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by violently accelerating a clock, but by employing fast clocks that nature provides. Earth is bombarded from outer space by highly energetic particles moving at nearly the speed of light.3 Most of them do not reach the ground, because they react with oxygen and nitrogen nuclei in the upper atmosphere and produce new particles, among them the muons. Muons are a heavy kind of electron and quite similar to them, except that they are unstable: A muon at rest decays after just a millionth of a second, producing an electron and two other stable particles called neutrinos. The decay time may be used as a unit of time telling us when a millionth of a second has passed at the speed of a muon. By the standards of modern technology, this “muon clock” is not very precise. But muons can be brought to high velocities much more easily than atomic clocks, and a free supply of them is showered down on Earth in a quickly moving state every day in the form of natural cosmic radiation.

Cosmic muons lead to an impressive confirmation of special relativity and its transformability of space and time. Even racing at such high velocities as they acquire in the upper atmosphere, the muons’ lifetime of a millionth of a second would not be nearly enough for them to reach the ground. And yet detectors do register many of these particles, even though they are supposed to have decayed along the way. The resolution of this problem is that a millionth of a second, within which a muon at rest would decay, seems much longer for a muon traveling at high speed and watched from the ground. Thanks to the high muon velocity, from the particles’ viewpoint enough space is transformed into time for them to reach the ground before their decay.

Measurements with atomic clocks or of muons were not available when Einstein developed his theory of special relativity. Rather, he derived his equations for the transformation of space and time from a deep consideration of the theory of light, introduced in 1861 by James Clerk Maxwell. (As a mathematical curiosity, the same transformation law, but without a physical interpretation, had already been found by Hendrik Antoon Lorentz.) The process of applying such principles independently of observations can be compared with Newton’s realization of his own theory’s incompleteness. Newton’s law of gravity was, at its inception and long thereafter, highly successful in the description of astronomical observations; it was centuries before the first minute and unexplained deviations from the law were observed. Even so, as mentioned above, Newton was not completely happy, for his law looked too animalistic. What makes two masses attract each other even when they may be arbitrarily far apart? This flaw, already looked upon with suspicion by Newton, becomes acute in special relativity.

In Newton’s understanding of separate space and time, there is no problem in principle with his gravitational law; there may at best be an aesthetic one. In special relativity, however, the law flatly becomes inconsistent. Newton’s gravitational force depends on the distance between two bodies in space, but there is no quantity related to time. If one tries to combine this with a transformability of space and time, a strict application of the law would mean that the gravitational force had to depend on the state of motion, e.g., the velocity of a measurement apparatus: A change in the velocity must transform space in time, causing Newton’s law to be time-dependent. The smaller spatial distance would then be compensated by the larger time lapse in such a way that all observers, moving at different speeds, would calculate the correct force. But this requirement was not taken into account when Newton formulated his law; thus the need to extend Newton’s theory.

A similar situation is realized in the theory of electromagnetism. Coulomb’s law for the electrostatic attraction (or repulsion) of two charged bodies, so called after its formulator, Charles Augustin de Coulomb, is very similar to Newton’s for the gravitational attraction of two masses. One simply