To build on the above premise for my own theory of how energy is extracted from these fractional state hydrogen atoms in a cavity or catalyst, I assume a relativistic solution for fractional quantum states inspired by Jan Naudts paper (5 August 2005). "On the hydrino state of the relativistic hydrogen atom". First however I must digress,The twin travelling near C would perceive the other twin and all physical properties back on earth as occurring at a rate of multiple seconds per second. Additionally Lorentz contraction of objects travelling at significantfractions of light speedcauses the objects observed by the travellingtwin to appear smaller (actuallyboth twins would observe contraction as the effect is due to "distance" on the time axis). Fractional quantum state hydrogenexhibits increased reaction rate and contraction and is based on relativistic math suggesting something similar to an event horizon should be expected. The argument becomes whether a Casimir cavity can create "equivalence" where inside the cavity becomes a protected harbor that views outside the cavity just as we view an event horizon. An observer outside the cavity defines our 1 second per second reference frame to measure differences in "equivalent" acceleration rate between an event horizon or a Casimir cavity. I am proposing the rate inside a Casimir cavity from our perspective becomes multiple seconds per second inverse to the Casimir restriction of longer wavelength vacuum fluctuations. This is referred to as "up conversion" by QED and causes the ratio of short to long vacuum fluctuations inside a Casimir cavity to increase as the distance between plates is reduced. By extension I would predict the ratio of short to long vacuum fluctuations approaching an event horizon to decrease.
Like the twin approaching C we see matter inside the cavity occurring at multiple seconds per second because we are greatly accelerated by a default time rate (or ratio of vacuum flux) relative to the protected harbor inside the cavity. The difference in rate results in time dilation and Lorentz contraction. The fractional quantum state atom remains stationary to an observer outside the cavity in XYZ coordinates but not time. the outside of the cavity has equivalent acceleration only a fraction of an event horizon but it still far exceeds the damped acceleration caused inside the cavity by Casimir plates. This creates a delta in acceleration through equivalence with the unlikely property that the observer and the effect can be spatially local and stationary to each other separated by only Casimir plates as opposed to huge gravity wells needed for an event horizon. I am proposing that the change in ratio of short to long vacuum fluctuations which defines a Casimir cavity is evidence for this difference in equivalent acceleration and that we accept time dilation and contraction inside a Casimir exclusion field just like we accept it in an event horizon.
The Mills theory, Haisch-Moddel patent and my own theory are all quite similar in requiring monatomic gas into a rigid cavity and then diverge in their explanation of the excess heat. My theory for excess heat diverges when monatomic gas contracts to fractional quantum states and starts to permeate deeper into smaller geometry cavities than the molecular gas. The smaller local geometry further contracts the atom allowing even deeper penetration, it contracts so much further than the molecular gas when an appropriate rigid cavity material is selected that I ignore the molecular gas except as a reservoir for disassociating atoms. Like a Pd membrane in reverse, a fractional state molecule that forms from these tiny atoms in these tiny cavities or lattices becomes confined, essentially trapped inside a membrane. Opposing forces that normally result in catalytic action can now be leveraged to produce heat. Heat and gas law provide motion to the fractional state molecule within the confines of the membrane which varies the Casimir force on the molecule. The force exerted on the atoms to change fractional state is converted by the molecule to break the covalent bond which pushes the atoms out of confinement long enough to change fractional states before reforming a new fractional molecule, giving off a photon and becoming confined once again. This cycle continues until the atoms escape or the membrane /cavity melts down.
To be clear I don't believe a fractional quantum state actually allows the orbital to ever get any closer to the nucleus from a 4D perspective. Lorentz contraction is relativistic and allows the 3D perspective to fall below ground state while keeping the minimal displacement on the time axis. Bourgoins' 2007 paper inverse Quantum Mechanics of the Hydrogen Atom seem to prove the 137 fractional states claimed by Mills but it is a relativistic solution.
XYZT coordinates of orbital to nucleus no linear motion is arbitrarily [0,0,Bohr radius, 0] to [0,0,0,0]
XYZT coordinates of orbital to nucleus linear motion approaching C is [0,0,0,Bohr radius] to [0,0,0,0]
Casimir cavities create a "gravity Hill" vs. "gravity Well"
1. A 2005 math paper by Jan Naudts "On the hydrino state of the relativistic hydrogen atom" contends the controversy over fractional quantum states overlooks relativistic effects inside a Casimir cavity.
2. A 2007 paper by Ron Bourgoin, "Inverse Quantum Mechanics of the Hydrogen Atom : A General Solution" confirms 137 fractional quantum states claimed by Mills.
3. I propose the orbital appears to collapse spatially below Bohr radius because the "displacement" to the nucleus has been partially converted to temporal units from our perspective. The fractional quantum state only exists from our perspective outside the cavity, like the relativistic "Twin Paradox" it is unphysical to think the twins are actually shrinking or accelerating relative to their own frame. The claims that the hydrino are "unphysical" are absolutely correct. They exist as hydrogen relative to their own frame but exhibit real effects through time dilation and Lorentz contraction just like the returning twin when they exit the cavity.
4. Prevenslik work replicating Casimir effect through "up-conversion" indicates nature has method to convert IR >> VUV via conservation of energy. I posit this method is relativistic based on 1-3 above and therefore all frequencies (entire spectrum including virtual photons) are translated by the exclusion field to a different frame such that they "appear" up-converted from our perspective.
5. Christian Beck papers, Measureability of vacuum fluctuations and dark energy and  Electromagnetic dark energy propose virtual photons below 1.7Thz more gravitationally active than those above. I posit therefore the ratio of short to long virtual photon wavelengths (>1.7Thz)/(<1.7Thz) decreases approaching event horizon to reflect a higher population of virtual photons below 1.7thz with increasing gravitational activity.
6. I postulate my relativistic "up-conversion" in a Casimir cavity changes this ratio of virtual photons (>1.7Thz)/(<1.7Thz) in the opposite direction creating a gravity "Hill" or lack of gravitationally active virtual photons as opposed to a gravity "Well". The "Hill" is less gravitationally active making space outside the cavity appear more active in the same way we perceive an event horizon. This creates an opportunity for "equivalence" with an abrupt boundary without the typical astronomical distances or crushing gravity. The hydrogen inside the cavity is nearly stationary relative to hydrogen outside in the XYZ coordinates but not T!