Turn the dials. Every reading on this console is computed live from the formulas shown beside it, and each instrument marks where it simplifies. A reference instrument, drawn as a hardware design study, sits in the same chain of state, so what you feel under your hand is the mathematics of a metric that carries a scale factor. Built for physics students who learned relativity the usual way and want to know what changes when the ruler itself becomes a field. The framework is Norbert Schwarzer's; the reduction to these instruments is the companion paper's.
Take the metric you know and multiply it by a function of a scalar field f. The physical metric becomes
F multiplies the whole metric, so it is a conformal factor: a proper length scales as √F, a frequency as 1/√F. The master dial sets the field amplitude Δf. Turn it and the ruler on the far side of the seam changes; the walker in the viewport keeps taking strides of one proper metre, and you watch how much map each stride covers.
Top: the field you set. Middle: the conformal factor F and the local ruler √F. Bottom: a map in coordinate units with a walker taking strides of one proper metre; the glowing band is the seam. Where F is small the ruler is coarse and a stride covers more map. A step across the seam is the whole idea in one motion.
The physics dials above set the state a seam would need. This panel is a hardware design study: a sealed bench instrument, 28 × 18 × 9 cm and 4.2 kg, drawn as it would have to be if the framework were right, so that its assumptions can be criticised as engineering rather than as prose. It does not test the theory; it presupposes it. The checks are the four measurements in the supplement, and they use instruments that already exist. The cradle carries the same four dials as instrument 01, kept in step both ways, plus a destination preset and a baseline dial that turns only when both sign-offs are set. The instrument reports through a single hardened port, and a bench check decides whether the reading locks.
Design study The substrate, materials and readings below are an engineering fill-in, published for critique. Nothing on this page reports a measurement taken with this instrument.
In the scaled-metric picture proper time scales as √F exactly as proper length does. The instrument's phase differential between the stored baseline and the local field is that ratio. The reference crystal, read as a nitrogen-vacancy diamond lattice, has a zero-field splitting near 2.870 GHz whose position shifts by 1/√F, so the crystal is a direct readout of the seam setting: a city-scale seam (one part in a thousand) moves the line by about 1.4 MHz, a bench magnetometer's job; an intercontinental seam (one part in a trillion) moves it by about 1.4 mHz, an atomic clock's job. The phase-differential sensor array is the weak-measurement channel that reads the ratio without collapsing the reference. The core cell, on a restricted water–diamond hypothesis, is a coherent domain of structured water, which is the object Schwarzer's equations describe; its residual jitter is the fulcrum jitter of instrument 02. Because space and time rescale together, a seam gives a clock-rate difference across the boundary, never a displacement along the timeline. The design measures and references; it generates nothing.
Status of this panel: a hardware design study, published for critique. It has not been built or validated, and nothing here reports a measurement taken with it.
Hover a bay in the 3D view to see its material. The NV-diamond choice is what ties the box to the dial physics: its reference line shifts as 1/√F, so the crystal reads the seam setting directly.
In the scaled-metric field equations the dimension number appears explicitly. As n grows, the term nonlinear in the gradient of f gains weight while the curvature terms recede (the framework's account of why gravity is weak), the exponent 4/(n−2) shrinks so the scale factor answers less to f, and the action's offset from its extremum, the ever-jittering fulcrum, fades toward the classical stationary principle.
Schematic Weights are drawn as gradient ∝ n, curvature ∝ 1, fulcrum offset H ∝ 1/n. These are the trends the framework states; the exact coefficients are in the source text.
Watch the bead. At low n it rides high on the slope and jitters; at high n it settles into the extremum and the wobble fades. That is the classical limit arriving under your hand.
The tension the companion paper reports is under your fingers: a strong scale response (large exponent) wants small n; weak gravity (small curvature weight) wants large n. Turn the dial and watch one improve as the other worsens.
The Casimir energy density between plates a distance d apart falls as d−4 and is measured to about a percent between 0.1 and 6 µm. A 30 m Morris–Thorne throat needs about 3.2 × 1040 J/m³ of negative energy over its own volume. If vacuum energy is scale-dependent, the dependence must stay hidden where Casimir is measured and switch on above it. Set the onset and the exponent and see whether the gap closes.
The shaded band is where Casimir has been measured; any trial law must sit on the textbook line there. The instrument does not claim the vacuum does this. It shows what it would have to do, which is a question a laboratory can put at tens to hundreds of micrometres.
Conservation of angular momentum for a triad of fixed mass gives ω ∝ r−2 in a torque-free collapse. If the effective mass carries a factor of the scale factor, meff ∝ F(r)q with F ∝ rp, the rule becomes ω ∝ r−(2+qp). A keyed animation most naturally holds ω constant. The bench generates a track with a hidden exponent and tracking noise; fit it by hand, then reveal.
Left: ω/ω0 against r/r0 on log axes, so a power law is a straight line with slope −k. Right: the triad at the current frame. The same measurement on real footage is the sharpest test the companion paper proposes, and it needs no absolute scale.
With G = F g, show that proper lengths scale as √F and frequencies as 1/√F. Then turn the master dial to a seam with Ffar/Fnear = 4 and confirm the readouts.
A seam is set so that one proper metre on the far side spans ten kilometres of near-side map. What ratio Fnear/Ffar is needed, and with n = 4, Cf = 1, what Δf? Can the dial reach it?
On the dimension dial, find the smallest n at which the gradient term outweighs curvature 10:1, and the exponent there. Then find the n at which the exponent drops below 0.2. Why does the companion paper call this a tension?
On the scale test, set the onset to 1 µm and find the exponent that closes the gap. Why is that excluded, and what onset does the companion paper adopt?
Generate five tracks at 4 % noise and 24 frames. Fit each by hand, then least-squares, then reveal. How often can your hand tell k = 2 from k = 2.5? Repeat at 12 % and 8 frames.
Using the master dial, explain why a domain wall in f needs no negative energy, and why the same framework makes a curvature throat harder rather than easier.