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Haisch-Bernard: Primer

Project: US Patent 7,379,286 B2, "Quantum Vacuum Energy Extraction", inventors Bernard Haisch (Redwood City, CA) and Garret Moddel (Boulder, CO), assignee Jovion Corporation, Menlo Park; filed 26 Sep 2005, granted 27 May 2008 [read: Patent7379286 p.1]. Also in the folder: a one-page conference abstract by Haisch and Moddel, "Indirect extraction of zero-point energy from the quantum vacuum: Patent 7,379,286" [read: Haisch_abstractSSE10 p.1], and Robert L. Forward, "Extracting electrical energy from the vacuum by cohesion of charged foliated conductors", Physical Review B 30, 1700 (1984) [read: Forward1984 p.1].

Sources. No source gap: all three documents have readable text. The patent and Forward's paper are scans read by OCR (optical character recognition), and their equations and numbers were checked against page images by the deep readers. This primer also draws on the Investigator's downloaded papers (research/files/), chiefly the co-inventor's experimental test, Dmitriyeva and Moddel, Physics Procedia 38, 8-17 (2012), and the review by Moddel and Dmitriyeva, Atoms 7, 51 (2019).

Source tags. [read] = from a project document or a downloaded paper in research/files/; [web] = Internet source with URL; [memory] = general knowledge, with confidence; [calc] = arithmetic done for this primer, reproduced in example.py.

Interested parties. Haisch and Moddel are the inventors; Jovion is the assignee, and Moddel declares a Jovion stockholding in the 2019 paper [read: Atoms 2019, via Investigator]. Google Patents also records an assignment to the Regents of the University of Colorado on 2008-06-10 [web: https://patents.google.com/patent/US7379286B2/en, via Investigator]. Their descriptions of what the device does are their own characterisation. Forward's paper was funded by the US Air Force Rocket Propulsion Laboratory and Hughes Aircraft [read: Forward1984 p.3]; he has no stake in this patent.

Verdicts in this primer are the arbiter's (arbiter.md, including its "QE revision" section). The primer adds no new verdicts. After the quality check (qe.md), patent pages 10-12 and 17-21 were deep-read from page images, so the patent's own cutoff convention, its hydrogen cavity size, its later embodiments and its granted claims are now covered here.

1. The idea in one paragraph

Empty space is not perfectly empty: quantum physics says the electromagnetic field always jiggles a little, even at absolute zero. This background is called the zero-point field, and its energy the zero-point energy. Between two metal plates very close together, some of that jiggling is shut out, and the plates are pushed together (the Casimir effect, which is real and measured). Haisch and Moddel start from a minority theory, stochastic electrodynamics, in which an atom's electron is a tiny classical planet that would spiral into the nucleus by radiating, except that it is kept in orbit by soaking up energy from the zero-point field. If you push a gas atom into a narrow gap where part of that field is shut out, they reason, the electron should sink to a lower orbit and give off energy as heat. When the atom leaves the gap, the full field outside would lift the electron back up for free. Pump gas round and round through a sponge of tiny gaps and you have a heat source fed by the vacuum: "extracting energy locally and replenishing it globally" [read: Patent7379286 printed col. 4]. Forward's 1984 paper, also in the folder, is a different and more modest idea: a stack of charged metal foils that the Casimir force squeezes together, doing electrical work like a battery being discharged. The arbiter's finding is that the Casimir effect and cavity-shifted atomic energies are real, but the energy shifts they produce in a 0.1-micron gap are about a hundred-millionth of what the patent assumes, and a static gap cannot give a net energy gain over a full in-and-out cycle. The co-inventor's own experiment saw a small infrared signal, a thousand or more times below the prediction, with most trends the reverse of what the idea predicts.

2. What you need to know first

Energy levels and photons. An atom's electron can only have certain energies. When it drops from a higher level to a lower one it gives off a photon (a packet of light) with energy E = hf, where h = 6.626×10⁻³⁴ J·s is Planck's constant and f is the frequency in hertz (Hz). Energies at the atomic scale are measured in electron-volts: 1 eV = 1.602×10⁻¹⁹ J. Hydrogen's electron is bound by 13.6 eV. For comparison, the thermal energy of a molecule at room temperature is kT ≈ 0.026 eV, where k = 1.381×10⁻²³ J/K is Boltzmann's constant and T the temperature in kelvin. Read: Krane, Modern Physics, chapters on the Bohr model and the hydrogen atom; or Serway, Moses and Moyer, Modern Physics.

The Bohr model. Bohr (1913) pictured hydrogen's electron in a circular orbit of radius a₀ = 0.529 Å (1 Å, an ångström, is 10⁻¹⁰ m), moving at speed v = αc, where c = 3.00×10⁸ m/s is the speed of light and α ≈ 1/137 is the fine-structure constant (a pure number that measures the strength of the electric force between charges). The angular momentum m v a₀ equals ħ = h/2π, the "reduced Planck constant" (m is the electron mass). Quantum mechanics later replaced the orbit with a probability cloud, but the numbers a₀, αc and 13.6 eV survive. Read: Krane, as above.

Larmor radiation. Any accelerating charge radiates. The power, from Maxwell's equations, is the Larmor formula P = q²a²/(6πε₀c³), where q is the charge, a the acceleration and ε₀ = 8.854×10⁻¹² F/m the permittivity of free space. An electron in a circular orbit is always accelerating (towards the centre), so classically it should radiate and spiral into the nucleus in about 10⁻¹¹ s. This "collapse problem" is one of the original reasons quantum mechanics was needed. Read: Griffiths, Introduction to Electrodynamics, chapter 11 (Radiation).

Modes of a box, and the harmonic oscillator. Light inside a box with mirror walls can only exist as standing waves that fit the box, called modes. Between two parallel mirrors a distance d apart, a wave travelling straight across must have a whole number of half-wavelengths across the gap, so the longest wavelength that fits is 2d. Each mode behaves like a mass on a spring (a harmonic oscillator). In quantum mechanics the lowest energy of an oscillator of angular frequency ω is not zero but ½ħω: this is the zero-point energy. Read: Griffiths, Introduction to Quantum Mechanics, chapter 2 (the harmonic oscillator); any optics text on standing waves.

Potential energy and conservative forces. If a force can be written as F = −dU/dz for some potential energy U(z), then the work done moving along any path depends only on the start and end points. Going around a closed loop, the net work is zero. Gravity and the electrostatic force are of this kind. This is the single most important idea for judging this patent. Read: Taylor, Classical Mechanics, chapter 4 (Energy); Kleppner and Kolenkow, An Introduction to Mechanics.

Detailed balance. In a system at one uniform temperature (thermal equilibrium), every microscopic process happens just as often as its reverse. If atoms entering a region give up energy, atoms leaving it take the same energy back at the same rate, so no net heat flows. This is the microscopic reason the second law of thermodynamics forbids running a heat engine from a single-temperature reservoir. Read: Schroeder, An Introduction to Thermal Physics, chapters on the second law and on heat engines.

Gas flow in tiny channels. The mean free path is how far a gas molecule travels between collisions; about 70-80 nm for argon at 1 atmosphere and room temperature [memory, medium; arbiter computes ~78 nm]. When a channel is narrower than this, molecules hit the walls more than each other (free-molecular or Knudsen flow), and ordinary pipe-flow formulas no longer apply. Read: Karniadakis, Beskok and Aluru, Microflows and Nanoflows (for depth); Schroeder for kinetic theory basics.

3. The textbook view

3.1 Zero-point energy is real

The electromagnetic field is a collection of modes, each a harmonic oscillator with lowest energy ½ħω. Summed over all modes, the zero-point energy per unit volume is formally infinite, but only differences in it are observable. Two observed consequences matter here [memory, high]:

  • The Lamb shift. Hydrogen's 2S and 2P levels, equal in the simplest quantum theory, are split by about 1 GHz (about 4×10⁻⁶ eV) because the electron is jostled by vacuum fluctuations. The 1S level is shifted by about 8.17 GHz, or 3.4×10⁻⁵ eV [calc from 8.17 GHz]. This was a founding success of quantum electrodynamics (QED), the quantum theory of light and charges.
  • Spontaneous emission. An excited atom decays because it is coupled to the vacuum modes. Change the modes (put the atom in a mirrored cavity) and the decay rate changes. This "cavity QED" is a large, mainstream field.

3.2 The Casimir effect

Two parallel, uncharged, perfectly conducting plates at separation d attract. The energy per unit area and the pressure are

u = −π²ħc / (720 d³), P = π²ħc / (240 d⁴).

Here u is energy per area (J/m²), P is pressure (Pa = N/m²). One way to picture it: the plates exclude modes with wavelengths longer than 2d from the gap, so the outside pushes harder than the inside. Forward writes the same formulas with h instead of ħ: u = −πhc/(1440 d³) and P = πhc/(480 d⁴), which are identical once h = 2πħ is substituted [read: Forward1984 page image p.1; checked symbolically in example.py].

Size check [calc]: at d = 1 μm, P = 0.0013 Pa; at d = 100 nm, P = 13 Pa (about a ten-thousandth of an atmosphere); at d = 20 nm, P = 8,100 Pa. The force grows steeply as the gap closes. It has been measured to a few per cent since the late 1990s (Lamoreaux 1997; Mohideen and Roy 1998) [memory, high].

Two real-world limits. First, a metal is a mirror only for light below its plasma frequency, above which it becomes transparent: about 15 eV for aluminium, 8-9 eV for gold and silver [web: https://arxiv.org/pdf/0908.1126, via arbiter]. A metal gap cannot exclude modes with photon energies above this. Forward states the matching limit for the force law: it holds only down to a_min = λ_min/2π, where λ_min is the shortest wavelength the plate material reflects [read: Forward1984 Eq. 4]. Second, the Casimir force is conservative: it comes from an energy u(d) that depends only on the gap, so letting plates snap together and then prying them apart again returns zero net energy.

3.3 Atoms near walls: the Casimir-Polder shift

A single ground-state atom near a mirror also has its energy lowered slightly, because the mirror changes the vacuum modes the atom feels. This is the Casimir-Polder (CP) interaction, the atom-wall cousin of the Casimir force and of the van der Waals force between molecules. At distances z large compared with the atom's own transition wavelengths divided by 2π (the "retarded" regime), QED gives [memory, high for the formula]

U(z) = −3ħc α_vol / (8π z⁴),

where α_vol is the atom's static polarizability volume (how easily its electron cloud is pulled aside by an electric field, in m³): 0.205 ų for helium, 1.64 ų for argon, 4.04 ų for xenon [web: https://arxiv.org/pdf/2006.15448, via arbiter]. (The same formula is often written 3ħcα/(32π²ε₀z⁴) with the SI polarizability α = 4πε₀α_vol.) The energy depends only on position, so it is a potential energy and the force −dU/dz is conservative.

This shift was measured: Sukenik, Boshier, Cho, Sandoghdar and Hinds (Phys. Rev. Lett. 70, 560, 1993) sent ground-state sodium atoms through a micron-wide gold cavity and found the QED prediction for both the size and the distance dependence [web: https://digitalcommons.odu.edu/physics_fac_pubs/7/]. So the inventors are right that "Lamb shifts can be controlled" by cavities [read: Haisch_abstractSSE10 p.1]. The question is only how big the shift is (Section 5).

3.4 Stochastic electrodynamics (SED)

SED is a research programme (Marshall, Boyer and others from the 1960s) that asks how much of quantum behaviour can be reproduced by classical particles bathed in a classical, random electromagnetic field whose spectrum is chosen to match the quantum zero-point energy, ½ħω per mode [read: Patent7379286 printed cols. 1-3; memory, high for the history]. It is a legitimate, published line of work, outside the mainstream, with real successes: it reproduces the Casimir force, van der Waals forces and the blackbody spectrum [memory, medium]. For hydrogen it offers an appealing picture. A classical electron at the Bohr orbit radiates 4.67×10⁻⁸ W by Larmor's formula [calc]. If the random field feeds it the same power on average, the orbit is stable. Boyer (1975) and Puthoff (1987) obtained a Bohr-sized balance this way, and Cole and Zou (2003-2004) simulated the orbit and got a probability distribution resembling the quantum ground state for a time [read: Patent7379286 printed col. 3].

The known difficulties [web and read as tagged]: - Puthoff's balance used a harmonic-oscillator approximation; Haisch himself calls this "a weakness" on his website [web: http://www.calphysics.org/zpe.html, via Investigator]. - Longer simulations find that SED hydrogen eventually self-ionises (the electron escapes), and relativistic corrections "have little effect" on this [web: https://arxiv.org/abs/1506.06787, Nieuwenhuizen and Liska]. - Cetto and de la Peña (1988), working within SED on atoms near conducting objects, report that their results "coincide with previous quantum calculations" [web: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.37.1952, abstract only, via arbiter]. The arbiter reads this as: SED done carefully gives the same tiny QED-sized shifts, not eV-sized ones [web: abstract only; inference, since no reviewer has read the paper]. Moddel and Dmitriyeva's own wording is narrower: they cite this work as showing that "under particular simplifying assumptions this shift is not predicted" [read: Atoms 2019]. Both readings stay on the table until the full paper is read. - No SED treatment of many-electron atoms exists; the patent says the extension "has not yet been proven theoretically" [read: Patent7379286 printed col. 5].

In standard quantum mechanics, the ground state does not radiate at all: there is no lower state to drop to, so no balance is needed. The vacuum field does matter (it causes the Lamb shift and spontaneous emission), but it does not hold the ground state up.

4. Where the inventors depart

The patent's chain of reasoning, set beside the textbook at each link.

Step Patent Textbook (and the reviews)
1. Atom stability Hydrogen's orbit at a₀ is held up by a balance of Larmor emission and zero-point absorption (SED) [read: printed col. 3] In QED the ground state cannot radiate; nothing needs to hold it up. SED's balance is a real research model with a long-time stability problem (Section 3.4).
2. The key wavelength The orbit is sustained by zero-point radiation at "2·π·0.529·137 = 455 Å" [read: page image, printed col. 3; the OCR text shows "22", the image shows π] Correct arithmetic: 2πa₀/α = 455.6 Å. Its photon energy is 27.2 eV [calc].
3. What the gap removes "Suppression of zero-point radiation at this wavelength and shorter" in a Casimir cavity makes the electron decay [read: printed col. 3]. The patent's own convention: modes "whose wavelengths are longer than the separation of the plates" are excluded, and suppression "will be strongest for wavelengths of d or greater" [read: page images pp.10-11]. For hydrogen it specifies "a Casimir cavity of d=250 A or thereabouts" [read: page image p.11, col. 4] The phrase "and shorter" is loosely worded, but the patent's numbers remove the longer wavelengths, which is the right direction. The difference is the convention: for ideal mirrors the cutoff is λ = 2d (half a wavelength must fit), while the patent uses λ = d, a factor of 2 more generous, without saying so. Under the textbook 2d rule hydrogen's 455 Å needs d ≤ 228 Å; the patent's 250 Å is within about 10% of that [calc]. The objections that remain: no metal reflects 27 eV light (Section 3.2), and nothing in the patent computes how much energy the suppression releases. The 0.1 μm figure is the patent's noble-gas figure and its "tail" argument (row 4), not its hydrogen figure.
4. Bridging the gap Partial suppression on a "stairway" at d/n, and the electron's tail out to five Bohr radii, may allow "0.1 microns-0.2 microns" [read: printed col. 3]. It also appeals to a named theorist: "According to a Jordan Maclay, who has done theoretical Casimir cavity calculations, a long cylindrical cavity results in an inward force ... this implies that a cylindrical cavity of diameter 0.1 micron would yield the desired decay" [read: page image p.11, col. 4] Not computed in the patent. Near a mirror the field changes by a few per cent and oscillates in sign with wavelength, so a broad-band effect largely averages out [physicist.md, order of magnitude]. The Maclay passage is the applicants' characterisation of his work: no paper is cited, Maclay is not in the patent's reference list, and the step from "inward force" to "electron decay" is the applicants' own. What Maclay actually calculated is an open lead.
5. Heavier atoms A fully shielded outer electron at radius r scales as λ ∝ r^(3/2), so Ar, Kr, Xe need larger gaps; "a crude assumption" [read: printed col. 4]. Hydrogen is set aside (it is a two-atom molecule, so "a dissociation process would need to precede an injection") and the working gases are He, Ne, Ar, Kr, Xe at d = 0.1 μm [read: p.11] The patent's own scaling puts Ar, Kr and Xe wavelengths (240-347 nm) above a 0.1 μm gap's textbook 200 nm cutoff, and all five gases (156-347 nm) above the patent's own 100 nm cutoff [calc]. At these wavelengths (3.6-8 eV) metals such as aluminium do reflect, so the metal-transparency objection is weaker for the actual working gases than for hydrogen [arbiter, memory, medium]. Many-electron SED is not derived.
6. Energy released "Since the binding energy of the electron is 13.6 eV, we assume that the amount of energy released ... would be on the order of 1 to 10 eV" [read: printed col. 4]. And how it comes out: "no matter how quickly the atom is injected ... the process will be a slow one as experienced by the orbiting electron. We therefore assume ... gradual release of energy in the form of heat, rather than a sudden optical radiation signature" [read: p.11] An assumption, not a derivation. QED gives about 10⁻⁹ to 10⁻⁸ eV in a 0.1 μm gap (Section 5); SED probably agrees, per the arbiter's inference from the Cetto and de la Peña abstract (Section 3.4). The "slow process, heat not spectral lines" premise is the patent's own reason to look for heat; it is why the 2012 test used an infrared heat detector, and why the inventors never ran a spectroscopic search. It is itself untested.
7. On exit "The electron would absorb energy from the zero-point field and be re-excited to its normal state" [read: printed col. 4] If the energy depends on position, it is a potential U(z). What is released going in is paid back coming out; the loop sums to zero.
8. Thermodynamics "Extracting energy locally and replenishing it globally", like taking "thimbles-full of water from the ocean"; Cole and Puthoff showed no violation [read: printed cols. 3-4] The vacuum is the lowest-energy state of the field; there is no lower state to draw it down to. Detailed balance applies at one temperature. The inventors themselves later list both objections as unresolved (below).
9. Making the exit asymmetric (later embodiments) The patent concedes that if release and re-supply are "both local" or "both global", "no net energy is provided. To avoid these possibilities, we provide an asymmetry" [read: page image p.18]. FIG. 8: an absorbing glass layer lines the channel just upstream of the conducting cavity, on sapphire, "within roughly one emission wavelength" of the emitting atoms; nothing absorbs downstream; "the conducting layer length is chosen so that the emerging atoms do not have substantial access to radiation emitted from the absorbing regions" [read: page images pp.18-19]. FIGS. 5-7 move the walls instead of the gas: a stretched photonic-crystal polymer with 200 nm gas gaps, and a MEMS (micro-electro-mechanical system) polysilicon plate rocked by voltage, needing "very little energy" [read: p.17]. No numbers for the absorber or conductor length, and no measurement, for any of these FIG. 8 is the inventors' best-engineered answer to the exit objection, and the right idea for an energy trap: put the sink where atoms emit, none where they refill. The arbiter's weighing: the absorber is itself a thermal emitter in the band it absorbs (Kirchhoff's law); a 2 μm conductor stripe is shorter than a far-infrared wavelength, so exiting atoms stay within reach of the absorber; 1-10 eV photons (124 nm to 1.24 μm) mostly pass through both glass and sapphire (both are largely transparent above about 0.2 μm [memory, medium]), so the far-infrared materials choice does not match; and if the "global" supply is ordinary room-temperature radiation, a single-temperature loop gives no work. Verdict: Never properly tested (nobody built FIG. 8), and under thermal-equilibrium physics Refuted by calculation; it survives only as the hypothesis that the zero-point field is a non-thermal reservoir (Cole and Puthoff 1993, unread). Moving walls: if atom energy depends on spacing, the gas presses on the walls and the actuator repays on reopening what was released on closing; at 1 eV per atom that extra pressure is about 40 atm [calc]. Verdict: Refuted by calculation (higher confidence than the gas-flow case)
10. Scope All atoms, not just hydrogen ("not yet been proven theoretically"); molecular bonds ("An analogous process is also believed to underlie molecular bonds"); liquid working fluids (ethylene glycol up to about 100 °C, sodium) [read: pp.12, 17] Claimed scope with no argument given; Never properly tested.

The inventors' own caveats, kept in the record. The co-inventor's 2019 paper names the exit problem directly: "one might argue ... they would have to surmount a potential hill to exit the cavity ... Still, we cannot totally rule out this potential hill argument", and says it is "not clear whether equilibrium considerations render it incapable of providing harvestable energy" [read: Atoms 2019, sections 2.3.8 and 2.3.10]. Haisch in 2009: the team had "not yet been able to prove anything in the laboratory", and sporadic signals "can't be ruled out as experimental error" [web: https://www.nextbigfuture.com/2009/02/jovion-corporation-gets-patent-for-zero.html, via Investigator]. These are honest statements and a learner should give the inventors credit for them.

What the patent legally claims. None of the 20 claims contains "net", "gain" or an output figure. Claims 1 and 19 require a fluid that releases energy on entering a Casimir cavity, a collector, and re-intake of energy on leaving; claims 15, 16, 18 and 20 add relative movement between cavity and fluid; claim 20 replaces the cavity with any "mechanism" that changes the atoms so they release energy. The FIG. 8 asymmetry appears in no claim [read: page images pp.19-21, deep read]. So the granted scope is "release, then re-intake", narrower than the title and the summary's "from replacements for small batteries to power plant sized generators" [read: p.12]. The verdicts here judge the title claim of a continuing net supply.

The related patents the applicants set aside. The patent lists Shoulders (US 5,018,180), Mead and Nachamkin (US 5,590,031) and Pinto (US 6,477,028; 6,593,566; 6,665,167) and dismisses each with one reason: it "does not deal with energy release from atoms in Casimir cavities" [read: page image p.12]. That is the applicants' characterisation (they have a stake via Jovion). Pinto's patents, as the applicants describe them, propose making a Casimir system "non-conservative", a different route to the same goal; they are kept in the record.

What the inventors get right. The zero-point field is real; the Casimir force is real; cavities really do shift atomic energy levels and change emission rates; SED is a serious if minority theory; and the Cole-Puthoff argument that zero-point energy is not thermal energy, so the usual heat-engine bound does not directly apply, is a published position [read: patent; memory, medium on Cole and Puthoff's content, which no reviewer read]. The departure is quantitative (how big the shift is) and logical (whether the exit is free).

Forward is different. Forward (1984) explicitly treats the vacuum-fluctuation field as "highly probable" to be conservative, "otherwise it would be possible to design machines using the Casimir force that would allow an infinite amount of energy to be extracted from the vacuum" [read: Forward1984 p.2]. His hydroelectric-dam analogy says the energy is put in when the foil stack is made, the way the sun lifts water to the lake. His device is a battery, not a source, and he never claims otherwise. The patent's description of it as "a simple, but not practical, energy extraction experiment" [read: printed col. 3] is fair only in that sense.

5. Worked example: the energy ledger of one atom entering a 0.1-micron gap

All numbers below are reproduced by example.py (run command in its header). Constants: ħ = 1.0546×10⁻³⁴ J·s, c = 2.998×10⁸ m/s, e = 1.602×10⁻¹⁹ C, ε₀ = 8.854×10⁻¹² F/m, mₑ = 9.109×10⁻³¹ kg, α = 1/137.036, a₀ = 0.5292×10⁻¹⁰ m.

Step A. Reproduce the inventors' starting numbers (they are right)

Orbit speed: v = αc = 2.998×10⁸ / 137.036 = 2.188×10⁶ m/s.

Orbit frequency: f = v / (2πa₀) = 2.188×10⁶ / (2π × 0.5292×10⁻¹⁰) = 6.58×10¹⁵ Hz. The patent prints 6.6×10¹⁵ s⁻¹. (matches)

Wavelength of light at that frequency: λ = c/f = 2πa₀/α = 455.6 Å = 45.6 nm. The patent prints 455 Å. (matches)

Photon energy at that frequency: hf = 27.2 eV. (Algebraically hf = α²mₑc², which is exactly twice hydrogen's 13.6 eV binding energy. A neat check.)

Larmor power: the acceleration is a = v²/a₀ = 9.05×10²² m/s², so

P = e²a² / (6πε₀c³) = 4.67×10⁻⁸ W = 2.9×10¹¹ eV/s.

At that rate the electron would radiate its whole 13.6 eV in 13.6 eV / P = 4.7×10⁻¹¹ s; the proper classical spiral-in time, a₀³/(4r_e²c) with r_e = 2.82×10⁻¹⁵ m the classical electron radius, is 1.6×10⁻¹¹ s [calc]. The patent's "less than one-trillionth of a second" is 16-47 times too short, a minor slip that does not affect the argument.

So far the patent and the textbook agree.

Step B. What does a 0.1 μm gap actually remove?

An ideal parallel-plate gap of width d removes modes with wavelengths longer than 2d (the textbook rule: half a wavelength must fit across). The patent uses a looser rule of its own, a cutoff at λ = d, "strongest for wavelengths of d or greater" [read: page image p.11]. Both are worked below.

  • Hydrogen. The patent pairs hydrogen with "a Casimir cavity of d=250 A or thereabouts" [read: page image p.11, col. 4], not with 0.1 μm. On the patent's rule, a 250 Å gap cuts off at 250 Å, so the 455 Å mode is removed. On the textbook rule it cuts off at 500 Å, so 455 Å still fits; removing it needs d ≤ 455/2 = 228 Å. The patent's 250 Å is within about 10% of that [calc]. So the geometry is nearly right. The real obstacle for hydrogen is the walls: they would have to reflect 27 eV light, which no metal does (aluminium stops reflecting near 15 eV). (For comparison, a 0.1 μm gap would leave hydrogen's 45.6 nm modes untouched on either rule; the patent offers 0.1-0.2 μm for hydrogen only through its uncomputed "tail" and "stairway" argument.)
  • Noble gases at d = 0.1 μm = 100 nm, with the patent's own heavier-atom scaling, λ = 45.6 nm × (r/a₀)^1.5 [calc from the patent's radii]. The textbook cutoff is 200 nm; the patent's is 100 nm:
Gas Patent radius r Scaled λ Gap needed, textbook (λ/2) Removed at 0.1 μm, textbook rule? Removed at 0.1 μm, patent's rule (λ ≥ d)?
He 1.2 Å 156 nm 78 nm no yes
Ne 1.3 Å 175 nm 88 nm no yes
Ar 1.6 Å 240 nm 120 nm yes yes
Kr 1.8 Å 286 nm 143 nm yes yes
Xe 2.05 Å 347 nm 174 nm yes yes

So under the patent's crude model, a 0.1 μm gap is the right size for argon, krypton and xenon on either rule, and for all five gases on the patent's rule; and those photon energies (3.6-8 eV) are low enough for a metal such as aluminium to reflect. This is the strongest form of the inventors' geometric case and it is worth seeing. (Note one oddity of that model: the same fully shielded electron would be bound by only 13.6 eV × a₀/r, about 3.5-4.5 eV for Ar-Xe [calc], less than the 10 eV upper figure the patent assumes is released. Real first ionisation energies are 12-16 eV [memory, high].) On the textbook rule it also predicts that helium should do least, which is the opposite of what the 2012 experiment saw (Step E); on the patent's looser rule helium is included, so that prediction is weaker.

What this step does and does not show: the geometry is not where the patent fails. The cutoff convention is a factor of 2 generous and the patent derives nothing, but its chosen gap sizes are roughly the right sizes. The decisive question is the size of the energy shift, which is Step C.

Step C. How much energy does the gap actually give the atom?

Here is where the ledger decides the matter. Three mainstream estimates, all for perfect mirrors, which overstate the effect:

C1. The whole Casimir energy in an atom-sized volume. At d = 100 nm the Casimir energy per area is π²ħc/(720 d³) = 4.33×10⁻⁷ J/m²; divide by d to get an energy density of 4.33 J/m³. In a volume a₀³ = 1.48×10⁻³¹ m³ that is 6.4×10⁻³¹ J = 4×10⁻¹² eV. (SED proponents reply that the orbit is fed by power flowing in at the speed of light, not by a stored amount, so this is a scale check, not a proof [contrarian.md].)

C2. The Casimir-Polder shift (the established, measured effect). For an atom at the centre of the gap, z = 50 nm from each wall, using U = 3ħc α_vol / (8πz⁴) for one wall and roughly doubling for two:

Argon: U = 3 × (1.0546×10⁻³⁴ × 2.998×10⁸) × 1.64×10⁻³⁰ / (8π × (5×10⁻⁸)⁴) = 1.556×10⁻⁵⁵ / 1.571×10⁻²⁸ = 9.9×10⁻²⁸ J = 6.2×10⁻⁹ eV (one wall), ≈ 1.2×10⁻⁸ eV (two walls).

Gas Shift, two walls (eV) Claimed 1 eV is this many times larger
He 1.5×10⁻⁹ 6×10⁸
Ar 1.2×10⁻⁸ 8×10⁷
Xe 3.0×10⁻⁸ 3×10⁷

C3. Scale markers. The hydrogen 1S Lamb shift, the effect the inventors cite as their model, is 3.4×10⁻⁵ eV. Room-temperature kT is 0.026 eV, so 1-10 eV is 39-387 kT: a chemical-bond-sized change, which would be glaring in the spectrum of every noble gas sitting in nanoporous materials such as zeolites and porous glass [physicist.md]. None has been seen [memory, medium].

Ledger so far: the assumed release is 1-10 eV; the computed, measured-type shift is 10⁻⁹ to 10⁻⁸ eV. The gap is 7 to 10 orders of magnitude. This is why the arbiter rates the strong form "Refuted by calculation (vs cavity QED)".

Step D. Exit: the closed loop

Suppose, generously, the shift were large. The atom's energy depends on where it is, so call it U(z). Going in from z_out to z_in the field does work U(z_out) − U(z_in) on the atom (released as heat or light). Coming out it does U(z_in) − U(z_out). The sum is exactly zero; example.py does this symbolically. A free re-excitation on exit would need a non-conservative energy source, which is the step the patent asserts and the 2019 paper concedes it "cannot totally rule out" failing.

And atoms do not just flow once through: at 300 K their mean speeds are 1,260 m/s (He), 399 m/s (Ar) and 220 m/s (Xe), against the patent's drift of 0.1 m/s. The rate at which atoms hit and cross any boundary by thermal motion (n v̄/4 per unit area, n the number density, v̄ the mean speed) is 550-3,150 times the drift flux [calc]. An atom crosses a 10 μm conducting stripe in 8-45 ns. If every boundary crossing released energy, plain thermal bouncing with no flow at all would release a thousand times more [mathematician.md]. The gas would be in equilibrium with the walls, exactly the detailed-balance situation.

The patent's own answers to the exit problem (pp.17-19; see Section 4, row 9). Moving walls. If the walls move instead of the gas, the same ledger appears as a force: an atom whose energy E depends on wall spacing pushes on the walls with F = −dE/dz, so the actuator repays on reopening what was released on closing. At the patent's 1 eV per atom and 1 atm (n = 2.5×10²⁵ m⁻³ at 293 K), the extra pressure is n × E = 2.5×10²⁵ × 1.6×10⁻¹⁹ J ≈ 4×10⁶ Pa, about 40 atm; at the Casimir-Polder size (10⁻⁸ eV) it is 0.04 Pa [calc; example.py part F]. Either the shift is tiny or the drive faces a large extra load; "very little energy" cannot go with a large output. FIG. 8. The asymmetric absorber is a real attempt to make "local" release and "global" re-supply differ. It is the inventors' strongest design response, but no one has built it, and under thermal-equilibrium physics the absorber re-radiates what it absorbs; it would work only if the zero-point field is a non-thermal reservoir, the premise that rests on Cole and Puthoff (1993), which no reviewer has read.

Step E. Check the patent's own power arithmetic and the experiment

Patent arithmetic (it is correct given its assumption) [calc]: - Channels (10×10 cm plates, 5,000 strips, 0.1 μm gap, gas at 10 cm/s): 0.1 m × 10⁻⁷ m × 0.1 m/s × 2.69×10²⁵ m⁻³ × 5,000 = 1.34×10²⁰ transitions per second; × 1.602×10⁻¹⁹ J = 21.5 W per eV. Patent: 21-210 W. (matches) - Cube (1 cm³/s of gas, 500 cavity passes per atom): 1.34×10²² per second → 2,152 W per eV. Patent: 2,150-21,500 W. (matches)

The pumping check. The patent scales a published flow measurement (Roy et al.: 1 atm across 60 μm at 10 cm/s) to its 1 cm block at 1 cm/s: 101,325 Pa ÷ 10 × (10,000 μm / 60 μm) = 1.69×10⁶ Pa ≈ 16.7 atm. It then prints "a pressure of 1700 Pa, corresponding to 17 atmospheres" and "1.7 milliwatts" [read: page image, printed col. 12]. - 1700 Pa is 0.017 atm; 17 atm is 1.7×10⁶ Pa. They differ by 1,000. - Power = pressure × volume flow: 1.69×10⁶ Pa × 10⁻⁶ m³/s = 1.7 W, not 1.7 mW. A gentler isothermal-compression estimate, p₀Q ln(p/p₀) = 101,325 × 10⁻⁶ × ln 16.7, is 0.29 W. - The patent compares this with the 2.2-22 kW cube; against its preferred 1 cm² bonded-wafer device (1-10 W at 8 atm, for which no calculation is given) the corrected pumping power is 3-170% of output. Net gain is not shown even on the patent's own assumptions.

The 2012 experiment (Dmitriyeva and Moddel, the co-inventor's laboratory) [read: Physics Procedia 38]: He, Ar, N₂ and Xe flowed through polycarbonate membranes with 0.1-0.4 μm pores at about 5 sccm (standard cubic centimetres per minute) and 4 torr. - Prediction at 1 eV per atom: 5 sccm = 2.24×10¹⁸ atoms/s → 0.36 W [calc]. The paper says "milliwatts", which implies only about 0.3% of atoms counting, a factor the paper does not explain [arbiter]. - Detected: about 10⁻⁷ W at the detector, "thousands times" below prediction. Trends: strongest for helium and for uncoated plastic, the reverse of prediction ("We do not know the reason"). - The authors' controls against ordinary explanations [read: 2012 paper, section 3.2]: - Joule-Thomson cooling (gas cooling as it expands through a restriction): the membrane was replaced by a 12.5 μm Mylar film with one 3 mm hole. The lock-in phase was "180° off" from the membrane runs, "indicating cooling", so the membrane signal is not Joule-Thomson. Helium gave too small a signal to measure in this control, as expected from its near-zero Joule-Thomson coefficient (this is about the control, not the membranes). - Friction heating: frictional power should grow as the square of the flow (like I²R in a resistor), but the measured power grew linearly. The authors note this "does not automatically disqualify" friction, because the chamber exchanged heat with the room. The gas order (helium largest, xenon smallest) is also the reverse of what friction predicts, though heat conduction in the gas might account for it. - Adsorption heating: the signal did not follow the filters' surface areas (9.42, 18 and 12.56 cm² for 0.1, 0.2 and 0.4 μm pores). - Turbulence: flow below 2 cm/s gives a Reynolds number (the ratio that predicts turbulence) far too low. - Plastic beating gold: the authors suggest emissivity "could explain" it. Plastic radiates infrared with emissivity about 0.95, gold 0.01-0.1, so the same heat would show up far more strongly from uncoated polycarbonate. - Their conclusion: "None of these clearly fit the data, but it is possible that a combination of effects could", and zero-point extraction "remains a possible explanation". - The 2019 follow-up (Fig. 9) [read: Atoms 2019, p.11]: for helium through uncoated 0.1, 0.2 and 0.4 μm membranes, "the highest signal was registered from the 0.1 µm filter". The authors give two readings: the smaller pores "suppress ZPFs having frequencies that more closely match the atomic outer orbital frequencies", or "the smaller diameters produce a higher pressure drop and could give rise to more frictional heating". This is the one trend in the direction the cavity hypothesis predicts. Neither reading was tested with a matched-flow-resistance control. - Mechanical power in: the simple product 5 sccm × 4 torr is 4.4×10⁻⁵ W [calc]; the paper gives about 2×10⁻⁵ W. Its own conclusion: "the power out was less than the power in and there is no need to invoke an additional power source", while zero-point extraction "remains a possible explanation" [read: 2012 p.13, p.16].

Bottom line of the ledger. The inventors' starting numbers (Step A) are correct; their gap sizes are roughly right under their own model, 250 Å for hydrogen and 0.1 μm for the noble gases, though their cutoff rule is a factor of 2 generous and hydrogen's 27 eV light passes through metal (Step B); but the energy the cavity actually exchanges with an atom is 10⁻⁹ to 10⁻⁸ eV, not 1-10 eV (Step C); what comes out on entry goes back on exit (Step D); the later moving-wall and asymmetric-absorber designs do not escape that ledger on equilibrium physics (Step D); and the one measurement found far less than predicted, with power out below power in, a signal its authors could not fully explain by ordinary heating, and one trend (smallest pores strongest, 2019) in the predicted direction (Step E).

6. Evidence table

Verdicts are from arbiter.md.

Claim Tested? Result Replicated? Verdict
1. Atoms lose 1-10 eV entering a ~0.1 μm cavity ("Casimir-Lamb shift") Yes, four attempts, none neutral: Puthoff, Little and Ibison synchrotron test (2002), "so far without success" [web: arXiv:1012.5264]; Dmitriyeva and Moddel (2012) gas-flow infrared test; Moddel and Dmitriyeva (2019) added helium data; Henriques MSc, Coimbra (2014), "some evidence of radiation" for Xe, nothing above noise with pre-excited Xe, detector judged insensitive [web: https://estudogeral.uc.pt/handle/10316/28082] 2012: signal real but ~10⁻³ or less of prediction; gas and coating trends reversed; controls ruled out Joule-Thomson cooling (opposite phase), turbulence and adsorption, and friction did not fit cleanly (linear, not quadratic, in flow); authors: "None of these clearly fit the data". 2019: highest helium signal from the smallest (0.1 μm) pores, read either as a cavity effect or as more friction at the larger pressure drop; overall "tantalizing but ... inconclusive". Mainstream CP shift computed at 10⁻⁹-10⁻⁸ eV. No independent replication of an energy release Strong form: Refuted by calculation (vs cavity QED) and Tested, not supported. Weak sub-eV form: Never properly tested (tested by its proponents, who stopped; not dismissed without testing)
2. Re-absorption on exit gives continuous net power, "extracted locally, replenished globally" No net-power measurement; the only power balance (2012). The patent's FIG. 8 asymmetric absorber and its moving-wall designs (FIGS. 5-7) were never built or measured Power out < power in No Strong form, flowing gas (symmetric or FIG. 8): Refuted by calculation under thermal-equilibrium physics (conservative potential, detailed balance), moderate confidence; the 2012 power balance Tested, not supported; FIG. 8 itself Never properly tested. Moving-wall forms: Refuted by calculation (conservative force over a closed cycle; higher confidence). Weak form (a non-equilibrium flow effect drawing on a non-thermal zero-point reservoir): Never properly tested
3. SED explains atomic stability; the hydrogen balance holds for all atoms SED hydrogen tested by simulation only (Cole and Zou 2003-04: ground-state-like for a time; Nieuwenhuizen and Liska 2015: self-ionisation persists) Mixed for hydrogen; no theory for many-electron atoms Simulations by several groups SED hydrogen: Historically superseded but instructive. All-atoms extension: Never properly tested
4. Patent power figures (21-210 W; 2150-21500 W; 1-10 W) and 1.7 mW pumping No device built or measured Output arithmetic reproduces from the assumed 1-10 eV; pumping is 1.7 W (or ~0.3 W), not 1.7 mW n/a Pumping: Internally inconsistent (1700 Pa vs 17 atm). Outputs: correct as arithmetic, conditional on claim 1
5. Forward (1984) foil-stack "vacuum-fluctuation battery" Casimir force measured (Lamoreaux 1997; Mohideen and Roy 1998) [memory, high]; device never built (no source found) Equations correct (Eq. 2 drops a sign; OCR "980" is 480) Force: yes, many groups Force: Established. Device as energy store: Plausible, untested. As a net source over a cycle: Refuted by calculation (Forward does not claim it). Metal values at 1-20 nm: Never properly tested (as of 1984)

The record after 2012 (absence of evidence). The Colorado gas-flow work stops after the 2012 paper; the 2019 paper reuses 2010-12 data plus one helium run. Funding on record: DARPA via SPAWAR grant N66001-06-1-2026 (from 2006), CU proof-of-concept money conditional on milestones, about $200,000 private money by 2009 with about $10 million sought, a HUB Lab contract to Jovion (2010-12) [web: Investigator notes in research/]. Jovion's website (© 2023) has an empty "Progress" link; Hathaway Research International lists the project with no results [web: Investigator]. Google Patents shows the patent "Active" to 2026-11-30 [web: https://patents.google.com/patent/US7379286B2/en]; an unresolved "2011-12" legal event may or may not be a fee lapse. The arbiter weighs five explanations: (a) the effect did not hold up and was dropped (supported by out < in, reversed trends, Haisch's 2009 caution, the 2019 closing remark that fundamental constraints may preclude extraction); (b) funding ran out (the $10M ask with no visible award); (c) trade secrecy (no evidence beyond silence; the published papers are candid, and Moddel states he plays no active role in Jovion); (d) the effort moved to Moddel's metal-insulator-metal (MIM) Casimir-cavity devices (documented: Phys. Rev. Research 3, L022007, 2021; patent family US 11,133,758 with a projected, not measured, "up to 250 W" per 10×10 cm array); (e) the ambiguous heating artefacts made a clean follow-up too costly. The arbiter judges (a), (b) and (d) together fit best, and found no evidence of suppression. Records that would decide: USPTO maintenance-fee and assignment history, the DTIC/DARPA final report, Jovion filings, CU technology-transfer files.

Other material kept in the record (whatever the verdict): Moddel et al. 2021, Phys. Rev. Research 3, L022007 (a mainstream American Physical Society journal), reporting observed conductance increases with thinner Casimir cavities and "anomalous offsets in the current and voltage" in metal-insulator-metal devices; a different mechanism from this patent, but a measured anomaly by the co-inventor, beside the projected (not measured) 250 W above [web: https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.L022007, via Investigator]; a 2009 talk at the Los Alamos National Laboratory (LANL) Center for Nonlinear Studies (CNLS) "Workshop on New Frontiers in Casimir Force Control", Santa Fe (abstract book saved in research/files/, image-only, unread) [web: https://cnls.lanl.gov/casimir/proceedings001.PDF, via Investigator]; the patent's priority date, 2004-09-27, from a provisional application not in the folder [web: Google Patents, via Investigator]; the STAIF-2006 (Space Technology and Applications International Forum) review of experimental concepts for studying the quantum vacuum, Davis, Teofilo, Haisch, Puthoff and others, cited as ref. [3] in the 2012 paper and probably describing the planned experiment (the Investigator's reading; not read) [web: http://www.calphysics.org, via Investigator]; the Davis-Puthoff AIAA (American Institute of Aeronautics and Astronautics) book chapter linked from Jovion's zero-point page, which reproduces Davis and Puthoff's "On Extracting Energy from the Quantum Vacuum" (unread) [web: https://www.jovion.com/zpe/, via Investigator]; Dmitriyeva's 2012 PhD thesis, which ran the zero-point test alongside low-energy nuclear reactions (LENR) work on hydrogen loading into palladium, in the same lab with the same calorimetric skills, and the 2019 paper's acknowledgement of funding from Coolescence, a LENR company [web: colorado.edu thesis PDF, via Investigator]; the Jordan Maclay citation (Section 4, row 4; the applicants' characterisation); Haisch's calphysics.org caveats; Cole and Puthoff (1993), "Extracting energy and heat from the vacuum", Phys. Rev. E 48, 1562 (the inventors' cited thermodynamic basis; unread by all reviewers); third-party patents citing Haisch-Moddel (US20190207537A1, US20180059704A1, US20230208321A1); a 2009 blog commenter's link to BlackLight Power "hydrino" claims (the commenter's characterisation, not the inventors'); Kotov et al. (2025), a mainstream cavity-modified ground-state theory citing Moddel et al. 2021 (unread; its stance is unknown).

7. What a learner should take away

Solid. - Zero-point energy, the Casimir force and cavity-modified atomic energies and decay rates are real, measured physics. The inventors' starting point is not fantasy. - The SED numbers in the patent (455 Å, 6.6×10¹⁵ Hz, Larmor balance at the Bohr orbit, angular momentum ħ) are correct, and the SED picture is a genuine, instructive attempt to get quantum results from classical physics plus a random field. - Forward's equations and his conservative-field, battery framing are sound.

Wrong, and why it is instructive. - Size. The 1-10 eV figure is assumed from the 13.6 eV binding energy, not calculated. The calculated cavity shift is a hundred-millionth of that. Lesson: when a paper says "we assume" before its key number, find out what the theory actually gives; here a one-line formula settles it. - The cutoff rule. Between ideal mirrors the longest wavelength that fits is 2d, not d; the patent uses d without saying so, a factor of 2 generous. And a gap only removes a mode if its walls actually reflect at that wavelength: no metal reflects hydrogen's 27 eV light. Lesson: picture which standing waves fit in the box, then check that the box is a box at that wavelength. (The patent's gap sizes are otherwise roughly right; its wording "this wavelength and shorter" is loose, not its numbers.) - The exit. A position-dependent energy is a potential; a closed loop returns zero. This is the same logic that defeats every static-magnet and static-Casimir perpetual-motion scheme, and Forward stated it plainly in 1984. Lesson: always ask what happens on the return stroke. - Pumping. A 1000× unit slip (1700 Pa vs 17 atm) flattered the output-to-input ratio. Lesson: carry units through every line.

Genuinely open (small, but open). - What produced the 2012 infrared signal, with helium strongest and plastic beating gold? Ordinary heating is the leading candidate, and emissivity may explain plastic over gold (the authors' suggestion), but the authors' own controls ruled out Joule-Thomson cooling, turbulence and adsorption, and friction did not fit cleanly. The 2019 result that the smallest pores gave the most helium signal fits either a cavity effect or more friction. The pore-size scan with matched flow resistance that would decide was never done. - Whether the FIG. 8 asymmetric-absorber design does anything: nobody has built it. - Whether some sub-eV, non-equilibrium flow effect exists in nanopores: never properly tested. - What Cole and Puthoff (1993) and Cetto and de la Peña (1988) derive in full, and how their assumptions compare with the patent's. - Why the gas-flow line went silent, and what the DARPA final report says.

8. Check yourself

  1. A gap between two ideal mirrors is 0.1 μm wide. What is the longest wavelength of light that can form a standing wave straight across it? Is a 45.6 nm wave excluded?
  2. Using U = 3ħc α_vol/(8πz⁴), estimate the Casimir-Polder shift of a xenon atom (α_vol = 4.04×10⁻³⁰ m³) 25 nm from one wall. How many times smaller is it than 1 eV?
  3. An atom's energy inside a gap is lower than outside by ΔU. Explain in two sentences why letting gas flow in and out of the gap at one temperature gives no net heat, and name the principle.
  4. The patent says pumping 1 cm³/s against 17 atm costs 1.7 mW. Recompute it. What went wrong?
  5. Forward's foil battery really does turn Casimir attraction into electrical energy. Why is it a battery rather than a source?

9. Further reading

Mainstream. - D. J. Griffiths, Introduction to Electrodynamics (radiation and the Larmor formula, ch. 11) and Introduction to Quantum Mechanics (harmonic oscillator, hydrogen). - P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic Press, 1994): zero-point energy, Lamb shift, Casimir effect, and a fair discussion of SED. The patent itself cites it [read: printed col. 5]. - S. K. Lamoreaux, "Demonstration of the Casimir force in the 0.6 to 6 μm range", Phys. Rev. Lett. 78, 5 (1997) [memory, high]; U. Mohideen and A. Roy, Phys. Rev. Lett. 81, 4549 (1998) [memory, high]. - C. I. Sukenik et al., "Measurement of the Casimir-Polder force", Phys. Rev. Lett. 70, 560 (1993) [web: https://digitalcommons.odu.edu/physics_fac_pubs/7/]. - D. V. Schroeder, An Introduction to Thermal Physics (second law, detailed balance). - L. de la Peña and A. M. Cetto, The Quantum Dice: An Introduction to Stochastic Electrodynamics (Kluwer, 1996) [memory, high]: the standard book on SED, by researchers within the field. - T. M. Nieuwenhuizen and M. T. P. Liska, "Simulation of the hydrogen ground state in stochastic electrodynamics-2" (2015) [web: https://arxiv.org/abs/1506.06787].

The inventors and related work. - B. Haisch and G. Moddel, US Patent 7,379,286 B2 (2008); project folder. - B. Haisch and G. Moddel, "Indirect extraction of zero-point energy from the quantum vacuum: Patent 7,379,286" (conference abstract, probably SSE 2010; date inferred by the Investigator); project folder. - O. Dmitriyeva and G. Moddel, "Test of zero-point energy emission from gases flowing through Casimir cavities", Physics Procedia 38, 8-17 (2012) [web: https://www.colorado.edu/faculty/moddel/media/59; copy in research/files/]. - G. Moddel and O. Dmitriyeva, "Extraction of zero-point energy from the vacuum: assessment of stochastic electrodynamics-based approach as compared to other methods", Atoms 7, 51 (2019) [copy in research/files/]. - B. Haisch, zero-point energy pages at http://www.calphysics.org/zpe.html [web]. - D. C. Cole and H. E. Puthoff, "Extracting energy and heat from the vacuum", Phys. Rev. E 48, 1562 (1993) [memory, high for the citation]. - H. E. Puthoff, "Ground state of hydrogen as a zero-point-fluctuation-determined state", Phys. Rev. D 35, 3266 (1987) [memory, high]. - R. L. Forward, Phys. Rev. B 30, 1700 (1984); project folder.

Answers

  1. The longest wavelength is 2d = 200 nm. A 45.6 nm wave is shorter than that and fits (many half-wavelengths across the gap), so it is not excluded. Excluding it needs d ≤ 22.8 nm, and walls that reflect 27 eV light, which metals do not. (The patent itself does not use 0.1 μm for hydrogen: it proposes d = 250 Å, close to the 228 Å needed, with its own looser cutoff rule λ = d.)

  2. z = 2.5×10⁻⁸ m, so z⁴ = 3.91×10⁻³¹ m⁴. U = 3 × 3.162×10⁻²⁶ J·m × 4.04×10⁻³⁰ m³ / (8π × 3.91×10⁻³¹ m⁴) = 3.83×10⁻⁵⁵ / 9.82×10⁻³⁰ = 3.9×10⁻²⁶ J ≈ 2.4×10⁻⁷ eV. That is about 4 million times smaller than 1 eV. (The retarded formula is only roughly valid this close; a non-retarded estimate gives a similar order.)

  3. If the energy depends only on position, it is a potential energy, and the energy released entering is exactly the energy needed to leave, so a closed in-out cycle does zero net work. At one temperature each crossing inward is matched by a crossing outward at the same rate (detailed balance), so no net heat flows; this is the second law of thermodynamics at the microscopic level.

  4. 17 atm = 17 × 101,325 Pa ≈ 1.7×10⁶ Pa; × 10⁻⁶ m³/s = 1.7 W. The patent wrote 1700 Pa (0.017 atm) instead of 1700 kPa, a factor of 1000. Against the patent's preferred 1-10 W device, 1.7 W (or 0.3 W for isothermal compression) is not negligible.

  5. The Casimir force is conservative: its energy depends only on the plate spacing. Letting the foils collapse releases the energy that was stored when the foils were made (or last pushed apart); pushing them apart again costs at least that much. Forward's own hydroelectric analogy says this: the dam runs on water the sun lifted.