Phase Transition of Gravity: From Quantum Graviton to Classical Spacetime——Emergence of General Relativity from Time-Body Freezing in Self-Construction Theory

Abstract: The core dilemma of quantum gravity lies in the apparent irreconcilability between the graviton predicted by quantum field theory and the curved spacetime described by general relativity (GR). Within the framework of the Self-Construction Theory (SCT), this paper proposes that gravity is essentially a manifestation of the same entity—the time-body (3-simplex)—at different freezing stages. The time-body is the fundamental unit of three-dimensional spatial extension; its collective vibrations correspond to massless spin-2 particles (gravitons), while the continuum limit of its static configuration yields the spacetime metric and curvature. The time-body undergoes a continuous phase transition (the fourth phase transition) at the energy scale $E_4\approx2.4\times10^{-3}\,\text{eV}$. Before freezing, time-body vibrations are active and gravity is transmitted in the form of quantum gravitons, with significant quantum effects. After freezing, independent vibration modes are completely suppressed; gravity is no longer mediated by particles but emerges as the classical dynamics of spacetime geometry—namely, general relativity. This paper derives the critical behavior of time-body freezing from the relaxation equation, proves that the continuum limit from the discrete Regge action to the Einstein-Hilbert action automatically holds after freezing, and gives the SCT expression for Newton's gravitational constant $G = \frac{K^2}{16}e^{-120}/m_0^2$. The cosmological constant $\Lambda$ naturally emerges as the information compression energy remaining from time-body freezing, and its value agrees with observations. This paper further presents a testable prediction: the spacing of resonance peaks in the primordial gravitational wave spectrum is determined by the eigen-spectrum combination $120=5!$ and the golden ratio $\phi$, and can be tested by experiments such as LISA and CMB-S4. The quantum-classical transition of gravity is not at the Planck scale but a continuous phase transition near the extremely low scale $2.4\times10^{-3}\,\text{eV}$.

Keywords: phase transition of gravity; time-body freezing; graviton; general relativity; Self-Construction Theory; quantum gravity; dark energy