CST Time-Machine Simulator — Rings • Photons • 4 Clocks

Advanced Physics Layer — SR • GR • Sidereal Drift • Star Map • E↔m CST stays the narrative layer; physics adds the engineering layer behind the rings.

Special Relativity — Velocity Time Dilation

Ship velocity (fraction of c)

0.0% c γ = 1.0000

CST Δt (ideal)

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Proper Δt′ (SR)

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Uses Δt′ = Δt·√(1 − v²/c²) to show relativistic slippage on long, fast arcs.

Gravitational Time Dilation — Deep Wells

Reference body

GR factor √(1 − 2GM/rc²)

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CST Δt baseline

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Δt′ near body (GR)

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Applies Δt′ = Δt·√(1 − 2GM/rc²) to compare “far-away” vs “deep-well” clocks.

Sidereal vs Solar — Star Drift

Per-day drift (solar−sidereal)

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Accumulated drift over |Δt|

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Sidereal day ≈ 23h 56m 4.1s. The small offset compounds; big |Δt| → large sky drift.

Star Mapping & Light-Time

Right Ascension α (hours)

Declination δ (deg)

Distance d (light-years)

Unit vector (x,y,z)

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Light-time delay t = d/c

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Uses x = cosδ·cosα, y = cosδ·sinα, z = sinδ and t = d/c (here d in light-years → years of delay) for a real sky backbone.

Energy ↔ Mass Budget — Time-Machine Field Load

Effective payload mass m (kg)

100 kg E = —

Field Load Index (Δt ⊗ m)

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This panel uses E = m·c² as a design “budget” — not literal mass-to-pure-energy conversion. The Field Load Index grows with both |Δt| and effective mass, hinting at how much energy a realistic CST time bubble would need to stay coherent while carrying ship + memories + data.

The engine remains theoretical until a lab prototype exists, but this ties your rings and beams to an explicit energy–mass story that engineers can tune.

White = stable equilibrium • Red = traveling • Rings bob faster in transit; particles & photons accelerate

How This Time Machine Model Works — Clocks, Equilibrium & Equations

Clocks used (always live):

UTC Cosmic Clock — Universal reference for synchronization.
Current Local Clock — Your device’s local time.
Destination Clock — Target local date/time you dial.
Δt Clock — Signed difference from now → destination, which smoothly goes to zero during travel.

Equilibrium condition (visual demo): The machine holds a stable field when thermal, rotation, and phase terms are small. During travel, energy rises and the beam glows red; upon arrival, it returns to white, indicating equilibrium.

Key relations (illustrative):

Δt = t_dest − t_now
Δt′ = Δt·√(1 − v²/c²) (special relativity, high velocity arcs)
Δt′ = Δt·√(1 − 2GM/rc²) (general relativity, deep gravity wells)
LOD(Δt) ≈ 24 h + (1.7 ms / 100 yr) × (Δt / yr) (tidal friction trend → future days slightly longer)
rotFactor(Δt) = 24 h / LOD(Δt)
ω_⊕(Δt) = 2π / (86400 s · rotFactor)
P ∝ |Δt| · (1 + |rotFactor−1|·k) (more offset → more power to maintain the bubble)
x = cosδ·cosα, y = cosδ·sinα, z = sinδ (RA/Dec → 3D star coordinates)
t = d/c (light-time delay from stars; here d in light-years ≈ years of signal lag)
E = m·c² sets an energy–mass budget: the simulator’s Field Load Index scales with effective payload mass and |Δt|, making the rings feel like a machine a lab could, in principle, cost out.

Cosmic motion notes: For geologic-scale jumps, you must account for Earth’s rotation change (LOD) and long-term orbital/axial effects. In this demo, the rings’ bob and intensity encode that: larger |Δt| → faster bobbing and brighter beam. Historically, tidal friction slows Earth’s rotation; orbital period changes are smaller but can be modeled if desired.

Interpretation: If the destination is far, |Δt| is large → the simulator shows higher field activity (faster bob, photons, particles). When you press Travel, Δt converges toward zero, the beam transitions red→white, and the rings/particles return to stable rates, indicating synchronized arrival.

In this version, your CST ring is the poetic “cosmic story” layer. The SR/GR blocks, sidereal drift, star-mapping, and energy–mass budget form the engineering notes that could turn the story into a prototype — still theoretical, but now tied tightly to real physics.