Dear Cristi,
Wow! (or maybe, as Neo would say in "The Matrix", Whoa!) What a densely packed, ambitious essay!
As always, your present a lot of fascinating topics in interesting and insightful ways. I like how you state right away that it is hard to define "fundamental", and that, anyway, "reality tends to ignore our definitions"...
Your analysis of the relevance of isomorphism to fundamentality is thought-provoking. By the way, nice illustration of isomorphism with the Sum 15/Tic-Tac-Toe example.
I like how you frame the astounding weirdness of wavefunction "collapse": "the wavefunction spreads and interferes, but if you catch it, you catch the entire particle, not only that part of its wavefunction you thought was there."
Nice discussion also of the relativity of fundamentalness, with the example of points vs lines.
And now, for the main idea: the germ/seed that can unfold into an entire universe, or even a whole set of multiverses... Intriguing! In the same way that a holomorphic function car be recovered just by knowing the derivatives of all orders at a single point, the entire universe could be recovered from knowing everything there is to know at a given point... That's non-locality with a vengeance! :)
I have to confess that, from the bottom of page 5 to the bottom of page 8, the density, complexity, and unfamiliarity (for me) of many concepts made it hard to follow your argument. I have downloaded your 2017 paper, "The Standard Model Algebra", and will certainly study it to get a better idea... I am fascinated by potential deeper-level explanations of the Standard Model, so I am looking forward to it.
In your ambitious footnote 8 (on free will), you write:
"If we want to turn the picture upside-down and consider that our choices also determine the germ, then would it be possible that our local actions determine the germ here, and by this the state of the universe everywhere?"
I find this intriguing, since it resonates somehow with my ideas about "co-emergence" that I presented in my essay in the last FQXi contest. You also write:
"Or maybe each agent is free, but if their choices conflict with each other, then the germs of the two agents turn out to unfold in distinct universes, so again their choices don't conflict with each other."
I also find this interesting, as it reminds me of the Q-Bism like idea that the Universe only makes sense one observer at a time (the theme of Amanda Gefter's fascinating book, "Tresspassing on Einstein's Lawn").
In closing this already quite long comment(!), I have two questions concerning the last part of your article, "Indra's net" (lovely analogy, by the way!).
1) You say that the information about the whole universe could be encoded at each point, in higher derivatives of the field at that point. By information, do you mean the laws, or the initial conditions as well? Or is it that the initial conditions are irrelevant because you are thinking of the whole universe as infinite, so every possible initial "local" condition happens infinitely often, so everything averages out to zero information overall in initial conditions?
2) You say there is no need for a mechanism to unfold the state of the universe out of the germ, since the germ already contains everything that happens in the universe... Is it a similar claim than when someone who believes that the universe is a simulation says that there is no need for an actual computer to run the simulation, since the "consequences" of the simulation exist whether or not it is run?
Congratulations once again for a strong entry. I am glad your essay is doing so well in the community vote, and I wish you good luck in the "finals"!
Marc
