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sim_48_nordtvedt_lunar_ranging_2026
PASS
0.6s - peak 0.0 MB

today's EP-violation signal = 0 exactly,

Purpose

Compute the Nordtvedt equivalence-principle parameter η=4(βPPN1)(γPPN1)\eta = 4(\beta_{\mathrm{PPN}}-1)-(\gamma_{\mathrm{PPN}}-1) for SVT and compare to the LLR bound η=(0.8±1.3)×104\eta=(-0.8\pm 1.3)\times 10^{-4} and the next-generation APOLLO/ELRAD target η3×105|\eta|\le 3\times 10^{-5}.

What it proves

In the IR-protected regime (sim_46) SVT sits at γ=β=1\gamma=\beta=1 exactly, so ηSVT(z=0)=0\eta_{\mathrm{SVT}}(z{=}0)=0 — trivially below every existing and forecasted LLR bound. Unlike chameleon models that predict η>0\eta>0 via scalar coupling to nuclear binding energy, SVT's null is a structural prediction of the IR fixed point. The non-trivial content is the drift: dη/dz\mathrm{d}\eta/\mathrm{d}z turns on immediately above zIRz_{\mathrm{IR}}, so APOLLO / ELRAD can either see the drift (detection) or tighten the bound on zIRz_{\mathrm{IR}} (constraint).

Relation to current theory

LLR has been the tightest gravity test for 55 years and has ruled out most scalar-tensor Nordtvedt signals. SVT's temporal screening makes it maximally consistent with LLR *today* while leaving a detection channel open in next-generation retroreflector experiments — the postdiction-then-prediction pattern Dr. Turyshev's paper specifically asks for.

Key equation
ηSVT(z=0)=4(βSVT1)(γSVT1)=0\eta_{\mathrm{SVT}}(z{=}0) = 4(\beta_{\mathrm{SVT}}-1)-(\gamma_{\mathrm{SVT}}-1) = 0

Plots

sim_48_eta_of_z.png
sim_48_eta_of_z.png
sim_48_mass_composition.png
sim_48_mass_composition.png
sim_48_nordtvedt_compare.png
sim_48_nordtvedt_compare.png

Scalar metrics

Chameleon predicted eta0.00001
Vainshtein predicted eta0
deta/dz at z_IR (SVT)0.0884

stdout tail

=================== VALIDATION ===================
  LLR eta    : (-8.00e-05 +/- 1.30e-04)
  APOLLO target : |eta| <= 3.0e-05
  Chameleon predicted eta  : 1.0e-05
  Vainshtein predicted eta : 0.0e+00
  SVT predicted eta(z=0)   : 0.0e+00
  deta/dz at z_IR (SVT)   : 8.84e-02
  SVT within LLR 1-sigma  : PASS
  SVT within APOLLO target: PASS
  SVT eta flat at z=0     : PASS
  SVT has non-zero drift  : PASS
  Overall                 : PASS

  SVT Prediction: today's EP-violation signal = 0 exactly,
  non-zero drift switches on for z > z_IR. APOLLO / ELRAD will
  either see the drift or tighten z_IR.
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