Problem of time

In theoretical physics, scientists face a profound conceptual conflict known as the problem of time. This conflict arises because our two most successful descriptions of nature do not agree on how time works. Quantum mechanics, which describes the very small, treats time as a universal and absolute background. In this view, time is an external parameter that stays steady while systems change. Conversely, general relativity, our theory of gravity and the large-scale universe, views time as malleable and relative. In general relativity, time is a coordinate that can stretch or bend. This fundamental disagreement makes it difficult to understand if time is a real, distinct phenomenon or just an appearance.

To understand the conflict, we must look at how each theory uses time. In the standard Copenhagen interpretation of quantum mechanics, time is a special background parameter. All measurements of observables, which are physical properties, occur at specific instants of time. Probabilities are assigned to these measurements based on that fixed timeline. The math used here, called Hilbert space, relies on a set of observables that commute at a specific time. In contrast, general relativity does not use time as a unique background. Instead, the field equations are formulated in terms of spacetime. At a cosmic scale, general relativity describes a closed universe with no external time. These two roles for time are incompatible, creating a barrier for physicists.

A major part of this mystery is the frozen formalism problem. In non-relativistic quantum mechanics, equations include time evolution. This means an energy operator characterizes a system, and a wavefunction evolves as time passes. However, when applying these ideas to the whole universe, the math changes. In general relativity, the energy operator becomes a constraint in the Wheeler–DeWitt equation. In this equation, the wavefunction of the universe is constant. This means the cosmic wavefunction is frozen and does not evolve. This leads to a strange paradox where the universe appears static at a cosmic level, even though things seem to change at smaller scales.

Several researchers have proposed ways to bridge this gap through entanglement. Don Page and William Wootters suggested that time might be an emergent phenomenon. They proposed that observers inside the universe experience evolution due to energy entanglement. This occurs between an evolving system and a clock system, both located within the universe. While the overall system remains timeless, the internal parts experience time through this link. In 2013, a team at the Istituto Nazionale di Ricerca Metrologia in Turin, Italy, tested this. Ekaterina Moreva, Giorgio Brida, and their colleagues used photons to perform an experimental test. They confirmed that time is an emergent phenomenon for internal observers but is absent for external ones.

Other mathematical approaches attempt to solve the problem by changing how we calculate motion. Jorge Pullin and Rodolfo Gambini developed a consistent discretizations approach. They use lattice approximation techniques to avoid the inconsistencies found in standard canonical approaches. In the canonical approach, discretizing equations often makes them impossible to solve simultaneously. By discretizing the action of the theory instead, they ensure the equations remain consistent. This allows the theory to be quantized more easily. This method involves picking a physical variable to act as a clock. This leads to the Montevideo interpretation of quantum mechanics, which uses the quantum nature of clocks to explain measurement limitations.

Different thinkers also propose structural changes to how we view the passage of time. Avshalom Elitzur and Shahar Dolev suggest that spacetime itself might be subject to change. They argue that quantum-mechanical experiments might provide evidence of inconsistent histories. Meanwhile, Lee Smolin proposes the idea of a "thick present." This view suggests that two events in the present can be causally related. This differs from the "block universe" view, where all time exists eternally. Marina Cortês and Smolin also argue that certain discrete dynamical systems show time asymmetry. This asymmetry supports the idea of an objective passage of time rather than a static universe.

Advanced theories continue to explore the relationship between gravity and scale. Charles Wang and his co-workers have looked at scale invariance in loop quantum gravity. They suggest the problem of time might relate to an underlying scale invariance of gravity-matter systems. In scale-invariant models, a conserved Weyl current can give rise to a harmonic time. This might even lead to a quantized version of time. Finally, Carlo Rovelli and Alain Connes proposed the thermal time hypothesis. They use a statistical mechanics model of gravity to characterize thermodynamic time. This approach views time as a vector flow of a statistical state, offering another possible way to reconcile the laws of physics.