Dear Jonathan Dickau,
I very much enjoyed your excellent essay; you say "things from the Mandelbrot set ... teach lessons in physics." I would say that you gain insight from the Mandelbrot set and teach yourself. Regardless, your focus on asymmetry is fruitful. I had not thought of the
"near perfect symmetry at higher magnification... [and] asymmetrical at lower magnification."
I agree with you that "entropy can be characterized by spreading and sharing." As I've noted in earlier essays, energy is transmitted through space and time. If that energy crosses a systemic threshold and effects a change in structure of the system, then that 'in-formation' of the system is a record of information. One can show that Bekenstein's holographic entropy formula based on "screens storing information" can be derived exactly in terms of energy only, never mentioning, using, or even conceiving of information.
My point is that if energy is fundamental, and one can define an abstraction, say information or entropy, and derive abstract results, then a clever person can often begin with the abstraction and work back toward the fundamental as if it "emerges from" the abstraction, as Verlinde does. Barbour does something similar with time.
The same applies to 'quantum information', as you so well describe at the top of page 3. I of course do not deny the obvious usefulness of the abstraction of information, but what is fundamental is energy.
Jacobson asks "how did classical general relativity know that horizon area would turn out to be a form of entropy?" As I noted, the horizon formula can be derived strictly as a distribution of energy. Since thermodynamic entropy is derived in terms of energy distributions, and since formulaic similarity between 'thermodynamic entropy' and 'information entropy' leads [as ET Jaynes notes] to "proving nonsense theorems", it should not be surprising that clever persons can run the derivations backwards, from abstract to fundamental. Here fundamental is made to seem to "emerge" from abstraction. That appears to be quite the fashion in physics today. Hence Jacobson and Verlinde.
You, on the other hand, observe:
"...that asymmetry is as fundamental to physics as symmetry takes some getting used to."
Hooray for you. You mentioned SU(3)xSU(2)xU(1) is fundamental, but SU(3) is a valid symmetry only for equal masses, yet it is applied in cases where masses differ by two orders of magnitude. As you note,
"there is a tendency in physics to oversimplify."
You "see condensation as a general feature of all theories of emergent and induced gravitation." While I wholly reject "emergent gravitation", I heartily concur with you on the importance of 'condensation'. And I do agree with you that
"Asymmetry is as much a fundamental to physics as symmetry is."
I think this is a major contribution to this particular essay contest.
Gravity is fundamental, not emergent, and the key asymmetry is that expressed in the gravito-magnetic equation
curl C = - mv
where C is the gravito-magnetic field, m is the mass/energy density and v is the velocity. The - represents the fundamental asymmetry that is left-handed circulation. This underlies the asymmetric left-handedness of the universe from galaxies to neutrinos to biology. If Mandelbrot brought you to this insightful understanding, you have used it well.
Congratulations on a superb essay,
My very best regards,
Edwin Eugene Klingman