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But Einstein had little further experimental guidance as to how Newton’s theory was to be extended. There were merely tiny observed deviations in some planetary trajectories, in particular in Mercury’s orbit, which, as noticed first by Urbain Le Verrier in 1855, seemed to shift compared to Newtonian calculations by the small amount of 43 arc seconds (about one one-hundredth of a degree) per century. The influence of Venus, the planet closest to Mercury, was already factored in, as were small perturbations such as possible irregularities in the shape of the sun, without managing to reconcile the observations with theoretical considerations. Only Einstein was able to explain the shifted trajectory in a natural way by using his new equations of motion in general relativity.

Fortunately, new data soon arrived that were also incompatible with Newton’s law but that had already been predicted correctly by Einstein. These were tiny shifts, or bending, experienced by starlight in close passage around the sun. Measured by Arthur Eddington during a total solar eclipse in 1919, these shifts led to the first triumphant verification of general relativity. (By now, more precise measurements of this type have been performed using radio waves emitted by quasars, as done for the first time by Edward Fomalont and Richard Sramek in 1976.) If deviations between Einstein’s predictions and those observations had occurred, Einstein’s theory would have been long forgotten, despite his quip “If nature does not coincide with theory, it is all the worse for nature” (“Wenn die Natur nicht mit der Theorie übereinstimmt, so ist dies um so schlimmer für die Natur”).

In 1960, Robert Pound and Glen Rebka performed the first test of general relativity in an experiment on earth, and this test, too, was passed with highest marks. Here, the transformation of time at different altitudes, implying different positions in space-time, was measured. Farther away from the center of the earth, the gravitational force is weaker, which geometrically implies, as we will soon see, a changed form of space-time. Time progresses differently at higher altitudes, becoming faster than at lower ones. This speed-up is normally not noticeable, but it can be detected by sensitive measurements. To that end, Pound and Rebka exploited the Mössbauer effect, endowing some crystals with very finely tuned frequencies for the emission and absorption of light. Matter such as an atom can usually emit and absorb light near certain frequencies in the so-called spectrum, as it is used in fluorescent lights or lasers. The reason for the select set of frequencies is the quantum nature of matter (the topic of the next chapter). Since single atoms or molecules, on which such measurements would be performed, move in a gas, emission and absorption processes occur in different states of motion; the atoms, after all, move due to heat. Emission and absorption take place at different velocities; and according to special relativity, the progress of time, thus the frequency as the number of oscillations per unit of time, depends on the state of motion. Therefore, light is emitted and absorbed not at fixed and precise frequencies, but in frequency intervals of finite width.

In bodies subject to the Mössbauer effect, emission and absorption happen not at single atoms but at the entire crystal. As a whole, the crystal moves less than atoms in a gas. Accordingly, emission or absorption frequencies are much more precise. Special relativity no longer implies deviations of frequencies; but when a light-emitting crystal and an absorbing one of the same type are positioned at different altitudes, general relativity comes into play. Time progresses differently for the emitting crystal than it does for the absorbing one, causing a frequency mismatch in the light that reaches the absorbing crystal. A great enough mismatch prevents the light from being absorbed, and this is exactly what one can detect without even using large differences in altitude: The height of a building of several stories is sufficient.

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