Condensed Geometry II: New Constraints, Temporal Confinement Phase and Structure and Interpretation of Space and Time
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In this paper we basically intend to deductively study aspects and physical behavior of time in the Quantum Mechanical and Loop Quantum Gravity regime and the physical interpretations therein. The implicit gauge invariance of the vortical time is deduced. A new form of the Hamiltonian constraint is produced and the corresponding Vector or Diffeomorphism constraint is also introduced, the Gauss constraint being found to be the same as that in the original. The new consequences are discussed. The paper presents fresh new ideas and interpretations as well as perspectives on the spatial as well as the now introduced temporal aspects of Loop Quantum Gravity. In this we basically intend to deductively study aspects and physical behavior of Time in the Quantum Mechanical and Loop quantum gravity regime and the physical interpretations therein. In what follows, we provide a systematic mathematico-physical treatment of the vortical aspect of quantum gravity or a test quantum system, relative to space, as the time for that system. The implicit gauge invariance of the vortical time is deduced. A general theory of implicit and explicit gauge invariance is proposed. The gauging out of the acausality gauge degree of freedom is deduced and the causal direction of time is shown to nucleate out as a self ordered criticality due to a “tweaking” field which is shown to be a form of magnetic phase transition. This magnetic phase arising in the Kodama holomorphic wave functional universe, arises naturally due to the Ashtekar “magnetic” field in general. Also the wave-particle duality of gravity/ geometry as a quantum system is interpreted in terms of the physical role played by time. The long standing problem of the interpretation of the quantum mechanical time-inverse temperature has apriori been resolved with a heuristic interpretation. As an epilogue, the Pauli theorem on time as an operator has been discussed along with the standard proof.
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