This always bugs me. Quantum Mechanics isn't actually that difficult. It has some nasty maths, yes, but that's mostly slog work, rather than an impossibility. 90% of it is the Schroedinger's equation + boundary conditions.
The main issue is that you have to abandon the particle model of reality. This is deeply engrained into our brains. If you try and understand it as "Particles + extras", you will fail. You have to think of it as "Waves + extras". It then, suddenly makes logical sense.
It does have some interesting implications, however, about deeper reality however. E.g. what exactly IS decoherence, from a physical point of view. Also, what is physically happening, dimensionally, when a wave is complex, or even pure imaginary. These are beyond the scope of QM however.
The big problem isn't that the math is hard, or that's often impossible to visualise. The problem is that a whole bunch of charlatans intentionally misinterpret what "observing" is in QM, to make money off of gullible victims.
To elaborate on this, the Schrödinger equation, which describes the dynamics of a single particle, is a wave equation and hence a lot of classical intuition from e.g. electrodynamics can be applied.
It is many-body systems, i.e. systems composed of many interacting particles, which is not only mathematically complex but can also defy classical expectations due to emerging phenomena, etc.
The problem of quantum mechanic is that the physics it shows us is not intuitive, and it sometimes breaks other laws of physics.
Quantum intrication means that information travels faster than light for example. Counterfactuality also breaks causality.
It's not the maths that are the problem, it's that it doesn't make physical sense in the world we currently understand. And the equations explain nothing. They merely describe a a world that doesn't make sense.
Quantum mechanic is like having a machine from the future that does cool things, but you don't understand how it works. It's like people did chemistry before they understand what chemistry was. We do uber cool things with it, but it is a spotlight on our ignorance at the same time.
Actually, I think it's time to reveal, that to some people QM is actually pretty intuitive.
It's just that the masses and the news media don't understand it, so they assume that nobody does. The particle worldview is deeply ingrained into many people's brains, because it's deeply useful to them on a day-to-day basis. If you loosen that requirement, then there's literally nothing standing in your way to accept a wave-worldview.
What about the Copenhagen interpretation debate? What about the non-locality?
These are academic debates, not people ones. Saying that quantum mechanic is intuitive is arrogant at best. You may have a perfect understanding of the current theory and how to use it, and you maybe comfortable using it everyday, but then you should be aware of the limits shouldn't you?
Yeah ok, I get your input. The point is, that most of the arguments, that say that QM is "unintuitive", boil down to the fact that some people are simply unwilling to accept that the world is "not made of particles".
Some people adhere to this worldview like to a religion. You cannot argue with religion. Therefore, for most people, there is little hope to come to terms with QM. However, I am saying, that if you "give up" on a particle worldview, then QM isn't so super weird as lots of people always make it seam.
Yeah, there's some strange issues going on. But I'm saying, that a lot of these aren't so mad to think about if you give up on your particle worldview. Coherence, for example, boils down to a system which isn't simply described by "that atom goes there and this atom goes here". It's different, but consistent. It still reveals a consistent model with a measurable outcome. Just that this model is like taking public transport instead of riding your own car. Sometimes, you gotta mix things up to see the bigger picture.
I get what you're saying, but I can't help but think quantum physics is a weird beast. Somehow it is the opposite of relativity that's purely geometric, although in 4d.
To go in your direction, I think the probabilistic nature it the biggest weird thing of quantum mechanic. And you can absolutely admit it and live with it, but for many people, that will be a tough thing to do, and they'll rather think that our knowledge is too limited to understand the reality of things. And it's hard to blame them for that.
IMO we lack some good sci-fi to explore and familiarise these things.
I definitely agree it's unintuitive to the layman. We never have to deal with large scale wave interactions, on the classical physics level. I disagree, however, that we can't understand it. It does make sense, it just doesn't map to our default particle mindset.
I disagree that it breaks the laws of physics though. It just shows some flaws in our methodology. E.g. the speed of light isn't a limit on fundamental speed, but of information. It just happens that the only time we can have transmission without information is via decoherence.
QM is definitely incomplete. We know the what, but not the why. That applies to most of physics however. Newtonian physics is the same. We know what happens, but not why. It's just that Newtonian physics is intuitive to our savannah running brain, while QM requires more mental work.
QM is the only bit of physics where something can still be both physical and have zero information content. Therefore it's the only place where the difference matters between C being a universal Vs a limit for information.
Also waves are non local, an exponential decay never actually reaches zero. Accepting this is critical to QM making sense. It's just very alien to our natural sensibilities.
As for the conflict with GR, both theories are known to be incomplete since neither predict each other. Knowing how both differ is one of the few known holes in physics. Interestingly, both theories are ridiculously accurate, within their domains, making the job all the harder.
Quantum entanglement is when the quantum states of two or more objects become linked in such a way that the state of one object seems to instantly affect the state of the other object, regardless of the distance between them. this does not mean that information can travel faster than the speed of light, that's a misconception.
Entanglement is a probabilistic process, it does not transmit classical information faster than the speed of light. The measurement result of a quantum system is inherently random, and it cannot be controlled or transmitted deterministically. The apparent faster-than-light transmission in entangled systems is the result of quantum correlation, and it does not equip systems with a faster way to communicate classical information across spacetime.