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Has anyone else (without a background in physics) kind of given up trying to understand developments in physics? It seems like the reporting is usually complete

Has anyone else (without a background in physics) kind of given up trying to understand developments in physics? It seems like the reporting is usually completely inaccurate or a metaphor at best. And that to have some grasp of it requires having a solid foundation in undergrad physics at a minimum. I'm just wondering if I'm being lazy by not trying hard enough or efficient. It's definitely not for lack of curiosity, but I also don't like to fool myself into thinking I understand something that I don't.

abeppu 5y ago
> I'm just wondering if I'm being lazy by not trying hard enough or efficient. Leonard Susskind at Stanford has a series of courses specifically aimed at helping people get up to speed in understanding modern physics. Every several months I work up the enthusiasm to watch several lectures, and then I get distracted and forget it all. Clearly, it's because I'm not trying hard enough because there are so many other things to also be curious about. https://theoreticalminimum.com/ https://theoreticalminimum.com/ But I also wish that physics were less focused on understanding extremes, and more interested in understanding physical systems closer at hand. There are interesting recent-ish results found in the behavior of crumpling paper, collapsing piles of sand, or the 'legs' of wine in a glass. I suspect that we could have much richer conceptual tools for thinking about the physical world actually around us if only more resources went into looking at it, rather than into exploring how laws do or don't break down in extreme conditions that don't naturally exist near earth.
- TheCowboy 5y ago
  I can relate to this. It might seem stupid but understanding this made me change the way I tied my shoes, and my laces come undone way less frequently now. https://news.berkeley.edu/2017/04/11/shoe-string-theory-science-shows-why-shoelaces-come-untied/ https://news.berkeley.edu/2017/04/11/shoe-string-theory-scie... (Also thanks to everyone for their responses, a lot of good stuff to check out.)
  - fho 5y ago
    Mandatory link to Ian's Shoelace Site: https://www.fieggen.com/shoelace/ https://www.fieggen.com/shoelace/
    - jrace 5y ago
      This site helped me to realize I had been tying one of my shoes wrong my entire life.
- gumby 5y ago
  > But I also wish that physics were less focused on understanding extremes To defend this approach: Extrema are a good way to get a handle on a problem, which can then be extended. In programming we almost always have to handle the null case ("what if the graph is unpopulated?") and often an extreme case as well ("What if we end up with 10 million users? How to we quickly respond to XXX"). In physics, like so many other domains, the poles are often the most enlightening region. However, as you say, work on those extrema rarely translates into more common situations until a breakthrough happens.
  - moonchrome 5y ago
    >In programming we almost always have to handle the null case ("what if the graph is unpopulated?") and often an extreme case as well ("What if we end up with 10 million users? How to we quickly respond to XXX"). Even the extreme case has to be somewhat realistic to be worth considering. Physics has gone way past that point once they started building accelerators larger than cities to detect subatomic reactions. Not saying it's not worth investigating but it's not at all comparable to any practical domain, at this point it's l'art pour l'art.
    - svachalek 5y ago
      It's realistic, they are learning about the particles that make up everything on Earth. But not necessarily pragmatic, in that there aren't likely new uses for that knowledge in the foreseeable future. Still, imagine what we can do once we've achieved a model of how it all really works.
      - moonchrome 5y ago
        I don't really know how the model enables much if it requires that kind of effort to test the predictions. If the predictions implied something more practical you could test that. I think the time where this kind of physics breakthroughs lead to anything useful is gone. At the same time I think there's stuff that's much more practical with still a lot of discoveries to be made - like superconductivity.
    - 5y ago
- tobmlt 5y ago
  >>> I suspect that we could have much richer conceptual tools for thinking about the physical world actually around us if only more resources went into looking at it What I hear in this statement is more towards the domains of research engineering as opposed to theoretical physics. Sand piles are of course the bridge between the two ;)
  - whatshisface 5y ago
    >Sand piles are of course the bridge between the two ;) Bridges are an engineering topic, most coastal areas lie on sedimentary rocks, and wormholes, a theoretical physics topic, are also called "Einstein–Rosen bridges." In other words, while bridges are bridges between sand piles and sand piles, sand piles are bridges between bridges and bridges.
    - tobmlt 5y ago
      Yes. You took the entropy right out of my mouth.
  - abeppu 5y ago
    I was thinking more along the lines of complex system research, self-organizing criticality etc. E.g. https://en.wikipedia.org/wiki/Abelian_sandpile_model https://en.wikipedia.org/wiki/Abelian_sandpile_model This can be a scientific rather than an engineering discipline, insofar as it's concerned with understanding the behavior of systems, rather than creating a solution which makes a system behave according to our wishes. We have a limited understanding of "order" or patterns arising out of systems with many aggregating interactions, and often focusing on relatively idealized and isolated systems.
- hellbannedguy 5y ago
  Are these videos working for you guys?
  - pas 5y ago
    For me Firefox blocks the YT embeds: https://www.youtube.com/embed/a6ANMKRBjA8?version=3&modestbranding=1&hd=1&showsearch=0&showinfo=0&rel=0 https://www.youtube.com/embed/a6ANMKRBjA8?version=3&modestbr...
- zopa 5y ago
  Quantum gravity gets the headlines, but only a pretty tiny minority of physicists actually work on stuff like that. Most people are researching problems much closer to hand. Basically the utopia you're looking for is already here.
- sharikone 5y ago
  Let's be real. There are more physicists than fitting research problems. That's why your average physics PhD graduate is typically employed outside of the field they learned and earns less than an average React programmer. That said, theoretical physics has the goal of understanding reality from a reductionist point of view. At the scales that goes from the nucleus to the Solar system there are few questions left. We know the Standard Model and GR and they fit the data perfectly. Of course some questions remain for how things interact when there are many of them (e.g. warm superconductivity) but there are few questions about fundamental laws You can think about it like bootstrapping an open source system (it was in the homepage today). There are still many technical hurdles downstream but we are interested in reducing the binary blob from which all starts to its perfect minimal form. And the only places we still have not figured out well are things at the limit of our instrument capacity. Black holes (GR and relativity, we still cannot figure out that and proving black hole seems experimentally challenging), exotic particles (what are quarks composed of?), dark matter (why far away galaxies seem to rotate so quickly?), dark energy, inflation, that stuff. I think physics should be smaller, it has too many graduates. But actually these problems should be researched. They are the fundamental questions that remain and there is a reason that the layman considers this stuff to be "real physics" and not origami folding
  - avmich 5y ago
    > That's why your average physics PhD graduate is typically employed outside of the field they learned and earns less than an average React programmer. Ha, I used to think that a big chunk of physicists by education are employed outside of the field they learned and earn top 10% salary of the industry doing software in financial companies. Heard more than once that computer science is easier than physics. Physical background helps hugely with software.
    - porknubbins 5y ago
      How would physics help with software though? My impression from trying physics is that its just that if you are smart enough to do physics you are smart enough that software engineering is not really hard but at most merely complicated.
- pas 5y ago
  wine legs on applied science: https://www.youtube.com/watch?v=s6w0tSg-msk https://www.youtube.com/watch?v=s6w0tSg-msk ! And let me randomly throw in metallic water too: https://www.youtube.com/watch?v=Vdz18ibX7rE https://www.youtube.com/watch?v=Vdz18ibX7rE
DontGiveTwoFlux 5y ago
I worried about this too. But I think my attitude has changed after watching lots of the PBS Space Time youtube channel. They do a great job of breaking down these concepts at a level where highly interested non-physicists can get what feel like the real details without dumbing it down too much. They have good videos on many physics topics, and regularly explain new discoveries. https://youtu.be/QLSIZg0npuA https://youtu.be/QLSIZg0npuA
- stronglikedan 5y ago
  PBS Space Time seconded. I recommend taking the rabbit-hole approach with them - i.e., blocking out a considerable more amount of time than the length of the video you're about to watch. They always reference past videos that expand on the building blocks of whatever the topic is in the video you're watching, and it helps to go watch those if it's a new topic to you, before continuing with the current video. I absolutely love that channel.
  - not_kurt_godel 5y ago
    Thirding PBS Space Time, and seconding taking time to really focus and treat watching them like studying. I became really interested in physics about 2 years ago. Initially the content was really challenging but I forced myself to rewatch many of the vids several times and it was ultimately very rewarding. I have a good enough grasp on the core concepts that I'm able to explain them to friends in-depth and it makes for great conversations, especially when people are in a state of mind to pontificate about the nature of the universe hehe.
    - stevenhuang 5y ago
      Fourthing as well. Think I've watched (heard) every episode at least twice now. They really calm the mind I find, as I frequently drift off to sleep with it in the background, dreaming about Space Time.
- zbendefy 5y ago
  Not a physicist but I find the Science Asylum also pretty good: https://youtu.be/Q2OlsMblugo https://youtu.be/Q2OlsMblugo
mrfox321 5y ago
The main issue is that quantum mechanics and {special | general} relativity are non-intuitive. Any classical analogy is a leaky abstraction at best. There are communicators who can pierce through this effectively. However, they tend to be researchers who do not have the time to spend writing pop-sci articles.
- marbu 5y ago
  You are right about quantum mechanics and general relativity, which requires more advanced math, and it's hard to create good and useful analogies without it. That said, if you can handle basic high school math, you don't need any leaky abstractions for special relativity: explain experiment with speed of light measurement and it's consequences, then explain thought experiment about the light clock and mathematically derive time dilatation out of it.
  - enkid 5y ago
    Special relativity may not require a lot of math, but it's results are still very unintuitive.
- lanstin 5y ago
  And sadly quantum mechanics is the simple and obvious version of quantum field theory, which is what the standard model is. Electron energies around a proton in the atom are one thing, but particles as fields and renormalization kill. Tho Feynman wrote a non maths book on QED.
celticninja 5y ago
Not given up but I would like to find a physicist on twitter who can layman's terms some of thes developmemts.
- devoutsalsa 5y ago
  I like Sabine Hossenfelder: - https://twitter.com/skdh?s=20 https://twitter.com/skdh?s=20 - https://www.youtube.com/c/SabineHossenfelder https://www.youtube.com/c/SabineHossenfelder
  - T-A 5y ago
    Well, then: http://backreaction.blogspot.com/2020/11/the-black-hole-information-loss-problem.html http://backreaction.blogspot.com/2020/11/the-black-hole-info...
    - celticninja 5y ago
      Thank you
immmmmm 5y ago
PBS space time is the best ressources out there. i have a phd in this kind of things and still learn a lot. but you're right, while nature is fundamentally weird to our brains (and often involve very complex maths), physicists (including myself) are typically very bad at explaining things in a simpler language. one of the reason i stopped was the very little (between 10 and 100) people around the world i could talk of my work.
- PartiallyTyped 5y ago
  I second PBS space time, and would also like to mention the notorious Sabine Hossenfelder, she has a great educational youtube channel and does a good job at explaining things to the lay person.
  - immmmmm 5y ago
    i do partially agree. while it was once a very good educational channel, it has often been very opinionated, sometimes in good, but also in somewhat narrow ways. for instance repeating that modified gravity is great and that strings/supersymmetry/etc is bad is a bit weak especially on a science education channel. i have worked with strings and some of her criticism if founded, repeating over the years that people that work in those domains are intellectual fraudsters (i'm barely exaggerating) is wrong and especially damaging on an educational channel. consequently, there a whole mob of youtube commenters that repeat this (with no context) to whoever wants to hear that. the same happened with Smolin and his book, following Green's book. TBH LQG is not yet there (despite recent interesting progress) and Calabi Yau compaction don't yield the universe we observe. Modified gravity doesn't seem to work too well too.. so yes, if you remain critical of what she says :)
    - naasking 5y ago
      > Modified gravity doesn't seem to work too well too.. I mean, it works out basically as well as dark matter. Both are consistent with some observations, and inconsistent with others. Last time this happened we simply postulated wave-particle duality, which is alone the same lines as what Sabine is pursuing.
sharikous 5y ago
It is actually a very famous controversy in physics between Hawking and Leonard Susskind. https://en.wikipedia.org/wiki/The_Black_Hole_War https://en.wikipedia.org/wiki/The_Black_Hole_War And if you care about understanding physics you absolutely have to check Susskind's "the theoretical minimum" videos. He explains advanced concepts with remarkable clarity. You really can grok string theory if you watch some of his series
pyb 5y ago
This is the frontier of knowledge. By definition, things that theoretical physicists themselves barely understand. For instance, this physicist reportedly "Discovered an Escape From Hawking’s Black Hole Paradox". If true (I presume it is), this implies that other physicists before her didn't understand the black hole paradox all that well! It also implies that you'll never get a crystal clear understanding of it from reading popular science.
SubiculumCode 5y ago
My favorites are the articles about a new math discovery...no clue...but I like cheering for them!
lordnacho 5y ago
Isn't it like this with any serious subject? You need to have read quite a few books to get it? One positive thing is that if you just pick up the university books/papers, there's no exam. You can just read them for understanding the concepts instead of for passing tests. I picked up a book about relativity (both) years after graduating, and it was an interesting read. I won't claim to understand how Ricci tensors work, but it made sense at the time.
- crazygringo 5y ago
  > Isn't it like this with any serious subject? You need to have read quite a few books to get it? No, I'd say physics/math is uniquely hard in this regard. A lot of stuff in the humanities, you can still get the gist of a paper even if you're not precisely familiar with the field, authors, etc. Then read a couple of textbooks, a handful of survey articles, all of which is a few days' reading, and you'll understand nearly of all it. But physics? A well-educated layperson can read a paper and not have the slightest idea what any of it means, no clue whatsoever. And a few days' reading isn't going to help much -- it's quite likely to need a couple years' of study at a minimum to understand the context of the paper. Remember, math/physics isn't just its own subject, it's its own language. For most people, the average math/physics paper might as well be written in Chinese. While a history, sociology, or political science paper is incredibly more accessible.
  - lordnacho 5y ago
    On second thought this is a good point. I think of it as mathy stuff being very deep, while humanities stuff is very broad. So you can stick your feet in the math end of the pond and not reach the bottom, but wherever you stick your feet in in humanities, you'll get it, but you can still wade a long way to places you haven't been.
phendrenad2 5y ago
Yeah. I wish magazines would do more work bridging the gap between scientist and layperson. Most articles are either "completely inaccurate or a metaphor at best" as you say, or they're just an unabashed, untranslated interview with a key scientist (like this article).
ben_w 5y ago
The latest developments (with a few exceptions) generally really are impenetrable without a solid foundation in undergrad physics, which meant that many of my trips to Physics Stack Exchange have given me a direct personal experience of being on the dumb side of the Dunning-Kruger effect. The good news is, as others have already suggested, this level of education is now very accessible by e.g. YouTube channels: https://youtube.com/c/pbsspacetime https://youtube.com/c/pbsspacetime https://youtube.com/c/SabineHossenfelder https://youtube.com/c/SabineHossenfelder https://youtube.com/playlist?list=PL701CD168D02FF56F https://youtube.com/playlist?list=PL701CD168D02FF56F (Susskind, The Theoretical Minimum: Quantum Mechanics) I would add the channels: https://youtube.com/user/EugeneKhutoryansky https://youtube.com/user/EugeneKhutoryansky https://youtube.com/user/minutephysics https://youtube.com/user/minutephysics and the MOOC Brilliant.org That said, I’m still definitely in the “undrergrad” level despite all this; I can recognise the equations of GR and QM, but not use them, and there’s plenty which I know I must be misunderstanding.
- queuebert 5y ago
  > The good news is, as others have already suggested, this level of education is now very accessible by e.g. YouTube channels: With the caveat that you must work on on every problem set you are confronted with. An essential part of a physics education is struggling over extremely hard problem sets. (I'm assuming/hoping these channels offer decently hard problem sets.) This more than lectures teaches you how to flail about in unknown areas of physics and to gauge your own understanding. This I think is a physicist's superpower.
  - ben_w 5y ago
    > An essential part of a physics education is struggling over extremely hard problem sets Indeed; this is where brilliant.org makes its sales pitch. And, thankfully, when its physics courses went beyond my level of mathematics, it also has a mathematics course which I’m hoping will get me up to the right level.
drran 5y ago
If you cannot understand it, then probably it doesn't matter for you, because you have no problem to solve. Most of the time, physicists are trying to invent a mathematical formula or construct to elegantly describe a physical process, to make an accurate prediction. Just imagine, that we have a game, where we want to accurately predict next frames of a video. It's an interesting game on its own, because you need to understand deeply what happens on the video to be able to accurately predict behavior of all objects, animals, and persons in the video. Such game requires a lot of skill, to accurately guess and predict, but most of the time it's not important for us, mere mortals. For example, we put a lot of effort into OpenGL, PBR, physic engines, etc. to make realistic games. Do you feel obligated to study all of that when you are interested in a realistic fly simulation? Do you feel obligated to study construction of AK when you like to play a 3D shooter? If you really want to understand physics, then I suggest to perform experiments, or play with a physical simulation, or, even better, to implement your own physical simulation. Look, for example, at this beautiful simulation of black hole done in OpenGL shader: https://ebruneton.github.io/black_hole_shader/demo/demo.html https://ebruneton.github.io/black_hole_shader/demo/demo.html https://www.youtube.com/watch?v=_hhOd7GDboM https://www.youtube.com/watch?v=_hhOd7GDboM https://github.com/ebruneton/black_hole_shader https://github.com/ebruneton/black_hole_shader https://ebruneton.github.io/black_hole_shader/paper.pdf https://ebruneton.github.io/black_hole_shader/paper.pdf
marcyb5st 5y ago
I am one of these with a background in physics, but have been out of the circle for the last 10y. I highly recommend the videos from PBS Space Time on YT. They have playlists on various topics and, if you are willing to put the mental effort, can give a solid foundation and allow to understand to some extent papers/theories like the one reported here.
WindyLakeReturn 5y ago
I would suggest starting with YouTube. Start consuming a variety of videos from different sources and you'll begin picking things up and gaining enough knowledge to start identifying bad info. You can start with lectures of complex topics by physicists meant for the general public. Their is a lot of handwaving to remove the math and oftentimes they go into personal beliefs concerning theoretical physics, but they are very good at identifying each time they do so. PBS spacetime is one that seems informative while giving enough clarifications. Including looking into a few pop sci theories, explaining what they would mean, and ending with why science don't consider them as serious explanations. You can also find some more math heavy explanations and slowly build your math skills to be good enough to understand the physics that uses it.
DantesKite 5y ago
That's why I like Quanta Magazine. They do a great job of laying down enough material to get a sense of what's going on.
- stevenhuang 5y ago
  Especially in this article, the explanation of the proposed breakthrough was pretty clear: Old: Errant entropy curve (Hawking's entropy calculation) due to wrong black hole surface area used New: Resolved entropy curve (Page curve) via quantum-corrected surface area (quantum extremal surface)
  - raattgift 5y ago
    I'm glad you thought the article's explanation was "pretty clear". For me it was less clear in part because it raised the question: "what is a quantum extremal surface?", which doesn't really seem to be answered in the Quanta article. Perhaps I could persuade you to try your hand at your terse sort of summary for the interviewee's two-author paper https://arxiv.org/abs/1408.3203 https://arxiv.org/abs/1408.3203 (Engelhardt & Wall, E&W2014) defining quantum extremal surfaces, and having done so return to and similarly summarize the part of the Quanta Magazine article where the interviewee is asked (several years later) about applicability of these defined surfaces outside higher-dimensional anti-de Sitter space supporting a conformal field theory on its timelike (n-1)-spherical boundary, Maldacena-style. (cf. end p.23 E&W2014 and their footnote 6). Such a summary could enlighten one or both of us, and perhaps other readers, and at the very least I'd be grateful (since I have no idea how to capture what quantum extremal surfaces are in only a line of text). (The open access https://link.springer.com/article/10.1140/epjc/s10052-020-08437-2 https://link.springer.com/article/10.1140/epjc/s10052-020-08... is likely to be of some help, its SdS_4 spacetime being a decent approximation of a late-time isolated galaxy cluster in an expanding Robertson-Walker universe. Our standard cosmology models our universe in a way which one might describe reasonably as expanding RW -> dS_4 equipped with a dusty distribution of matter such that at late times most mass -> "dust grains" that resemble SdS's Schwarzschild submanifold. Cf. https://en.wikipedia.org/wiki/De_Sitter%E2%80%93Schwarzschild_metric https://en.wikipedia.org/wiki/De_Sitter%E2%80%93Schwarzschil... ).
anigbrowl 5y ago
Kind of, as you say it is time-consuming to keep up. A bigger problem is that it's not obvious what the impact of many discoveries would be on daily life; physics sometimes seems to have been stuck in an era of diminishing returns after important breakthroughs that led to a short era of rapid innovation - sort of how nuclear fusion has been 20 years away my whole life. I've often felt part of the problem here is the relative decrease of manned missions in space, which are not the best bang for the buck in scientific terms, but at one time created a widespread of view of 'humanity's future in space' that provided the motivation for and wide public interest in many scientific endeavors. Nowadays, there's a widespread feeling that planet earth has got very crowded and there aren't as many opportunities for big new discoveries (the sort that can be appreciated by anyone without specialist education/training), that the long-term viability of our habitat is Not Great, and that the prospect of space exploration is too remote and costly to have any impact on the lives of ordinary people, but is limited to a microscopic scientific or financial elite. Of course, this is somewhat irrational; as a society we've chosen to have ubiquitous worldwide real-time communications devices that would have once seemed limited to star Trek. Computing has made big science small enough to fit in our pocket and allowed anyone who is really interested to be a software maven. But it's not as spectacular as the future anticipated a few decades ago.
omgJustTest 5y ago
Startswithabang and other science educators, particularly Veritasium, do excellent jobs. It's complicated and worth the time to understand what they present.
wrycoder 5y ago
Natalie Wolchover is one of the finest science journalists around, especially for physics. You can rely on her.
hinkley 5y ago
Isn’t it kinda true that A Brief History of Time was so important in part because it successfully dumbed down a bunch of esoteric physics? Maybe we are just reverting to the mean? I recall years ago mentioning offhand to someone that I read SIGPLAN proceedings and their eyes bugged out and they asked if I could understand those. I said “only about 3/4s” but I knew exactly what he meant. Learn to human.
toast0 5y ago
> I'm just wondering if I'm being lazy by not trying hard enough or efficient. I don't think anyone else specifically said this, so allow me to be one of the few who say you're being efficient. Sure, you could spend time to understand this stuff, and yes it's important knowledge for the world/society, but knowing about black holes really isn't going to change anything you do, unless you're a physicist or working on something involving deep space (and likely not really then either). Sometimes esoteric knowledge is useful in other areas, and sometimes learning esoteric knowledge is fun or helpful to build learning skills, but sometimes it's just more junk to fill your brain sponge with. If it doesn't tickle your interest, leave it be and it's fine. If it becomes useful, chances are over time more ways to explain it will have been made and some might be more comprehendable by you.
codethief 5y ago
> I'm just wondering if I'm being lazy by not trying hard enough or efficient. It's definitely not for lack of curiosity, but I also don't like to fool myself into thinking I understand something that I don't. I don't think you're lazy or not trying hard enough. The truth is just that… it's a hard and long road. Even more so when you're studying by yourself. I took about the straightest path you can take to learning Quantum Mechanics and General Relativity (and all the math you need for it), attending classes and sitting down on my butt every day for 3 to 4 semesters. There are ways to shorten it but I'm not sure how rewarding that would be. It also depends on what you mean by "understanding". If you really want to understand things at the deepest level possible, there's no way around a university-level education. I'm saying "university-level", not "university", because one could certainly learn these things on one's own. But to be honest with you I think chances of pulling this off are very small, mostly because physics outsiders don't have access to the same resources or social networks as enrolled students, which makes studying even more frustrating. Anyway, FWIW here's a roadmap for learning General Relativity at the deepest-possible level along with the minimum timeframe needed (IMO) and the most important topics / keywords you really need to understand well: Linear Algebra (1-2 semesters): vector spaces, linear maps, dual maps, matrices, symmetric bilinear forms – These things lay the foundation for pretty much anything in math and are needed to understand differentiation in several variables (see below) as well as pretty much anything in Differential Geometry and Relativity. Real Analysis (1-2 semesters): Mostly differentiation of functions of one to several variables + a bit of integration theory – needed for pretty much anything in Differential Geometry and Relativity (especially coordinate changes and manifolds) but also in mechanics. Differential Geometry aka (Semi-)Riemannian Geometry (1 semester): manifolds, tensors, metric, connections, geodesics, curvature – These concepts are at the heart of General Relativity Mechanics (1-2 semesters): Newtonian Mechanics, Lagrangian Mechanics, Special Relativity (all with a focus on both theoretical and experimental physics) – without these there's no hope of understanding (or appreciating) the physics content of GR General Relativity (1 semester) (Side note: Don't let anyone tell you that you don't really need Differential Geometry and all the other math to understand Relativity. They're lying and probably don't really understand Relativity, either.) For quantum mechanics it's a bit shorter because the math is not as involved (at least to understand the basic concepts: Linear Algebra: (1-2 semesters): (finite-dimensional) vector spaces, linear maps, dual maps, matrices, symmetric bilinear forms – No way around this. 99% of quantum mechanics is encoding fuzzy concepts in linear algebra. Mechanics (1 semester): Newtonian Mechanics, Lagrangian Mechanics Quantum Mechanics Bonus: Hilbert space theory, basics in functional analysis
CephalopodMD 5y ago
Yes. This is nonsense to me. That said, check out scienceclic. They do good run downs of BOTH the metaphorical stuff AND the math that underpins it. PBS spacetime is a fun place to check out too. Between the two of them, you should have enough of an idea of these things to wax scientific at a cocktail party.

abeppu 5y ago

> I'm just wondering if I'm being lazy by not trying hard enough or efficient. Leonard Susskind at Stanford has a series of courses specifically aimed at helping people get up to speed in understanding modern physics. Every several months I work up the enthusiasm to watch several lectures, and then I get distracted and forget it all. Clearly, it's because I'm not trying hard enough because there are so many other things to also be curious about. https://theoreticalminimum.com/ https://theoreticalminimum.com/ But I also wish that physics were less focused on understanding extremes, and more interested in understanding physical systems closer at hand. There are interesting recent-ish results found in the behavior of crumpling paper, collapsing piles of sand, or the 'legs' of wine in a glass. I suspect that we could have much richer conceptual tools for thinking about the physical world actually around us if only more resources went into looking at it, rather than into exploring how laws do or don't break down in extreme conditions that don't naturally exist near earth.

TheCowboy 5y ago
I can relate to this. It might seem stupid but understanding this made me change the way I tied my shoes, and my laces come undone way less frequently now. https://news.berkeley.edu/2017/04/11/shoe-string-theory-science-shows-why-shoelaces-come-untied/ https://news.berkeley.edu/2017/04/11/shoe-string-theory-scie... (Also thanks to everyone for their responses, a lot of good stuff to check out.)
- fho 5y ago
  Mandatory link to Ian's Shoelace Site: https://www.fieggen.com/shoelace/ https://www.fieggen.com/shoelace/
  - jrace 5y ago
    This site helped me to realize I had been tying one of my shoes wrong my entire life.
gumby 5y ago
> But I also wish that physics were less focused on understanding extremes To defend this approach: Extrema are a good way to get a handle on a problem, which can then be extended. In programming we almost always have to handle the null case ("what if the graph is unpopulated?") and often an extreme case as well ("What if we end up with 10 million users? How to we quickly respond to XXX"). In physics, like so many other domains, the poles are often the most enlightening region. However, as you say, work on those extrema rarely translates into more common situations until a breakthrough happens.
- moonchrome 5y ago
  >In programming we almost always have to handle the null case ("what if the graph is unpopulated?") and often an extreme case as well ("What if we end up with 10 million users? How to we quickly respond to XXX"). Even the extreme case has to be somewhat realistic to be worth considering. Physics has gone way past that point once they started building accelerators larger than cities to detect subatomic reactions. Not saying it's not worth investigating but it's not at all comparable to any practical domain, at this point it's l'art pour l'art.
  - svachalek 5y ago
    It's realistic, they are learning about the particles that make up everything on Earth. But not necessarily pragmatic, in that there aren't likely new uses for that knowledge in the foreseeable future. Still, imagine what we can do once we've achieved a model of how it all really works.
    - moonchrome 5y ago
      I don't really know how the model enables much if it requires that kind of effort to test the predictions. If the predictions implied something more practical you could test that. I think the time where this kind of physics breakthroughs lead to anything useful is gone. At the same time I think there's stuff that's much more practical with still a lot of discoveries to be made - like superconductivity.
  - 5y ago
tobmlt 5y ago
>>> I suspect that we could have much richer conceptual tools for thinking about the physical world actually around us if only more resources went into looking at it What I hear in this statement is more towards the domains of research engineering as opposed to theoretical physics. Sand piles are of course the bridge between the two ;)
- whatshisface 5y ago
  >Sand piles are of course the bridge between the two ;) Bridges are an engineering topic, most coastal areas lie on sedimentary rocks, and wormholes, a theoretical physics topic, are also called "Einstein–Rosen bridges." In other words, while bridges are bridges between sand piles and sand piles, sand piles are bridges between bridges and bridges.
  - tobmlt 5y ago
    Yes. You took the entropy right out of my mouth.
- abeppu 5y ago
  I was thinking more along the lines of complex system research, self-organizing criticality etc. E.g. https://en.wikipedia.org/wiki/Abelian_sandpile_model https://en.wikipedia.org/wiki/Abelian_sandpile_model This can be a scientific rather than an engineering discipline, insofar as it's concerned with understanding the behavior of systems, rather than creating a solution which makes a system behave according to our wishes. We have a limited understanding of "order" or patterns arising out of systems with many aggregating interactions, and often focusing on relatively idealized and isolated systems.
hellbannedguy 5y ago
Are these videos working for you guys?
- pas 5y ago
  For me Firefox blocks the YT embeds: https://www.youtube.com/embed/a6ANMKRBjA8?version=3&modestbranding=1&hd=1&showsearch=0&showinfo=0&rel=0 https://www.youtube.com/embed/a6ANMKRBjA8?version=3&modestbr...
zopa 5y ago
Quantum gravity gets the headlines, but only a pretty tiny minority of physicists actually work on stuff like that. Most people are researching problems much closer to hand. Basically the utopia you're looking for is already here.
sharikone 5y ago
Let's be real. There are more physicists than fitting research problems. That's why your average physics PhD graduate is typically employed outside of the field they learned and earns less than an average React programmer. That said, theoretical physics has the goal of understanding reality from a reductionist point of view. At the scales that goes from the nucleus to the Solar system there are few questions left. We know the Standard Model and GR and they fit the data perfectly. Of course some questions remain for how things interact when there are many of them (e.g. warm superconductivity) but there are few questions about fundamental laws You can think about it like bootstrapping an open source system (it was in the homepage today). There are still many technical hurdles downstream but we are interested in reducing the binary blob from which all starts to its perfect minimal form. And the only places we still have not figured out well are things at the limit of our instrument capacity. Black holes (GR and relativity, we still cannot figure out that and proving black hole seems experimentally challenging), exotic particles (what are quarks composed of?), dark matter (why far away galaxies seem to rotate so quickly?), dark energy, inflation, that stuff. I think physics should be smaller, it has too many graduates. But actually these problems should be researched. They are the fundamental questions that remain and there is a reason that the layman considers this stuff to be "real physics" and not origami folding
- avmich 5y ago
  > That's why your average physics PhD graduate is typically employed outside of the field they learned and earns less than an average React programmer. Ha, I used to think that a big chunk of physicists by education are employed outside of the field they learned and earn top 10% salary of the industry doing software in financial companies. Heard more than once that computer science is easier than physics. Physical background helps hugely with software.
  - porknubbins 5y ago
    How would physics help with software though? My impression from trying physics is that its just that if you are smart enough to do physics you are smart enough that software engineering is not really hard but at most merely complicated.
pas 5y ago
wine legs on applied science: https://www.youtube.com/watch?v=s6w0tSg-msk https://www.youtube.com/watch?v=s6w0tSg-msk ! And let me randomly throw in metallic water too: https://www.youtube.com/watch?v=Vdz18ibX7rE https://www.youtube.com/watch?v=Vdz18ibX7rE

DontGiveTwoFlux 5y ago

I worried about this too. But I think my attitude has changed after watching lots of the PBS Space Time youtube channel. They do a great job of breaking down these concepts at a level where highly interested non-physicists can get what feel like the real details without dumbing it down too much. They have good videos on many physics topics, and regularly explain new discoveries. https://youtu.be/QLSIZg0npuA https://youtu.be/QLSIZg0npuA

stronglikedan 5y ago
PBS Space Time seconded. I recommend taking the rabbit-hole approach with them - i.e., blocking out a considerable more amount of time than the length of the video you're about to watch. They always reference past videos that expand on the building blocks of whatever the topic is in the video you're watching, and it helps to go watch those if it's a new topic to you, before continuing with the current video. I absolutely love that channel.
- not_kurt_godel 5y ago
  Thirding PBS Space Time, and seconding taking time to really focus and treat watching them like studying. I became really interested in physics about 2 years ago. Initially the content was really challenging but I forced myself to rewatch many of the vids several times and it was ultimately very rewarding. I have a good enough grasp on the core concepts that I'm able to explain them to friends in-depth and it makes for great conversations, especially when people are in a state of mind to pontificate about the nature of the universe hehe.
  - stevenhuang 5y ago
    Fourthing as well. Think I've watched (heard) every episode at least twice now. They really calm the mind I find, as I frequently drift off to sleep with it in the background, dreaming about Space Time.
zbendefy 5y ago
Not a physicist but I find the Science Asylum also pretty good: https://youtu.be/Q2OlsMblugo https://youtu.be/Q2OlsMblugo

mrfox321 5y ago

The main issue is that quantum mechanics and {special | general} relativity are non-intuitive. Any classical analogy is a leaky abstraction at best. There are communicators who can pierce through this effectively. However, they tend to be researchers who do not have the time to spend writing pop-sci articles.

marbu 5y ago
You are right about quantum mechanics and general relativity, which requires more advanced math, and it's hard to create good and useful analogies without it. That said, if you can handle basic high school math, you don't need any leaky abstractions for special relativity: explain experiment with speed of light measurement and it's consequences, then explain thought experiment about the light clock and mathematically derive time dilatation out of it.
- enkid 5y ago
  Special relativity may not require a lot of math, but it's results are still very unintuitive.
lanstin 5y ago
And sadly quantum mechanics is the simple and obvious version of quantum field theory, which is what the standard model is. Electron energies around a proton in the atom are one thing, but particles as fields and renormalization kill. Tho Feynman wrote a non maths book on QED.

celticninja 5y ago

Not given up but I would like to find a physicist on twitter who can layman's terms some of thes developmemts.

devoutsalsa 5y ago
I like Sabine Hossenfelder: - https://twitter.com/skdh?s=20 https://twitter.com/skdh?s=20 - https://www.youtube.com/c/SabineHossenfelder https://www.youtube.com/c/SabineHossenfelder
- T-A 5y ago
  Well, then: http://backreaction.blogspot.com/2020/11/the-black-hole-information-loss-problem.html http://backreaction.blogspot.com/2020/11/the-black-hole-info...
  - celticninja 5y ago
    Thank you

immmmmm 5y ago

PBS space time is the best ressources out there. i have a phd in this kind of things and still learn a lot. but you're right, while nature is fundamentally weird to our brains (and often involve very complex maths), physicists (including myself) are typically very bad at explaining things in a simpler language. one of the reason i stopped was the very little (between 10 and 100) people around the world i could talk of my work.

PartiallyTyped 5y ago
I second PBS space time, and would also like to mention the notorious Sabine Hossenfelder, she has a great educational youtube channel and does a good job at explaining things to the lay person.
- immmmmm 5y ago
  i do partially agree. while it was once a very good educational channel, it has often been very opinionated, sometimes in good, but also in somewhat narrow ways. for instance repeating that modified gravity is great and that strings/supersymmetry/etc is bad is a bit weak especially on a science education channel. i have worked with strings and some of her criticism if founded, repeating over the years that people that work in those domains are intellectual fraudsters (i'm barely exaggerating) is wrong and especially damaging on an educational channel. consequently, there a whole mob of youtube commenters that repeat this (with no context) to whoever wants to hear that. the same happened with Smolin and his book, following Green's book. TBH LQG is not yet there (despite recent interesting progress) and Calabi Yau compaction don't yield the universe we observe. Modified gravity doesn't seem to work too well too.. so yes, if you remain critical of what she says :)
  - naasking 5y ago
    > Modified gravity doesn't seem to work too well too.. I mean, it works out basically as well as dark matter. Both are consistent with some observations, and inconsistent with others. Last time this happened we simply postulated wave-particle duality, which is alone the same lines as what Sabine is pursuing.

sharikous 5y ago

It is actually a very famous controversy in physics between Hawking and Leonard Susskind. https://en.wikipedia.org/wiki/The_Black_Hole_War https://en.wikipedia.org/wiki/The_Black_Hole_War And if you care about understanding physics you absolutely have to check Susskind's "the theoretical minimum" videos. He explains advanced concepts with remarkable clarity. You really can grok string theory if you watch some of his series

pyb 5y ago

This is the frontier of knowledge. By definition, things that theoretical physicists themselves barely understand. For instance, this physicist reportedly "Discovered an Escape From Hawking’s Black Hole Paradox". If true (I presume it is), this implies that other physicists before her didn't understand the black hole paradox all that well! It also implies that you'll never get a crystal clear understanding of it from reading popular science.

SubiculumCode 5y ago

My favorites are the articles about a new math discovery...no clue...but I like cheering for them!

lordnacho 5y ago

Isn't it like this with any serious subject? You need to have read quite a few books to get it? One positive thing is that if you just pick up the university books/papers, there's no exam. You can just read them for understanding the concepts instead of for passing tests. I picked up a book about relativity (both) years after graduating, and it was an interesting read. I won't claim to understand how Ricci tensors work, but it made sense at the time.

crazygringo 5y ago
> Isn't it like this with any serious subject? You need to have read quite a few books to get it? No, I'd say physics/math is uniquely hard in this regard. A lot of stuff in the humanities, you can still get the gist of a paper even if you're not precisely familiar with the field, authors, etc. Then read a couple of textbooks, a handful of survey articles, all of which is a few days' reading, and you'll understand nearly of all it. But physics? A well-educated layperson can read a paper and not have the slightest idea what any of it means, no clue whatsoever. And a few days' reading isn't going to help much -- it's quite likely to need a couple years' of study at a minimum to understand the context of the paper. Remember, math/physics isn't just its own subject, it's its own language. For most people, the average math/physics paper might as well be written in Chinese. While a history, sociology, or political science paper is incredibly more accessible.
- lordnacho 5y ago
  On second thought this is a good point. I think of it as mathy stuff being very deep, while humanities stuff is very broad. So you can stick your feet in the math end of the pond and not reach the bottom, but wherever you stick your feet in in humanities, you'll get it, but you can still wade a long way to places you haven't been.

phendrenad2 5y ago

Yeah. I wish magazines would do more work bridging the gap between scientist and layperson. Most articles are either "completely inaccurate or a metaphor at best" as you say, or they're just an unabashed, untranslated interview with a key scientist (like this article).

ben_w 5y ago

The latest developments (with a few exceptions) generally really are impenetrable without a solid foundation in undergrad physics, which meant that many of my trips to Physics Stack Exchange have given me a direct personal experience of being on the dumb side of the Dunning-Kruger effect. The good news is, as others have already suggested, this level of education is now very accessible by e.g. YouTube channels: https://youtube.com/c/pbsspacetime https://youtube.com/c/pbsspacetime https://youtube.com/c/SabineHossenfelder https://youtube.com/c/SabineHossenfelder https://youtube.com/playlist?list=PL701CD168D02FF56F https://youtube.com/playlist?list=PL701CD168D02FF56F (Susskind, The Theoretical Minimum: Quantum Mechanics) I would add the channels: https://youtube.com/user/EugeneKhutoryansky https://youtube.com/user/EugeneKhutoryansky https://youtube.com/user/minutephysics https://youtube.com/user/minutephysics and the MOOC Brilliant.org That said, I’m still definitely in the “undrergrad” level despite all this; I can recognise the equations of GR and QM, but not use them, and there’s plenty which I know I must be misunderstanding.

queuebert 5y ago
> The good news is, as others have already suggested, this level of education is now very accessible by e.g. YouTube channels: With the caveat that you must work on on every problem set you are confronted with. An essential part of a physics education is struggling over extremely hard problem sets. (I'm assuming/hoping these channels offer decently hard problem sets.) This more than lectures teaches you how to flail about in unknown areas of physics and to gauge your own understanding. This I think is a physicist's superpower.
- ben_w 5y ago
  > An essential part of a physics education is struggling over extremely hard problem sets Indeed; this is where brilliant.org makes its sales pitch. And, thankfully, when its physics courses went beyond my level of mathematics, it also has a mathematics course which I’m hoping will get me up to the right level.

drran 5y ago

If you cannot understand it, then probably it doesn't matter for you, because you have no problem to solve. Most of the time, physicists are trying to invent a mathematical formula or construct to elegantly describe a physical process, to make an accurate prediction. Just imagine, that we have a game, where we want to accurately predict next frames of a video. It's an interesting game on its own, because you need to understand deeply what happens on the video to be able to accurately predict behavior of all objects, animals, and persons in the video. Such game requires a lot of skill, to accurately guess and predict, but most of the time it's not important for us, mere mortals. For example, we put a lot of effort into OpenGL, PBR, physic engines, etc. to make realistic games. Do you feel obligated to study all of that when you are interested in a realistic fly simulation? Do you feel obligated to study construction of AK when you like to play a 3D shooter? If you really want to understand physics, then I suggest to perform experiments, or play with a physical simulation, or, even better, to implement your own physical simulation. Look, for example, at this beautiful simulation of black hole done in OpenGL shader: https://ebruneton.github.io/black_hole_shader/demo/demo.html https://ebruneton.github.io/black_hole_shader/demo/demo.html https://www.youtube.com/watch?v=_hhOd7GDboM https://www.youtube.com/watch?v=_hhOd7GDboM https://github.com/ebruneton/black_hole_shader https://github.com/ebruneton/black_hole_shader https://ebruneton.github.io/black_hole_shader/paper.pdf https://ebruneton.github.io/black_hole_shader/paper.pdf

marcyb5st 5y ago

I am one of these with a background in physics, but have been out of the circle for the last 10y. I highly recommend the videos from PBS Space Time on YT. They have playlists on various topics and, if you are willing to put the mental effort, can give a solid foundation and allow to understand to some extent papers/theories like the one reported here.

WindyLakeReturn 5y ago

I would suggest starting with YouTube. Start consuming a variety of videos from different sources and you'll begin picking things up and gaining enough knowledge to start identifying bad info. You can start with lectures of complex topics by physicists meant for the general public. Their is a lot of handwaving to remove the math and oftentimes they go into personal beliefs concerning theoretical physics, but they are very good at identifying each time they do so. PBS spacetime is one that seems informative while giving enough clarifications. Including looking into a few pop sci theories, explaining what they would mean, and ending with why science don't consider them as serious explanations. You can also find some more math heavy explanations and slowly build your math skills to be good enough to understand the physics that uses it.

DantesKite 5y ago

That's why I like Quanta Magazine. They do a great job of laying down enough material to get a sense of what's going on.

stevenhuang 5y ago
Especially in this article, the explanation of the proposed breakthrough was pretty clear: Old: Errant entropy curve (Hawking's entropy calculation) due to wrong black hole surface area used New: Resolved entropy curve (Page curve) via quantum-corrected surface area (quantum extremal surface)
- raattgift 5y ago
  I'm glad you thought the article's explanation was "pretty clear". For me it was less clear in part because it raised the question: "what is a quantum extremal surface?", which doesn't really seem to be answered in the Quanta article. Perhaps I could persuade you to try your hand at your terse sort of summary for the interviewee's two-author paper https://arxiv.org/abs/1408.3203 https://arxiv.org/abs/1408.3203 (Engelhardt & Wall, E&W2014) defining quantum extremal surfaces, and having done so return to and similarly summarize the part of the Quanta Magazine article where the interviewee is asked (several years later) about applicability of these defined surfaces outside higher-dimensional anti-de Sitter space supporting a conformal field theory on its timelike (n-1)-spherical boundary, Maldacena-style. (cf. end p.23 E&W2014 and their footnote 6). Such a summary could enlighten one or both of us, and perhaps other readers, and at the very least I'd be grateful (since I have no idea how to capture what quantum extremal surfaces are in only a line of text). (The open access https://link.springer.com/article/10.1140/epjc/s10052-020-08437-2 https://link.springer.com/article/10.1140/epjc/s10052-020-08... is likely to be of some help, its SdS_4 spacetime being a decent approximation of a late-time isolated galaxy cluster in an expanding Robertson-Walker universe. Our standard cosmology models our universe in a way which one might describe reasonably as expanding RW -> dS_4 equipped with a dusty distribution of matter such that at late times most mass -> "dust grains" that resemble SdS's Schwarzschild submanifold. Cf. https://en.wikipedia.org/wiki/De_Sitter%E2%80%93Schwarzschild_metric https://en.wikipedia.org/wiki/De_Sitter%E2%80%93Schwarzschil... ).

anigbrowl 5y ago

Kind of, as you say it is time-consuming to keep up. A bigger problem is that it's not obvious what the impact of many discoveries would be on daily life; physics sometimes seems to have been stuck in an era of diminishing returns after important breakthroughs that led to a short era of rapid innovation - sort of how nuclear fusion has been 20 years away my whole life. I've often felt part of the problem here is the relative decrease of manned missions in space, which are not the best bang for the buck in scientific terms, but at one time created a widespread of view of 'humanity's future in space' that provided the motivation for and wide public interest in many scientific endeavors. Nowadays, there's a widespread feeling that planet earth has got very crowded and there aren't as many opportunities for big new discoveries (the sort that can be appreciated by anyone without specialist education/training), that the long-term viability of our habitat is Not Great, and that the prospect of space exploration is too remote and costly to have any impact on the lives of ordinary people, but is limited to a microscopic scientific or financial elite. Of course, this is somewhat irrational; as a society we've chosen to have ubiquitous worldwide real-time communications devices that would have once seemed limited to star Trek. Computing has made big science small enough to fit in our pocket and allowed anyone who is really interested to be a software maven. But it's not as spectacular as the future anticipated a few decades ago.

omgJustTest 5y ago

Startswithabang and other science educators, particularly Veritasium, do excellent jobs. It's complicated and worth the time to understand what they present.

wrycoder 5y ago

Natalie Wolchover is one of the finest science journalists around, especially for physics. You can rely on her.

hinkley 5y ago

Isn’t it kinda true that A Brief History of Time was so important in part because it successfully dumbed down a bunch of esoteric physics? Maybe we are just reverting to the mean? I recall years ago mentioning offhand to someone that I read SIGPLAN proceedings and their eyes bugged out and they asked if I could understand those. I said “only about 3/4s” but I knew exactly what he meant. Learn to human.

toast0 5y ago

> I'm just wondering if I'm being lazy by not trying hard enough or efficient. I don't think anyone else specifically said this, so allow me to be one of the few who say you're being efficient. Sure, you could spend time to understand this stuff, and yes it's important knowledge for the world/society, but knowing about black holes really isn't going to change anything you do, unless you're a physicist or working on something involving deep space (and likely not really then either). Sometimes esoteric knowledge is useful in other areas, and sometimes learning esoteric knowledge is fun or helpful to build learning skills, but sometimes it's just more junk to fill your brain sponge with. If it doesn't tickle your interest, leave it be and it's fine. If it becomes useful, chances are over time more ways to explain it will have been made and some might be more comprehendable by you.

codethief 5y ago

> I'm just wondering if I'm being lazy by not trying hard enough or efficient. It's definitely not for lack of curiosity, but I also don't like to fool myself into thinking I understand something that I don't. I don't think you're lazy or not trying hard enough. The truth is just that… it's a hard and long road. Even more so when you're studying by yourself. I took about the straightest path you can take to learning Quantum Mechanics and General Relativity (and all the math you need for it), attending classes and sitting down on my butt every day for 3 to 4 semesters. There are ways to shorten it but I'm not sure how rewarding that would be. It also depends on what you mean by "understanding". If you really want to understand things at the deepest level possible, there's no way around a university-level education. I'm saying "university-level", not "university", because one could certainly learn these things on one's own. But to be honest with you I think chances of pulling this off are very small, mostly because physics outsiders don't have access to the same resources or social networks as enrolled students, which makes studying even more frustrating. Anyway, FWIW here's a roadmap for learning General Relativity at the deepest-possible level along with the minimum timeframe needed (IMO) and the most important topics / keywords you really need to understand well: Linear Algebra (1-2 semesters): vector spaces, linear maps, dual maps, matrices, symmetric bilinear forms – These things lay the foundation for pretty much anything in math and are needed to understand differentiation in several variables (see below) as well as pretty much anything in Differential Geometry and Relativity. Real Analysis (1-2 semesters): Mostly differentiation of functions of one to several variables + a bit of integration theory – needed for pretty much anything in Differential Geometry and Relativity (especially coordinate changes and manifolds) but also in mechanics. Differential Geometry aka (Semi-)Riemannian Geometry (1 semester): manifolds, tensors, metric, connections, geodesics, curvature – These concepts are at the heart of General Relativity Mechanics (1-2 semesters): Newtonian Mechanics, Lagrangian Mechanics, Special Relativity (all with a focus on both theoretical and experimental physics) – without these there's no hope of understanding (or appreciating) the physics content of GR General Relativity (1 semester) (Side note: Don't let anyone tell you that you don't really need Differential Geometry and all the other math to understand Relativity. They're lying and probably don't really understand Relativity, either.) For quantum mechanics it's a bit shorter because the math is not as involved (at least to understand the basic concepts: Linear Algebra: (1-2 semesters): (finite-dimensional) vector spaces, linear maps, dual maps, matrices, symmetric bilinear forms – No way around this. 99% of quantum mechanics is encoding fuzzy concepts in linear algebra. Mechanics (1 semester): Newtonian Mechanics, Lagrangian Mechanics Quantum Mechanics Bonus: Hilbert space theory, basics in functional analysis

CephalopodMD 5y ago

Yes. This is nonsense to me. That said, check out scienceclic. They do good run downs of BOTH the metaphorical stuff AND the math that underpins it. PBS spacetime is a fun place to check out too. Between the two of them, you should have enough of an idea of these things to wax scientific at a cocktail party.