{"id":277506,"date":"2025-11-07T15:48:15","date_gmt":"2025-11-07T15:48:15","guid":{"rendered":"https:\/\/www.newsbeep.com\/us\/277506\/"},"modified":"2025-11-07T15:48:15","modified_gmt":"2025-11-07T15:48:15","slug":"physicists-take-the-imaginary-numbers-out-of-quantum-mechanics","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/us\/277506\/","title":{"rendered":"Physicists Take the Imaginary Numbers Out of Quantum Mechanics"},"content":{"rendered":"

A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth with accurate calculations of hydrogen\u2019s emission and absorption of light. There was, however, a snag. The central equation of quantum mechanics featured the imaginary number i, the square root of \u22121.<\/p>\n

Physicists knew i\u00a0was a mathematical fiction. Real physical quantities like mass and momentum never yield a negative amount when squared. Yet this unreal number that behaves as i2 = \u22121 seemed to sit at the heart of the quantum world.<\/p>\n

After deriving the i-riddled equation \u2014 essentially the law of motion for quantum entities \u2014 Erwin Schr\u00f6dinger expressed the hope that it would be replaced by an entirely real version. (\u201cThere is undoubtedly a certain crudeness at the moment\u201d in the equation\u2019s form, he wrote in 1926.) Schr\u00f6dinger\u2019s distaste notwithstanding, i stuck around, and new generations of physicists took up his equation without much concern.<\/p>\n

Then, in 2021, the role of imaginary numbers in quantum theory attracted newfound interest<\/a>. A team of researchers proposed a way to empirically determine<\/a> whether i is essential to quantum theory or a mere mathematical convenience. Two teams<\/a> quickly<\/a> followed up to perform the intricate experiments and found supposedly unequivocal evidence that quantum theory needs i.<\/p>\n

This year, however, a series of papers has overturned that conclusion.<\/p>\n

\"Black-and-white <\/p>\n

Erwin Schr\u00f6dinger was dissatisfied that his eponymous equation used complex numbers. He hoped to find a replacement for it. But his equation has stuck around.<\/p>\n

In March, a group of theorists based in Germany rebutted<\/a> the 2021 studies, putting forward a real-valued version of quantum theory that\u2019s exactly equivalent to the standard version. Two theorists in France followed up with their own formulation<\/a> of a real-valued quantum theory. And in September, another researcher approached the question from the perspective of quantum computing and arrived at the same answer: i isn\u2019t necessary for describing quantum reality after all.<\/p>\n

Although the real-valued theories avoid explicit use of i, they do retain hallmarks of its distinct arithmetic. This leads some to wonder whether the imaginary aspect of quantum mechanics \u2014 or even reality itself \u2014 is truly vanquished.<\/p>\n

\u201cThe mathematical formulation does guide what we infer about the nature of the physical world,\u201d said Jill North<\/a>, a philosopher of physics at Rutgers University.<\/p>\n

Impossible Values<\/p>\n

Living in Amsterdam in 1637 at the peak of tulip mania (the Dutch frenzy for flowers which led to impossibly valued tulip bulbs), Ren\u00e9 Descartes grappled with equations whose solutions also seemed to have impossible values. Using x3 \u2212 6×2 + 13x \u2212 10 = 0 as an example, Descartes wrote that its solutions \u201care not always real; but sometimes only imaginary. \u2026 There is sometimes no quantity that corresponds to what one imagines.\u201d The three numbers you can plug in for x are 2, 2 \u2212 i and 2 + i. The latter two numbers, each of which has both a real part and an imaginary part in the form a + ib, came to be called complex numbers.<\/p>\n

Descartes viewed them with derision, but complex numbers were later adopted for their utility in fields as diverse as geometry, optics and signal analysis.<\/p>\n

Schr\u00f6dinger grudgingly acknowledged their ease of use in quantum theory. His equation governs the evolution of the wave function, an entity representing the possible quantum states of an object. (These states can interfere destructively and constructively like waves.) Schr\u00f6dinger\u2019s wave function was complex-valued, even though actual measurements of quantum systems always return real values. \u201cQuantum theory really is the first physical theory where the complex numbers seem to be right smack in the middle of the theory,\u201d said Bill Wootters<\/a>, a quantum information theorist at Williams College.<\/p>\n

One way to represent a complex number like a + ib is as a point on a plane, where a is the position on the x-axis (which can be thought of as the real number line) and b is the position on an imaginary y-axis. Each complex number is an arrow, called a vector, pointing from the origin to the complex coordinate (a, b). These complex vectors obey the unusual math of complex numbers: Multiplying by i, for example, rotates the vector 90 degrees.<\/p>\n

These properties made them a natural fit for the quantum states of the wave function \u2014 also vectors obeying odd combination rules.<\/p>\n","protected":false},"excerpt":{"rendered":"A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory…\n","protected":false},"author":2,"featured_media":277507,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[49],"tags":[199,79],"class_list":{"0":"post-277506","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-physics","9":"tag-science"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/277506","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/comments?post=277506"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/277506\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media\/277507"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media?parent=277506"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/categories?post=277506"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/tags?post=277506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}