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[Let's start with the bad news, and lots of it. The only suitable reflector for circa 100 nm-gapped Casimatter fabrication (which is as small as can be optically diddled given dielectric electronic bandgaps) is vacuum-deposited aluminum with a 60:40 MgF2:LiF alloy dielectric, as below. When you integrate the Casimir force expression over the gap distance (which gives energy: force through a distance) and multiply by the total surface area contained within one cubic centimeter of Casimatter (go ahead, it's high school calculus and algebra)... you get nothing - less than a part per quadrillion mass-equivalent relative exclusion. Casimatter is crap, even in theory. Bummer. All these fancy words sum to nothing, just like Official Truth about the Ozone Hole.]
Acceleration versus applied force is inertial mass; acceleration in a gravitational field is gravitational mass. The Equivalence Principle asserts the masses are indistinguishable. General Relativity posits gravitation as minimal paths (geodesics) traced along the shape of space, but neglects inertia. Bernhard Haisch, Hal Puthoff, Alfonso Rueda, and other stochastic electrodynamics fans propose inertia's origin http://www.jse.com/haisch/zpf.html The quantum vacuum has zero point fluctuations. Accelerating within ZPF induces proportional resistance - inertia (Phys. Rev. A 49 678 (1994), Science 263(5147) 612 (1994)).
Classical vacuum contains neither mass nor energy. Heisenberg Uncertainty Principle in the quantum vacuum demands the product of uncertainties of energy and time be a small but finite number. The classical harmonic oscillator includes an uncertainty of 0.5 photon/allowed electromagnetic mode. Where do vacuum ZPF hide?
ZPF explain the Lamb shift, electron anomalous g-factor, Rabi oscillations (single atom laser), and Casimir effect. ZPF do not appear Doppler shifted and are Lorenz-invariant: intensity varies as the cube of ZPF frequency (or inverse cube of its wavelength). The grain of space appears near 10-33 cm, the Planck length. Integrating intensity over all possible frequencies gives 1094 gm/cm3. Nuclear density is 2x1014 gm/cm3.
Accelerating within ZPF may elicit inertia. Screening ZPF may separate inertial and gravitational masses if gravity is not ZPF- related. If ZPF mediates both the Equivalence Principle prevails (Phys. Rev. A 39 2333 (1989), Ibid. 47 3454 (1993));
(pi)c5 2(pi)(lambda)2c3
Newton's G = ---------------- = -------------------
(h-bar)(omega)2 h
(2)(3.14159)([(1.61605x10-33 cm)2](2.99792x1010 cm/sec)3
= --------------------------------------------------------------
(6.6260755x10-27 erg-sec)
G = 6.672571x10-8 erg-cm/g2 (ZPG model - empirically incorrect)
G = 6.674215x10-8 erg-cm/g2 (quadrupole torsion balance)
Phys. Rev. Lett. 85(14) 2869 (2000)
Science 288(5468) 944 (2000)
G = 6.67407x10-8 erg-cm/g2 (mass balance)
Phys. Rev. Lett. 89 161102 (2002)
where c=lightspeed, (h-bar) is Planck's constant (6.6260755x10-27 erg-sec) divided by 2(pi), and omega is the frequency of the Planck wavelength (lambda), 1.61605x10-33 cm. There is a debate over the presence of an additional factor of pi which, as the Planck constant is expressed in terms of G, would rescale the Planck length to 9.1176x10-34, a factor of sqrt(pi) smaller.
Call ZPF-depleted matter "Casimatter." If unified, Casimatter's measured mass and weight still would be too small for the atoms contained. Differential mass measurement before and after thermal (700 C for aluminum) or other Casimatter disruption is problematic. Chemical determination is insufficiently sensitive.
If mass and weight are not unified, can the Equivalence Principle be finessed? Mass can fall too slowly - feathers falling in air. Mass cannot free fall in vacuum too quickly, maybe.
ZPF is radiation, as in photons and waves. There is a node at a perfectly electrically conductive reflective surface. Given two plane parallel grounded metal mirrors in close apposition (narrow gap) without an optically absorbing medium between them,
1) Only integral multiples of half wavelengths are resonantly allowed for radiation with half wavelengths equal to the gap or smaller. Longer wavelengths are absolutely excluded (etalon - the more reflections the tighter the specification to 20% of all shorter wavelengths also excluded), and
2) Radiation whose half wavelength exceeds the gap is excluded.
Unaltered ZPF outside the gap pushes in, attenuated ZPF in the gap pushes out. The plates appear to attract varying inversely with the fourth power of their separation - the Casimir effect.
H.B.G. Casimir, Proc. Kon. Ned. Akad. Wetensch. B51 793 (1948)
Contemporary Physics 33(5) 313 (1992)
Sov. Phys.-Dokl. 12(11) 1040 (1968)
Proc. Royal Soc. A 312 435 (1969)
Ann. Phys. (NY) 56 474 (1970)
Phys. Rev. E 48(2) 1562 (1993)
Edward G. Harris, A Pedestrian Approach to Quantum Field
Theory. Wiley-Interscience, NY 1972, pp. 108-9
Measured to within 5% of theory, Phys. Rev. Lett. 78 5 (1996)
Phys. Rev. Lett. 81 4549 (1998)
Measured to within 1% of theory, Phys. Rev. A 59(5) R3149 (1999)
Imperfect mirrors, Phys. Rev. Lett. 81 3815 (1998)
Temperature above 0 K, Phys. Rev. A 57 1870 (1998)
Curved mirrors, Amer. J. Physics 65 381 (1997))
Spherical dielectrics, J. Phys. A: Math. Gen. 32 535 (1999)
Hellmann-Feynman model, Int. J. Chem. 7 1 (2004)
With a ZPF wavelength limit of 10-33 centimeter (remember - intensity varies as the inverse CUBE of the wavelength!) and a practical reflection limit of around 10-5 cm gap for aluminum at its plasmon frequency cutoff, how much eldritch squeeze obtains under ideal conditions?
A(pi)2(h-bar)c
Fc = ---------------
(240)a4
where A is area; "a" is the transparent separation of parallel flat 100% conductive 100% reflective grounded plates at 0 K; "h-bar" is Planck's constant divided by 2(pi); "c" is lightspeed.
If "a" is measured in micrometers the Casimir force is (0.01300 dyne/cm2)/a4 or (1.3x10-7 newton/cm2)/a4. An average apple weighs a newton (coincidence?). A 500 nm (wavelength of green light) gap gives 0.208 dyne/cm2. A 100 nm gap (extreme ultraviolet approaching soft x-ray) gives 130 dyne/cm2 (a milli-apple/cm2). That is 33 times the weight of aluminum foil/cm2.
Correction factors obtain for two dielectric plates (dd) or one metal and one dielectric (md) plate (where e is the dielectric constant; Phys. Rev. B. 30(4) 1700 (1984), JETP 2 73 (1956)):
Fc(e-1)2 Fc(e-1)
Fdd = -----------f(dd) Fmd = ---------f(md)
(e+1)2 (e+1)
e <3.5 4 5 8 10 25 50 infinity
----------------------------------------------------------
f(dd) 0.35 0.38 0.38 0.4 0.43 0.5 0.6 1.0
f(md) 0.48 0.5 0.52 0.55 0.58 0.7 0.8 1.0
How can bulk matter exclude ZPF? Aluminum, density 2.7 g/cm3, is the only metal amply reflecting deep into the ultraviolet, 93% between 100 and 120 nm. Magnesium fluoride is a vacuum-deposited dielectric transparent in the deep UV, 80% transmittance at 115 nm (http://www.crystran.co.uk/). Go much deeper (10.9 eV; J. Appl. Phys. 38 1701 (1967)) and photons are energetic enough to be absorbed by exciting electronic transitions. Magnesium fluoride has density 3.177 g/cm3 and a refractive index of 1.63 at 121 nm. Imagine a flat, wide ring within a two sector vacuum deposition chamber. Resistance heating deposits 10 nm/sec Al and 2 nm/sec MgF2. High frequency magnetron sputtering is much faster. A 30 second/paired layer deposition cycle with excellent thickness control is entirely nominal.
One sector continuously deposits 70 nanometers of aluminum onto a rotating ring (AIP Handbook 3rd Ed., Section 6, for 99+% of theoretical reflectance vs transmission), promptly covered by 37 nanometers of magnesium fluoride in the other sector in a never ending bifilar spiral. The optical path between aluminum mirrors is the gap (37 nm) times refractive index (1.63) which is 60.3 nm or 1/2(121 nm). Deposited thin film dielectrics tend to be slightly porous with slightly lower refractive indices than bulk material. Allow a safety margin for the 115 nm cutoff. Dice the ring, release the backing, and hold sheets of Casimatter. Viewed broadside Casimatter is an overcoated aluminum mirror (J. Opt. Sci. Am. 51 719,913 (1961), ibid. 53 620 (1963)).
Casimatter, average density 2.86 g/cm3, is 38 wt-% ZPF-depleted magnesium fluoride. A centimeter thickness needs 93,460 layers whose summed noise (dirt, non-ideal deposition) ruins flatness. Ten paired layers deposited/minute is ten days of continuous running. A human hair is 60 microns in diameter. Hair-thick self-supporting if fragile Casimatter plates need 560 paired layers. 560 is a large number, but not impossible in running time (five hours at a leisurely pace) or physical structure.
Lithium fluoride goes to 110 nm with refractive index 1.777 and density 2.639 g/cm3 but is hygroscopic, degrading in humidity. Vacuum deposit alternating layers of 31 nm LiF and 70 nm aluminum to obtain Casimatter of average density 2.68 of which 30 wt-% is ZPF-depleted lithium fluoride. A hair-thickness plate requires 595 paired layers with 40% more effect than the 121 nm etalon.
The Casimatter composite suffers from mismatch of linear thermal coefficients of expansion of its components. As newly fabricated Casimatter cools aluminum layers will shear deform from unequal contraction versus dielectric layers:
LINEAR SHEAR ELASTIC
DENSITY RI EXPANSION MODULUS LIMIT
COMPONENT g/cm3 121 nm x106/K GPa GPa
========================================================
Aluminum 2.70 23.1 24 0.13
MgF2 3.177 1.630 13.7 55 50.
LiF 2.639 1.624 37.0 55 11.
60:40 alloy 2.962 1.628 23.0
Rhenium 21.04 6.7 178
Does a miscible alloy of 60:40 MgF2:LiF exist and resist phase separation to give a thermal expansion mismatch of only 0.1x10-6/degree versus aluminum? Does it retain transparency in the extreme ultraviolet? It is a minor vacuum deposition chore to synthesize film alloy (bulk alloy crystallized via Stockbarger directional solidification is unlikely) and perform measurements of refractive index, transmission/wavelength, and thermal linear expansion coefficient. Given weight-averaged refractive indices for 121 nm (1.628) and densities (2.962), 37 nm of fluoride alloy alternating with 70 nm of aluminum give Casimatter of average density 2.79 gm/cm3of which 37 wt-% is ZPF-depleted fluoride alloy. A hair-thickness plate requires 560 paired layers.
1) Thinning aluminum barriers with the next layer(s) taking up the leakage reduces the net Casimir Effect faster than it increases the ZPF-excluded mass ratio.
2) Extremely small optical gap fabrication is insufficient. 55 nm aluminum is transparent (refractive index of 0.753, absorption coefficient of 0.021, reflectance of 0.02) but rhenium is reflective (refractive index of 0.55, absorption coefficient of 0.97, reflectance of 0.34). 80 nm of rhenium alternating with 36 nm of aluminum give Casimatter of average density 13.29 gm/cm3 of which 5.5 wt-% is ZPF-depleted aluminum. With an etalon gap ratio of 54/121 = 0.446 the ZPF exclusion will be 25.2 times as great for an overall bulk enhancement factor of 3.7 versus aluminum plus fluoride alloy, less reflectance and transmittance inefficiencies which kill the idea. Mismatched linear thermal coefficients of expansion of aluminum and rhenium compromise the physical integrity of 520 bifilar layers summing to 60 microns in thickness and square centimeters in extent.
3) Use aluminum as transparent spacer for a 10 nm gap and 30 nm of fluoride alloy as dielectric walls to give Casimatter of average density 2.90 of which 23 wt-% is ZPF-depleted aluminum. 1500 bifilar layers sum to a 60 micron thickness. The gap would be 1/12 as large: (.23/.37)(124)[(5.912)/(7.912)](.39) for 2800 times the ZPF exclusion versus the conservative case, depending upon how thick a dielectric continuum constitutes a "wall." Risky.
Given Casimatter plates thick as a human hair and a couple of centimeters on a side, expected potential divergence of inertial and gravitational masses will be very small - parts-per-billion or less. Two sensitive analytical techniques are appropriate.
Fashion Casimatter into hollow corner cubes and drop them in a vacuum chamber as one leg of an interferometer. Computer counts of fringe shifts/time derives acceleration. Alternate with drops of ordinary hollow corner cubes of the same dimensions and mass. Dr. James Faller of the University of Colorado has gravimeters of surpassing sensitivity and precision:
"Continuous gravity observations using Joint Institute for Laboratory Astrophysics absolute gravimeters" J. Geophys. Res. 97 12437 (1992), J. Geophys. Res. 98(B3) 4619 (1993) A hundred JILA installations measure gravity worldwide to a few microgals (10-8meter/sec2; 1 gee = 980 microgals) precision.
Alternatively, Play gravitation (gravitational mass) against centripetal force (inertial mass) in an Eotvos balance,
Eotvos experiment Ann. Physik. 68 11 (1922)
"Eotvos Balance" Am. J. Phys. 27(5) 336 (1959)
Scientific American 205(6) 84 (1961)
Phys. Rev. Lett. 59(6) 609 (1987)
Nature 347 261 (1990)
Phys. Rev. Lett. 78 2523 (1997)
What alternative view is possible? Blackbody radiation arises from charged quantum oscillators in walls (Planck) or photon gas statistics in cavities (Bose). The same answer obtains either way, but which one is the correct interpretation? Yes.
The Feynman-Hellman theorem, Phys. Rev. 56 340 (1939) and Int. J. Chem. 7 1 (2004), asserts that two reflective conductive plates' proximity causes redistribution of charge. The force between the plates is classical, acting between redistributed charges. The Casimir effect is modeled as two enormous inert atoms (bound plasmas) inducing reciprocal polarization and experiencing van der Waals attraction from an integrated Lennard-Jones potential. No ZPF are required.
Casimir energy between two points is the free energy of two quantized fluctuating dipole moments coupled by dipole-dipole radiation interaction (zero frequency being static interaction). This treatment exactly scales to the parallel dielectric plate case (Physica A 153 420 (1988), ibid. 259 165 (1998)).
Casimatter could be an ice pick driven by a sledgehammer, or just a big water balloon. It depends whether you are funded to look at Casimatter or engineer something with it.
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