Why Quantisation Exists: Thresholds and Events

This guide explains why discrete thresholds must exist for events and propagation at a foundational level, without assuming quantum mechanics or deriving specific constants. It establishes the conceptual necessity of quantisation before any continuum recovery or saturation mechanisms are introduced.

1. The Core Question

Physical events occur. Things change discretely. Measurements yield definite outcomes.

The question is not whether discreteness exists — that is empirically established — but why discreteness is structurally necessary at all.

What would a universe without discrete thresholds look like, and why does that possibility fail?

2. The Wall Analogy: Understanding Thresholds

Consider a brick wall under stress:

Small stresses can be absorbed elastically across the wall’s structure
The wall flexes slightly, redistributes load through mortar joints
No permanent change occurs; no crack forms

But beyond a certain crack threshold:

Stress exceeds what the wall can locally buffer
A crack must form — a discrete, irreversible structural change
The crack propagates independently until it reaches a boundary or is absorbed elsewhere

The crack threshold is not arbitrary. It reflects:

How stiff the bricks are
How many internal degrees of freedom the joints have
How stress redistributes through the structure

Crucially: if there were no threshold, stress could be absorbed by ever-finer adjustments indefinitely, and no crack would ever form.

3. Three Concepts: Branching, Deferred Mismatch, and Forced Commitment

Before proceeding, we must distinguish three related but distinct concepts:

3.1 Branching

Branching occurs when multiple admissible continuations are simultaneously compatible with existing structure.

A single configuration can support multiple future paths
These paths may later merge if they remain mutually compatible
Branching does not require cracks or discrete events
Example: An electron traveling through a double slit admits multiple compatible continuation paths

3.2 Deferred Mismatch

Deferred mismatch arises when local constraint satisfaction creates unresolved mismatch that cannot be absorbed immediately.

The mismatch is real and persistent
It must propagate as an independent carrier (a “crack”)
It carries obligations for future resolution
Example: A photon as a propagating packet of deferred mismatch

3.3 Forced Commitment

Forced commitment occurs when compatibility can no longer be maintained across alternative paths or unresolved mismatch.

Multiple branches or deferred commitments cannot all be jointly satisfied
The structure must partition into mutually incompatible configurations
This is not stochastic choice — it is structural necessity
Example: Measurement as closure-triggered commitment

4. The Necessity of Thresholds

4.1 Without Thresholds: The Frozen Universe

If mismatch could always be absorbed by arbitrarily small adjustments:

No stress would ever exceed buffering capacity
No deferred mismatch would ever crystallize into propagators
No forced commitments would ever occur
No discrete events would ever happen

This is a frozen universe — one where:

There is no alphabet of causal events
No definite punctuation marks separating past from future
No resolution into distinct outcomes

Physical reality as we observe it requires that buffering has limits.

4.2 The Role of Planck’s Constant ℏ

Planck’s constant ℏ sets the empirical scale of the minimum discrete unit in our universe:

The smallest packet of deferred mismatch that can propagate independently
The minimum “action” required to force an irreversible event
The threshold below which mismatch is absorbed elastically, above which it must propagate

Crucially: We are not deriving ℏ here. We are explaining why a constant of this type must exist at all.

The specific value of ℏ in our universe is an empirical fact. CD explains:

Why some threshold must exist (structural necessity)
What role it plays (minimum deferred mismatch packet size)
How it relates to other mechanisms (saturation, capacity, continuum structure)

But it does not claim to derive ℏ from first principles.

5. What This Means for Events and Interference

5.1 Events Happen When Buffering Fails

An event occurs when:

Local mismatch exceeds buffering capacity
A commitment must be forced
The structure partitions irreversibly

This is not:

Random collapse
External measurement
Observer intervention

It is structural resolution triggered by constraint saturation.

5.2 Interference Exists Because Branching Exists

Interference occurs when:

Multiple branches remain compatible
They retain shared ancestry
They can merge without violating constraints

Interference does not require deferred mismatch or cracks. It requires only:

Branching (multiple admissible continuations)
Compatibility preservation across branches
Shared structural history

Electrons interfere. Molecules interfere. Large aggregates can interfere if isolated.

The limiting factor is not “being a crack” — it is whether branch histories remain mutually admissible.

6. Below-Threshold Mismatch

6.1 What Happens to Stress Below the Threshold?

In the wall analogy:

Below-threshold stress is absorbed elastically
It spreads across the wall without trace
It does not need to propagate as a crack
It does not need to be resolved later

The same holds for informational structure:

Below-threshold mismatch is buffered within existing structure
It does not crystallize into a propagator
It does not create deferred obligations
It is simply locally absorbed

6.2 Not Every Mismatch Must Propagate

There is no requirement that “every mismatch must propagate.”

Only structurally significant mismatch — that which exceeds local buffering capacity — becomes a propagator.

This is why:

Not every interaction emits radiation
Not every fluctuation becomes causal
Not every disturbance leaves a trace

7. Constants as Load-Bearing Properties

The value of ℏ (and other fundamental constants) encodes load-bearing properties of the universe:

ℏ → minimum unit of deferred mismatch
c → maximum reconciliation propagation rate
G → gravity coupling (emergent from closure availability)

These constants are not arbitrary parameters. They reflect:

The structural capacity of informational substrate
The saturation limits of constraint resolution
The geometry of admissible continuations

But they are empirical — we measure them, we do not derive them from pure logic.

CD’s contribution is explaining why constants of these types must exist, not computing their numerical values.

8. Relationship to Later Mechanisms

This guide establishes why thresholds exist at a conceptual level.

Later mechanisms build on this foundation:

8.1 Continuum Recovery (C-series papers)

How discrete substrate permits continuous approximations
When threshold effects become negligible
How carrier structures emerge

8.2 Saturation Mechanisms (M-SAT-GEN)

How ℏ enters as the size of minimal deferred mismatch in continuum regimes
Dimensionless saturation ratios (capacity vs generation)
Why dark matter halo cores form where they do

8.3 Event Structure (Q-series)

Formal treatment of closure and commitment
Branching vs partition conditions
Born rule emergence from compatibility geometry

But none of these require knowing ℏ first. This guide explains the necessity of some threshold, not its specific value.

9. Summary

Why quantisation exists:

Buffering must have limits, or no events would occur
Discrete thresholds are structurally necessary for causal punctuation
ℏ is the empirical scale of minimum deferred mismatch in our universe

What this is not:

Not a derivation of ℏ from axioms
Not a claim that ℏ is unique or inevitable
Not dependent on quantum mechanics, continuum structure, or GR

What it enables:

Explains why discrete events are necessary, not accidental
Grounds later work on saturation and capacity limits
Justifies treating ℏ as a structural parameter, not a tunable constant

This is conceptual bedrock for understanding why our universe has discrete structure at all.