Ex-News Junkie
Curved Space in Polar Coordinates
Wed Aug 2, 2017 5:57pm

If there is only one spatial dimension, how can it lead to the curved space of general relativity?

Well, if the other dimensions are angular (circular), then instead of being linear, maybe all the dimensions are actually Logarithmic Spirals, with the angular dimensions being circles (special cases), and the relative velocity of the two particles determining the tightness of the spiral curvature of the radial (spatial) dimension...

There's some imagination... Chew on that!

"A logarithmic spiral, equiangular spiral or growth spiral is a self-similar spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous spiral".

"The exponential function exactly maps all lines not parallel with the real or imaginary axis in the complex plane, to all logarithmic spirals in the complex plane with centre at 0."

"The function x ↦ x k {\displaystyle x\mapsto x^{k}} x \mapsto x^k, where the constant k {\displaystyle k} k is a complex number with a non-zero imaginary unit, maps the real line to a logarithmic spiral in the complex plane."

"The golden spiral is a logarithmic spiral that grows outward by a factor of the golden ratio for every 90 degrees of rotation (pitch about 17.03239 degrees). It can be approximated by a "Fibonacci spiral", made of a sequence of quarter circles with radii proportional to Fibonacci numbers."

Logarithmic spirals describe the shapes of galaxies, storms, seashells, and sections of the fractal known as the Mandelbrot Set.

  • A shot in the darkEx-News Junkie, Wed Aug 2 5:41pm
    What if space-time is in polar coordinates instead: - angle a - angle b - radius R (a single spatial distance between any two particles) plus time t (a scalar time dimension that gives us relative... more
    • Curved Space in Polar Coordinates — Ex-News Junkie, Wed Aug 2 5:57pm
      • The Big BangEx-News Junkie, Wed Aug 2 6:30pm
        So maybe mass determines the tightness of the spiral dimensions, which in turn determines whether the spiral manifests as an angular dimension (or imaginary, or lateral dimension) or whether the... more
        • After all is said and doneEx-News Junkie, Thu Aug 3 5:33pm
          I have no idea what I'm talking about! I would need a degree in math and a degree in physics (at least) to begin to comprehend general relativity and the standard model and all the other grand... more
          • Phenomena I've attempted to addressEx-News Junkie, Thu Aug 3 7:07pm
            - a mechanism for the early hot dense state of universe as a very large particle shower trapped in a very small (but inflating) space, both resulting from the energy released when a circular... more
            • Prime numbersEx-News Junkie, Sat Aug 5 1:17pm
              More thoughts on how the universe is easier to understand if it is represented using polar coordinates, where there is only one dimension of space, and therefore space can only be curved if it is a... more
              • String TheoryEx-News Junkie, Mon Aug 28 3:13pm
                What if everything in the cosmos is a string? 3-dimensional space could be an illusion... It could be two angular dimensions and one radial dimension, i.e. spherical coodinates. The angular... more
                • S(pring) TheoryEx-News Junkie, Mon Aug 28 6:27pm
                  A string that vibrates is acting like a spring. Springs store energy. Hooke's Law: E = k . x^2 ... So when a particle travels through space it is transferring energy in & out of the spring, to & from ... more
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