🌀 Special & General Relativity

What you’ll learn

1. The Problem with LightExplain the ether problem and why the Michelson-Morley null result demanded new physics.Maxwell's theory gave light a fixed speed but no obvious reference frame, so physicists invented the ether. Michelson and Morley's 1887 interferometer found no trace of Earth's motion through it, and the crisis was resolved only in 1905 by a young patent examiner in Bern.
2. 1905: Two Simple PostulatesState special relativity's two postulates and derive that simultaneity is relative.Physics looks identical in all uniformly moving frames, and everyone measures light at the same speed c. Together these force the relativity of simultaneity and make c an unbreakable speed limit — one now built into the very definition of the metre.
3. Time Dilation Is RealQuantify time dilation via the Lorentz factor and review its experimental proofs.Moving clocks run slow by the factor γ, negligible at everyday speeds but huge near c. Cosmic-ray muons reaching sea level, the Hafele-Keating flying-clock experiment of 1971, and the slightly younger returning astronauts of today all measure exactly this effect.
4. E = mc²Explain mass-energy equivalence and its scale, from the Sun to reactors and PET scans.Einstein's September 1905 paper showed mass and energy interconvert at the rate c², about 90 terajoules per gram. Fusion powers the Sun by destroying four million tonnes of mass a second, fission reactors run on the mass defect, and PET scanners image the body with annihilation energy.
5. SpacetimeDescribe Minkowski spacetime, the invariant interval, and light's finite speed as a window into the past.Minkowski showed in 1908 that relativity is geometry: observers slice four-dimensional spacetime into 'space' and 'time' differently, but the spacetime interval is invariant. Finite c makes astronomy time travel — deep telescope images show the universe billions of years ago — and light cones enforce causality.
6. The Happiest ThoughtState the equivalence principle and its two signature consequences: universal free fall and gravitational time dilation.Free fall locally erases gravity — Einstein's 'happiest thought' — because gravity accelerates everything identically, as Apollo 15's hammer-and-feather drop showed on the Moon. It follows that clocks deeper in gravity tick slower, an effect NIST has measured over a height of 33 centimetres.
7. General Relativity: Gravity as GeometryPresent the 1915 field equations' core idea and the first confirmations: lensing and Mercury.General relativity replaces the force of gravity with curved spacetime: matter tells spacetime how to curve, spacetime tells matter how to move. The theory immediately explained Mercury's anomalous 43 arcseconds-per-century precession, and gravitational lenses now make the curvature directly visible.
8. Putting Einstein to the TestReview the classic tests: the 1919 eclipse, modern light-deflection measurements, lensed quasars, and Gravity Probe B.Eddington's 1919 eclipse plates confirmed light bending and made Einstein famous; radio interferometry has since verified the deflection to better than 0.01%. The Einstein Cross shows one quasar lensed into four images, and Gravity Probe B confirmed the geodetic and frame-dragging effects of spinning Earth.
9. Black Holes and Gravitational WavesConnect black holes, gravitational waves, and pulsar timing as strong-field tests of general relativity.The Event Horizon Telescope imaged M87's 6.5-billion-solar-mass black hole in 2019, LIGO caught spacetime ripples from merging black holes in 2015, and binary pulsars have tracked gravitational-wave energy loss since 1974. In gravity's most extreme regimes yet observed, Einstein's equations keep passing.
10. Relativity in Your PocketShow relativity as working infrastructure, from GPS clock corrections to cosmology.GPS satellite clocks are pre-tuned for a net +38 microseconds per day of relativistic drift; uncorrected, positions would err by about 10 km per day. On the largest scales, the expanding universe and the cosmic microwave background are governed by the same 1915 equations.

Questions this course answers

Grounded in trusted sources

• Albert Einstein, 'On the Electrodynamics of Moving Bodies', Annalen der Physik 17 (1905)
• Albert Einstein, 'Relativity: The Special and the General Theory' (1916)
• Dyson, Eddington & Davidson, Philosophical Transactions of the Royal Society A 220 (1920)
• Hafele & Keating, Science 177 (1972)
• Abbott et al. (LIGO/Virgo), Physical Review Letters 116 (2016)
• Event Horizon Telescope Collaboration, Astrophysical Journal Letters 875 (2019)
• Neil Ashby, 'Relativity in the Global Positioning System', Living Reviews in Relativity 6 (2003)
• Kip Thorne, 'Black Holes and Time Warps' (W. W. Norton, 1994)

Every Wunder lesson is built from real, reputable sources — never invented.

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