CH. 01
Time Dilation
A clock on a fast spaceship ticks slower than the one in your kitchen. Not by illusion -- by ledger. Spacetime is one fabric, and what you spend on motion you cannot also spend on time.
Δt′ = Δt / √(1 − v²/c²)
CH. 02
Gravitational Lensing
Light has no preference. It travels straight -- through space that isn't. Around a heavy mass, the geodesics curve, and the photon obediently follows. We call the resulting smear an arc, a ring, a cross.
θ = 4GM / (c² b)
CH. 03
The Spacetime Fabric
Imagine a sheet stretched flat. Drop a marble. The sheet dimples. Roll a pebble nearby and it spirals inward -- not pulled, but coasting a path that was always going to end here. Gravity is geometry.
Rμν − ½ gμν R = 8πG Tμν
CH. 04
Frames of Reference
There is no preferred observer. The platform moves past the train, and the train moves past the platform, and the laws of physics do not flinch. Relativity is the polite refusal to claim a center.
x′ = γ(x − vt)
CH. 05
Quantized Spacetime
At the smallest scales, even smoothness might be an illusion -- a mosaic of Planck-scale tiles whose edges we cannot yet see. Relativity and quantum mechanics still negotiate over the lease.
ℓP = √(ℏG/c³) ≈ 1.6 × 10−35 m