The constraints arising from the quantum mechanical symmetry on wavefunctions, and the effect of the constraints on the structures and internal notions of quantum states are studied.
The measurement problem in quantum mechanics and the embedding of observers in general relativity jointly point to the awkward position of the observer in physical theory: traditional theories place the observer outside the system, but in a self-contained universe, the observer must be internal to the physical world. This paper models the observer as a local subnet inside an emergent spacetime constraint network, whose internal constraint structure forms a compressed generative model of the external network state. The measurement event is reinterpreted as a non-equilibrium phase transition of the internal constraint conffguration when the constraint propagation between the observer subnet and the target subnet reaches a critical threshold, and wavefunction collapse is reduced to a sudden transition of a local subnet from a symmetric multi-basin state to a single-basin broken-symmetry state. Based on a formalisation of the microscopic dynamics of constraint networks, symmetry and conservation laws, and the emergence of an arrow of time, this framework uniffes the historical interpretation of decoherence with active inference in the free energy principle, and argues that a self-referential universe can contain a self-referential subnet, thereby making physical laws cognisable. Physics and cognitive science achieve a deep unity at the ontological level of constraint networks.
Whether the total angular momentum of the photon can be separated into spin and orbital parts has been a long-standing problem due to the constraint of transversality condition on its vector wavefunction. A careful analysis shows that the situation arises from a misuse of the constraint in quantum mechanics. To use the constraint properly, we convert the vector representation into a two-component representation in which the wavefunction is not constrained by any conditions. Upon doing so, we not only separate the spin conceptually from the orbital angular momentum but also identify the Berry gauge in which the two-component wavefunction can be canonically quantized. A corollary is that only in one particular Berry gauge can a radiation field be canonically quantized in terms of the plane waves. The degree of freedom to fix the Berry gauge, which reflects a symmetry of the constraint, turns out to have observable quantum effects.