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Area of Science:

  • Quantum Gravity
  • Theoretical Physics
  • Mathematical Physics

Background:

  • The
  • problem of time
  • poses a significant challenge in reconciling general relativity and quantum mechanics.
  • Existing quantum gravity approaches often struggle with defining a consistent time evolution parameter.

Purpose of the Study:

  • To introduce and explore the implications of an unconstrained Hamiltonian structure within manifestly covariant quantum gravity theory (CQG-theory).
  • To establish a dynamical evolution parameter that resolves the conceptual difficulties associated with time in quantum gravity.

Main Methods:

  • Formulation of CQG-theory with an unconstrained Hamiltonian structure.
  • Identification of a 4-scalar proper time parameter (s) as the dynamical evolution parameter.
  • Analysis of the observable character of the evolution parameter and its relation to the cosmological constant.

Main Results:

  • CQG-theory features an unconstrained Hamiltonian structure in evolution form.
  • A 4-scalar proper time (s) is identified as the dynamical evolution parameter for the quantum wave function.
  • The evolution parameter (s) is shown to be observable and functionally dependent on the cosmological constant via quantum-vacuum interactions.

Conclusions:

  • The identified proper time parameter (s) overcomes the
  • problem of time" in quantum gravity.
  • CQG-theory provides a viable mathematical framework consistent with general relativity and canonical quantum mechanics.
  • This approach offers a path towards a logically and physically consistent theory of quantum gravity.