Deriving Physics from Information: Six Axioms, Zero Equations

Both pillars of modern physics — Special Relativity (E=mc^2) and Quantum Mechanics (the Schrodinger equation) — are derivable from 6 informational axioms that encode zero known physics equations. The derivation produces 9 genuine results, 1 novel testable prediction, and a structural resolution of the quantum gravity unification problem.

Six statements. No physics assumed.

P1 through P5 were stated first. P6 was identified as the minimal additional axiom needed after P1-P5 proved insufficient to derive the c^2 exponent.

These are not primes. They are composites of the primitives.

In natural units: mass IS energy. The c^2 in E = mc^2 is a unit conversion artifact from measuring space and time in different scales.

The chain: Bilinearity leads to a quadratic metric, which gives us Noether's theorem, which yields E = mc^2.

1. P6 gives a quadratic metric. Bilinear composition induces a bilinear form on void. Bilinear forms are quadratic.

2. P2 gives mixed signature. Irreversibility distinguishes time from space. You can reverse spatial direction but not temporal. The metric has signature (-,+,+,+).

3. P5 gives c as the metric coefficient. The bandwidth bound sets the conversion between space-bits and time-ticks.

4. Steps 1-3 derive the Minkowski metric. Not assumed — follows from P2, P5, P6.

5. P1 gives conservation. Bounded state in void persists through time.

6. Noether's theorem applied to time-translation symmetry for stationary existence: conserved energy = existence times c^2.

No step encodes E = mc^2. Each step applies a primitive axiom or a mathematical theorem to the previous step's output.

1. Metric + P1 give action. Free-particle action in the Minkowski metric derived above.

2. P3 + P4 give the path integral. Discrete void means finite paths between points. The existence-field at a point = sum over all causal paths weighted by action.

3. Path integral gives Schrodinger. Expanding the propagator to first order in time yields the equation. Standard result (Feynman and Hibbs, 1965).

P3 (quantization) and P6 (bilinearity) together predict that the product operator deviates from bilinearity when boundary-bits approach the minimum void quanta.

Consequence: energy-dependent photon speed for high-energy photons. Testable via gamma-ray burst observations with the Fermi telescope.

Existing modified dispersion relation theories propose this phenomenologically. The primitive framework derives it structurally: the product must become nonlinear where discreteness dominates.

c is not a speed. It is a bandwidth — the maximum rate at which boundary-structure can propagate through causal sequence. Nothing exceeds c because the void's partition capacity is finite.

The conflict arises because quantum mechanics assumes discrete spacetime (P3 + P4) while general relativity assumes smooth geometry (P6). In the primitive framework, both are consequences of the SAME axiom set. The conflict only appears when bilinearity meets discreteness at the Planck scale.

The "problem of quantum gravity" is not a conflict between two theories. It is the question: what does the product look like when boundary-bits approach their minimum? The primitives predict this breakdown. They do not resolve it — that requires knowing the nonlinear structure of the product at the minimum.

1. Can P6 be derived from P1-P5, making it a theorem rather than an axiom?
2. Does the framework predict the specific value of c, or only its existence?
3. What determines the spatial dimension (3+1 vs other)?
4. Can gravity (GR field equations) be derived beyond the structural argument?
5. What is the nonlinear structure of the product at the minimum? This IS quantum gravity.
6. Can the framework derive the Standard Model particle spectrum?