The Pais Patent Gravitational-Wave Bench
Chapter 23 of In Plain Sight asks why LIGO does not go off the scale when the Navy's patented generator runs. The generator patent prints the figures an answer has to start from: 'on the order of 10³³ W/m²' of electromagnetic flux, a static field 'on the order of 10¹⁰ Tesla', and 'power levels on the order of 10¹⁰ watts' of gravitational waves through the Gertsenshtein effect, on an equation it takes from a 2008 JASON report. Run as written, in SI, over a square metre and a metre of field, the three figures close on each other: 1.2 × 10¹⁰ W comes back. Evaluated as the report does, in its own units, the same expression gives 4π/μ₀, ten million, more. Beside the inputs: the highest steady field a laboratory has reported is 45.5 T, the patent's is 2.2 × 10⁸ times it and sits inside the magnetars' range; the CoReLS laser's focus reached 1.1 × 10²⁷ W/m², the patent's flux is a million times it. The patent's own 10³⁵ gravitons a second fix its wave at 151 MHz, 3 × 10⁴ times above the top of LIGO's design band; at that frequency ten gigawatts is 3 × 10⁻²⁸ at Livingston, 1,570 km away. Carried into the band at 100 Hz the same power is 4.5 × 10⁻²², nearly half GW150914's peak and held steady, heard in five thousandths of a second. A one-tonne disc of the craft patent's size at 30,000 rpm, all its mass off centre, radiates 6.8 × 10⁻²⁵ W by the quadrupole formula, 34 orders under the patent's figure, with its rim at 6,283 m/s. The report's sentence and the patent's rebuttal hang at equal size.
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Open the interactive ▸ What you're looking at
The Chain is the generator patent’s own arithmetic drawn left to right: electromagnetic flux times area, the Gertsenshtein factor (4πG/c⁴)B₀²L² in both unit systems, the gravitational-wave power out, and the strain that power makes at one kilometre, at LIGO Livingston and at LIGO Hanford. Under it three log ladders set each input beside the measured world: the field beside 45.5 T, 1,200 T, the Schwinger field and the magnetars; the flux beside the Sun’s surface, the CoReLS laser’s focus and the Schwinger intensity; the frequency beside LIGO’s band and GW150914’s sweep. Every box follows the dials.
The Spectrum is strain against frequency, both axes log, from 1 Hz to 10¹² Hz: LIGO’s design curve (a target, labelled DESIGN), GW150914’s peak as a gold bar across 35 to 250 Hz, the O1 all-sky limits, a one-year line the bench computes, the patent’s band shaded, the dialled power at both detectors as h ∝ 1/f, and a what-if marker that carries the same power into the band at a frequency you choose, with the seconds to signal-to-noise 8. The Rotor spins a disc of the craft patent’s size, 2 m at 30,000 rpm, with the mass and ellipticity as dials, and draws its quadrupole power on one bar with the report’s two ceilings, the patent’s ten gigawatts and GW150914’s peak luminosity.
The Bubble is the craft patent’s Equation 1 at its own example, a disc of 2 m radius charged to 50,000 C/m² and spun at 30,000 rpm: the flux it gives, the power off both faces beside the Sun, the Three Gorges Dam the book names and the world’s grid, the surface field beside air’s breakdown and the Schwinger field, the pressure on the face beside the Earth’s centre and the Sun’s, and the energy the charge costs to place. The File runs the sources on cards, the book, the two patents, the report and the measurements quoted, and closes on two cards at equal size: what the report says and what the patent says.
Why it is here
The book has a culture note on the site, the Culture 08 source note on In Plain Sight; chapter 23 carries one number an instrument can take over. Coulthart records a question sceptical scientists put to him: if the Navy's Dr Salvatore Pais's gravitational-wave generator 'truly were pumping out gravity waves', why do the LIGO receivers in Louisiana and Washington not go off the scale; he writes that 'No one knows enough yet in the white world of science to be able to answer that question'. The generator patent (US 10,322,827 B2, granted 2019) prints three figures of its own: an input electromagnetic flux 'on the order of 10³³ W/m²', a static field 'on the order of 10¹⁰ Tesla', and gravitational waves at 'power levels on the order of 10¹⁰ watts', strung on an equation it takes from page 10 of a 2008 JASON report. The site's Gravitational Waves bench runs from the detector to the source: LIGO's arm stretched by a wave that was measured. This one runs the other way: from a patent's own stated source to the detector.
So the instrument does one thing: it runs the patent's own figures through the patent's own equation, sets each input beside a measured record, and puts the output on LIGO's curve. It takes the three figures and the equation as the patent prints them (in both unit systems, since the patent itself notes a factor missing from the report's equation), the report's conversion and ceiling as the report prints them, LIGO's peak strain, sensitivity and limits as the papers print them, and 45.5 T, 1,200 T, 1.1 × 10²³ W/cm² and the magnetars' fields as their papers print them. It does not say whether the patents are right, whether a device was built, or which unit system to believe. The report's sentence and the patent's sit at equal size on the File; the reading is the reader's.
How it works
Everything on the bench is arithmetic on the patents’ own figures, the report’s own figures and the published measurements. The script that ships with the site re-derives every displayed number, and reproduces the patents’ and the report’s own printed figures, before the build is allowed to pass.
P_GW = [(4πG/c⁴) B₀² L²] P_EM · h₀ = √(8GP/c³) / (2πf r) · h₀ = 16π²G I ε f_rot² / (c⁴ d) · S = (σ²/ε₀) R ω
The chain. The generator patent writes P_GW = [(4πG/c⁴)B₀²L²]P_EM, taken from the report’s Equations (3-13) and (3-14), and states its inputs and output in SI units; evaluated as written, at 10¹⁰ T over a metre the factor is 1.04 × 10⁻²³, so at the bench’s 1.13 × 10³³ W/m², over a square metre, it gives 1.2 × 10¹⁰ W, on the order of the patent’s “10¹⁰ watts”. The report evaluates the same expression in its own units, 10⁻³⁵ at 10⁵ gauss over 10³ cm², which for the same field and length is 4π/μ₀ = 10⁷ times the SI reading; the patent itself says a factor “on the order of 10⁶”, the inverse of μ₀, is missing from the report’s equation. Evaluated as the report does, the same inputs give 1.2 × 10¹⁷ W. The bench prints both and chooses neither. The patent’s 10³⁵ gravitons a second at 10¹⁰ W put one graviton at 10⁻²⁵ J, which is hf at 151 MHz; the report’s own ceiling, 10⁻¹⁸ W at 10⁷ gravitons a second, implies the same frequency.
The strain of a wave. A source radiating power P in one polarisation at frequency f, isotropically, makes a strain amplitude h₀ = √(8GP/c³)/(2πf r) at distance r: the Isaacson flux (c³/16πG)⟨ḣ₊² + ḣײ⟩ set equal to P/4πr². Fed GW150914’s own peak luminosity, 3.6 × 10⁴⁹ W, and its 410 Mpc, the form gives 1.3 to 2.2 × 10⁻²¹ across the sweep against the measured 1.0 × 10⁻²¹. At 151 MHz the patent’s ten gigawatts is 4.7 × 10⁻²⁵ one kilometre away, 3.0 × 10⁻²⁸ at Livingston (1,570 km, a great circle from Naval Air Station Patuxent River) and 1.3 × 10⁻²⁸ at Hanford (3,599 km). At 100 Hz, inside the band, the same power is 4.5 × 10⁻²² at Livingston; against the design curve’s 4.1 × 10⁻²⁴/√Hz a source overhead reaches signal-to-noise 8 in 0.005 s.
The rotor and the bubble. A rigid body spinning at f_rot with moment of inertia I and ellipticity ε radiates h₀ = 16π²G I ε f_rot²/(c⁴d) (the known-pulsars paper’s Equations (4) and (5) combined) at power P = (32G/5c⁵) I² ε² Ω⁶. The patents give no mass, so the rotor’s is a dial: a 1,000 kg disc of 2 m at 30,000 rpm with ε = 1 gives 6.8 × 10⁻²⁵ W, 34 orders under 10¹⁰ W, and 6.5 × 10⁻³⁷ at 1 km; the mass that reaches ten gigawatts there is 1.2 × 10²⁰ kg. The craft patent’s Equation 1, S = (σ²/ε₀)Rω for a disc, at its own 50,000 C/m², 2 m and 30,000 rpm gives 1.77 × 10²⁴ W/m², its “10²⁴”: 4.5 × 10²⁵ W off both faces, 0.116 of the Sun’s luminosity; a surface field of 5.6 × 10¹⁵ V/m; 1.4 × 10²⁰ Pa on the face; 5.6 × 10²¹ J to place the charge.
Nothing is fitted. The only choices are the dials: the flux, the area, the field and its length, the frequency, the normalisation; the rotor’s mass, radius, spin, ellipticity and distance; the disc’s charge, radius and spin; the what-if frequency. Every finding is quoted at the patents’ own defaults and across them.
The dials that decide the result
The patent’s three figures and the frequency; the normalisation; the rotor; the disc; the what-if. Together they draw every version of the chain the patents’ own equations allow.
- The chain. Flux 10²⁰ to 10³⁵ W/m² (default the patent’s 1.13 × 10³³, from the craft patent’s example at 10¹¹ Hz); area 10⁻⁸ to 100 m²; field 1 to 10¹² T (default 10¹⁰); field length 1 cm to 10 m; wave frequency 10 MHz to 300 GHz, from the generator patent’s low end to the top of the craft patent’s microwave range, default the 151 MHz the graviton rate implies.
- The normalisation. The Gertsenshtein factor as the report evaluates it (the default) or as the patent writes it in SI; the two differ by 4π/μ₀ = 10⁷ for the same inputs, and both are always printed.
- The rotor. Mass 1 to 10⁵ kg (default 1,000; the patents give none), radius 0.1 to 5 m (default the craft patent’s 2), spin 100 to 100,000 rpm (default its 30,000), ellipticity 10⁻⁶ to 1 (default 1, the largest the formula allows), distance 1 m to 10⁴ km with Livingston and Hanford as presets.
- The disc. Surface charge 1 to 10⁵ C/m² (default the patent’s 50,000), radius 0.5 to 5 m, spin 1,000 to 100,000 rpm.
- The what-if. The frequency the patent’s ten gigawatts is carried to on the Spectrum, 20 to 2,000 Hz, default 100: the question on p. 290, asked of the band LIGO reads.
The claims, as they stand
The patents’ figures, the report’s, the book’s question and the board’s pitch one by one, and where each lands when the patents’ own equations are run.
| 'we can produce HFGW exhibiting power levels on the order of 10¹⁰ watts, for an input EM energy flux on the order of 10³³ W/m². In this case, B₀ is the magnetic flux density, on the order of 10¹⁰ Tesla' proposed by the generator patent, US 10,322,827 B2 | REPORTED | Entered as given. As the patent writes its equation, in SI, 1.13 × 10³³ W/m² over a square metre and 10¹⁰ T over a metre give 1.2 × 10¹⁰ W: the figure comes back from its own inputs. Evaluated as the report does, in its own units, the same inputs give 1.2 × 10¹⁷ W, 4π/μ₀ more; the patent itself names a factor “on the order of 10⁶”, the inverse of μ₀, as missing from the report’s equation. Both printed; neither chosen. |
| 'B₀ ... on the order of 10¹⁰ Tesla' proposed by the generator patent | MEASURED | 2.2 × 10⁸ times the highest steady field a laboratory has reported, 45.5 T (Hahn et al. 2019); 8.3 × 10⁶ times the record indoor pulsed field, 1,200 T (Nakamura et al. 2018); 2.3 times the Schwinger field; inside the range inferred for magnetars, 6 × 10⁸ to 2 × 10¹¹ T. |
| 'energy flux values in excess of 10³³ W/m² are feasible' proposed by the generator patent | MEASURED | 1.0 × 10⁶ times the CoReLS laser’s 1.1 × 10²⁷ W/m² (Yoon et al. 2021); 0.49 of the Schwinger intensity, where the patent itself says pair production begins; 1.8 × 10²⁵ times the Sun’s surface. A square metre at that flux carries 2.9 × 10⁶ Suns. |
| 'gravitational waves at the same frequency as the EM radiation' · 'low end microwave frequencies on the order of 10⁷ Hz' · '10³⁵ gravitons/sec' proposed by the generator patent | EXACT | The graviton rate at 10¹⁰ W puts one graviton at 10⁻²⁵ J, which is 151 MHz; the report’s own 10⁻¹⁸ W at 10⁷ gravitons a second implies the same. LIGO’s design curve ends at 5,000 Hz: the patent’s low end is 2,000 times above it, 151 MHz is 3.0 × 10⁴ times. At the patent’s own frequency the wave is not in the band the detectors read, whatever its amplitude. |
| 'why do the ... LIGO receivers in Louisiana and Washington not go off the scale' proposed by the question Coulthart reports (p. 290) | EXACT | Three answers in arithmetic. At the frequency the patent names, ten gigawatts is 3.0 × 10⁻²⁸ at Livingston (1,570 km) and 1.3 × 10⁻²⁸ at Hanford (3,599 km). That frequency sits above LIGO’s band. The same ten gigawatts at 100 Hz would be 4.5 × 10⁻²² at Livingston, 0.45 of GW150914’s peak and held steady, signal-to-noise 8 in 0.005 s against the design curve. |
| 'the energy level (gain in potential energy) capable of annihilating a planet such as the Earth is on the order of 10³² Joules (which may be achieved with the concept at hand)' proposed by the generator patent | EXACT | (3/5)GM²/R from the fact-sheet Earth is 2.24 × 10³² J, as the patent says. At the patent’s own ten gigawatts, delivering it takes 7.1 × 10¹⁴ years. |
| 'σ = 50,000 Coulombs/m², a disc ... radius of 2 m and an angular speed of 30,000 RPM' giving 'on the order of 10²⁴ Watts/m²' proposed by the craft patent, US 10,144,532 B2 | EXACT | Equation 1 at those inputs gives 1.77 × 10²⁴ W/m², reproduced. Off both faces that is 4.5 × 10²⁵ W, 0.116 of the Sun’s luminosity and 2.0 × 10¹⁵ times the Three Gorges Dam the book names; the surface field is 5.6 × 10¹⁵ V/m, 1.9 × 10⁹ times air’s breakdown; the pressure on the face 1.4 × 10²⁰ Pa, 3.9 × 10⁸ times the Earth’s centre; the charge costs 5.6 × 10²¹ J to place, fifty years of the world’s electricity. |
| F = 4πG B₀² L²/c⁴ ∼ 10⁻³⁵ 'for B₀ = 10⁵ Gauss and L² = 10³ cm²' · 'P_GW(out) ∼ 10⁻¹⁸ watts' · 'No foreign threat in HFGW is credible' proposed by the JASON report, JSR-08-506 (2008) | REPORTED | The 10⁻³⁵ is reproduced in the report’s units; the same inputs in the SI-as-written form give 10⁻⁴², 4π/μ₀ = 10⁷ below, which the patent describes as a factor on the order of 10⁶, the inverse of μ₀. The 10⁻¹⁸ W ceiling sits 6.2 orders above the bench’s rotor and 28 below the patent’s figure. The conclusions are printed as the report’s, with the patent’s rebuttal beside them. |
| 'run the quadrupole formula ... on the patent's own stated masses and rotation rates ... a gap of more than thirty orders of magnitude' proposed by this site's board, the pitch | REPORTED | Neither patent states a mass or a rotation rate for the generator; the craft patent’s 2 m and 30,000 RPM belong to a charged disc with no mass given. With the mass a dial, a 1,000 kg disc at that radius and spin, ε = 1, radiates 6.8 × 10⁻²⁵ W: 34 orders under the patent’s 10¹⁰ W in power, and 15 orders under GW150914’s strain at 1 km. The board’s “LIGO’s design strain (about 1e-21 at 100 Hz)” was GW150914’s peak, not a design figure; the design curve is 4.1 × 10⁻²⁴/√Hz at 100 Hz. |
| 'The JASON report considers relatively low EM energy fluxes, when compared with those generated by the physical mechanisms described in the inventor's aforementioned published paper (on the order of 10³³ W/m², and beyond). ... It is because of this fact, that the JASON report's conclusions must be revisited, are incorrect, and are directly in conflict with the current invention.' proposed by the generator patent | REPORTED | Printed as the patent’s, beside the report’s conclusions. The two documents disagree on the flux a generator can carry; the Chain’s flux ladder sets the patent’s 10³³ W/m² beside the CoReLS laser’s focus and the Schwinger intensity, and the bench rules on neither. |
| The rotor the formula allows proposed by this bench | MODELLED | At 2 m and 30,000 rpm the rim moves at 6,283 m/s and pulls 2.0 × 10⁶ g; a steel rim would carry 3.1 × 10¹¹ Pa against tabulated yields of 2.5 × 10⁸ to 1.65 × 10⁹ Pa. The mass that reaches ten gigawatts there is 1.2 × 10²⁰ kg, 1.7 thousandths of the Moon’s. |
| What the bench amounts to proposed by this bench | READING | The patent’s three figures close on each other in the unit system the patent uses, and each sits beside the measured record it exceeds; the wave they describe sits above LIGO’s band and, inside it, would be heard within a second. Whether the patents are right, whether a device was built, and which unit system to believe, the documents do not settle, and the bench does not. |
Try this
- Start on the chain. Switch the normalisation from the report’s to as written and watch the output fall from 1.2 × 10¹⁷ W to 1.2 × 10¹⁰ W, the patent’s own “on the order of 10¹⁰ watts”; nothing else moves.
- Bring the field down to earth. Drag B₀ to 45.5 T, the laboratory’s steady record, and the flux to the CoReLS laser’s 10²⁷ W/m²; read the output.
- Open the spectrum. Find the amber dot at 151 MHz, far to the right of the violet curve; then drag the what-if dial from 100 Hz to 1,000 Hz and watch the seconds to signal-to-noise 8 change.
- Spin the rotor. Set the ellipticity to 10⁻⁶, a neutron star’s, and watch the power bar drop another twelve orders; then set the distance to Livingston.
- Bill the bubble. Drag the surface charge down to 1 C/m² and watch the disc’s output fall from a tenth of a Sun to 1.8 × 10¹⁶ W, 4.7 × 10⁻¹¹ of it.
- Finish in the file. The question, the patents, the report, the measurements, Sheehy, Pais, Coulthart; then the two cards at equal size.
Accuracy
The honest line between what is quoted, what is measured, what is a design target, what is established physics, what is arithmetic, what is a choice, and what is a reading:
| Feature | Status | What that means |
|---|---|---|
| The patents | Reported | US 10,322,827 B2: 10³³ W/m², 10¹⁰ T, 10¹⁰ W, 10³⁵ gravitons a second, 10⁷ Hz and 300 MHz to 300 GHz, the Gertsenshtein equation as written and its note on the missing factor, the 10³² J planet figure. US 10,144,532 B2: Equation 1, 50,000 C/m², 2 m, 30,000 RPM, 10²⁴ W/m², the 1 C/m² example at 10¹¹ Hz, the 10¹⁸ V/m Schwinger figure. Read in full; quoted as printed; no mass, size or rate for the generator anywhere in them. |
| The book and the report | Reported | The question on p. 290, the four patents as the book lists them, Sheehy's letter, Pais's and his critics' sentences, Coulthart's doubts and closing question (pp. 288 to 302); the JASON report's conclusions, its Equation (3-14) at 10⁵ gauss over 10³ cm², its 10⁻¹⁸ W ceiling and its 10³⁸ W for propulsion (JSR-08-506). Each sentence carried as its author's. |
| LIGO and the laboratory | Measured | GW150914's 1.0 × 10⁻²¹ peak, 35 to 250 Hz, 410 Mpc and 3.6 × 10⁴⁹ W; O1's 10⁻²³/√Hz at 100 Hz and its all-sky limits of 4 × 10⁻²⁵ and 1.5 × 10⁻²⁵; 45.5 T (Hahn et al. 2019); 1,200 T (Nakamura et al. 2018); 1.1 × 10²³ W/cm² (Yoon et al. 2021); magnetar fields of 6 × 10⁸ to 2 × 10¹¹ T (Kaspi and Beloborodov 2017; the McGill magnetar catalogue). |
| LIGO's design curve | Design | LIGO-T1800044-v5, 5 to 5,000 Hz, thinned to about 150 log-spaced rows of the file, each checked against it: a target, not a measurement, and labelled so wherever it is drawn. |
| The physics | Established | The Isaacson flux of a wave and the single-polarisation strain it gives; the rotating body’s quadrupole strain and power; the Schwinger field computed from CODATA; great circles on a 6,371.0088 km sphere. |
| The arithmetic | Exact | The chain in both unit systems, the strain at 1 km and at the two detectors, the seconds to signal-to-noise 8, the rotor's power and strain, the bubble's flux, power, field, pressure and charge energy, every ratio on the ladders. No parameter is fitted. |
| The dials | Modelled | The device's place (NAS Patuxent River), the emitting area, the field length, the rotor's mass and ellipticity, a source overhead with coherent integration, the what-if frequency. The patents give none of them; each is labelled on the bench and quoted across its range. |
| What it amounts to | Reading | Whether the patents are right, whether a device was built, which of the two unit systems the equation should be read in, and what the book’s question deserves as an answer are readings, and the bench declines to make them for you. |
In one line: The patents’ figures are taken as printed and run through the patents’ own equations in both unit systems; each input is set beside a measured record; the report’s and the book’s sentences are carried as theirs; every choice is named as a dial; and whether the patents are right, whether a device was built, and which unit system to believe are left where the documents leave them. The reading is yours.
Sources
- Coulthart, R. (2021) In Plain Sight: An Investigation into UFOs and Impossible Science, HarperCollins Australia: chapter 23, "Dr Salvatore Pais's Puzzling Patents" (pp. 288 to 302).
- Pais, S. C. (2019) "High Frequency Gravitational Wave Generator", US Patent 10,322,827 B2, filed 14 February 2017, granted 18 June 2019, assignee the United States of America as represented by the Secretary of the Navy, Google Patents: 10³³ W/m², 10¹⁰ T, 10¹⁰ W, Equations 1 to 4, the citation of and answer to the JASON report.
- Pais, S. C. (2018) "Craft Using an Inertial Mass Reduction Device", US Patent 10,144,532 B2, filed 28 April 2016, granted 4 December 2018, Google Patents: Equation 1 and its two examples, the Schwinger figure, the 'vacuum plasma bubble/sheath'.
- Eardley, D. et al. (2008) High Frequency Gravitational Waves, JSR-08-506, JASON, The MITRE Corporation, for the Office of the Director of National Intelligence, approved for public release: the abstract and conclusions, section 3.3's Equations (3-13) to (3-15), Equations (3-24) and (3-25), section 5's 10³⁸ W.
- Abbott, B. P. et al. (2016) "Observation of Gravitational Waves from a Binary Black Hole Merger", Physical Review Letters 116, 061102, arXiv:1602.03837: the peak strain 1.0 × 10⁻²¹, 35 to 250 Hz, 410 Mpc, the peak luminosity 3.6 × 10⁵⁶ erg/s.
- Abbott, B. P. et al. (2016) "GW150914: The Advanced LIGO Detectors in the Era of First Discoveries", Physical Review Letters 116, 131103, arXiv:1602.03838: 10⁻²³/√Hz at 100 Hz.
- Abbott, B. P. et al. (2017) "All-sky search for periodic gravitational waves in the O1 LIGO data", Physical Review D 96, 062002, arXiv:1707.02667: 20 to 475 Hz, the worst-case limit of 4 × 10⁻²⁵ near 170 Hz and 1.5 × 10⁻²⁵ for circular polarisation.
- Abbott, B. P. et al. (2017) "First Search for Gravitational Waves from Known Pulsars with Advanced LIGO", The Astrophysical Journal 839, 12, arXiv:1701.07709: Equations (4) and (5), together the rotating body's strain.
- Aasi, J. et al. (LIGO Scientific Collaboration) (2015) "Advanced LIGO", Classical and Quantum Gravity 32, 074001, arXiv:1411.4547: the 4 km arms, the band's 10 Hz low end.
- Barsotti, L., Fritschel, P., Evans, M. & Gras, S. (2018) "Updated Advanced LIGO sensitivity design curve", LIGO-T1800044-v5, the file aLIGODesign.txt, dcc.ligo.org: the design strain amplitude spectral density, 5 to 5,000 Hz.
- Sathyaprakash, B. S. & Schutz, B. F. (2009) "Physics, Astrophysics and Cosmology with Gravitational Waves", Living Reviews in Relativity 12, 2, arXiv:0903.0338: section 2.6, Equations (14) to (18), the flux of a wave.
- Hahn, S. et al. (2019) "45.5-tesla direct-current magnetic field generated with a high-temperature superconducting magnet", Nature 570, 496 to 499; Nakamura, D. et al. (2018) "Record indoor magnetic field of 1200 T generated by electromagnetic flux-compression", Review of Scientific Instruments 89, 095106; Yoon, J. W. et al. (2021) "Realization of laser intensity over 10²³ W/cm²", Optica 8, 630.
- Kaspi, V. M. & Beloborodov, A. M. (2017) "Magnetars", Annual Review of Astronomy and Astrophysics 55, arXiv:1703.00068; Olausen, S. A. & Kaspi, V. M. (2014) the McGill magnetar catalogue, physics.mcgill.ca: surface dipole fields of 0.061 to 20 × 10¹⁴ G.
- NASA/NSSDC Sun, Earth and Moon fact sheets (D. R. Williams); CODATA 2022 (NIST); Wikipedia "LIGO", "Naval Air Station Patuxent River", "Schwinger limit", "Dielectric strength", "Earth's inner core", "Electricity generation" and "Steel", read 2 October 2026.
- Signals from the Periphery, Culture 08, the source note on In Plain Sight; INST-15 Gravitational Waves, this bench's sister.