Quantum Mechanics in symmetry language
arXiv:1305.4349
Abstract
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better understood in this view. In particular, the abstract concept of symmetry provides a basis-independent definition for observables. Moreover, we show that the apparent projection/collapse of the state as the final step of measurement or decoherence is the result of breaking of symmetries. This phenomenon is comparable with a phase transition by spontaneous symmetry breaking, and makes the process of decoherence and classicality a natural fate of complex systems consisting of many interacting subsystems. Additionally, we demonstrate that the property of state space as a vector space representing symmetries is more fundamental than being an abstract Hilbert space, and its integrability can be obtained from the imposed condition of being a representation of a symmetry group and general properties of probability distributions.
20 pages, 1 figure. v6 significantly different from v5, and includes new ideas related to quantum gravity
References in corpus (16)
- Dynamics of dark energy
- Reference frames, superselection rules, and quantum information
- Quantum teleportation using active feed-forward between two Canary Islands
- Planck 2013 results. XXIII. Isotropy and statistics of the CMB
- Quantum teleportation and entanglement distribution over 100-kilometre free-space channels
- Planck 2018 results. VII. Isotropy and Statistics of the CMB
- Conditional probabilities with Dirac observables and the problem of time in quantum gravity
- Planck 2013 results. XXVI. Background geometry and topology of the Universe
- Experimental implementation of a Kochen-Specker set of quantum tests
- Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics
- Energetic Causal Sets
- Action principle for cellular automata and the linearity of quantum mechanics
- Spin foam models as energetic causal sets
- And what if gravity is intrinsically quantic ?
- Toward the unification of the postulates of Quantum Mechanics
- Phase transitions and equilibrium measures in random matrix models