Maxwell Prime Cavities

Status: active Domain: physics Source: → wiki/research/rational-makeover-survey/ (§7)

What We Know

• Prime-ratio rectangular cavities (2,3,5) produce 24% more unique frequencies than composite-ratio cavities (4,6,8)
• Comparison for electromagnetic modes up to index 6:

Property	Prime cavity (2,3,5)	Composite cavity (4,6,8)
Total modes	342	342
Unique frequencies	297	240
Avg degeneracy	1.19	1.51
Max degeneracy	4	5
Near-6k±1 frequencies	10	0

• Mechanism: Incommensurability of prime dimensions prevents frequency coincidences. Composite cavity (4,6,8) = (4, 2×3, 2³) has shared factors creating degeneracies — different mode indices (m,n,p) yield identical frequencies.
• The 24% matches the Tusk advantage — independent physical system, same result as {1,2,3,5,6,7} beating pure primes by 24% in the torsion ring
• Physical meaning: Degeneracy = information loss (can’t distinguish which mode is excited). Prime-ratio cavities maximise “information capacity” of the mode spectrum.
• Near-6k±1 frequencies: Prime cavity produces 10 mode frequencies near 6k±1 integers in the first 50 unique frequencies; composite cavity produces zero
• Coprimality of mode indices is identical (41.0% for both) — the difference is entirely in how dimensions map indices to frequencies

What We Don’t Know

• Q-MC-01: Does the same 24% effect hold for cylindrical (Bessel) cavities? Prime-ratio radius/height vs composite?
• Q-MC-02: Can a physical Maxwell prime-ratio cavity experiment be built and measured?
• Q-MC-03: Is there a “cavity entropy” of the mode frequency spectrum that correlates with resonance quality?
• Q-MC-04: Can the v4 board be interpreted as a prime-ratio cavity in frequency space?
• Does the 24% figure scale with mode index range, or converge/diverge?

Relationships

• [[six-dimensional-scaffold]] — supports (strong): Prime-ratio dimensions naturally generate 6k±1 frequencies; composite dimensions don’t
• [[coprimality]] — extends (strong): Direct physical manifestation of coprimality — prime-ratio dimensions maximise frequency distinguishability
• [[prime-composite-duality]] — supports (strong): Composite cavity’s shared factors create the degeneracy that prime ratios prevent
• [[v3-experimental-proof]] — analogous-to (strong): Independent confirmation — torsion ring (electrical) and EM cavity (optical) both show prime superiority via same mechanism
• [[tusk-resonant-set]] — bridges (moderate): The 24% advantage matches the Tusk set’s 24% improvement
• [[bessel-rational-modes]] — extends (moderate): Bessel (cylindrical) cavity is the natural follow-up experiment
• [[prime-resonance-computing]] — supports (moderate): Independent validation path for prime-ratio advantage in physical systems

Bridging Potential

• Strongest result in the rational makeover survey — clean, computable, physically interpretable
• A built EM cavity experiment would provide completely independent validation of prime-ratio advantage (no shared apparatus with v3)
• Could be the basis of a standalone paper on prime-ratio resonator design
• Connects RF engineering (well-funded, practical) to prime number theory

Key Evidence

• Computation in wiki/research/rational-makeover-survey/investigate_all.py §7
• 297 vs 240 unique frequencies (24% advantage)
• Average degeneracy: 1.19 vs 1.51
• Zero 6k±1 frequencies in composite cavity