Status: CANONICAL Paper: 24 — A Transformation-Based Definition of Local Lorentz Invariance and Its Connection to Frame Dragging
Frame dragging (Lense-Thirring effect) in GR arises from the off-diagonal g_{tφ} metric components near rotating masses. SSZ does not modify the angular structure but affects the time component through Ξ.
For a rotating mass (Kerr-like geometry):
- The angular momentum J creates an off-diagonal metric term
- SSZ modifies the g_tt component: g_tt = -(1 - 2Ξ(r)) instead of -(1 - r_s/r)
- The g_{tφ} cross-term is treated via standard PPN orbit machinery
Frame dragging is a timelike orbit observable → uses PPN (β, γ), NOT Ξ-only.
SSZ maintains local Lorentz invariance by construction:
- The speed of light c is locally invariant everywhere
- Effects arise from geometry/path + clock mapping, not local speed changes
- The transformation between frames preserves the local light cone structure
The transformation-based definition (Paper 24) shows that SSZ's modified time dilation is compatible with local Lorentz invariance because Ξ enters as a position-dependent scale, not a velocity-dependent one.
| Observable | Method | SSZ vs GR |
|---|---|---|
| Lense-Thirring precession | PPN | Identical (weak field) |
| Geodetic precession | PPN | Identical (weak field) |
| Frame dragging near NS | PPN + Ξ correction | Different (strong field) |
In the weak field (where frame dragging has been measured, e.g., Gravity Probe B), SSZ = GR exactly.
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