As a non-physicist, QM only clicked for me when I learned the linear algebra of one- and two-qubit systems and observables on those systems [1]. The math is accessible at a pre-calculus level, and the most "counter-intuitive" aspects of QM (interference, the uncertainty principle, entanglement) make perfect sense in this framework. I think it's the best starting point for understanding what QM really says.

[0] That's not to say they aren't important historically or for a complete understanding of QM. I'm talking about conceptual understanding for someone, especially an amateur, encountering QM for the first time.

[1] Chapter 2 of Nielsen and Chuang is what did it for me. It's heavygoing if you've never seen linear algebra before, but I don't know of a clearer explanation of the postulates of quantum mechanics.

Basic Concepts Of Quantum Mechanics by L. V. Tarasov

https://archive.org/details/tarasov-basic-concepts-of-quantu...

The dialogues of the author engages with various personas and the reader that are interspersed as Prelude and Interludes are really enlightening.

For example:

Classical Physicist: Can one seriously speak about an object without having an idea of what it looks like? Isn’t it strange that we study, for example, the behaviour of an electron in a crystal while we don’ t even know what an electron actually is?

Author: I don’t agree that we don’t even know what an electron is. I have just indicated a number of precisely determined characteristics and properties of an electron. More detailed properties of microparticles in general and electrons in particular were considered in the preceding sections of the book (and will be considered in the following sections). In fact, we know quite a lot about the electron and know, in particular, about its behaviour in a crystal. This is evidenced by the large number of semiconducting devices fabricated and used by us in practice. As you will see, the absence of a “physically intuitive” model of the electron has in no way turned out to be a serious obstacle. We may even go a step further and state that an understanding of natural phenomena in which Planck’s constant plays an important role is possible only through a significant rejection of a graphic description. By the way, this idea was given by Heisenberg, in whose works much attention was given to questions of the use of physically intuitive methods.

I think these lectures are a good intro to QM. This statement feels very emotional though. Many-worlds just states there is no such thing as wave function collapse. The many worlds are a logical conclusion following. Copenhagen simply refuses to elaborate to when wave-function collapse happens, which to me is not a complete theory.

You could have some critique of many-worlds in relation to statistics, although I think many people have given quite satisfactory explanations.

Many worlds is just bare bones QM.. If any other theory is proposed, it should be falsifiable (like pilot wave theory for example). Doesn't mean it won't be difficult to measure.

If anyone is interested in self-studying quantum physics, QFT for the Gifted Amateur [1] is very well regarded.

1: https://academic.oup.com/book/36442?login=false

https://scholarpedia.org/article/Bell's_theorem

"The number of different wavelengths of electromagnetic radiation, N(λ)dλ, with wavelengths in a small interval between λ and λ + dλ, (dλ means a small interval in wavelength) can be shown to be proportional to 1/λ⁴."

doesn't make sense. It should not talk about a number of wavelengths, but the number of allowed standing-wave modes (number of eigenmodes that a mathematical solution to the electric field in the relevant situation has) in the small wavelength interval.

This doc is the first one I've seen that explains upfront what a wave means here: "The quantity which travels in this way is known as a 'disturbance'. Precisely what this disturbance is depends on the wave," and for EMR, "it is an electric field and a magnetic field which are perpendicular to each other and also perpendicular to the direction of the wave." So now I'm going to read the rest.

I don't have much to add on the article itself except that it's almost certainly worth reading.

It was also weird to know that then as it still is today, the only wave function that can be solved is single atom hydrogen.

That's a pretty bold assumption.

- Richard Feynman

The math does indeed work, and many experiments and practical uses seem to show that there is something to quantum broadly. But to throw determinism out the window and believe that quantum is fundamentally probabilistic, and that one can never really run scientific experiments because observing state collapses superposition, has always seemed asinine to me.

I could be completely wrong, but it's always seemed obvious to me that the need for probabilities in quantum is a clear indicator that something is missing in the theory. I'm never surprised when a person can't understand quantum as its described today.

When the "measurement"/"interaction" has a catastrophic :) impact on what you want to understand, won't be easy to "understand" anything.

On the bright side, the universe did throw at us some nibbles through that 'catastrophic' fog which can be "useful".

I think, it is important to teach the mathematical emergence of our classic physics from quantum physics (well... not gravity ofc).

Another important thing to teach kids: the difference between models and reality. We were lucky this emergent physics was not chaotic and have had strong predictability and has been very stable... well we would not exist otherwise.

It sounds all superior and mysterious to quote Feynman here, but the fact is many people absolutely do understand quantum mechanics.

It doesn't. It's model. All models are wrong (including quantum mechanics and attention) but some are useful. You understand the domain of the model, the problems it can solve, the math behind the models and use the model to make predictions. If you are competent at linear algebra and functional analysis, you can do quantum mechanics.

If you make the error of believing that quantum mechanics is ontological god's honest truth of nature, you will end up with blunders like using it to explain consciousness like Prof Penrose. His math was impeccable, but he was making a category error.

Tl;dr spacetime does not exist as a global background where things are "placed", it is not ontic. "Things" are first, and spacetime is derived from interaction statistics of "things". This eliminates nearly all naive paradoxes like double slit etc. Now, these "things" are somewhat complicated and non-intuitive (e.g. there are no individual "particles", they are a limit of discrete distributions), but that's a good start.

My theory: The reason we perceive collapse as irreversible is because the computational complexity of reversing the equations is very high. Especially as the state converges towards an eigenvalue of the measurement operator, it becomes more difficult to reverse. This is similar to how a hash function is reversible in principle but not practice. My two cents.

Many worlds and such are just pseudo religious nonsense.

1) Disregard many worlds as a purely remaining mathematical outcome of bounded probability rather than discrete reality. (No 1 thing exists just 1ish things but ultimately that doesn’t mean there are many versions of any give 1)

2) just accept you can’t find the “stuff” of reality. You simply measure increasingly small probability domains which interact with other probability domains

3) time is the sequential working out of probability of anything existing and other things that might exist co defining themselves.

4) space is just the interaction of these probabilities working themselves out into a stable projection.

Just because at a quantum scale everything becomes potential doesn’t mean all potential has been manifested.

It baffles me that so many serious scientists don’t understand this basic tenet.

It's useful, not metaphysically real. (Hot take btw) This is called Instrumentalism. The belief that it's real is called Scientific Realism. However over and over again, science can't cover edge cases, and we find better fitting models. The Copernician revolution is a good example of this dichotomy.

2. Academia basically forces you to believe the doctrine or you fail the class. From philosophy to physics to sociology. If you read the philosopher survey, you will find trendy things being quite high. It's a religion in itself.

Bonus 3: Philosophical Pragmatism and Instrumentalism generally solves this, but is intellectually a dead end. There is a reason analytic philosophy continues despite gaping holes in linguistics (late Wittgenstein) that ruin it. But at the same time, best fits might be missing a new paradigm. I wish I could tell people to ask AI to explain Hegel to understand, but I think people need to read it themselves.

Tl;dr: quantum mechanics is the best we have. It's definitely wrong, but it's the most useful we have.

Uh oh, some people have no sense of humor =\

> but we have to live with this strange idea if we accept that Quantum Physics describes Nature correctly.

That depends on how you define nature, world and universe. For me nature is defined by things that can be perceived by human senses.