The Metric Appearance Bench: Table 1 Seen from Outside

THE METRIC APPEARANCE BENCH · D132, TABLE 1, p. 9
How a craft in an engineered metric would appear to a remote observer: four sentences of D132 (pp. 12 to 14) and one of D128 (p. 14)
two coefficients from the paper's own table, √g₀₀ and √(−g₁₁), with a tie that holds g₀₀ · (−g₁₁) = 1; the rows applied one at a time, as the paper applies them
the sentences are reported; the bands, the constants and the masses are tabulated
Wien, Planck, the rows and the lens equation are exact; the hull's temperature and the stage are modelled
for each sentence: which coefficient, which column of Table 1, which setting
stand on the range · hear it · read its glow · bend the stars · climb the ladder · open the file

Evidence

fact ⇄ what kind of claim · live

D132 (29 March 2010): Table 1 (p. 9); the time row's ten seconds and five (p. 8); the ear and the glow (p. 12, Figure 1); the size (p. 13); the index and the lens (pp. 10, 14)

the paper's own words with their pages

REPORTED

D128 (11 March 2010), p. 14: the heat spectrum 'blue-shifted', and 'microwave, visible, UV, soft X-rays'

the human tissue paper's words

REPORTED

D139 (6 April 2010), p. 30: Equation (9), 1.35 × 10²⁷ kg and 0.71 M_J per metre of throat, its caveat and Table 2

the wormholes paper's figures as printed

REPORTED

c, G, h, k, σ and Wien's b: CODATA 2022 at NIST

the constants' pages, each value on its line

TABULATED

Jupiter 1.90 × 10²⁷ kg, Earth 5.97 × 10²⁴ kg, the Sun's 5,772 K: NASA's fact sheets

the masses on the Lens view's axis

TABULATED

The hearing range, 20 to 20,000 Hz (the hearing range page)

the Ear's strip

TABULATED

The voice band, 300 to 3,400 Hz (the voice frequency page)

the Ear's darker band

TABULATED

The eye, 380 to 750 nm (the visible spectrum page)

the glow's visible window

TABULATED

The bands from 10 pm to 1 mm (the electromagnetic spectrum page's table); microwaves 1 mm to 1 m (the microwave page)

the Spectrum's ribbon

TABULATED

The soft and hard X-ray boundary, 0.1 to 0.2 nm (the X-ray page); the ultraviolet page's 100 to 400 nm

noted on the File; the ribbon takes the table's edges

TABULATED

Wien: λ_peak = b/T, and b/(fT) seen from outside

the peak and its band

EXACT

Planck's law; the received curve f · B(ν/f, T) = B(ν, fT)/f²

the frequency, energy and time rows together

EXACT

Stefan-Boltzmann: σT⁴; received ×f², a true fT body ×f⁴

the power factor

EXACT

The Schwarzschild radius r_s = 2GM/c²

M_bh, the mass whose r_s is the drawn radius

EXACT

The deflection α = 4GM/(c²b)

the bend at the rim

EXACT

The Einstein radius in its far-source form, θ_E = √(4GM/(c²D)), the stars at infinity

the ring and M_rim

EXACT

The point-mass lens equation θ = β + θ_E²/θ and its two images

the dome's shader

EXACT

Table 1's rows at the dials: time ÷f, frequency ×f, energy ×f, length ÷s, velocity ×f/s, mass ×s²/f

arithmetic on the table; nothing fitted

EXACT

Standard gravity, 9.80665 m/s² (ISO 80000, the standard gravity page)

the accelerations printed in g

TABULATED

Kim et al.'s Planckian locus splines

the colour's check, within 0.0011

TABULATED

The sRGB matrix and transfer (the 2003 amendment)

the colour on the screen

TABULATED

Wyman, Sloan and Shirley (2013): the CIE 1931 colour matching fit

the colour of a Planck spectrum

TABULATED

The hull a blackbody at T, 300 K by default (the paper gives no temperature); the point mass at the craft's centre; the tie on by default

the bench's dials, each named

MODELLED

Staging: the desert floor at night, the dome's latitude 35° N and sidereal time 6 h, the craft's 40 m height (lifted to clear the floor when the drawn sphere is larger), the eye's 1.6 m, the faint stars, the 800 K glow threshold; the ground not lensed

the Range's stage, each item named

MODELLED

Which column of Table 1 each sentence sits in, and what, if anything, a craft did

the question this bench leaves to you

READING

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