In our earlier paper, Void Anchoring, Action Quantization, and the Mass Scale, we proposed a simple but radical idea: mass emerges from irreversible information updates occurring on a discrete substrate. In that framework, a particle is not fundamentally a tiny solid object, but a repeating pattern of committed state transitions. Its rest mass is determined by how those transitions accumulate relative to the fundamental tick structure of the substrate.
Two ingredients governed the result. The first was the void coupling probability — the likelihood per substrate tick that the system enters a configuration capable of contributing to an irreversible update. The second was the anchoring depth — the number of successful micro-events required before a full, irreversible bit-flip is completed. Mass scaled as the ratio of these two quantities. The structure was internally consistent and remarkably robust. It respected action quantization, reproduced correct dimensional behavior, and aligned naturally with inertial mass.
But there was an open question. What determines the coupling probability itself?
In the original anchoring paper, this probability was defined statistically, but not dynamically derived. The architecture of mass was in place, but one of its key components remained unexplained.
The new paper, Void Coupling as Phase Coherence, addresses that gap directly. Instead of treating void coupling as a free parameter, we reinterpret it as phase coherence between the interface mode and the void substrate. In simple terms, a particle-like mode and the underlying substrate each carry oscillatory structure. When these oscillations are well synchronized, alignment events become common. When synchronization weakens, alignment becomes sparse.
We introduce a single quantity — a coherence measure — that quantifies how well the two oscillations track one another. From this coherence measure, we derive the probability that the system enters an alignment window capable of producing an irreversible micro-event. The mass formula remains structurally unchanged. What changes is that the coupling probability is no longer an unexplained input; it becomes a computable consequence of synchronization dynamics.
Nothing in the original Void Anchoring framework is discarded. The anchoring depth still measures how many micro-events are required for commitment. The action per committed flip remains quantized. The scaling relation between commitment density and mass remains intact. The coherence paper does not replace the anchoring paper — it supplies its missing dynamical layer.
Seen together, the two papers form a coherent progression. Void Anchoring established the structural bridge from irreversible information to mass. Phase Coherence explains what governs how frequently commitment opportunities arise within the substrate’s discrete evolution.
This upgrade also strengthens the explanatory reach of the framework. It introduces a natural synchronization threshold: when coherence collapses, effective coupling vanishes and mass disappears. It provides a mechanism for decay widths: particles in intermediate coherence regimes become sensitive to small fluctuations. And it offers a natural route to the enormous hierarchy of particle masses. Small differences in internal synchronization structure become amplified exponentially as internal complexity grows. That amplification explains why, for example, the top quark is roughly 340,000 times heavier than the electron.
Importantly, this work does not attempt to replace the Higgs mechanism at the level of established particle physics. Instead, it offers a possible deeper interpretation of what determines the strength of a particle’s interaction with the Higgs field. In the Standard Model, the Yukawa couplings that determine fermion masses are empirical inputs. In the coherence–anchoring picture, those couplings correspond to underlying synchronization and anchoring properties of the mode. The exponential hierarchy of masses becomes a reflection of internal coherence structure rather than a list of unexplained numbers.
General Reader Summary
Here is the simple version.
The Void Anchoring paper proposed that mass comes from irreversible information updates. A particle is a repeating pattern of state transitions on a deeper substrate. Its mass depends on how many substrate ticks are required to complete one full, committed update.
The new Phase Coherence paper explains why some particles complete those updates more readily than others. The answer is synchronization. When a particle’s internal oscillation is strongly synchronized with the substrate, opportunities for irreversible updates arise frequently within the substrate’s discrete evolution. If the anchoring depth is shallow, those opportunities accumulate quickly and the particle has higher mass. If synchronization is weak or anchoring is deep, updates require many substrate ticks to complete and mass is small.
Mass, in this picture, is not a mysterious intrinsic substance. It is the density of committed information updates relative to the substrate’s discrete evolution.
Stable particles correspond to high-coherence modes that resist fluctuation. Unstable particles sit at intermediate coherence, where small disturbances strongly affect the accumulation of commitment. And the enormous differences in particle masses emerge naturally from how internal complexity suppresses synchronization.
Taken together, the two papers present a unified view: mass is what irreversible information looks like when it becomes dynamically synchronized with the fabric of reality.