M4: is psi an internal triplet or a spatial displacement?

[dmobius3]

Hi @jeffsyee,

A definition question about M4 for the MIT (M8) column. Per the platform's cross-model rule it is yours to settle, not ours to assume: https://github.com/openwave-labs/openwave/blob/main/dev_docs/CROSS_MODEL_TESTING.md

M8 tests each family in MIT's three flat SU(2) connections on S3/2I. A field can be twisted by such a connection only if it carries an internal representation the connection acts on. The pinned wave_engine.py evolves a single 3-component field psi by a componentwise vector Laplacian (no div/curl), seeds it as a radial, longitudinal displacement psi = A*profile(r)*r_hat, and takes the potential on |psi|^2. That reads like a physical spatial displacement, but it could be three internal scalar components that are merely seeded radially. The platform rule is explicit that a component count and our reading of the code do not settle this; your word does.

So is psi:

1. three internal scalar components,
2. a geometric spatial displacement vector, or
3. an already soldered field (an internal index tied to the spatial one by design)?

Why a one-line answer is enough, i.e. the registered branch it closes:

• "internal triplet" -> M8 activates the M4 first-occurrence table (already computed and cross-checked against MIT's mass-spectrum) as the certification fixture, and M4 enters the three-connection test natively.
• "geometric displacement", or no reply -> the platform default stands: native and untwisted, three-connection compatibility recorded "not applicable", which is a neutral status on this platform, not a failure. Any soldering to make it testable would be a separate, pre-registered object that we own, not a change to M4.

We are not modifying wave_engine.py or the M4 dynamics either way.

Thanks, Blake

[xrodz]

Hi @dmobius3, since we helped @jeffsyee build the M4 engine, here is some engine-level context while the question is in flight. Jeff, as the EWT model author, is the person to definitely settle it.

What the engine itself commits to, for what it is worth:

• psi carries a spatial length unit: the buffers are psi_am, displacement in attometers scaled for f32 precision (medium.py). Internal scalar components would have no reason to be measured in attometers.
• psi physically moves the medium's granules: the granule render position is grid position + boost * psi / dx (wave_engine.py, sample_position_to_render). The renderer treats psi as a displacement of a granule in space, which is the EWT granular-medium picture.
• The seeding speaks the language of spatial vectors: the base wave is a "radial (longitudinal) displacement psi = A profile(r) r_hat", and longitudinal vs transverse is only meaningful when the field's direction lives in the same space as the propagation direction.
• The componentwise Laplacian with no div/curl is a registered numerical scope decision (M4 upgrade substrate for EWT: vector-field, fully non-linear, PDE solver (port the M5-class engine) #203), not an ontology statement, so its absence is not evidence either way.

So the engine, as built, implements your reading 2 (geometric spatial displacement). But the engine is our implementation of the theory, not the theory: whether EWT means psi as a literal displacement of the granular medium is the author-gated part. Over to Jeff.

[jeffsyee]

@dmobius3, thanks for the question. To connect the M4 simulation explicitly to the theory: in EWT, psi represents the geometric spatial displacement of the medium. Its three components describe displacement in physical space; they are not three internal scalar components or an internal index soldered to the spatial one. Wave amplitude is the maximum magnitude of that displacement.

Therefore, the explanation from @xrodz accurately reflects the intended EWT ontology. He deserves credit for building the initial M4 model, with @lsmolinski extending it, while I provided guidance on its theoretical basis.

I use “granules” for the constituents of the medium, following terminology coined by Gabriel LaFrenière and used in earlier Wave Structure of Matter research. In EWT, the physical displacement of these granules—and the resulting wave amplitude—is used throughout calculations involving particles, photons, and forces.

[dmobius3]

@xrodz @jeffsyee

Sounds good, gents. That closes this Q&A.

On S3/2I, native M4 remains untwisted, so three-connection compatibility are “not applicable” rather than a failure. M4 stays in the M8 program as a dynamical comparison model.

The remaining curved-quotient operator choice is now an M8 specification task, not an open author question or a blocker on this thread.

Thanks again 🍻