When learning quantum mechanics, you have to let go of the commonly-held belief (often unknown to the holder) that everything in our world can be explained in terms of concepts that are familiar to us and our human-sized environment. You cannot reason your way through QM with classical analogies. You find the wave-particle duality confusing; why? Only because you cannot imagine a human-sized object that is both a particle and wave. Let go of both of those concepts - forget about particles and waves as you know them - and accept that QM objects fall into new ontological categories which do not map well onto any classical concept. This is fine! As a child, you learned new ontological categories all the time. Everything was alien to you. You've learned new categories before, and you can learn them again.
If we cannot use the language of everyday experience to understand quantum mechanics, what can we use? The answer is math. We have found math to be an incredibly effective language for describing quantum mechanical phenomena. Superposition isn't really like a particle being "in two different places at the same time", it's a complex linear combination of state 0 and state 1. There are differences between those things, and the differences are fundamental to understanding quantum mechanics.
A corollary to the inability to meaningfully explain QM with classical analogies is that all pop science dealing with QM is absolute, irredeemable garbage and always will be. Stop reading it.
There is a similar problem with Special Relativity and Classic Newtonian Mechanics. Let's pick an usual object like a pool ball. To understand it completely you must apply Special Relativity, but for everyday calculation you can approximate its behavior with Classic Mechanic and the approximation is good to play pool, throw it at a target and whatever you usually need. Moreover, you can apply all the theory of a Rigid Body and analyze how it rotates. The problem is that there are no rigid bodies in Special Relativity, because any change must affect all the ball instantly. So a rigid body is sometimes a very good approximation, but there are no true rigid bodies.
In a quantum object in some experiments they can be approximated very well as a particle, and in other experiments they can be approximated very well as a wave. But this are only two good approximations that make the calculations much easier but are not the exact behavior of the object.
I think that at the beginning of discovery of quantum mechanics nobody know what was happening and only know that some object were weird and sometimes they ware well approximated as particles and sometimes they ware well approximated as waves. Later they discovered the "true" nature of these object that sometimes can be approximated as a wave or as a particle, but it is much more difficult to explain to someone that doesn't want to learn the math.
Just to somewhat gently push back on this a little bit, math is probably not enough if you want someone to really get how quantum mechanics work at a fundamental level.
So quantum superposition isn't just two things at the same time, it's a complex equation that combines the two states. Great. Except that non-math majors don't think of linear equations as a singular 'thing' that describes a state. That in itself is a huge paradigm shift for people like me. I'm not used to having an axis in an equation not refer to a continuous range that I can move through.
There's a comic[0] on this springs to mind, that being able to plug equations into something is not the same as understanding it. Most tutorials or technical articles I read about quantum mechanics skip concepts and assume that showing the math is enough. In doing so, they skip all of the hard, useful parts of education and focus only on the language and terminology we can use to talk about something.
I spent a lot of time in physics, statistics, and calculus where I understood the math and not the concepts. I graphed things in 4 dimensions before I encountered Flatland, but I didn't understand the 4th dimension before Flatland. I worked with complex numbers all the time in calculus, but I didn't start to understand complex numbers until years later when I started watching Numberphile.
So I'm at least a little bit skeptical of claims that that quantum mechanics are different. We've had to build new paradigms to understand a lot of stuff in the past; concepts like infinity don't map to tangible analogies, but we can still build tutorials and scenarios that demonstrate interesting behaviors and properties.
Right now the only people I can find trying to do that for quantum are the pop-science writers, and like you said they're mostly all crap. It's kind of frustrating.
I think quantum mechanics really is different. Consider a fundamental aspect of the quantum world, familiar to anybody reading Scott Aaronson's blog: the 2-norm.
People are familiar with how probability works in the classical world. For a given event with several different possible outcomes, like flipping a coin, the probability of those outcomes sums to 1 (here, 1/2 + 1/2 = 1).
In the quantum world, probability doesn't work like that. Rather, the sum of the absolute value of the probability squared equals one. A quantum coin flip has probability (actually called amplitude) 1/sqrt(2) for heads and 1/sqrt(2) for tails. |1/sqrt(2)|^2 + |1/sqrt(2)|^2 = 1.
This has huge implications. It means probabilities can be negative, since |-1/sqrt(2)|^2 + |-1/sqrt(2)|^2 = 1 (actually it goes further - the probabilities can be complex numbers!). It means negative probabilities can interfere and cancel out positive probabilities. And a whole bunch of other wild stuff. All of quantum mechanics (or so Scott claims) follows from this.
I submit that a world where something as basic as the probabilities of all outcomes summing to 1 not holding is a world so alien that attempts to explain it in terms of our own experience will only end in confusion.
Sure, but we don't need to explain everything in terms of our world to still try to explain concepts. We can use contradictions, or games[0], or experiments, or any number of mechanisms.
Infinity doesn't really map to anything else that I understand. Some of the better tutorials I've gotten on infinity are literally just saying, "hey, look at this scenario. Do you think it works the same way as with really big numbers? Well it DOESN'T! Now watch me shove even more guests into your hotel! :)"
I'm not pushing back against the idea that quantum mechanics is a completely new paradigm, I'm pushing back against the idea that math, by itself, is a good enough mechanism for teaching new paradigms.
The math/pop-science dichotomy actually reminds me a bit of my early physics lessons on electricity. I'd either get a really awful analogy (electricity is just like water flowing through a pipe), or I'd get the formula to add up the resistors and calculate voltage and then get told, "well, this is all you're going to need to know for the test."
Neither approach was concerned with understanding how electricity worked; one just said "think of it as something else", and the other said "don't think about it."
The problem is that our best way to describe QM is using math, and the experiments can only verify that the predictions made with math agree with the results.
There are many interpretations of what the math mean, like many words or wave function collapse. But the interpretations are equivalent, in any experiment they use the same math to get the same results.
So you may like one interpretation or the other, but the only sure part is the math.
Games, analogies, think experiments are nice and are useful to understand how to apply the math and get an intuitive idea of how the math work and how some approximations may simplify the calculations.
I still sometimes move my finger in circles to think and do calculations about spin, in spite the spin of a particle is not exactly equal to the spin of a ball. It's a nice analogy and (for me) it's useful, but the real particles don't behave like balls or moving finger.
Another important part is to understand how to translate an actual lab setup to math and how to relate the result of the calculation and the experiments.
I totally agree, the poster understands the calculation rules, but calls the wave function or amplitudes the probabilities, where practically everyone calls their norm squared the probability (or probability density)
It was for pedagogical purposes. I mentioned they were actually called amplitudes. For the intended audience, the difference doesn't matter. Scott Aaronson uses a similar tactic on p110 of Quantum Computing Since Democritus.
As you mentioned Numberphile, what do you think of the YouTube channel PBS Space Time? It helped me finally grok quite a few bits of physics that never made sense to me before.
Everett was a physicist. So was Einstein, Schrodinger, Bohm and DeBroglie. Not all physicists have been sold on the Copenhagen interpretation of QM, where classical concepts don’t apply. That’s just one interpretation.
Everything also seems to behave like a split is happening. They are equally valid explanations, and neither has any supporting evidence that isn't shared by the other. We should probably assume the simpler explanation is more likely, but it's not even clear which explanation is simpler. :/
This dispute isn't about the probabilities or the math, it's about what the probabilities/math are modeling. Is it a non-classical wave-function woo that collapses, including backwards in time? Is it evidence for multiple realities? Is there a pilot wave or other hidden variables? Or is it mostly a matter of ignorance of the exact state of the quantum system, requiring us to use probabilities?
Consider particle decay: it's a fundamentally random event - there is not enough internal structure to suppose the existence of some internal timer, nor is there enough worlds to fill the eternity during which the particle can "choose" to decay at any moment.
For pop books I've only read Brian Greene. I don't think they were helpful for learning quantum mechanics; the reader just stumbles through bewildering scenario after scenario and has forgotten them all within a week.
QED is great, I think it really gets across one way of thinking about these things.
Agree with @ahelwer that Brian Greene isn't terribly useful. Have not read Zee & Smolin's popular books... but for what it's worth, Zee is a serious guy & writes great textbooks, Smolin is not.
If we cannot use the language of everyday experience to understand quantum mechanics, what can we use? The answer is math. We have found math to be an incredibly effective language for describing quantum mechanical phenomena. Superposition isn't really like a particle being "in two different places at the same time", it's a complex linear combination of state 0 and state 1. There are differences between those things, and the differences are fundamental to understanding quantum mechanics.
A corollary to the inability to meaningfully explain QM with classical analogies is that all pop science dealing with QM is absolute, irredeemable garbage and always will be. Stop reading it.