Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5

Imaginary numbers may be essential for describing reality

#1
C C Offline
https://www.quantamagazine.org/imaginary...-20210303/

EXCERPTS: 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.

[...] the real formulation of quantum mechanics has lingered as evidence that the complex version is merely optional. Teams including Vértesi and McKague, for instance, showed in 2008 and 2009 that — without an i in sight — they could perfectly predict the outcome of a famous quantum physics experiment known as the Bell test.

The new research, which was posted on the scientific preprint server arxiv.org in January, finds that those earlier Bell test proposals just didn’t go far enough to break the real-number version of quantum physics. It proposes a more intricate Bell experiment that seems to demand complex numbers.

[...] Even without recruiting an Alice, a Bob and a Charlie to actually perform the experiment that the new paper imagines, most researchers feel extremely confident that standard quantum mechanics is correct and that the experiment would therefore find the expected correlations. If so, then real numbers alone cannot fully describe nature. “The paper in fact establishes that there are genuine, complex quantum systems,” said Valter Moretti, a mathematical physicist at the University of Trento in Italy. “This result is quite unexpected to me.”

Nevertheless, odds are that the experiment will happen someday... (MORE - details)
Reply


Possibly Related Threads…
Thread Author Replies Views Last Post
  Article Might there be no quantum gravity after all? + Problem yields numbers too big for our C C 0 97 Dec 6, 2023 12:48 AM
Last Post: C C
  Imaginary numbers are real? + Mass & angular momentum, left ambiguous, get defined C C 1 91 Jul 15, 2022 01:35 PM
Last Post: Kornee
  Quantum theory needs complex numbers + Is the universe actually a fractal? C C 0 85 Dec 16, 2021 04:05 AM
Last Post: C C
  How many numbers exist? Infinity proof math + Nanosphere at the quantum limit C C 0 77 Jul 16, 2021 06:03 PM
Last Post: C C
  Young physicist ‘squares the numbers’ on time travel + Mathematical ‘Hocus-Pocus’ C C 1 275 Sep 30, 2020 12:11 AM
Last Post: confused2
  What if a nuclear bomb was detonated in Marianas Trench? + Imaginary numbers intro C C 0 289 Jul 24, 2018 03:35 AM
Last Post: C C
  Mystery numbers explained + Maker of Patterns: Freeman Dyson's collection of letters C C 0 309 May 4, 2018 09:29 PM
Last Post: C C
  Where do numbers come from? + Quantum superposition could unravel ‘grandpa paradox’ C C 62 9,953 Jun 7, 2017 12:50 PM
Last Post: Secular Sanity



Users browsing this thread: 1 Guest(s)