CASIMIR FORCE CONTROL · 3D NANOSTRUCTURE APPARATUS

Shelden et al., Nano Lett. 2025, 25, 9254–9261 · gold sphere rs=33.1 µm · k=0.3 N/m · PFA + Lifshitz/Drude · DOI ↗

SEPARATION d80.0 nm

FORCE GRADIENT δF— mN/m

vs PLATE×0.24

PLATE CONTRIB.15 %

APPARATUS · SIDE VIEW (not to scale)● OSCILLATING

FORCE-GRADIENT SPECTRUM · δF vs d

GEOMETRY

PILLAR RADIUS  rp600 nm

300 · 600 · 1200 · 3000 nm fabricated · h_p=120 nm

SET SEPARATION  d80.0 nm

30 nm ←——→ 3000 nm (log)

MAXWELLX · INTERACTIVE FIELD PHYSICS ATLAS

Strange physics, made inspectable.

Every model shows its source, equation, assumption, limitation, and next experiment. Touch the apparatus above; the numbers update live. Then open any door below.

ACTIVE MODULE · RESEARCH STATUS

Casimir Force Control Enabled by 3D Nanostructures

Shelden et al., Nano Letters, 2025 · DOI 10.1021/acs.nanolett.5c01101 ↗

ESTABLISHEDGeometry modifies Casimir force behavior — measured for pillars, hollow cylinders, and arrays.

MODELINGThis apparatus is a MaxwellX educational approximation (PFA + illustrative geometry modifier).

CURRENT STAGEEducational model and research-stage measurement path.

NEXT TESTReproduce published geometry-force curves computationally, then measure through an AFM/KPFM partner.

EQUATION

FPFA(d) = ∫S Pplate–plate(H(x)) dA

ASSUMES

Sphere radius R ≫ gap d; locally flat surface; gold described by a Lifshitz/Drude permittivity.

LIMITATIONS

A publication-grade model needs full Lifshitz pressure, real-material permittivity, roughness, and patch-potential correction. The geometry modifier here is illustrative.

EXPLORE THE ATLAS — model doors

01MODELING

Vacuum Bookkeeping

Negative-energy density, the order-of-magnitude ladder, and the quantum-interest wall.

02MODELING

Casimir Apparatus

Sphere-plane PFA force, gradient maps, and the not-to-scale apparatus diagram.

03EXPERIMENTAL PATH

Field Geometry Sandbox

Electrode/coil geometry → local |E| and gradient maps. Exposure mapping only.

04HYPOTHESIS

Bioelectric Response Atlas

Frequency × geometry response-window matrix. Partner-lab territory; no treatment claim.

05ESTABLISHED

Micro/Nanomotor STRIDE Lab

Symmetry, topology, interface, energy matching — light into directed motion.

06STANDARD

Energy Accounting Bench

Energy into load vs every artifact. Signals earn status through calibration, controls, and repeat measurement.

07STANDARD

Measurement Integrity Lab

The 16-item checklist every signal must clear before it earns a claim.

08FRONTIER HORIZON

Frontier Systems Notebook

The far horizon — autonomous systems and the constraints that bound them.

Modeling anchor after Shelden, Spreng, Garrett, Rahman, Kim & Munday, Casimir Force Control Enabled by 3D Nanostructures, Nano Letters (2025). doi.org/10.1021/acs.nanolett.5c01101 ↗

MODELING · EDUCATIONAL MODEL

Casimir Force Apparatus

A credible interactive anchor for the Boundary Signature Program. Choose a geometry and separation; read the proximity-force-approximation force, its gradient, and an illustrative geometry modifier. The next stage is solver validation and measurement.

GEOMETRY

SEPARATION d{{ apD }} nm

SPHERE RADIUS R{{ apR }} µm

PILLAR RADIUS rp

PILLAR HEIGHT{{ apH }} nm

ARRAY GAP g{{ apGap }} nm

MATERIAL

r_p, height, gap, and material feed the full model (not the PFA toy). They are recorded here for the measurement protocol.

IDEAL PLATE PRESSURE

{{ out.apPlate }}

SPHERE–PLANE FORCE (PFA)

{{ out.apForce }}

FORCE GRADIENT |G|

{{ out.apGrad }}

GEOMETRY MODIFIER

{{ out.apMod }}

MODIFIED FORCE

{{ out.apForceMod }}

MODIFIED GRADIENT

{{ out.apGradMod }}

THE MAXWELLX RESEARCH HANDLE

Design H(x). Predict the force signature. Measure it.

FPFA(d) = ∫S Pplate–plate(H(x)) d²x

Divide the geometry into tiny local patches, compute the plate–plate pressure at each local gap H(x), integrate over the interacting surface, and compare the predicted signature to measurement.

LIMITS OF THIS MODEL

Educational model. A publication-grade modeling requires full Lifshitz pressure, real-material permittivity, surface roughness, patch-potential correction, and full geometry. The sphere–plane PFA assumes R ≫ d and treats the surface as locally flat.

F ≈ −π³ħcR / (360 d³) |G| ≈ π³ħcR / (120 d⁴)

MODELING · IDEAL-PLATE EXACT EXPRESSIONS

The Vacuum Keeps Its Books

Casimir negative-energy density is real, but small and constrained. The wall is beautiful — it tells us exactly where serious measurement begins.

PLATE GAP d{{ vacD }} nm

10 nm10 µm

ENERGY DENSITY  u(d) = −π²ħc / (720 d⁴)

{{ out.vacU }}

PRESSURE  P(d) = −π²ħc / (240 d⁴)

{{ out.vacP }}

|u| vs gap

ORDER-OF-MAGNITUDE LADDER

QUANTUM-INTEREST WARNING

Negative-energy pulses are constrained by quantum inequalities (Pfenning & Ford 1998): a region of negative energy must be paid back, with interest, by surrounding positive energy. The deeper the dip, the briefer and more bounded it must be. The ladder above is the demonstrated regime; warp-scale requirements sit many orders of magnitude beyond it. This is where serious measurement begins, not where physics ends.

EXPOSURE MAPPING · EDUCATIONAL MODEL

Field Geometry Sandbox

Source geometry changes local exposure. The same nameplate frequency and amplitude produce very different field and gradient maps depending on the electrode or coil. This tool maps local exposure conditions.

SOURCE GEOMETRY

FREQUENCY

WAVEFORM

DELIVERY

MEDIUM

ESTIMATED CURRENT DENSITY

relative tier for this delivery mode

HEAT RISK INDICATOR

conductive medium + higher f raises risk

Map shows |E| from a toy source model — an educational model. Use it to reason about where exposure concentrates, then verify with calibrated probes before any biological work.

HYPOTHESIS · EXPERIMENTAL PATH · PARTNER-LED BIOLOGY RESEARCH

Bioelectric Response Atlas

Cells are one entry point into MaxwellX. Frequency is a coordinate; geometry is the address. The research hypothesis: at the same frequency and nominal field strength, changing field geometry can change cellular response, because cells experience the local field map — not the nameplate setting.

The matrix below is illustrative. It maps where to look for response windows; it maps response windows across geometry and frequency, and it contains no measured data.

Plates

Point–line

Ring

Pancake

Helmholtz

Fig-8

Ferrite

{{ row.freq }}

SELECTED WINDOW

Atlas axes

RESEARCH PATH

MaxwellX is not offering medical treatment. Any biological work requires qualified lab partners, IRB / ethics review where applicable, sterile technique, proper assays, safety review, and regulatory compliance. The four geometries that matter are source geometry, field geometry, medium geometry, and biological geometry.

MEASUREMENT STANDARD · CALCULATOR

Energy Accounting Bench

If MaxwellX ever explores electrical output, this is how a signal earns the word "energy." Enter what you measured; the bench computes energy into the load and forces every plausible artifact onto the table before any claim.

VOLTAGE{{ ebV }} V

CURRENT{{ ebI }} µA

LOAD RESISTANCE{{ ebR }} MΩ

DURATION{{ ebT }} s

TEMPERATURE Δ{{ ebDT }} °C

Dark condition Shielded Control geometry run Loaded (vs open-circuit)

POWER INTO LOAD  P = V·I

{{ out.ebPower }}

ENERGY INTO LOAD  E = P·t

{{ out.ebEnergy }}

CAPACITIVE DISCHARGE (1 pF est.)

{{ out.ebCap }}

THERMAL CONTRIBUTION

ARTIFACT CHECKLIST — all cleared before a signal earns status

□{{ a }}

Measurement uncertainty is illustrative here; a real bench reports it per-channel with calibration traceability.