In theoretical physics, the problem of time is a conceptual conflict between quantum mechanics and general relativity.
[1][2] This problem raises the question of what time really is in a physical sense and whether it is truly a real, distinct phenomenon.
Furthermore, the Hilbert space used in quantum theory relies on a complete set of observables which commute at a specific time.
The field equations of general relativity are not parameterized by time but formulated in terms of spacetime.
At the cosmic scale, general relativity shows a closed universe with no external time.
over space evolves in time, t. In general relativity the energy operator becomes a constraint in the Wheeler–DeWitt equation:
Somehow, at a smaller scale, the laws of physics, including a concept of time, apply within the universe while the cosmic level is static.
The issue remains an open question closely related to attempted theories of quantum gravity.
In 2013, at the Istituto Nazionale di Ricerca Metrologica (INRIM) in Turin, Italy, Ekaterina Moreva, together with Giorgio Brida, Marco Gramegna, Vittorio Giovannetti, Lorenzo Maccone, and Marco Genovese performed the first experimental test of Page and Wootters' ideas.
These limitations are very natural in the context of generally covariant theories as quantum gravity where the clock must be taken as one of the degrees of freedom of the system itself.
This approach was considered for some time to be impossible, as it seems to require first finding the general solution to Einstein's equations.
[24] Motivated by the Immirzi ambiguity in loop quantum gravity and the near-conformal invariance of the standard model of elementary particles,[25] Charles Wang and co-workers have argued that the problem of time may be related to an underlying scale invariance of gravity–matter systems.
[29] As a global continuous symmetry, scale invariance generates a conserved Weyl current[26][27] according to Noether’s theorem.
[30] In the context of loop quantum gravity, Charles Wang et al. suggest that scale invariance may lead to the existence of a quantized time.
Physical time flow is modeled as a fundamental property of the theory, a macroscopic feature of thermodynamical origin.