LFM How-To: Strong Equivalence Principle (SEP) in LFM

Today we test a classic GR cornerstone in LFM: the Strong Equivalence Principle (SEP) via a Nordtvedt-style thought experiment. In GR, self-gravitating bodies fall the same way regardless of how much gravitational binding energy they contain. If SEP fails, two bodies with identical mass but different internal structure would accelerate differently in an external field.

THE QUESTION
Does LFM preserve SEP?
If χχ responds only to total energy density, the answer should be YES.

THE LFM MECHANISM
We evolve two fields only:

Matter field (GOV-01):

∂2E∂t2=c2∇2E−χ2E∂t2∂2E​=c2∇2E−χ2E

Substrate field (GOV-02):

∂2χ∂t2=c2∇2χ−κE2∂t2∂2χ​=c2∇2χ−κE2

Key point: χχ is sourced by E2E2 only. There is no term that depends on composition, pressure, or internal binding structure.

THE EXPERIMENT (CONCEPTUAL SETUP)
We simulate two bodies with equal total E2E2 but different internal structure:

Body A: compact, single peak
Body B: extended, multi-peak (same total energy)

Both are placed in the SAME external χχ gradient (a background well), then released.

SEP PASS CRITERION
If both bodies follow the same trajectory (same acceleration), SEP holds.

SEP FAIL CRITERION
If internal structure changes the fall rate, SEP is violated.

WHAT YOU SHOULD EXPECT IN LFM

• The force comes from the χχ gradient
• χχ is sourced only by total E2E2
• Therefore, the acceleration depends on total energy, not structure
• Result: SEP holds (Nordtvedt parameter η≈0η≈0)

WHY THIS MATTERS
Nordtvedt is one of the most sensitive SEP tests in GR.
Lunar Laser Ranging constrains SEP violations to tiny levels.
If LFM passes this, it clears a key GR test without dark matter particles.

WHAT TO LOOK FOR IN OUTPUT

• Center-of-mass position of both bodies vs time
• Overlap of trajectories within numerical tolerance
• No differential acceleration

PHYSICS POINT
This is not "GR by assumption." It follows directly from the LFM coupling:

1. GOV-01 propagates EE
2. GOV-02 responds to E2E2 only
3. No extra term distinguishes structure
4. Therefore, SEP should emerge