Space and time are not the fundamental background of the universe, but instead emerge from a mathematical process of zooming in and out.
April 25, 2026
Original Paper
Scale Duality and Emergence of Lorentzian Signature
SSRN · 6563280
The Takeaway
This paper demonstrates that the Lorentzian signature, the way our universe treats time differently than space, is a result of fractal geometry. As you move between different scales of reality, the mathematical properties of the universe naturally rotate into the specific structure we experience every day. This suggests that the very nature of our 4D reality is a fixed point that the universe inevitably settles into as it grows. It links the messy, jagged world of fractals with the smooth, elegant curves of Einstein's gravity. This discovery implies that time itself might just be a byproduct of the universe's internal scaling laws.
From the abstract
We present the completion of the Fractal Time framework by establishing a rigorous duality between Mandelbrot's fractal geometry (scale-up) and Perelman's Ricci ow (scale-down). The duality is mediated by a unitary operator K derived from the Fractal Flow Equation k dQ/dk = −C(k) Q(1 − Q), where Q(k) is the quantum fuzziness and C(k) the topological complexity function. We show that K maps the Hausdorff dimension D to 6 − D, explaining the inverse and idempotent behavior observed between t