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Quantum Mechanics Is Not That Hard to Understand

Alexander Turishchev

Published Mar 22, 2026• 0 citations
Publisher

Abstract

In this text, I don’t want to add anything new to quantum mechanics.I just want to help people understand it, to make learning a little easier.For example, a child, a teenager, or anyone curious about the subject — they want to know and understand.But right now, quantum mechanics is presented in such a way that after reading, a person still can’t find a simple answer to the question: “what actually is this?”That’s why I want to make it easier for everyone who wants to understand.

DOI
10.5281/zenodo.19166119

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Ask me anything

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In this text, I don’t want to add anything new to quantum mechanics.I just want to help people understand it, to make learning a little easier.For example, a child, a teenager, or anyone curious about the subject — they want to know and understand.But right now, quantum mechanics is presented in such a way that after reading, a person still can’t find a simple answer to the question: “what actually is this?”That’s why I want to make it easier for everyone who wants to understand.
This book attempts to explain the core of physics, the origin of everything and anything. It explains why physics at the most fundamental level, and especially quantum mechanics, has moved away from naïve realism towards abstraction, and how this means that we can begin to answer some of the most fundamental questions which trouble us all, about space, time, matter, etc. It provides an original approach based on symmetry which will be of interest to professionals as well as lay people. In the book, virtually no prior knowledge is assumed, but the readers are allowed to participate in a discussion of very deep ideas. Throughout the book, the readers are guided through some important ideas which need to be explained mathematically. The key fact is that the mathematics is not about calculation but about concepts. Much of it can be simplified using coloured text and diagrams. This means that ideas which are important to everyone who wants to know how the universe is structured are not glossed over as being too difficult for anybody but the experts. This book is written for a wide audience. Experts will gain a great deal, but so will lay readers. This would be an ideal book for students to read before progressing to another book by the author, The Foundations of Physical Law.
In the last two chapters, we talked about computational complexity up till the early 1970s. Here, we'll add a new ingredient to our already simmering stew – something that was thrown in around the mid-1970s, and that now pervades complexity to such an extent that it's hard to imagine doing anything without it. This new ingredient is randomness . Certainly, if you want to study quantum computing, then you first have to understand randomized computing. I mean, quantum amplitudes only become interesting when they exhibit some behavior that classical probabilities don't : contextuality, interference, entanglement (as opposed to correlation), etc. So we can't even begin to discuss quantum mechanics without first knowing what it is that we're comparing against. Alright, so what is randomness? Well, that’s a profound philosophical question, but I’m a simpleminded person. So, you’ve got some probability p , which is a real number in the unit interval [0, 1]. That’s randomness. But wasn’t it a big achievement when Kolmogorov put probability on an axiomatic basis in the 1930s? Yes, it was! But in this chapter, we’ll only care about probability distributions over finitely many events, so all the subtle questions of integrability, measurability, and so on won’t arise. In my view, probability theory is yet another example where mathematicians immediately go to infinite-dimensional spaces, in order to solve the problem of having a nontrivial problem to solve! And that’s fine – whatever floats your boat. I’m not criticizing that. But in theoretical computer science, we’ve already got our hands full with 2n choices. We need 2ℵ0 choices like we need a hole in the head.
To remind you, this book is based on a course I taught in 2006. On the last day of class, I followed the great tradition pioneered by Richard Feynman, in which the last class should be one where you can ask the teacher anything. Feynman's rule was that you could ask about anything except politics, religion, or the final exam. In my case, there was no final exam, and I didn't even make politics or religion off-limits. This chapter collects some of the questions people asked me, together with my responses. Student: Do you often think about using computer science to limit or give us a hint about physical theories? Do you think that we'll be able to discover physical theories which give more powerful models than quantum computation? Scott: Is BQP the end of the road, or is there more to be found? That's a fantastic question, and I wish more people would think about it. I’m being a bit of a politician here and not answering directly, because obviously the answer is “I don't know.” I guess the whole idea with science is that if we don't know the answer, we don't try to sprout one out of our butt or something. We try to base our answers on something. So, everything we know is consistent with the idea that quantum computing is the end of the road. Greg Kuperberg had an analogy I really liked. He said that there are people who keep saying that we've gone from classical to quantum mechanics so what other surprises are in store? But maybe that's like first assuming the Earth is flat, and then on discovering that it's round, saying who knows, maybe it has the topology of a Klein bottle. There's a surprise in a given direction, but once you've assimilated it, there may not be any further surprise in that same direction.