Scale Invariance: Self-Similarity of the Physical World

Scale Invariance: Self-Similarity of the Physical World by Richard N. Henriksen (Hardback, 2015)
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Scale Invariance: Self-Similarity of the Physical World by Richard N. Henriksen (Hardback, 2015)

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marcfaggionato.com/images/come-posso/4904.php Could anybody tell me what does scale invariance means? Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center , please edit the question.

Scale invariance can be thought of as ' self-similarity '. What this really means is that regardless of how much you zoom into or out of an object be it a function, or a physical object, or the like it looks exactly the same.

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Fractals are good examples of self-similarity. Shown below is an animation of the self-similarity of the Mandelbrot set :. Another well known example of scale invariance in physics is the Wiener process , which is a continuous-time stochastic random process.

Fractals and Scaling: Self-Similarity Dimension Quiz 3 (Solution)

It's also often called standard Brownian motion. No matter how much you zoom into a Wiener process you still get quantitatively the same thing:. In quantum field theory, scale invariance has an interpretation in terms of particle physics.

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In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved. My last example though scale invariance shows up in many places in physics and astronomy is something in which I personally study as a researcher, and that is the self-similarity of the dark matter halo profile. The dark matter halos surrounding dwarf galaxies up to the largest bound structures in the universe galaxy clusters , all seem to follow a fairly simple density profile.

As far as I know, people still don't completely understand why, physically speaking, this profile is what you observe in large gravity only simulations over many decades of mass.

The underlying physics is simple, it's just gravitational interactions between particles, but the intuition as to why they form these structures in bulk has not been properly explained. Sign up to join this community.

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