This paper presents Time-Update-Density Field Theory, a framework based on the Universe Finite Principle, which states that physical infinities do not exist in nature. The theory proposes that time is not a fundamental background parameter but emerges from the local update structure of space. The central concept is the time-update-density field ν, representing the local spatial update frequency. The local space-update time is defined by: dt = 1/ν The theory further proposes an Energy–Update Density Equivalence Principle, in which local energy density (ρₑ) and local time update density (ν) are interpreted as equivalent descriptions of a common underlying physical structure: ρₑ → ν → t Matter time is described by: dτₘ = (1/ν) √(1 − Vₘ²/c²) where Vₘ is the velocity of matter relative to the spatial update structure. Gravity is interpreted as a spatial gradient of time update density: g = −c² ∇ln(ν) Under the Universe Finite Principle, spatial updating possesses a maximum frequency νmax = c/lp which naturally leads to the minimum time interval dtmin = tp where lp and tp denote the Planck length and Planck time. The theory predicts that black holes do not contain mathematical singularities. Instead, gravitational collapse approaches a finite update-saturation state, leading to finite black-hole cores. Such finite-core structures may produce gravitational-wave echo signals following black-hole mergers, providing a possible observational test of the theory. The central hypothesis of the theory is that energy density, time update density, and time progression are different manifestations of a common underlying physical structure.
Toshihiro Tanaka (Mon,) studied this question.