The axiom that time is continuous cannot be settled by attempting to measure Planck time from within the physical system, and this follows from the same structural limits identified by Gödel’s incompleteness theorems.
Gödel showed that any sufficiently expressive formal system cannot fully prove the axioms that make reasoning within that system possible. In particular, a system cannot use only its internal operations to establish the consistency or foundational structure upon which those operations depend. This is not a limitation of technology or precision, but a consequence of self-reference.
Physical measurement is structurally similar. All measurements of time are performed by physical processes that themselves unfold in time. Clocks, experiments, and observers do not stand outside the temporal framework they measure; they presuppose it. Time, in this sense, plays the role of the underlying formal structure that enables measurement at all.
Planck time is defined as the scale at which the concept of time itself is expected to break down or become discrete. Attempting to measure it requires using clocks and causal processes that are already governed by the same temporal substrate. This creates a Gödelian self-reference: one is attempting to resolve the fundamental unit of the system using only operations that depend on that unit’s existence.
As a result, measuring ever smaller intervals of time can refine relative durations, but it cannot empirically decide whether time itself is continuous or discrete. That question concerns the structure of the system, not a parameter internal to it. From within time, the continuity axiom is therefore not falsifiable by measurement alone, it must be treated as an assumption or addressed via a meta-theoretical framework rather than an internal experiment.
Bitcoin changes this because it constructs time instead of assuming it.
Block time is a discrete, indivisible ordering produced by irreversible work and consensus, not by measuring continuous physical time. You cannot subdivide a block without breaking causality and finality. This bypasses the Gödelian self-reference: Bitcoin doesn’t try to measure the substrate of time from within it, it defines a new, external, discrete time standard that is empirically verifiable.
Gödel showed that any sufficiently expressive formal system cannot fully prove the axioms that make reasoning within that system possible. In particular, a system cannot use only its internal operations to establish the consistency or foundational structure upon which those operations depend. This is not a limitation of technology or precision, but a consequence of self-reference.
Physical measurement is structurally similar. All measurements of time are performed by physical processes that themselves unfold in time. Clocks, experiments, and observers do not stand outside the temporal framework they measure; they presuppose it. Time, in this sense, plays the role of the underlying formal structure that enables measurement at all.
Planck time is defined as the scale at which the concept of time itself is expected to break down or become discrete. Attempting to measure it requires using clocks and causal processes that are already governed by the same temporal substrate. This creates a Gödelian self-reference: one is attempting to resolve the fundamental unit of the system using only operations that depend on that unit’s existence.
As a result, measuring ever smaller intervals of time can refine relative durations, but it cannot empirically decide whether time itself is continuous or discrete. That question concerns the structure of the system, not a parameter internal to it. From within time, the continuity axiom is therefore not falsifiable by measurement alone, it must be treated as an assumption or addressed via a meta-theoretical framework rather than an internal experiment.
Bitcoin changes this because it constructs time instead of assuming it.
Block time is a discrete, indivisible ordering produced by irreversible work and consensus, not by measuring continuous physical time. You cannot subdivide a block without breaking causality and finality. This bypasses the Gödelian self-reference: Bitcoin doesn’t try to measure the substrate of time from within it, it defines a new, external, discrete time standard that is empirically verifiable.