciseness to get easiness to understand - like every teaching book should.

So, no. It's perfectly possible to explain it without the bad analogies.

But the complaint that started this whole thread is "why can't physicists explain why it's hard to add in extra neutrinos to the Standard Model?" Understanding the reason requires 2-3 semesters of relativistic quantum field theory, a subject which in turn requires relativity, quantum mechanics, and classical field theory.

Seriously, any resource that legitimately explains all of this, without bad analogies, and assuming no prerequisites, would end up precisely as hard to read (or likely harder) than the ~10,000 pages of textbook people currently study. The textbooks have already been optimized for ease of learning, there is no magic way to make a hard thing easy.

Because there are not enough letters in the Latin alphabet? You could of course use words instead of single letters, but I think most people that do numeric computing would agree that the transliteration of formulas into programming language syntax using ASCII makes things less readable.

Using different alphabets (we don't just use Greek, there's also Fraktur, bold letters, etc, though physicists tend to prefer markers like vector arrows, dots, hats, ...) allows for a compact way to namespace symbols.

If I do linear algebra and see an expression like

    A u = λ v + μ w

This is a video of Feynman's answer to an interviewer asking about what and why you feel something when you put two magnets together https://www.youtube.com/watch?v=MO0r930Sn_8. It's a great description of the problems inherent to explaining this sort of thing to people. (Also, if anyone knows a video/essay/talk along these lines by a less sexist person, I'd love a link.)

Feynman managed to do this with quantum electrodynamics, in "QED: The Strange Theory of Light and Matter." That layperson book shows an inefficient yet accurate way to calculate path integrals of Feynman diagrams without any calculus, and uses the exact analogy of a clock spinning for phase. I understood it without any background in the math.

There's also four lectures on QED for grad students, which is the "formal" version of pretty much the same content, featuring math.

Why can't someone take the QED approach for the whole standard model? Symmetry groups can be explained visually. I think the physicists just can't be bothered, and/or they underestimate the intelligence of uninformed but curious laypeople.

Roger Penrose is another example of a physicist who does this right, in Cycles of Time for instance.

Feynman had a rare talent for explanation, which few physicists have. This talent is just as real as his talent for physics.

The number of family of neutrinos was deduced for the first time in LEP experiments (in the 90s, the predecessor of LHC at CERN) : It was not known before whether there were 2, 3, or 4 family of neutrinos. If you want to learn more : http://pdg.lbl.gov/2020/reviews/rpp2020-rev-light-neutrino-t... a review about this subject. In summary, the combined result from LEP experiments is N_neutrinos = 2.984 +- 0.008. If you are interested, you can see the experimental plot that shows the fit and the difference between of a SM with 2, 3, and 4 neutrinos : https://arxiv.org/pdf/hep-ex/0509008.pdf Page 36 Figure 1.13, the data points are in red with their error bars (extremely important to pay attention to them and their size !) and the curves are the SM prediction for 2, 3, and 4 neutrinos.

In my opinion, this is a very nice plot that shows how different is the SM with 4 neutrino. This is why the SM is with 3 neutrinos and not otherwise, it is because the experimental data that were used to infer all the free parameters of the SM. The last ones were related the Higgs boson, and now everything is fixed.

To accommodate a 4th neutrino, then we would need to go beyond SM.

It is logically possible that the neutrino of the fourth generation is very heavy. In that case

- the constraint on the number of neutrinos from collider experiments is relaxed because the ultra-heavy neutrino's contribution to the observable would be extremely suppressed (because the collision energy was too low to be sensitive).

- the cosmological constraints are relaxed because the heavy neutrinos are already frozen out by the time of the electroweak phase transition in the early universe.

- the mixing constraints... well, right now it seems that the mixing matrix between the generations is unitary---there's no "leak" into a fourth generation. But our experimental precision is mediocre because precisely measuring the mixing is difficult (though there are experiments under way). It is also logically possible for there to be a fourth generation but that the neutrino doesn't mix at all---its mixing with the lighter neutrinos is precisely 0. While it's perfectly possible logically, we physicists do not like this kind of "fine tuning" without some explanation of how it could happen. In the SM the neutrino masses/mixings are input parameters, not things determined dynamically---they are axioms, so to speak. So any explanation of the mixing being really small would need to invoke more beyond-the-Standard-Model physics than "it's the same but there's a fourth generation".

The short answer is, it doesn't. The Standard Model, AFAIK, does not rule out the existence of more neutrinos (or more generally, more "generations" of leptons and quarks than the three we know); there is no hard and fast limit in the math of the Standard Model on the number of generations. So I think the article's statement is, if taken literally, false. (Unfortunately, this kind of thing is common in pop science articles, even in magazines like Scientific American that used to be better at avoiding such things.)

I think a better way of stating our best current knowledge would be that we have only observed three generations, and if a fourth generation does exist, all of the particles in it would have to be very massive--massive enough to have not been detected in any of our current experiments up to and including the LHC. Most physicists appear to think it's unlikely that a fourth generation exists given those limits, but I'm not aware of any theoretical argument that definitely rules it out.

Quantum mechanics attracted a lot of mystical woo early in its development, because it was so deeply unfamiliar from classical physics, but we've been at it for over a century now. We've moved way, way past the weirdness of quantum erasers and other examples that get promoted in pop science books. As I said, that doesn't mean all of the questions are answered, but a lot of questions are answered. You just can't understand the answers by expressing them in purely conventional terms, as pop science books try to do.

So physicists don't come out of school wearing pointy hats and feeling like the keepers of arcane knowledge. They can do quantum mechanics and apply it. That's not forbidden knowledge. It just takes work. Nobody ever promised you an understanding of physics from comfortably reading about it at a middle-school level, any more than you'd expect to learn dishwasher repair or glassblowing just from breezy introductions to it.

The information is accessible, and lots of "Quantum mechanics for dummies" books can actually give you a good handle on it. Yes, it takes math, but not very advanced math. Yes, you have to learn a new language, but that's to be expected. Novel ways of viewing the universe require new ways of talking about it. It's right there, publicly accessible.

No, they don't in fact. Most of them even admit that they don't understand it at all, yet it works for them so far, except when it comes to the precise origin of gravity. Some say that the reason why quantum mechanics and gravity couldn't be reconciled until today, because nobody on earth truly knows how exactly quantum mechanics works yet.

An average child can easily be beaten in chess by the average adult. An average adult is easily beaten by the average professional chessplayer. The average professional chessplayer is beaten by the grand master easily.

Now the grand master physicists are the grand masters and professionals, playing against a child. The standard model is a grand-master level of chess play and we're the children moving the figures somewhat randomly. It is likely that the average person is simply not on the level of expert knowledge in the field to even begin understanding the strategy.

In the process of learning it myself I tried to do my bit towards that by writing a little game. Sorry for the Java

http://tropic.org.uk/~crispin/quantum/

I'm not the only one

https://quantumgame.io/

https://github.com/stared/science-based-games-list

I do share your frustration with the mysteries of the Standard Model (and hope to understand them one day)

Still not going to install anything Java, but I hope my comments were helpful!