ELECTROMAGNETISM & RELATIVITY - Chapter 10 (Capstone), Exercise 1 Solution ========================================================== The Real Ratio Behind the Eddington Eclipse Test PROBLEM ------- Calculate the ratio of the real general-relativistic light-bending prediction (1.75 arcseconds) to the Newtonian prediction (0.83 arcseconds). How close is this ratio to exactly 2, and why does this specific factor-of-two difference make the 1919 eclipse test such a clean way to distinguish between the two theories? SOLUTION -------- Dividing the general-relativistic prediction by the Newtonian one: ratio = 1.75 / 0.83 ratio = 2.108 (approximately) ANSWER: The ratio is approximately 2.11 - very close to exactly 2, consistent with general relativity's own real prediction of exactly double the Newtonian deflection. This specific factor-of-two difference made the 1919 test unusually clean because the two competing predictions were not subtly different (which would have required extremely precise measurement to distinguish) - they differed by roughly a full factor of two. Even with the real measurement uncertainty involved in photographing faint starlight during a brief total eclipse, a result landing close to 1.75 arcseconds versus one landing close to 0.83 arcseconds would be clearly distinguishable, rather than requiring an impossibly precise instrument to tell the two theories apart. ---- WHY THIS WORKS AS AN ANSWER A large, clean ratio between two competing theoretical predictions is exactly what makes an experimental test decisive rather than ambiguous - real measurement always carries some uncertainty, so a subtle predicted difference risks a result that could plausibly be explained by either theory within the margin of error. Here, the near-exact factor-of-two gap meant Eddington's real 1919 measurements could confirm general relativity specifically, not just confirm that "some" gravitational light bending occurred (which even Newtonian physics, treating light as subject to gravity, would have predicted too, just at half the size).