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.
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.