“What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers,” he wrote to Hendrik Lorentz in 1926. When Erwin Schrödinger derived the equation that now bears his name, he hoped to scrub the i out. Physicists have never been entirely sure what to make of this. The so-called Schrödinger equation describes how the wave function changes in time - and this equation features an i. The wave function forecasts possible outcomes of measurements, such as an electron’s possible position or momentum. In quantum mechanics, the behavior of a particle or group of particles is encapsulated by a wavelike entity known as the wave function, or ψ. “The world is such that it really requires these complex” numbers, he said. “These complex numbers, usually they’re just a convenient tool, but here it turns out that they really have some physical meaning,” said Tamás Vértesi, a physicist at the Institute for Nuclear Research at the Hungarian Academy of Sciences who, years ago, argued the opposite. Provided that quantum mechanics is correct - an assumption few would quibble with - the team’s argument essentially guarantees that complex numbers are an unavoidable part of our description of the physical universe. Yet physicists may have just shown for the first time that imaginary numbers are, in a sense, real.Ī group of quantum theorists designed an experiment whose outcome depends on whether nature has an imaginary side.
No instrument has ever returned a reading with an i.
Sometimes, so-called complex numbers, with both real and imaginary parts, such as 2 + 3 i, have streamlined calculations, but in apparently optional ways. For physicists, however, real numbers sufficed to quantify reality. Imaginary numbers, labeled with units of i (where, for instance, (2 i) 2 = -4), gradually became fixtures in the abstract realm of mathematics. Mathematicians started calling those familiar numbers “real” and the apparently impossible breed of numbers “imaginary.” Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.Īll the numbers on the number line, when squared, yield a positive number 2 2 = 4, and (-2) 2 = 4.
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