>>12256025Quantum theory is a theory of vector spaces. This is a fact.
The "true reality" may be different. In fact it certainly has to be. But in the appropriate limits, it reduces to the model that we call "quantum mechanics", and this model is a mathematical one.
Don't confuse models for reality. Physics, and all of science, is just model building. I am discussing the model, because the best we can do to describe reality.
>>12256052The space of quantum states is continuous by any definition you might cook up. I don't understand what you're trying to argue here. Electron transitions occur because the electrons interact through the EM field. You can write down e.g. a Jaynes-Cummings model and see that the "spontaneous transition" is just a coarse grained description of unitary generated by an interaction term which entangles the electron's and EM field's Hilbert spaces. Suffice it to say, unitary dynamics are surely continuous.
>where is the continuity...Every path from the north to the south pole on the Bloch sphere. This is *literally* the distinguishing feature of qubits from classical bits.
>>b-b-but my high energy measurements...Total non-sequitur, has nothing to do with my post, and is honestly nonsensical in and of itself. Suggests to me that you don't actually know physics besides some freshman level material.
Even the simplest possible system (2-level) has an infinite number of possible states. This isn't a surprising or controversial statement in the least.
>>12257944The space of (pure) d-dimensional quantum states is basically just a complex unit sphere in d dimensions. States move along this sphere by the Schrodinger equation, which describes unitary transformations. Unitaries are basically just complex-valued generalizations of rotations.
Look up a picture of the Bloch sphere, which describes a 2-dim quantum system. Every pure state is a point on the surface of that sphere. All dynamics are described by rotations of between those points.
