Can someone without knowledge base understand quantum mechanics?

I think this question needs to have a reasonable definition first. What is “reading”?

Many people say that you have never studied calculus, algebra, or complex functions, and you absolutely cannot understand quantum mechanics, which is of course true. But the question is, if we define the concept of “understanding” extremely harshly, even if you learn all the above knowledge, do you “understand” quantum mechanics? We can go on to say, how can you not learn functionals, group theory, tensor computation, differential manifolds, gauge field theory… Even if you rise to the forefront of the field, before you fully understand quantum gravity, Who dares to say that he completely “reads” what he can do? In the end it comes down to what Feynman said “no one really understands quantum mechanics”.

Now when ordinary people mention that they want to read a little bit of quantum theory, many people jump out and say that if you don’t learn this or that, you can’t really understand it. This trend seems a bit extreme. According to this logic, we can also ask: Middle school students can’t solve Maxwell’s equations, so do they have no right to try to understand the fact that “light is an electromagnetic wave”? Middle school students don’t understand the principle of least action, can’t write Laplace and Hamilton’s equations, so why don’t they even learn Newton’s three laws? Even pushed to the extreme, you can ask: Can primary school students “understand” 1+1=2?

Many people may have heard this joke, saying that a Russian mathematician went to a French elementary school and asked the elementary school students: 1 plus 2 equals how much? Elementary school students say I don’t know the exact answer, but I know that 1 plus 2 must be equal to 2 plus 1. Ask him why? He said: “It’s not obvious yet? Because integers form an abelian group under addition.

This joke is of course used to laugh at the Bourbaki school in France. According to this school, even simple mathematics must be learned from the “most essential” and “deepest” foundation. However, practice clearly tells us that this does not work. Feynman stated clearly in his lectures on physics that we cannot lay out the most “basic” and “essential” advanced laws right away, but must start with some easier-to-understand, “approximately correct” laws. . This is also for college physics students. For lower-level groups of people, for the purpose of more popular science, this should not be a problem. Many more accessible means and metaphors, although technically “mistakes”, are absolutely needed and should not be grounds for scolding.

Any learning requires attention to methods and methods, and needs to conform to the laws of cognition. The kindergarten teacher tells you that 3 cannot be subtracted by 5, because a small number cannot be subtracted from a large one. Then in elementary school, the teacher tells you: Actually, yes, because there are still negative numbers. At the same time, the elementary school teacher said that the square root of negative numbers cannot be taken, because the square of any number is positive. However, when you get to middle school, the new teacher tells you: In fact, you can, because there is another thing called imaginary numbers. So, are all the previous teachers lying to you? Are they all misleading their children? Of course not. With the increase of knowledge, you will naturally overturn some previous conclusions, which is a learning process in itself.

Many people always say bitterly that it is inadvisable and harmful for ordinary people to accept some conclusions wholeheartedly without sufficient mathematics People do not intend to engage in full-time scientific research work at all, they just want to learn more knowledge and open their eyes. Even if you really want to do this, can some simplified “misdescriptions” in middle school textbooks or popular science books destroy a real physics genius? Without even the most basic ability to continue learning and correcting mistakes, can such a person be called a “true physics genius”? Middle school textbooks still tell us that “electrons revolve around the nucleus”, and they also carefully drew layers of Bohr atomic orbits in the diagram. How many future quantum physicists have this destroyed? Another example is the formula E=mc^2 that everyone knows, why do you not strictly distinguish between dynamic mass and static mass? Why not write this formula in full form? You can even say that the universe as a whole has no translational symmetry, so there is no conservation of energy, so this formula is wrong, and whoever remembers this formula will make a big mistake, become a laughing stock, or even destroy it Future academic career…

As for?

So I think it’s not a sin to teach ordinary people, middle school students, and even elementary school students about the theory of relativity, quantum physics, etc. (Not to mention that “Quantum Physics for Babies” is already available now.) Of course, as a student, you also need to have a clear understanding that learning is hierarchical, and the “quantum mechanics” understood on the basis of elementary school is different from that of “quantum mechanics”. The “quantum mechanics” understood on the basis of middle school, university, and even doctoral students is not the same thing, and even many specific conclusions may be contradictory or even diametrically opposite. From the most superficial, easy-to-image, and cool-sounding “wave-particle duality”, “Schrödinger’s cat”, “parallel universe”, etc., to more abstract wave functions, Schrödinger equation, and then go up a level, you will understand that this is essentially the mapping of the state vector in the Hilbert space, including what is an operator, what is an eigenstate, what is a density matrix, etc., and then above There are more advanced nouns, such as U(1) group, SU(2) group, etc. However, the more you go to the upper level, your understanding will be deeper and more “basic”. With the deepening of these understandings, you will gradually realize that many of the previous “understandings” are actually wrong, incomplete, or have a lower-level understanding.

For example, many people may have heard that quantum mechanics is uncertain, and the Schrödinger cat represents a state of probability, and so on. The “determined” state, even quantum mechanics itself is completely possible to be “determined” (there is only unitary evolution), the so-called uncertainty is just some kind of “explanation” of quantum mechanics (represented by the Copenhagen interpretation) . However, this “rejection” itself is a process of learning, and when you understand the problem in depth, you can better understand why there is such a different understanding. This kind of “wrong simplification” is innumerable in primary and secondary education, and it is not clear how many people have to go to compete with primary school teachers? Why get tangled up in issues like relativity or quantum theory?

So I think everyone should calm down. It is not a bad thing for students to read popular science about cutting-edge theories out of interest, but it is important to understand that only a superficial and possibly “wrong” understanding can be gained from it. Don’t just think that you have mastered the truth of the universe, let alone create your own “theories” by taking it for granted. And people who really study this field don’t have to worry too much about this “mistake”. From the point of view of mass education, the appropriate sacrifice of accuracy is necessary, and has always been so. When children grow up, they will naturally understand that the earth is not really “round”, and it does not “revolve around the sun”, and there is no need to get angry and blame this knowledge for how wrong it is.

It’s like an elementary school teacher teaching addition, she tells you: one apple plus one apple equals two apples, so 1+1=2. If a math professor insists on rushing up and yelling that you are wrong! If you don’t teach set theory, don’t introduce the ZFC axiom system, and don’t talk about Peano’s axioms, how can you make them really understand why 1+1=2? So, do you think the primary school teacher has a problem, or the math professor?

Source: Zhihu

Author: Cao Tianyuan Capo

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Further reading:

How to teach yourself quantum mechanics in high school?

What knowledge do you need to learn quantum mechanics?

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