Why we believe a big red sun will swallow us all up one day

That’s Maths: The essence of a good scientific theory is its power to predict future phenomena

The mathematical equations that express the laws of physics describe phenomena seen in the real world. But they also allow us to anticipate completely new phenomena. Early in his career Irish mathematician William Rowan Hamilton used the equations of optics to predict an effect called conical refraction, where light rays emerging from a biaxial crystal form a cone. This had never been seen before but, within a year, it was observed by his colleague Humphrey Lloyd, thrusting Hamilton into scientific prominence.

The essence of a good scientific theory is its predictive power. We develop the theory using observations of the world around us. Then we use it to account for new observations and also to predict entirely new phenomena. Prediction is the acid test of theory. The planet Neptune was mathematically predicted before it was directly observed. Newton's law of gravitation describes the motions of the planets around the sun. But, about two centuries ago, the orbit of Uranus was found to deviate from its predicted course.

What was wrong? Were the observations inaccurate or were Newton’s equations faulty? Neither of these: mathematical analysis showed that the orbital perturbations could be explained by another planet orbiting outside Uranus.

In 1845 astronomers Urbain Le Verrier and John Couch Adams independently calculated the position of such a planet. Within a week, Neptune was found less than one degree from Le Verrier’s computed location by an astronomer at the Berlin observatory. This was a dramatic confirmation of Newton’s theory of gravitation.

Le Verrier did not stop there. In 1859, he reported that the slow precession of Mercury’s orbit was not in agreement with Newtonian mechanics. But this time no new planet was found.

The solution was more sensational: Newton’s law of gravitation was imprecise. A new theory, Einstein’s general relativity, was needed.

This completely changed our view of space and time. It implied an orbit for Mercury in precise agreement with astronomical measurements. The new theory also predicted completely novel effects. One was the deflection from a straight path of starlight grazing the sun’s disk. The observation of this effect during a solar eclipse in 1919 was a triumph for relativity theory.

Another prediction made by Einstein in 1916 was that celestial bodies orbiting one another emit gravitational waves, ripples in the fabric of space-time. Indirect evidence of these waves was found in binary star systems that are spiralling inwards.

Further evidence emerged last St Patrick's Day, when astronomers at the Harvard-Smithsonian Center for Astrophysics released the "first direct image of gravitational waves" in the infant universe.

This evidence supports the theory of the Big Bang and cosmic inflation. However, the word “direct” is something of a misdirection: we still have not detected the energy of a gravitational wave passing the Earth. The search for this continues.

Another prediction is that radiating energy eventually will cause the Earth to drop into the sun. Relax: this should not happen for many trillions of years. Long before that – within just a few billion years – the sun will become a red giant and swallow us up.

Peter Lynch is professor of meteorology at University College Dublin. He blogs at thatsmaths.com