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Mathematics: “Particle collisions are somehow linked to mathematical ‘motives.’”

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From math and computer science writer Kevin Hartnett at Quanta:

Over the last decade physicists and mathematicians have been exploring a surprising correspondence that has the potential to breathe new life into the venerable Feynman diagram and generate far-reaching insights in both fields. It has to do with the strange fact that the values calculated from Feynman diagrams seem to exactly match some of the most important numbers that crop up in a branch of mathematics known as algebraic geometry. These values are called “periods of motives,” and there’s no obvious reason why the same numbers should appear in both settings. Indeed, it’s as strange as it would be if every time you measured a cup of rice, you observed that the number of grains was prime.

“There is a connection from nature to algebraic geometry and periods, and with hindsight, it’s not a coincidence,” said Dirk Kreimer, a physicist at Humboldt University in Berlin.

Now mathematicians and physicists are working together to unravel the coincidence. For mathematicians, physics has called to their attention a special class of numbers that they’d like to understand: Is there a hidden structure to these periods that occur in physics? What special properties might this class of numbers have? For physicists, the reward of that kind of mathematical understanding would be a new degree of foresight when it comes to anticipating how events will play out in the messy quantum world. More.

See also: Oxford mathematician John Lennox on fine tuning in the universe

and

Copernicus, you are not going to believe who is using your name. Or how.

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2 Replies to “Mathematics: “Particle collisions are somehow linked to mathematical ‘motives.’”

  1. 1
    bornagain77 says:

    as to:

    Strange Numbers Found in Particle Collisions – Nov. 2016
    An unexpected connection has emerged between the results of physics experiments and an important, seemingly unrelated set of numbers in pure mathematics.
    Excerpt: At the Large Hadron Collider in Geneva, physicists shoot protons around a 17-mile track and smash them together at nearly the speed of light. It’s one of the most finely tuned scientific experiments in the world, but when trying to make sense of the quantum debris, physicists begin with a strikingly simple tool called a Feynman diagram that’s not that different from how a child would depict the situation.
    Feynman diagrams were devised by Richard Feynman in the 1940s. They feature lines representing elementary particles that converge at a vertex (which represents a collision) and then diverge from there to represent the pieces that emerge from the crash. Those lines either shoot off alone or converge again. The chain of collisions can be as long as a physicist dares to consider.,,,
    Over the last decade physicists and mathematicians have been exploring a surprising correspondence that has the potential to breathe new life into the venerable Feynman diagram and generate far-reaching insights in both fields. It has to do with the strange fact that the values calculated from Feynman diagrams seem to exactly match some of the most important numbers that crop up in a branch of mathematics known as algebraic geometry. These values are called “periods of motives,” and there’s no obvious reason why the same numbers should appear in both settings. Indeed, it’s as strange as it would be if every time you measured a cup of rice, you observed that the number of grains was prime.
    “There is a connection from nature to algebraic geometry and periods, and with hindsight, it’s not a coincidence,” said Dirk Kreimer, a physicist at Humboldt University in Berlin.,,,
    For more than a century, luminaries like Carl Friedrich Gauss and Leonhard Euler explored the universe of periods and found that it contained many features that pointed to some underlying order. In a sense, the field of algebraic geometry — which studies the geometric forms of polynomial equations — developed in the 20th century as a means for pursuing that hidden structure.
    https://www.quantamagazine.org/20161115-strange-numbers-found-in-particle-collisions

    I liked the second comment in the comment section which stated this rather obvious conclusion:

    howard9
    “my first consideration to this is that these particle collisions do not seem random.”

    Seeing that randomness is a foundational cornerstone of the naturalistic/materialistic philosophy, I would say that finding that particle collisions, and the results thereof, to be non-random in their overall behaviour is a rather devastating finding for the naturalistic/materialistic philosophy.

    A few supplemental notes:

    As to Feynman’s Diagrams, as much as the diagrams may explain, it is also interesting to note what the diagrams don’t explain:

    Quantum Electrodynamics
    The key components of Feynman’s presentation of QED are three basic actions.[1]:85
    *A photon goes from one place and time to another place and time.
    *An electron goes from one place and time to another place and time.
    *An electron emits or absorbs a photon at a certain place and time.
    These actions are represented in a form of visual shorthand by the three basic elements of Feynman diagrams: a wavy line for the photon, a straight line for the electron and a junction of two straight lines and a wavy one for a vertex representing emission or absorption of a photon by an electron. These can all be seen in the adjacent diagram.
    It is important not to over-interpret these diagrams. Nothing is implied about how a particle gets from one point to another. The diagrams do not imply that the particles are moving in straight or curved lines. They do not imply that the particles are moving with fixed speeds. The fact that the photon is often represented, by convention, by a wavy line and not a straight one does not imply that it is thought that it is more wavelike than is an electron. The images are just symbols to represent the actions above: photons and electrons do, somehow, move from point to point and electrons, somehow, emit and absorb photons. We do not know how these things happen, but the theory tells us about the probabilities of these things happening.
    https://en.wikipedia.org/wiki/Quantum_electrodynamics#Introduction

    In fact, Quantum Electrodynamics is actually very friendly to Christian concerns:

    Double Slit, Quantum-Electrodynamics, and Christian Theism – video
    https://www.facebook.com/philip.cunningham.73/videos/vb.100000088262100/1127450170601248/?type=2&theater

    Leonard Euler was mentioned in the article. Leonard Euler, who was a devout Christian, was at the center of another amazing ‘coincidence’ that was also found in pure math:

    God by the Numbers – Connecting the constants
    Excerpt: The final number comes from theoretical mathematics. It is Euler’s (pronounced “Oiler’s”) number: e^pi*i. This number is equal to -1, so when the formula is written e^pi*i+1 = 0, it connects the five most important constants in mathematics (e, pi, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation). These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by pi; and analysis, by e, the base of the natural log. e^pi*i+1 = 0 has been called “the most famous of all formulas,” because, as one textbook says, “It appeals equally to the mystic, the scientist, the philosopher, and the mathematician.”,,,
    The discovery of this number gave mathematicians the same sense of delight and wonder that would come from the discovery that three broken pieces of pottery, each made in different countries, could be fitted together to make a perfect sphere. It seemed to argue that there was a plan where no plan should be.,,,
    Today, numbers from astronomy, biology, and theoretical mathematics point to a rational mind behind the universe.,,, The apostle John prepared the way for this conclusion when he used the word for logic, reason, and rationality—logos—to describe Christ at the beginning of his Gospel: “In the beginning was the logos, and the logos was with God, and the logos was God.” When we think logically, which is the goal of mathematics, we are led to think of God.
    http://www.christianitytoday.c.....ml?start=3

    The Baffling and Beautiful Wormhole Between Branches of Math
    Excerpt: But the weirdest thing about Euler’s formula—given that it relies on imaginary numbers—is that it’s so immensely useful in the real world. By translating one type of motion into another, it lets engineers convert messy trig problems (you know, sines, secants, and so on) into more tractable algebra—like a wormhole between separate branches of math. It’s the secret sauce in Fourier transforms used to digi­tize music, and it tames all manner of wavy things in quantum mechanics, electron­ics, and signal processing; without it, computers might not exist.
    http://www.wired.com/2014/11/eulers-identity/

    Moreover, Euler’s formula (the most famous of all formulas), is graphed out as a right handed spiral:

    picture
    http://www.wired.com/wp-conten.....uler_f.jpg

    The following images show the graph of the complex exponential function, e^{ix}, by plotting the Taylor series of e^{ix} in the 3D complex space (a helix)
    http://www.songho.ca/math/euler/euler.html

    “Coincidentally’, the predominant form of DNA is also a right handed spiral.

    In the following article, Adam Rutherford takes exception to the many incorrect examples of left handed DNA spirals he finds on the Internet and even at many reputable institutions:

    DNA’s twist to the right is not to be meddled with, so let’s lose the lefties – Adam Rutherford – 30 April 2013
    http://www.theguardian.com/sci.....t-to-right

    Correct DNA spiral – image
    http://images.wisegeek.com/dna-close-up.jpg

  2. 2
    EDTA says:

    Just within mathematics, there are quite a few interesting “coincidences” also:

    https://en.wikipedia.org/wiki/Mathematical_coincidence

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