Good piece, math-technical, worth a skim regardless. Intro below.
Imaginary Numbers May Be Essential for Describing Quantum Reality
A new thought experiment indicates that quantum mechanics doesn’t work without strange numbers that turn negative when squared.
Charlie Wood Contributing Writer Quanta Magazine
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.
All the numbers on the number line, when squared, yield a positive number; 22 = 4, and (-2)2 = 4. Mathematicians started calling those familiar numbers “real” and the apparently impossible breed of numbers “imaginary.”
Imaginary numbers, labeled with units of i (where, for instance, (2i)2 = -4), gradually became fixtures in the abstract realm of mathematics. For physicists, however, real numbers sufficed to quantify reality. Sometimes, so-called complex numbers, with both real and imaginary parts, such as 2 + 3i, have streamlined calculations, but in apparently optional ways. No instrument has ever returned a reading with an i.
Yet physicists may have just shown for the first time that imaginary numbers are, in a sense, real.
A group of quantum theorists designed an experiment whose outcome depends on whether nature has an imaginary side. 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.
“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. “The world is such that it really requires these complex” numbers, he said.
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 wave function forecasts possible outcomes of measurements, such as an electron’s possible position or momentum. The so-called Schrödinger equation describes how the wave function changes in time — and this equation features an i. ... '
No comments:
Post a Comment