- Think in the direction Energy → Mass → Curvature → Time. You choose the energy budget (flux, power, control gains) and see whether spacetime & quantum state can stay consistent.
- Enter steps, Δt, tolerances (εGR, εQM, εΔC), initial residuals, PD gains — these shape how quickly injected energy is converted into “mass-equivalent” curvature changes.
- Set photon–gravity inputs: base flux F₀, variability δI, redshift z, magnification M; optionally paste event times (e.g., solar flares) to drive flux via a kernel intensity.
- Click Run Simulation. If all residuals drop below tolerances for the hold window, you’ll see green badges (for this toy model).
- To make it a real verifier, swap in your GR/QM/CST kernels at the hooks—no UI changes needed.
\[ G_{\mu\nu} \;=\; 8\pi G\,T_{\mu\nu}, \quad E \;\longleftrightarrow\; m c^2 \] Linearized wave form (Lorenz gauge, $\bar h_{\mu\nu}=h_{\mu\nu}-\tfrac12\eta_{\mu\nu}h$):
\[ \square\,\bar h_{\mu\nu} \;=\; -16\pi G\,S_{\mu\nu}, \qquad S_{\mu\nu}=T^{\text{eff}}_{\mu\nu} \] with \[ T^{\text{eff}}_{\mu\nu}=\langle \hat T_{\mu\nu}\rangle + T^{\text{class}}_{\mu\nu} + T^{\text{EM}}_{\mu\nu} + F^{\text{CST}}_{\mu\nu} \] EM (photons) via flux — energy first, mass later
\[ F_{\mathrm{eff}}(t)=\frac{F_0\,[1+\delta I + \delta I_{\text{events}}(t)]\,M}{(1+z)^4}, \] \[ T^{\text{EM}}_{\mu\nu}\sim \frac{F_{\mathrm{eff}}}{c} \;\;\Rightarrow\;\; \rho_{\text{eff}} \sim \frac{F_{\mathrm{eff}}}{c^3} \] so injected photon energy sets an effective mass density and curvature.
\[ \dot{\hat\rho} = -\frac{i}{\hbar}\big[\hat H(g,A_\mu),\hat\rho\big] + \sum_j \kappa_j \mathcal D[L_j]\hat\rho + \mathcal L_{\text{CST}} \]
CST feedback (PD law, energy-shaped)
\[ F^{\text{CST}}_{\mu\nu} = -k_p\,\Delta h_{\mu\nu}-k_d\,\Delta \dot h_{\mu\nu}, \] \[ \Delta h_{\mu\nu}=h_{\mu\nu}-h^{\text{target}}_{\mu\nu}(t_{\text{CST}}) \] Here the PD gains map control energy into curvature corrections (effective mass re-balancing).
Point-process intensity (events → flux)
\[ \hat\lambda(t)=\sum_i K_h(t-t_i), \quad \delta I_{\text{events}}(t)=c_\lambda\,\hat\lambda(t) \] turning flare energy into extra curvature forcing.
Simulation & Physics Parameters
Residuals vs. Time (blink = energy)
hμν Snapshots & Spectra (pulsing with energy)
Snapshot: pre-control
Snapshot: post-control
Spectrum: pre
Spectrum: post
Input Power vs. Curvature Change (blinking = energy rate)
The brighter / faster the blink, the more aggressively energy is being pushed into curvature in this toy model.
Observable Checks
| Test | Target | Measured | Status |
|---|---|---|---|
| Solar-system orbits (fractional err/orbit) | < 1e-8 | — | — |
| Cosmology (FRW homogeneous limit) | match | — | — |
| Lab EM cavity (Δf vs small h) | linear | — | — |
Einstein Master Equation — Purpose
The calculator couples four pieces into one loop: (1) GR curvature via the Einstein equations, (2) Quantum state evolution via a Lindblad master equation, (3) Photon forcing via flux (EM stress–energy), (4) CST feedback control that damps metric error. In this energy → mass view, you start from energy inputs and watch how they would appear as effective mass, curvature, and clock shifts. When all three residuals fall below tolerance and stay there (hold window), the system is self-consistent for those inputs.
How to fill each label
- Steps (N): number of integration steps (e.g., 500).
- Δt: time step (dimensionless here; obey CFL in real solvers), e.g., 0.02.
- εGR, εQM, εΔC: tolerances for the GR residual, QM residual, and control error (e.g., 1e-6).
- Consecutive steps for “solved”: how many steps in a row must be under tolerance (e.g., 50).
- RGR(0), RQM(0): initial residual magnitudes at the start.
- ΔC(0): initial metric error norm (toy scalar here).
- h-spectrum imbalance: 0–1 slider that shapes the pre/post spectra visuals.
- PD gains kp, kd: proportional/derivative gains for CST control (energy you spend to push curvature back into line).
- Photon base flux F₀ [W/m²]: e.g., 1361 at 1 AU (TSI).
- Variability δI (fraction): slow baseline modulation (0.00–0.05 typical).
- Lensing M: magnification factor (≈1 near Earth; >1 if lensed).
- Redshift z: gravitational/cosmological redshift (near-Earth ≪1).
- Noise τ, σ: Ornstein–Uhlenbeck correlation time (s) and amplitude (fraction) for jitter.
- Event times (s): comma/space list of flare or burst times to spike flux.
- Kernel & h: choose Gaussian / Epanechnikov / Exponential; set bandwidth/decay in seconds.
- cλ: scales the event intensity λ̂(t) into fractional flux δIevents.
After you click Run Simulation, check badges and plots. To turn this into a proof for a real system, replace the three hook functions with your integrators.
Quick Fills (try these, then Run)
1) Sun–Earth (quiet Sun)
Stable baseline, minimal events; should damp smoothly.
2) Sun–Earth (flare events)
Adds bursty event times and larger variability.
3) Lab EM cavity (minimal flux)
Toy lab case: tiny flux & tighter tolerances.
After filling, press Run Simulation. Tweak gains or tolerances if residuals don’t converge with the toy kernels.
Click the button to auto-fill parameters that (with these toy kernels) pass:
Solar-system orbits < 1e-8, FRW limit “match”, and Lab cavity “linear”. Then press Run Simulation.
Relativistic Clock, Star Mapping & Light-Time Physics
1. Time Dilation (Velocity)
2. Gravitational Time Dilation (Deep Gravity Wells)
3. Star Coordinate Mapping (RA/Dec → 3D)
4. Sidereal Clock Adjustment
5. Light-Time Correction
You already built the vision. These pieces just lock it into the real sky: energy → mass → curvature → time, stitched with RA/Dec and light-time so your Interstellar Star Clock can live inside actual physics.