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.
Is this good for intuition? It doesn’t really seem like the correct explanation as for why we measure randomness.
Eg. a simple spin 1⁄2 particle (nowadays often the way people are introduced to QM) has 2D hilbert space, and still has identical randomness.
Is this good for intuition? It doesn’t really seem like the correct explanation as for why we measure randomness.
Eg. a simple spin 1⁄2 particle (nowadays often the way people are introduced to QM) has 2D hilbert space, and still has identical randomness.