Quantum Mechanics: the bad news: our ordinary world is made out of weird, fuzzy, unpredictable stuff. The good news: the weird, fuzzy, unpredictable stuff is made out of unfamiliar but perfectly sensible math.
Related Pages: Physics, Decoherence, Many-worlds interpretation, Configuration space, Egan's Law, Timeless Physics
The biggest conceptual difference between the world of quantum mechanics and the physical world at the level we typically interact with is that it's much harder to specify the state of a system. Classical systems like a bowling ball or a planet have well-defined positions and velocity, and the state of such a system can be completely specified by just those two quantities. Quantities like position and velocity are called vectors, and in a 3-dimensional world a vector has component along each of the 3 dimensions. The state of a classical point particle can thus be given by just 6 numbers.
In quantum mechanics, particles don't have both a well-defined position and velocity, and as a consequence, the vector that describes a quantum system can't be expressed in just 3 dimensions. In general, there is no upper limit on the number of dimensions a quantum system can have, and so while the state of our bowling ball exists in two 3D spaces (one for position and one for velocity), a quantum system, in general, exists in a space that's similar to the 3D space we're used to, but with an infinite number of dimensions. This space is called Hilbert space. In order to be able to write down answers without using infinite numbers, quantum systems are usually mapped to other "spaces" like the 3D position and velocity spaces that we mentioned before. But information can be lost in this mapping, the same way a low-resolution photograph won't fully capture a 3-dimensional object. As a consequence of the lossy nature of this transformation, instead of the position of a quantum particle we instead get a distribution of possible positions. This is why quantum mechanics is often described as random or unpredictable....