Choas and conservation

  • #1
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?
 

Answers and Replies

  • #2
Dr. Courtney
Education Advisor
Insights Author
Gold Member
3,332
2,512
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?

One needs to distinguish between physical symmetries and mathematical symmetries.

Noether's Thm can be stated informally as:

If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.

I haven't read the Strogatz book, but two questions that come to mind are:

Is the purported symmetry in fractals a continuous symmetry?

Is the purported symmetry in fractals a physical symmetry (really a perfect symmetry in a physical realization)?

A lot of purported symmetries in physical systems are neither exact nor continuous.
 
  • Like
Likes Michele Zappano
  • #3
Andy Resnick
Science Advisor
Education Advisor
Insights Author
7,665
2,416
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?

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.
 
  • Like
Likes Michele Zappano
  • #4
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.
perfect, thanks
 

Related Threads on Choas and conservation

Replies
1
Views
3K
Replies
13
Views
4K
Replies
2
Views
1K
Replies
9
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
3K
Replies
8
Views
2K
Replies
8
Views
3K
Replies
11
Views
1K
Top