Emergent Time: Hierarchy, Correlations, and Multiverses

1. Introduction

Time has long been considered a fundamental, universal entity. Modern physics challenges this assumption:

• General Relativity: time depends on the observer and gravity.
• Quantum Mechanics: equations are reversible; time is an external parameter.
• Canonical Quantum Gravity: Wheeler–DeWitt equation has no explicit time variable.

This synthesis presents a hierarchical and original vision of time as an emergent property, spanning quantum scales to correlated multiverses, highlighting theoretical assumptions and experimental limits.

2. Theoretical Foundations

2.1 Relativity (Einstein)

• Proper time: (d\tau^2 = g_{\mu\nu} dx^\mu dx^\nu)
• Time dilation: (\Delta t’ = \gamma \Delta t = \frac{\Delta t}{\sqrt{1 – v^2/c^2}})
• Gravitational time dilation: (d\tau = \sqrt{1 – \frac{2GM}{rc^2}} , dt)

2.2 Quantum Mechanics

• Schrödinger equation:
  (i\hbar \frac{\partial}{\partial t} |\psi(t)\rangle = \hat{H} |\psi(t)\rangle)
• Temporal symmetry: reversible.
• Page–Wootters mechanism (theoretical): emergent time via correlation
  (|\Psi\rangle = \sum_n |n\rangle_\text{clock} \otimes |\psi_n\rangle_\text{system})

2.3 Thermodynamics and Entropy

• Boltzmann entropy: (S = k_B \ln \Omega)
• Second law (isolated system): (\Delta S \ge 0)
• Arrow of time = monotonic increase of entropy.

2.4 Quantum Gravity and Emergentism

• Loop Quantum Gravity: space = spin network ((V,E))
• Holography: time emerges from correlations on a boundary
• Key idea: time may emerge from information and entanglement, active area of research.

3. Three Temporal Layers: « Temporal Onion »

3.1 Quantum Layer (core)

• Fast atomic transitions: (f \sim 10^{10}-10^{15} \text{Hz})
• Reversibility: no intrinsic arrow of time
• Entanglement → internal clock (Moreva et al., 2014)

3.2 Thermodynamic Layer (middle)

• Aggregation of quantum events
• Increasing entropy → arrow of time
• Macroscopic time as function of internal information: (t_\text{thermo} = F(S)) [illustrative]

3.3 Cosmological Layer (outer)

• Universe expansion: scale factor (a(t))
• Friedmann equation:
  (\left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3} \rho – \frac{k}{a^2} + \frac{\Lambda}{3})
• Cosmological time = integration of micro-events and global entropy

3.4 Interactions Between Layers

• Cumulative effect: micro-events → thermodynamic arrow → cosmological expansion
• Analogy: temporal onion with nested, correlated layers

4. Experiments and Evidence

Scale	Key Experiment	Observation	Reliability
Quantum	Moreva et al., 2014 — entangled photons	Emergent time via correlation (Page–Wootters mechanism)	~85% — limited scope
Quantum	Hafele–Keating, 1971 — atomic clocks on airplanes	Relativistic time dilation	~99% — replicated, GPS base
Thermodynamic	Statistical irreversibility (Boltzmann–Maxwell)	Macroscopic arrow of time via increasing entropy	~97% — consensus established
Cosmological	GPS — daily relativistic corrections	Gravitational and kinematic time dilation	~99%
Cosmological	Planck 2018 — CMB	Universe expansion, flat geometry	~98%
Cosmological	NIST/PTB optical clocks 2010–2020	Gravitational dilation at 33 cm altitude	~99%

5. Emergent Time: Information Network

• Theoretical hypothesis: fundamental universe = units of quantum information (« it from qubit »)
• Micro-ticks accumulate → macroscopic time
• Thermodynamic arrow = bias toward increasingly disordered states
• Conceptual formula [illustrative, unpublished]:
  (t_\text{macro} = \sum_i \Delta t_i^\text{quantum} \times f_\text{correlation}(i))

6. Speculative Extension: Correlated Multiverses

• Each universe = layer with its own laws and time
• Inter-universe correlations → subtle influence on time and entropy
• Global information network = multi-universe onion analog
• Cumulative, emergent, non-linear effects
• Ideas remain speculative and under active research

7. Conclusion

• Time = emergent effect, not fundamental
• Three nested scales: quantum, thermodynamic, cosmological
• Lower layer influences the next via correlations and aggregation
• Extension to correlated multiverses possible, unifying very fast and very slow via an information network
• Formulas and theoretical assumptions clearly labeled as illustrative or speculative

8. References

1. Einstein, A., Relativity: The Special and General Theory, 1916
2. Wheeler, J. A., DeWitt, B. S., Quantum Gravity, 1967
3. Moreva, E. et al., Time from quantum entanglement: experiment, Physical Review A, 89, 052122 (2014)
4. Rovelli, C., Quantum Gravity, 2004
5. Tipler, P. A., Llewellyn, R. A., Modern Physics, 2007