Ages & Lifetimes

Part 3: The Great Controversy — Lord Kelvin vs. The Geologists

In the late 19th century, Lord Kelvin (William Thomson) — one of the most respected physicists alive — calculated the Sun’s age from the best physics available: $\tau_\text{KH} \approx 20\text{–}30~\text{Myr}$. But geologists had a problem. Darwin’s theory of evolution needed hundreds of millions of years, and geologists studying rock layers, erosion, and sedimentation had independently concluded the Earth was at least hundreds of millions of years old, possibly billions. Kelvin’s response was blunt: the physics was clear, so the geologists were wrong. He even argued Darwin’s theory must be flawed for lack of time.

Kelvin was wrong — but not because his physics was wrong. His calculation was perfectly correct given his assumptions. This is a useful warning: correct math does not guarantee a complete model. Kelvin assumed gravitational contraction was the Sun’s only energy source. He couldn’t know there was a far more efficient source: nuclear fusion. The resolution came in the early 20th century — radioactivity (1896), Einstein’s $E = mc^2$ (1905), Eddington’s stellar-energy proposal (1920s), and Bethe’s proton-proton chain (late 1930s). Fusion converts about $0.7\%$ of hydrogen’s rest-mass energy to radiation, and that $0.7\%$ of $Mc^2$ is enormous compared to the gravitational energy $GM^2/R$.