Summary of the theory of emergent time

• [1] Emergent Time: A Causal-Machian Time Field Coupled to Matter
• [2] Planck-Scale Smearing of the Causal Time Field: Boundary Regularisation of the Emergent Time Theory
• [3] Quantum Field Theory Implications of the Emergent Causal Time Field
• [4] Cosmological Implications of the Causal-Machian Time Field
• [5] Commentary on the Model of a Causal-Machian Time Field
• [6] Time Bubble Nucleation on a Riemannian 3-Manifold: A Speculative Origin Scenario within the Emergent Causal Time Theory
• [7] A Smearing-Free Constraint-Pressure Mechanism for Dark Energy from Emergent Causal Time
• [8] A Z_3-Ring Parametrisation of the Fermion Masses and a Falsifiable Neutrino Spectrum
• [9] Particle Masses in Emergent Causal Time: the Geometric Content of $\eps=\sqrt2$ and a Map of the Standard-Model Mass Spectrum

Basic axioms and physical motivation

The theory of emergent time is based on two fundamental axioms: Time is coupled to matter and causality is preserved. Time is not understood here as an independent, absolute background, but rather as a physical quantity arising from the causal distribution of matter. Local time structures are determined by the matter within the past light cone.

From this follows a Machian interpretation of time: Local physical time is not entirely independent of the matter content of the universe. At the same time, the theory leads to a breach of global Lorentz invariance, as the causal distribution of matter provides a distinct cosmological reference frame, whilst local causality is to be preserved.

The physical motivation is to link time, gravity and the distribution of matter more closely. Instead of treating space-time merely as a passive stage, a causal time field is introduced, which reacts to matter and thereby influences the effective physical metric. The theory is not designed as a completely unambiguous construct: The axioms specify a direction but allow for different mathematical realisations.

Mathematical foundations, quantisation and initial applications

The first publication [1] formulates these physical principles within a mathematical structure. It introduces a causal-Machian time field that is coupled to matter, and shows how this can give rise to a modified form of the General Theory of Relativity can arise.

The second paper [2] supplements this structure with a Planck-scale-like smoothing of the causal time field. This smearing serves to regularise the sharp boundary of the light cone and prepares the theory for a quantised treatment.

The third publication [3] examines the consequences of these assumptions for quantum field theory. The focus is on how fields propagate on the effective metric determined by the emergent time field and what consequences this has for Standard Model couplings, causality and possible regularisation effects.

The fourth paper [4] applies the theory to cosmology. It examines what effects the causal-Machian time field might have on cosmological evolution, Hubble tension, structure formation and observable deviations from standard cosmology.

Classification of the theory and speculative origin scenario

The fifth publication [5] is a commentary on the classification of the first four papers. It clarifies, which statements are to be understood as core elements of the theory are to be understood, which assumptions remain model-dependent, and how the theory should be presented scientifically. It thus serves at the same time as a methodological bridge for a summarising presentation of the entire theory.

The sixth paper [6] develops a speculative scenario for its origin: a time-bubble nucleation on a Riemannian 3-manifold. This scenario presents an alternative to the classical description of the Big Bang. The observable temporal evolution arises from the formation of a finite time bubble within a substrate that was originally timeless or structured differently. This idea is explicitly Cosmology without quantisation and modified normalisation

The seventh publication [7] once again examines cosmological consequences, but this time without Planck-scale-like quantisation and with modified normalisation. Instead of retaining the cosmological constant, a causal constraint-pressure component is constructed from the retarded matter distribution.