The discussion centers on the relationship between fractal symmetry and Noether's Theorem, specifically addressing whether the self-similarity of fractals constitutes a continuous or physical symmetry. Noether's Theorem states that continuous symmetry properties correspond to conserved quantities over time. The conversation highlights the distinction between physical and mathematical symmetries, emphasizing that many purported symmetries in physical systems are neither exact nor continuous. Additionally, the concept of scale invariance, linked to conformal symmetry, is noted for its association with phase transitions and the generation of a conserved energy-momentum tensor.
PREREQUISITESPhysicists, mathematicians, and students interested in the intersection of symmetry, conservation laws, and fractal geometry.
Michele Zappano said:I was reading a Steven Strogatz book and he said that the self similarity of fractals is a symmetry. Has any conservation law been linked to this type of symmetry using Noether's Theorem?
Michele Zappano said:I was reading a Steven Strogatz book and he said that the self similarity of fractals is a symmetry. Has any conservation law been linked to this type of symmetry using Noether's Theorem?
perfect, thanksAndy Resnick said:This is at the edge of my understanding: scale invariance (self similarity) is associated with conformal symmetry:
https://en.wikipedia.org/wiki/Conformal_symmetry
These are typically associated with phase transitions, but I think you can also generate a conserved energy-momentum tensor from this.