The Gravity Lens — ring-former & mass-solver
A lens with no glass: mass curves spacetime, light bends, and the bending is the lensing. Set the mass and alignment on the left; on the right, an observer who sees only the bent light weighs the invisible mass — exactly — from the ring alone.
LIT Einstein radius θ_E∝√M · lens eq β=θ−θ_E²/θ · θ₊·θ₋=−θ_E² · μ=(u²+2)/u√(u²+4) FIG the seam · the read
◧ ring-former — the truth ring
◨ mass-solver — sees only bent light solving…
weighing the invisible…
Left — the ring-former (the truth): you place a mass and set the alignment . Light from a background source bends around the mass along curved geodesics. When source, lens, and observer are collinear (alignment→.99) the bent light closes into a full Einstein ring at radius θ_E∝√M; off-axis it breaks into two arcs / images . There's no focal point — a gravity lens focuses along a caustic, a line, not a spot. ·
Right — the mass-solver (the read): this observer never sees the mass . It sees only the bent light — the ring and the two images — measures their positions, and uses the product law θ₊·θ₋ = −θ_E² to recover θ_E, then M∝θ_E². The gauge shows the inferred mass matches the true mass exactly : you have weighed something invisible, purely by what it did to the light that passed near it. ·
That's the whole arc's ethic in its purest optical form: characterize the thing you cannot see by its effect on what you can read. The mass is the gap; the ring is its signature; the solver is the honest black-box read. LIT the lensing is real GR FIG the mapping to the seam.