Prompts for The Standard of Motion

The seed

Do you think the following article is a good seed for a blog essay about physics, information, and AI? https://arxiv.org/html/2609.15897v1

Other angles

Some other angles. I had a seminar which unified the different mechanics (classical mechanics, statistical mechanics, and quantum mechanics) into one picture. What’s the connection between algorithmic information theory and thermodynamics?

The seminar’s framework

I don’t remember but it wasn’t particularly fancy, it was putting them in a single Lagrangian / Hamiltonian framework.

Heller

Do you know about Michal Heller’s unification of Aristotelian, Newtonian and GR mechanics? Does it fit here too?

Wolfram and Newton

We have a deep dive into Wolfram Physics. Does it shed any light on Newtonian mechanics via its explanation of GR?

Motion is easy

So on Wolfram, what Newton shows is that motion is easy?

The test

That sounds like make-or-break. The model needs to establish a natural category of rules under which motion is easy. Some sort of graph-theoretic result.

Sources

Should I find a Michal Heller source for the essay?

I just downloaded a PDF under notes/private/

Working it out

Would you like to work out the essay here, though? Would we also need to introduce Lie algebras?

Provenance

I confirmed the name of the professor: Piotr Biler, but couldn’t locate the precise name of the seminar.

The seminar must have been the winter 2003/2004

Let’s make it “around 2003” as that’s certain (assuming it includes winter 2003/04)

Research reports

You can write reports under notes/research/ unless they’re throwaway

Life’s spaceships

I saved “List of spaceships” to private/

The qualitative theory

Does the qualitative theory of differential equations have any relevance to this discussion?

This was the seminar’s opening chapter IIRC, before introducing Largangian (? I don’t quite remember) and Hamiltonian (definitely) pictures.

Which speed is c

In Wolfram Physics, speed of light is something like the speed of the glider: slower than the speed of computation propagation “in principle”.

Are Life’s failures effective, i.e. can they be exploited? Could agar play the role of pure vacuum or is it structurally disqualified?

“what Gorard claims to have” – we should bring this up (primary source)

Re (1) – we shouldn’t claim that Gorard and Wolfram claim or insist that the physical speed of light is the rule application limit speed. I’ve heard them say that a computationally umbounded creatures could use our physics’ medium to communicate faster than the speed of light (presumably by a fixed factor?)

Pointing to the companion

When “the frame bundle of the frame bundle” first appears, it’s a good point to remind the reader the mathematical companion exists.

Fibers of absolute space

In the math companion: “whose fibers are the world lines of bodies at absolute rest” is a mental shortcut: the fibers are the colocated events, the fibers “cover” bodies at absolute rest but the bodies don’t exhaust the fibers? Anyways “body” is metaphorical too

A primer on bundles

Let’s add either a box or a section on bundles and connections to the math article (explain a bit of differential geometry to make it more self contained)

This is oddly written: *A vector field is a section of TX”

In the mathematics companion, can you expand this example a bit? “A manifold whose frame bundle has a global section is called parallelizable. The sphere is not: a global frame would include a nowhere-vanishing vector field.”

“which the hairy ball theorem rules out” – because of the smoothness requirement of any manifold

In the metaphoric terminology “However the sphere is combed (field continuity), a cowlick remains (zero).”

“The second law in Heller’s stylization is F=mv, a first-order equation: no force, no velocity.” What do you mean “no velocity”?

Let’s define a Hamiltonian in “One bracket, three mechanics” section of the math appendix and link again to the appendix from this section of the main article.

Can we give a brief intuition for what energy is? (For example, in terms of work; but maybe some other way.)

Reading Hamilton’s equations

I’d like to build more intuition for the particle Hamiltonian equations. I’m groping for: momentum-change is proportional to the release of potential energy; position-change is proportional to the kinetic energy in the direction of the momentum. Is that gibberish?

So Hamiltonian is more natural physically, but Largangian removes the need for the rotation? We could connect it to Lagrange multipliers from an earlier essay?

“has zero divergence, so its flow ϕ_t preserves phase-space volume” – this is very intuitive. Maybe it’s worthwhile to define divergence as it’s less familiar than gradient? And also another appearance of the rotation.

Lie algebras

Now we just need a short explanation of Lie algebras, it’s the last remaining scary word. Just a brief connection to the time group.

Great, also add a forward pointer to section 3 from either the first or the second mention of Lie in the companion.

Swirl and spread

Digression: what does whirl do, applying divergence via the cross-product?

Yes, let’s do that, thanks!

Generators

“the generator of time translation” – I wonder if we could squeeze in a brief intro to generators? exp as going from addition to multiplication which is composition etc.

“The book does not return exactly.” Is there a visual for this?

“the Jacobi identity” can we give the identity inline there?

In “The free particle as a realization”, let’s repeat “rotations J_i , spatial translations P_i, time translation H, boosts K_i” so that an unfamiliar reader who ended up there ahead of reading the main essay doesn’t bounce off?

Why does “The K_i are conserved” have both the partial derivative and the bracket?

What is H^2(g,g) in the stability intro in the compendium?

“semisimple” looks undefined

Signature and the fifth dimension

Does Wolfram Physics derive the Lorentz algebra with t < 0? Since t > 0 enables time travel.

No thanks. Where’s the extra dimension from for the deformed Poincaré algebra?

Silly analogy, but is it like in computer graphics converting affine into linear operators?

Yes, thanks!

Galilei and Bargmann

Can you again intuitively explain the difference between the Galilei and Bergmann algebras?

Yes, thanks!

Gaps, not quantization

“So ships fitting in a given box have speeds in a finite set.” This is not an interesting result. The interesting result is the ratio of available speeds as both space and time are scaled, no?

My point was it’s ok for speeds to be quantized when space is quantized. “Dense” speeds means there are no gaps where boosting means becoming a dramatically different particle.