# Can a layman learn GR and QM? REALLY learn? **URL:** \ **Category:** Factual Questions\ **Created:** [February 9, 2011, 10:03pm UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811 "2011-02-09T22:03:42Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![billfish678](https://avatars.discourse-cdn.com/v4/letter/b/7bcc69/32.png) [@billfish678](https://boards.straightdope.com/u/billfish678)\ **Post date:** [February 10, 2011, 12:59am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/21 "2011-02-10T00:59:06Z")
> [@brocks](#): > > If I understand you, you are saying that doing the math is necessary, but not sufficient. Conceded. > > But you also seem to be disparaging doing the math at all. I don’t get that. What is the alternative? Tell me why you think that. ---
**Author:** ![spenczar](https://avatars.discourse-cdn.com/v4/letter/s/858c86/32.png) [@spenczar](https://boards.straightdope.com/u/spenczar)\ **Post date:** [February 10, 2011, 12:59am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/22 "2011-02-10T00:59:48Z")
> [@billfish678](#): > > Did I say otherwise? > > Can you DO the math or do you GET the math? Or the physics? IME one ain’t the other. > > Sure, you need a mix, but if its mostly DO and little GET I don’t think you are going to reach any intellectual Nirvana because you can DO it. Or if you do, its certainly a different one than the getting it one. Okay. I’m not sure I know what you mean by “getting” math. It’s not the ability to do calculations, its not the ability to extrapolate to make interesting generalizations, and its not an appreciation of the beauty of the math. All of those are fun intellectually and they sure _feel_ like “getting” it, especially the last two. So what are you referring to, really, that is so unachievable by **brocks** in self-study? ---
**Author:** ![Tim\_T-Bonham.net](https://avatars.discourse-cdn.com/v4/letter/t/46a35a/32.png) [@Tim\_T-Bonham.net](https://boards.straightdope.com/u/Tim_T-Bonham.net)\ **Post date:** [February 10, 2011, 1:08am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/23 "2011-02-10T01:08:39Z")
> [@Enola\_Straight](#): > > Einstein himself believed relativity could be grasped by the average guy. And Ernest Rutherford, the ‘father of nuclear physics’, said _“If you can’t explain your physics to a barmaid it is probably not very good physics.”_ ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [February 10, 2011, 1:12am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/24 "2011-02-10T01:12:00Z")
> [@brocks](#): > > Is that five years for a PhD-track student, or for a guy doing what I’m doing (3 or 4 hours a day, no tutor)? > > And thanks for your remarks on the joy of the journey. Pretty much agrees with my previous post. And I would be very happy if “all” I get out of this is a really good understanding of special relativity, and a good BS detector for GR and QM. There’s different levels of understanding. All of them involve maths, but there’s still a choice on far you want to go I mean for example do you really want to learn all the numerical methods for solving particualrly difficult differential equations? Once you’ve got specisal relatvity nailed (not that difficult tbh) and you’ve also leanrt about vector spaces (absolutely necessary for quantum mechanics) try Bernard Schutz’s _A First Course in General Relativity_. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [February 10, 2011, 1:13am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/25 "2011-02-10T01:13:47Z")
I don’t understand why you are asking this question. If you want to do it and think you’ll enjoy the process, then just do it. You obviously decided to go ahead before you posted. If you’re asking whether you’ll succeed 15 years from now, then you’re not asking a question that any of us can answer. ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [February 10, 2011, 1:25am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/26 "2011-02-10T01:25:30Z")
I did my undergraduate degree in mathematics. I took some physics courses with the idea of getting a minor in physics. The (strictly undergraduate) college I went to wasn’t very big, but even it had a course in relativity and a course in quantum physics. You have an undergraduate degree in mathematics, so you’re smart enough to understand relativity and quantum mechanics. Look for the lowest-level textbooks you can find about relativity and quantum mechanics. (These will not be popular introductions to these subjects that skip the mathematics. You might want to read those first though, but then find the lowest-level textbooks you can obtain that have the mathematics in them.) If you don’t understand the physics or the mathematics in those books on quantum physics and relativity, look for lower-level books (but college-level books) on the physics and mathematics that you don’t understand in them. Work your way slowly but steadily through them. If you persist, you will eventually understand these subjects. ---
**Author:** ![billfish678](https://avatars.discourse-cdn.com/v4/letter/b/7bcc69/32.png) [@billfish678](https://boards.straightdope.com/u/billfish678)\ **Post date:** [February 10, 2011, 1:26am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/27 "2011-02-10T01:26:15Z")
> [@spenczar](#): > > Okay. I’m not sure I know what you mean by “getting” math. It’s not the ability to do calculations, its not the ability to extrapolate to make interesting generalizations, and its not an appreciation of the beauty of the math. All of those are fun intellectually and they sure _feel_ like “getting” it, especially the last two. > > So what are you referring to, really, that is so unachievable by **brocks** in self-study? I haven’t said ANYTHING is unachievable by Brocks. And did I say ANYTHING about the ability to extrapolate generalizations or a appreciation of the beauty of the math? No, I talked about solving problems and being able to DO the math. The ability to extrapolate and see the beauty would be some of my definitions of “getting it”, which are DIFFERENT from the ability to do the basic calcs now wouldnt it ? They must be because you listed them as distinctly different items now didn’t you? ETA. I see Exapno cut to the chase here. My points were these: The ability to do the problems doesn’t mean you’ll “get it”. If the years of math study won’t be inherently fun, the reward at the end might not be worth it. Even if the trip is fun, being able at the end to “do the problems” still doesnt mean you’ll “get it”. Given all this, perhaps another path (or destination for that matter) might be a better life choice for the OP. I guess next time somebody here wants to spend years of their lives doing something I’ll just go “hell yeah, go for it” rather than trying to point out possible pitfalls and making them think about the pro’s and the con’s and the process a bit. ---
**Author:** ![brocks](https://avatars.discourse-cdn.com/v4/letter/b/7feea3/32.png) [@brocks](https://boards.straightdope.com/u/brocks)\ **Post date:** [February 10, 2011, 1:26am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/28 "2011-02-10T01:26:44Z")
> [@Exapno\_Mapcase](#): > > I don’t understand why you are asking this question. If you want to do it and think you’ll enjoy the process, then just do it. You obviously decided to go ahead before you posted. > > If you’re asking whether you’ll succeed 15 years from now, then you’re not asking a question that any of us can answer. I wasn’t asking for permission, and I wasn’t asking whether I would succeed. I was asking whether it was a realistic goal for someone good, but not great, at math. If the answer is no, that won’t stop me, because I think determination might make up for lack of talent. There is also some evidence that my talent is sufficient, after all, because as noted earlier, I didn’t work as hard as I could have in college. But I did score 2400 on the GRE, back when it was Verbal-Math-Analytical, so who knows? ---
**Author:** ![brocks](https://avatars.discourse-cdn.com/v4/letter/b/7feea3/32.png) [@brocks](https://boards.straightdope.com/u/brocks)\ **Post date:** [February 10, 2011, 1:32am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/29 "2011-02-10T01:32:11Z")
> [@billfish678](#): > > I guess next time somebody here wants to spend years of their lives doing something I’ll just go “hell yeah, go for it” rather than trying to point out possible pitfalls and making them think about the pro’s and the con’s and the process a bit. I think the problem is that you haven’t pointed out any pitfalls; not really. For the life of me, I can’t understand how I could do something for 15 years without noticing that I’m not enjoying it. And I thought I made it pretty clear that satisfaction was the only reward I expected out of this. So what makes you think I’m going to come out of some kind of trance 15 years from now, and notice for the first time I’m not getting what I wanted out of it? Another of the reasons I didn’t study as much in college as I should have was I was into weightlifting. And there were always people, including in my immediate family, who would ask why I was spending so much time on that, when I could be doing other stuff. They always made it seem like I was taking time away from writing symphonies or performing Shakespeare, but the funny thing was, they spent most of _their_ time watching sitcoms. ---
**Author:** ![spenczar](https://avatars.discourse-cdn.com/v4/letter/s/858c86/32.png) [@spenczar](https://boards.straightdope.com/u/spenczar)\ **Post date:** [February 10, 2011, 1:37am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/30 "2011-02-10T01:37:52Z")
> [@billfish678](#): > > The ability to extrapolate and see the beauty would be some of my definitions of “getting it”, which are DIFFERENT from the ability to do the basic calcs now wouldnt it ? They must be because you listed them as distinctly different items now didn’t you? First of all, chill out, man. I didn’t kill your dog; I just asked for clarification. Perhaps the reason I thought you were dismissing math entirely was your response to my post. I said (in way more words) “Math is still good because it lets you extrapolate and see beauty” which you responded to with > [@](#): > > Can you DO the math or do you GET the math? Or the physics? IME one ain’t the other. > > Sure, you need a mix, but if its mostly DO and little GET I don’t think you are going to reach any intellectual Nirvana because you can DO it. Or if you do, its certainly a different one than the getting it one. That doesn’t read like agreement to me. I wasn’t sure _what_ you were saying, but you sure sounded convinced and angry, so I asked you to clarify. That’s all, take a deep breath. ---
**Author:** ![Simplicio](https://avatars.discourse-cdn.com/v4/letter/s/c37758/32.png) [@Simplicio](https://boards.straightdope.com/u/Simplicio)\ **Post date:** [February 10, 2011, 1:58am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/31 "2011-02-10T01:58:55Z")
> [@brocks](#): > > I wasn’t asking for permission, and I wasn’t asking whether I would succeed. I was asking whether it was a realistic goal for someone good, but not great, at math. I think the biggest thing is being able to _enjoy_ math. IMHO anyone reasonably intelligent thats willing to put the time in can figure out the math well enough to get a good handle on even upper level physics. But you have to be willing to sit there and bang your head around problems that might take a few hours, which means you more or less have to enjoy it. But you don’t need to be a super-genius or anything, and while its an acquired taste, if you enjoy it, its pretty easy to burn the time necessary to get a good understanding. As encouragement, my dept has a guy that took up physics as more or less a retirement project after being a lawyer for most of his life. The dept doesn’t pay him, but they gave him an office in return for his teaching a class. He’s not the worlds greatest researcher or anything, but he certainly knows enough to be conversant with Professors and Post-Docs in his area and understands the research being done in his area of interest. So what your contemplating is certainly do-able. ---
**Author:** ![davidm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/davidm/32/225_2.png) [@davidm](https://boards.straightdope.com/u/davidm)\ **Post date:** [February 10, 2011, 2:03am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/32 "2011-02-10T02:03:29Z")
The vast majority of quantum physicists started as laymen. Actually, all of them did. ---
**Author:** ![brocks](https://avatars.discourse-cdn.com/v4/letter/b/7feea3/32.png) [@brocks](https://boards.straightdope.com/u/brocks)\ **Post date:** [February 10, 2011, 2:07am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/33 "2011-02-10T02:07:56Z")
> [@These are my own pants](#): > > I mean for example do you really want to learn all the numerical methods for solving particualrly difficult differential equations? If it’s necessary to understand what I want to understand, then yes. But would it be necessary? If you have something like Maple or Mathematica to do the grinding for you, and assuming you understand why you want to solve this equation and how it is solved, do you lose anything by letting Maple do it for you? Is it any different than using a calculator, rather than pencil and paper, for long division, once you understand why and how the pencil and paper method works? ---
**Author:** ![brocks](https://avatars.discourse-cdn.com/v4/letter/b/7feea3/32.png) [@brocks](https://boards.straightdope.com/u/brocks)\ **Post date:** [February 10, 2011, 2:10am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/34 "2011-02-10T02:10:04Z")
> [@Simplicio](#): > > As encouragement, my dept has a guy that took up physics as more or less a retirement project after being a lawyer for most of his life. The dept doesn’t pay him, but they gave him an office in return for his teaching a class. He’s not the worlds greatest researcher or anything, but he certainly knows enough to be conversant with Professors and Post-Docs in his area and understands the research being done in his area of interest. > > So what your contemplating is certainly do-able. That is indeed very encouraging. May I ask why a physics dept would want a lawyer with no formal credentials in the field to teach a class? Or is it a law class? ---
**Author:** ![Simplicio](https://avatars.discourse-cdn.com/v4/letter/s/c37758/32.png) [@Simplicio](https://boards.straightdope.com/u/Simplicio)\ **Post date:** [February 10, 2011, 2:20am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/35 "2011-02-10T02:20:43Z")
> [@brocks](#): > > That is indeed very encouraging. > > May I ask why a physics dept would want a lawyer with no formal credentials in the field to teach a class? Or is it a law class? He’d already taught himself a sizable amount of physics when he came here, so apparently he convinced whoever he had to that he was qualified to teach it. And he did have a physics B.S. from however many decades ago, so he wasn’t completely without credentials. And there’s a PhD listed as his co-lecturer, though it appears the ex-lawyer does most of the actual work. It also probably helps that with the Recession, public universities can’t hire new faculty, and so departments have been engaging in some creative methods of expanding. So a guy that wants to come work for free looks pretty good, credentials be damned. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 10, 2011, 5:31am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/36 "2011-02-10T05:31:11Z")
> [@](#): > > The vast majority of quantum physicists started as laymen. Actually, all of them did. That’s what I was going to say: Clearly, it _is_ possible for a layman to learn what the experts do, or there wouldn’t be any experts. Now, obviously it’s going to be harder self-taught, but the fact that you have the motivation to do it will help tremendously. And it doesn’t have to be entirely self-taught, either: A lot of universities will have programs where older folks can audit classes for a discounted price, and for the introductory material, there’s always community colleges, which are cheap for everyone. As for how to go about matters: Special relativity, as others have mentioned, doesn’t require anything more than high school-level algebra. So bone up on your algebra, then look into SR. Note that the best books on SR are generally the first chapters of books on GR, since they’ll present it in a strong, general framework that you’ll later build on for GR. For instance, the Einstein summation convention will make tensors vastly easier to work with, and a good SR book will introduce it (even though it’s not really necessary at that level) to give you time to get comfortable with it. For quantum mechanics, I would recommend that you start with extensive study of classical wave theories. About 90% of the weirdness in QM stems directly from wave-particle duality, and the fact that QM is basically a wave theory. The Heisenberg uncertainty principle, for instance, shows up in a guitar string or in ripples on a pond, and nobody ever thinks it odd in those contexts. Once you’re completely comfortable with classical waves, then and only then should you actually crack open any book with “quantum” in the title. ---
**Author:** ![The\_Second\_Stone](https://avatars.discourse-cdn.com/v4/letter/t/bbe5ce/32.png) [@The\_Second\_Stone](https://boards.straightdope.com/u/The_Second_Stone)\ **Post date:** [February 10, 2011, 7:39am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/37 "2011-02-10T07:39:42Z")
I am a quantum mechanic by trade. There are no stray cats in our neighborhood. If something in your house is broken, I may or I may not be able to fix it. You won’t know until you try to use it. ---
**Author:** ![Chief\_Pedant](https://avatars.discourse-cdn.com/v4/letter/c/a6a055/32.png) [@Chief\_Pedant](https://boards.straightdope.com/u/Chief_Pedant)\ **Post date:** [February 10, 2011, 11:13am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/38 "2011-02-10T11:13:02Z")
> [@Stranger\_On\_A\_Train](#): > > Special relativity can be understood by anyone with a high school education and a little bit of intuition for mechanics. > > General relativity can be understood by anyone who has five years or so to study metric tensors, differential geometry on curved manifolds, and some pretty hefty vector calculus. > > Stranger I don’t agree with this. This sort of understanding is not nearly so much a function of time as it is of aptitude. A dullard such as I could spend a lifetime and not get a particularly strong grasp beyond the non-mathematical general concepts; a more capable brain for the math involved may not need five months. Our genetically-determined wiring sets an upper limit for our intellectual ability in any given area, and while it’s true more time will help, it’s a false premise that anyone can understand anything if they are simply given the time and circumstance. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [February 10, 2011, 11:19am UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/39 "2011-02-10T11:19:51Z")
> [@brocks](#): > > If it’s necessary to understand what I want to understand, then yes. > > But would it be necessary? If you have something like Maple or Mathematica to do the grinding for you, and assuming you understand why you want to solve this equation and how it is solved, do you lose anything by letting Maple do it for you? Is it any different than using a calculator, rather than pencil and paper, for long division, once you understand why and how the pencil and paper method works? That’s what I mean, it’s NOT really necessary. ---
**Author:** ![Quercus](https://avatars.discourse-cdn.com/v4/letter/q/7ab992/32.png) [@Quercus](https://boards.straightdope.com/u/Quercus)\ **Post date:** [February 10, 2011, 1:55pm UTC](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811/40 "2011-02-10T13:55:08Z")
> [@brocks](#): > > Is that five years for a PhD-track student, or for a guy doing what I’m doing (3 or 4 hours a day, no tutor)? > > And thanks for your remarks on the joy of the journey. Pretty much agrees with my previous post. And I would be very happy if “all” I get out of this is a really good understanding of special relativity, and a good BS detector for GR and QM. Hey, I have a physics degree and that’s about all I have right now. And it seems like a pretty good goal, by the way. My only addition is that if you’re going to be doing actual quantative QM problems, you’ll probably want to learn enough linear algebra to understand eigenvectors & eigenvalues. [Previous page](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811.md?page=1) [Next page](https://boards.straightdope.com/t/can-a-layman-learn-gr-and-qm-really-learn/570811.md?page=3)