In 30 seconds
The Frame-Budget Approach (FBA) builds physics operationally from the ground up: from distinguishable state “frames” and minimal updates we first define only an order (a sequence) — no presupposed “time coordinate”.
Each transition debits a budget (internal/external); via calibration this becomes measurable physics: proper time as an integrated internal budget flow and a signal front (light-cone logic) as a consequence of budget positivity.
An irreversible share of the internal budget additionally provides a natural bridge to the arrow of time, thermodynamics, and aging.
What is Part I about?
Part I establishes the concepts, minimal assumptions, and the operational grammar of the Frame-Budget Approach (FBA).
The guiding idea is:
We do not start from a predefined metric (“time as a coordinate”), but from what is operationally distinguishable in real protocols — and from what transitions cost. From distinguishability + bookkeeping (budget) + calibration we obtain, as consequences, proper time, a maximal propagation front (light-cone logic), and—under suitable limits—the familiar relativistic geometry.
Key ideas (6 points)
- Frames (state snapshots): A frame is an operationally “same” state relative to a chosen resolution / protocol boundary.
- Minimal events (ME): A minimal event is the smallest update that turns “same” into “different” under the chosen protocol.
- Order before clocks: Primarily, we have an order of updates (an index counts steps). Metric time emerges only after calibration.
- Budget as feasibility cost: Every transition debits a budget — typically split into internal (self-change of a system) and external (change of relations/position/order).
- Irreversibility carries arrows: A part of the internal budget may be irreversible. Operationally this yields an arrow of time; in FBA it also bridges to thermodynamics/aging.
- Calibration makes physics: Calibration (mapping “budget ↔ observable”) turns bookkeeping into testable statements: fronts/signal bounds, proper time, time dilation as budget reallocation, dissipation as aging.
Concepts you truly “have in hand” after Part I
Frame, minimal event, sequence/partial causal order, budget (internal/external/irreversible), calibration, front (signal front), proper time τ, aging A, admissible dynamics (as budget-constrained processes), composition/locality/no-signalling.
Mini formalism (only as much as needed)
External calibration (coordinate time & range):
Fix positive cost rates, e.g.
$$
\Delta B^{\mathrm{ext}}=\kappa_t\,\Delta t,\qquad
\kappa_x\,\|\Delta \mathbf{x}\|\le \Delta B^{\mathrm{ext}}.
$$
This immediately yields a front bound
$$
\|\Delta \mathbf{x}\|\le c\,\Delta t,\qquad
c:=\frac{\kappa_t}{\kappa_x}.
$$
Interpretation: a maximum propagation speed is not “added by hand” but follows from budget positivity + calibration.
Internal calibration (proper time):
Internal bookkeeping defines a system-bound step proper time, e.g.
$$
\Delta \tau_n=\frac{\Delta B^{\mathrm{int}}_n}{\kappa_\tau},\qquad
\tau[\gamma]=\sum_{n\in\gamma}\Delta\tau_n.
$$
That is: proper time is an integrated internal budget flow along a worldline γ.
Aging as an irreversible share:
One may isolate an irreversible contribution in the internal account and sum it along γ:
$$
A[\gamma]=\sum_{n\in\gamma}\Delta B^{\mathrm{irr}}_n.
$$
Reversible (unitary) contributions affect τ but not A; dissipation increases A.
What Part I delivers (and why it matters)
Part I is the foundation slab for Parts II–X:
- It defines the primitives (what is assumed vs. what is constructed?).
- It introduces a step–budget calculus (series/parallel/refinement), so statements remain stable under re-segmentation.
- It makes the front (signal bounds) a direct consequence of calibration and budget inequalities.
- It cleanly separates order (“which update follows which?”) from measure (“how much internal/external bookkeeping accrued?”).
- It shows how admissible dynamics can be framed as budget-constrained processes (bridging toward the later channel/GKLS parts).
- It provides a pass/fail checklist: the approach is built to be falsifiable if balance and consistency relations do not close for real protocols.
Reading path: where to go next
- Time/proper time/Minkowski: continue with Part II.
- Quantum channels & dynamics: Part III → Part IV.
- Spacetime/locality: Part V.
- Gravity: Part VI.
- Thermo & aging: Part VIII.
- Cosmology/tests: Part IX – Part X.