Being a physics grad student, I got used to the weird concepts behind quantum mechanics (used to doesn't mean I fully understand it though). What I mean is that I'm not surprised anymore by the fact that a quantum system might be in a superposition state, that a particle in a potential well has a discrete spectrum of energy, that some pairs of observables cannot both be measured with arbitrary precision, etc.
However, the problem arises when I'm talking about my work to my (non-physicists) friends and family. They are not used to think "quantum mechanically", so when I'm saying that Schrödinger's cat is really, simultaneously, both "alive" and "dead", they don't get my point as it just seems crazy. So I have been thinking for a while of what would be the easiest way to introduce them to the core principles of QM. (EDIT: This part seems to have upset people; I don't want to go into the details of distinguishing "simultaneously alive and dead until you measure" VS "superposition of alive and dead states", I mainly want them to understand that the outcome of the measure is indeterminate)
When they ask me "So what is QM all about?", I'd like to give them a short answer, a simple postulate/principle that, once accepted, makes most key features of QM seem more natural.
In my opinion, some of the "weird" ideas people find most difficult to accept (due to some popular pseudoscience) and/or that are central to QM are:
- Quantum superposition
- Complex amplitude/phase (as it leads to interference)
- Uncertainty principle
- Quantization of physical quantities/particles
My problem is that I can't explain how these ideas are related. If my friends accept that particles can be in two states at once, why couldn't they know both its position and momentum? Or if they accept that an electron has a super abstract property called a "complex phase", why should it lead to a discrete spectrum of energy?
Of course, I could just tell them that they need to accept it all at once, but then the theory as a whole becomes hard to swallow. In my opinion, QM sometimes suffers from a bad reputation exactly because it requires to put all our classical intuitions to scrap. While actually, I think it could make perfect sense even for a non-physicist given only 1 or 2 "postulates" above. I tried looking back at my own learning of QM with little success since undergrad students are often precisely bombarded with poorly justified postulates until they just stop questioning them.
A few more points:
- I don't want to get started on mathematical definitions, so nothing like "Quantum systems are in an infinite-dimensional Hilbert space" as it doesn't mean anything to my relatives. That includes pretty much all of the actual postulates of QM. I want my explanation to be more intuitive.
- I'd like to avoid any mumbo jumbo related to "wave-particle duality". I think (and I know I'm not the only one) that most explanations regarding this are inacurrate and actually inefficient at giving a good description of quantum behaviour, since most non-physicists aren't familiar with the properties of a classical wave anyway. And it's mostly used when talking about the position of a quantum particle; I've never heard someone say that spin "behaves like a wave" or "like a particle". I'm looking for something more fundamental, more universal.
- That being said, I think it's very important to include a discussion about the relative phase between two superpositioned states as it leads to quantum interference (perhaps the only "wave-like" feature that applies throughout QM). If there were only quantum superposition, quantum computing would be pretty much useless: even if we perform one billion calculations simultaneously, when measuring the system we would get a single random value. Our goal is to manipulate the system, to create destructive interference between the unwanted results in order to increase the probability of measuring the desired value. And that requires the notion of quantum phase.
- Uncertainty principle might be the toughest challenge here, since we can get the basic idea without invoking QM at all. First, even in classical mechanics, it's impossible to measure something with an arbitrarily big precision simply because of instrumental limitations. Second of all, it makes sense to get different results if we measure the position before or after the momentum ($[x,p]\neq 0$) since we interact with the system when making the first observation, leaving it in a different state afterward. How could I explain that there are more fundamental implications from QM?
- I wasn't sure about entanglement and quantization. The weirdness of entanglement doesn't come from how we achieve it, but from how we interpret it, which is still an unresolved issue as far as I know (Many-world? Copenhagen interpretation? etc). As for the quantization of particle properties, it doesn't seem like an intrinsic feature of QM, more of a consequence of boundary conditions. A free electron in a vaccum has a continuous energy spectrum, it's only when we put it in a potential well that some states are "forbidden" (not exactly forbidden of course; even Bohr explained the hydrogen atom in a semi-classical model using destructive interference between the state of the electron). Then, there is also the quantization of matter itself (photons, electrons, quarks, etc.) which is another story. But I think most people are familiar with the idea that matter is made of atoms, so it isn't a far stretch to include light as well. My point is that these two principles don't appear quite as essential as the other ones to understand QM.
I haven't found a satisfying answer in the similar posts of this forum (here, here or here for instance) since I'm more interested in the overall description of QM - not just of wavefunctions or superposition - and I don't want to get into the motivations behind the theory. Also, I'd like to give an accurate, meaningful answer, not one that leads directly to pseudoscientific interpretations of QM ("Particles are waves, and vice versa", "Everything not forbidden is mandatory", "Consciousness affects reality"; that kind of thing).
EDIT: Just to clarify my question perhaps, here what I would say concerning special relativity (SR).
The basic assumption of SR is that everyone always sees light traveling at the same speed, no matter what circumstances. So far so good.
Now imagine that I'm in a train going at 50 km/h and that I throw a ball in front of me at 10 km/h. From my perspective, the ball is going at 10 km/h. But for you, standing on the ground, the ball is going at 50+10 = 60 km/h with respect to you. It all makes perfect sense since you have to consider the velocity of the train. Good.
Now, let's replace the ball with a photon. Oh oh, according to our previous assumption, we will both see the photon travelling at the same speed, even though I am moving at 50 km/h. We cannot add my speed to your measurement as we did earlier. This implies that we both perceive time and space differently. Boom. And from this you can get to pretty much all of SR (of course, one should also mention that $c$ is the maximum speed).
This simple assumption implies the core of the theory. What would be the equivalent in QM, the little assumption that, when accepted, implies most of the theory?
@Emilio Pisanty I saw the post in your comment (it's one of the links at the end of mine). As I said, I'm not interested in why we need QM, I want to know/explain what fundamental assumption is necessary to build the theory. However it's true both questions are linked in some ways I guess.
EDIT 2: Again, I'm not interested in WHY we need QM. It's pretty obvious we'll turn to the theory that best describes our world. I want to explain WHAT is QM, basically its weird main features. But QM has a lot of weirdness, so if I simply describe the above phenomena one by one, it doesn't reflect the essence of the theory as a whole, it just looks like a "patchwork" theory where everyone added its magical part.
And I KNOW all about the QM postulates, but those are more a convention of how to do QM, a mathematical formalism, (we'll use hermitian matrix for observables, we'll use wavefunction on a complex Hilbert space to represent a particle, and so on) rather than a description of what QM is about, what happens in the "quantum world", what phenomena it correctly predicts, no matter how counterintuitive to our classical minds.
EDIT 3: Thank you all for your contributions. I haven't chosen an answer yet, I'm curious to see if someone else will give it a try.
There's a little point I want to stress: many answers below give a good description of the weird concepts of QM, but my goal is to wrap it all up as much as possible, to give an explanation where most of these are connected with as little assumptions as possible. So far @knzhou's answer is the closest to what I'm looking for, but I'm not entirely satisfied (even though there's probably no answer good enough). Most answers are very close to the wave-particle duality - which I'm not a fan of because people understand this as "Electrons are particles on week days and waves during the weekend". However perhaps it's unavoidable as it truly does include most of the phenomena listed above. Then I thought perhaps if we were talking about quantum fields rather than "waves of matter", the discussion would be less likely to lead to misinterpretation?
Also, for all those who said "Well QM is just incomprehensible for lay people" I think that's giving up too easily and it feels a little dishonest. QM is not a secret society for a special elite. I think it's important that researchers explain what is their goal and how they intend to achieve it to the general public. I think the 2nd question physicists are asked most often is "Why should my tax money pay for your work?". Do you really think an answer such as "Well... you couldn't understand it. Just trust me." is satisfying?
QM is counterintuitive, but well explained it can make sense, and I'm just looking for the easiest way to make people realize this without simply saying "Well forget anything you know". Also I think it is a theory that would be much easier to accept if people were more often exposed to these ideas. After all, children and high school students learn that the world is made of atoms and they accept it even though they cannot see atoms. Why then couldn't QM be part of the common scientific culture? It's true it may sound ridiculous at first to hear about superposition and indeterminate states, but it isn't by giving up and by saying "Well you need a degree to understand it" that we are going to change it and make it more appreciable.