Cosmology; universe based on math & quantum mechanics (Introduction)

by David Turell , Monday, February 17, 2020, 18:14 (1532 days ago) @ David Turell

Another article on the issue of a mathematical universe:

https://www.sciencenews.org/article/how-quantum-technique-highlights-math-mysterious-li...

"It has long been a mystery why pure math can reveal so much about the nature of the physical world.

"Antimatter was discovered in Paul Dirac’s equations before being detected in cosmic rays. Quarks appeared in symbols sketched out on a napkin by Murray Gell-Mann several years before they were confirmed experimentally. Einstein’s equations for gravity suggested the universe was expanding a decade before Edwin Hubble provided the proof. Einstein’s math also predicted gravitational waves a full century before behemoth apparatuses detected those waves (which were produced by collisions of black holes — also first inferred from Einstein’s math).

"Nobel laureate physicist Eugene Wigner alluded to math’s mysterious power as the “unreasonable effectiveness of mathematics in the natural sciences.” Somehow, Wigner said, math devised to explain known phenomena contains clues to phenomena not yet experienced — the math gives more out than was put in. “The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and … there is no rational explanation for it,” Wigner wrote in 1960.

***

"In an enormously complicated 165-page paper, computer scientist Zhengfeng Ji and colleagues present a result that penetrates to the heart of deep questions about math, computing and their connection to reality. It’s about a procedure for verifying the solutions to very complex mathematical propositions, even some that are believed to be impossible to solve. In essence, the new finding boils down to demonstrating a vast gulf between infinite and almost infinite, with huge implications for certain high-profile math problems. Seeing into that gulf, it turns out, requires the mysterious power of quantum physics.

***

"Today’s quantum computers are relatively rudimentary, but in principle, an advanced model could crack codes by calculating the prime factors for enormously big numbers.

"That power stems, at least in part, from the weird phenomenon known as quantum entanglement. And it turns out that, similarly, quantum entanglement boosts the power of MIP provers. By sharing an infinite amount of quantum entanglement, MIP provers can verify vastly more complicated proofs than nonquantum MIP provers. [MIP refers to a mathematical theorum about proofs]

***

"...pursuit of this discovery quite possibly will turn up deeper implications for math, computer science and quantum physics.

"It probably won’t shed any light on controversies over the best way to interpret quantum mechanics, as computer science theorist Scott Aaronson notes in his blog about the new finding. But perhaps it could provide some sort of clues regarding the nature of infinity. That might be good for something, perhaps illuminating whether infinity plays a meaningful role in reality or is a mere mathematical idealization.

"On another level, the new work raises an interesting point about the relationship between math and the physical world. The existence of quantum entanglement, a (surprising) physical phenomenon, somehow allows mathematicians to solve problems that seem to be strictly mathematical. Wondering why physics helps out math might be just as entertaining as contemplating math’s unreasonable effectiveness in helping out physics. Maybe even one will someday explain the other."

Comment: Note this last paragraph. God, the master mathematician, has used math to create the universe. A reality based on quantum mechanics can let us use quantum mechanics to solve how God does it. One might note the almost thirty-year-old book, "Fearful Symmetry. Is God a Geometer?"

https://www.amazon.com/Fearful-Symmetry-Geometer-Dover-Mathematics/dp/0486477584

"This fascinating study explores a fundamental paradox behind the patterns of the natural world, in which symmetrical causes lead to asymmetrical effects. Lesser and greater patterns—the structure of subatomic particles, a tiger's stripes, the shapes of clouds, and the vibrations of the stars—are produced by broken symmetry. This accessible exploration of the physical and biological world employs the mathematical concepts of symmetry to consider the deepest questions of modern physics."