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B What does it take to understand quantum mechanics?

  1. Aug 27, 2016 #1
    Lately I've taken a lot of interest in quantum mechanics but I have no formal schooling on the topic. Actually I dropped out of high school and joined the army, so besides using a map and compass or counting ammo I've had barely any use for math at all in about 10 years. But I've enjoyed quite a few articles and youtube videos on the double slit experiment, quantum entanglement, wave-particle duality, superstates and so on.

    So my question is, how long would it take me to learn the math, processes, experiments, etc. to understand and prove these things for myself? Let's assume that my math skills and overall intelligence is exactly average, whatever that might be. How many years of school and university would it take? And how hard would it be to learn on my own?
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  3. Aug 27, 2016 #2


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    A fairly normal academic path might be:
    - Year one: Basic differential and integral calculus, the stuff that is covered in a high school AP class or first-year college calculus.
    - Year two: Classical mechanics, special relativity, and E&M; multi-variable and vector calculus, elementary differential equations, complex numbers, and linear algebra.
    - Year three: Intro QM.
    So the answer to the "how many years?" question is something like "However long it takes to get to AP calculus, plus two". It's feasible to do this as a self-study (and then you can compress the schedule some) but it's still hard work.

    You might want to give Giancarlo Ghiradi's "Sneaking a look at God's cards" a try. It is far less mathematically demanding (no one is going to mistake it for a real textbook) but still provides an honest and solid overview of QM, something that you will never get from videos and articles.
  4. Aug 28, 2016 #3
    Great, thank you. I looked up the book, and I'm going to buy it, but first I want to make sure it's appropriate for a layman. I bought Quantum Mechanics: The Theoretical Minimum, which requires a basic understanding of calculus (something not advertised on the description and something I do not have.)
  5. Aug 28, 2016 #4
    Another starter book you could try -- https://www.amazon.com/Quantum-Reality-Philosophy-Jonathan-Allday/dp/1584887036/
    Last edited by a moderator: May 8, 2017
  6. Aug 28, 2016 #5
    I would do linear algebra in year one, just because matrices can appear in later topics. Also Nugatory's list makes it look easier than it is IMHO: "classical mechanics" actually includes analytical mechanics (Lagrangian and Hamiltonian), and "complex numbers" actually means "complex analysis". Both are very hard topics. Usually people don't bother as a hobby if they have to start from scratch, but hey, if you have a lot of free time it's better than watching tv all day...
  7. Aug 28, 2016 #6


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    Ghirardi requires no calculus, why I suggested it. It's still not an easy read; there are paragraphs that you'll go back over two or three times.

    (BTW, the reviews on amazon.com are pretty good at letting you know what you're in for, with both this book and Susskind)
    Last edited by a moderator: Aug 29, 2016
  8. Aug 28, 2016 #7


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    They are, but they're not needed to get through a first-year undergrad QM text. Of course you'll need them if you're going to move beyond that level - relatoivistic QM, QFT, the more complete and rigorous treatment you'll find in Ballentine and other graduate-level texts - but that's more than what OP is asking for.
  9. Aug 29, 2016 #8


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    Well, the good news is that all you need to understand quantum theory is math. Start with linear algebra and then extend it with Hilbert-space theory. My math professor used to say that (separable) Hilbert spaces are almost as simple as finite-dimensional ones. There are some subtleties about unbound self-adjoint operators which, however, almost never occur in the physicist's everyday work, and that's why physicists come very far even with a pretty hand-wavy use of generalized eigenvectors and eigenvalues. So you don't even need the fully rigorous treatment of Hilbert-space theory (although it doesn't hurt to learn them later to understand also the subtle points).

    The even better news is that you don't need any confusing philosophy at all. Reality is what's observable in nature (or in the lab with controlled experimental setups). The connection between the formalism of QT and real-world observation/experiments is given by Born's rule, and that's it (minimal statistical interpretation). Everything else is not physics but metaphysics, which may by entertaining but it's not necessary to understand physics.
  10. Aug 29, 2016 #9
    I should come clean here: I don't actually intend to learn the physics of quantum mechanics. I am simply awful at math. I was more just looking to gauge the amount of work it would take for an average person to prove some of the more "spooky" claims for himself.

    I was in jail for awhile in the states last year where a fire and brimstone priest came in one Sunday to give a lesson on Christianity. Personally I've been an atheist for a long time, but after the lesson in jail I asked some of the other inmates about their beliefs, and some of the things I heard were... Well, very interesting. One gentleman asked me, "You see how bright the moon gets at night? You think the sun does that? No way man," and he went on to inform me that the moon was actually a hollow space craft manned by aliens who had enslaved the human race, that mosquitoes and spiders are actually robot spies, that hallucinations from meth withdrawal is actually a glimpse at the real world, etc.

    Everyone in jail believed in both ghosts and Aliens. Of all the people I talked to, I was the only one who believed in Darwin's Theory of Evolution.

    Now I am a firm believer in science. But, as I am not a scientist, I am only exactly that: a believer, and after those conversations in jail I realized that it takes just as much faith for me to believe in quantum mechanics as it does for anyone else with my education to believe in ghosts or aliens or resurrection or anything like that. Now I believe it makes much more sense to believe in science than the supernatural, and I don't need to explain why to any of you here, but for an uneducated person like myself it absolutely takes faith.

    So my question was about what it would take to turn that faith into knowledge, and to be honest your answers are pretty intimidating, but they make perfect sense. It would be nice if all I had to do to understand QM was fast for a month or sacrifice a goat. I'd do that no problem. But the real path is just not in the cards for me, or at least not any time soon, so for now I'll just have to keep going on faith.
  11. Aug 29, 2016 #10
    Well, don't think that other "less spooky" or "not spooky" areas of science would take less work in the end :) the hardest problem in physics is turbulence, which for the layperson is trivial. Funny that your jail mates didn't find it an example of the occult that water comes out white and foamy instead of transparent if you open the faucet enough.
  12. Aug 29, 2016 #11
    Well I don't really recommend trying to understand quantum physics without any mathematical background. You don't need to know all of the precise and definite knowledge in mathematics to understand quantum physics, but you should at least know the idea of what it does. The learning stage of quantum physics is 99% math. As such, when you open any quantum physics textbook, they'll have so many more equations than pictures. You should at least be able to understand using your knowledge of mathematics how equations are derived, and what they imply (you don't need to do the math yourself though).

    Quantum physics is sometimes counter-intuitive if non-mathematical language is used. For example, I can tell you that exchange interaction can keep two atoms together by "exchanging electrons" (hence they are sometimes referred to as exchange force, though this is not correct to be precise). If you imagine this in your mind, this doesn't make sense at all. Why can two atoms be attracted and stay that way just by exchanging electrons? But if you look at the mathematical formulation of exchange interaction, it does indeed make sense. Exchange interaction is purely quantum mechanical phenomenon, and there is no analogy to classical mechanics.
    Meanwhile, when I tell you about magnetic attraction/repulsion, it is much easier to understand because you actually see this in macroscopic world; two magnets attract/repel depending on their orientation.

    I've seen people reading magazines for non-scientific public and interpret quantum mechanics in a hilariously wrong way. They claim that quantum mechanics are spooky magical world. I've seen worse where people fallaciously apply quantum mechanics to try to explain transcendence and God and claim that science have proven the existence of God.

    So if you want to "understand" quantum physics, you would need to know at least linear algebra and calculus. I suck terribly in math too bro and I have hard time understanding quantum physics too. Besides, I am a chemist, not a physicist.
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