Memorandum for the Record
Subject: The Conquest of Space-Time by The Metric Engineers In Their Unconventional Flying Objects From The World of Tomorrow.
http://www.skycaptain.com/
From: Sky Captain Smiling Jack Flash

Theorem: The observed QED Casimir force is NOT a zero point energy effect at all! It is an extremely weak Van Der Waals force only. The observed Casimir force is not important for metric engineering. I repeat. Now here this, Captain on board: The observed Casimir force is not important for the metric engineering of warp, wormhole and weapon. There is no zero point force here at all. The zero point force manifests in an entirely different way. All previous papers by everyone who have made the ZPF Casimir force claim based on mode-counting have made a mathematical error illustrated explicitly below.

The fallacy in Hal Puthoff's mode-counting argument is that whilst the outside of the plates do indeed have more modes that fit the boundary conditions than do the inside of the plates, NEVERTHELESS, the total incoherent completely random zero point energy density on both sides of the plates is identical with identical pressures, no matter what w is, because the additional EXTENSIVE space on the outside cancels the additional total energy EXTENSIVE effect of the additional outside modes on the INTENSIVE ZPF energy density. That is, the EXTENSIVE TOTAL ZPF energy scales identically to the total available space such that the ZPF energy density remains invariant! I show this rigorously for the 1D case that should describe the symmetry of ideal infinite flat parallel plates where only the distance perpendicular to the plates should affect the final result.

On Sept 2, 2004 Hal Puthoff challenged Sky Captain Jack to a Duel of Wits:

"It would seem that you insist that instead the w = -1 repulsive force is the important force on this level, previously neglected, so please show how to derive the attractive Casimir force by your counter-claim with its opposite-sign vacuum force."

BTW I never said that the direct gravity of ZPF had anything at all to do with the QED Casimir force, which is merely a very weak negligible Van Der Waal's force having nothing whatsoever to do with zero point energy.

OK, imagine a long closed EMPTY conducting uncharged cylinder with a movable piston inside it that partitions it into two volumes V(A) and V(B) with V(A) << V(B). There are more photon cavity modes that can fit inside the large V(B) than the small V(A). Therefore the sum of the TOTAL virtual photon zero point energies of hf/2 per mode is larger for V(B) than that of V(A). Of course, the REAL issue is the relative virtual photon energy densities. Let's make the problem even simpler by considering only one dimension of space so think of 1D lengths L rather than 3D volumes V. Imagine there is a short wave cut-off "a". We must fit the waves to obey the boundary conditions. The longest waves in each are 2L(A) and 2L(B) where L(A) << L(B).

I make the usual "mainstream" assumption of ZERO VACUUM COHERENCE in the model below.

The allowed standing wave cavity modes of the electromagnetic field oscillators have reciprocal wavelength "wave numbers" N(A)pi/2L(A) and N(B)pi/2L(B) respectively where N(A) and N(B) are positive integers. N(A)max ~ L(A)/a and N(B)max ~ L(B)/a in sense of "nearest integer to". This is the essentially the same as the musical harmonics on Orpheus's Lute studied by my Pythagorean ancestors who migrated to Ancient Greece from what is now Palestine/Israel.

However, I will now rigorously mathematically prove that the mode density in this 1D case is constant.

So we have total zero point energy in L(A) is ~ (1/2)hcSum npi/2L(A) from n = 1 to L(A)/a.

Note sum of first N integers is N(N + 1)/2

Therefore, the total zero point energy on the finite line segment L(A or B) is, assuming L(A or B) >> a

ZPE(A or B) ~ (1/2)(pihc/4L(A or B)){[L(A or B)/a][L(A or B)/a + 1] ~ (pi/8)(hc/a)(L/a)

Therefore the 1D Zero Point Energy Density is CONSTANT! That is divide by L

1D ZPE Density ~ (pi/8)(hc/a^2)

Note that this 1D "string" has a ZPE Density = String Tension, i.e. Energy per unit length, which is same as the Newtonian "force".

Even though there are more modes in the larger line segment, the available "space" is also larger! More modes in a larger space such that the density of virtual energy is constant! There is complete compensation. The ZERO POINT ENERGY DENSITY stays CONSTANT in BOTH PARTITIONS! It doesn't even matter what w is! It will be w = -1 for other reasons of general relativity. There is no zero point pressure differential at all! Now is this an artifact of making the problem 1 dimensional? Even if it is, the idealized Casimir force problem is for two infinite plane parallel thin plates and this should be a good symmetry approximation. Actually, the number of space dimensions should not matter because the mode density power scales the same way as the "space".

For example in 2D fdf that integrates to f^2 in 3D f^2df that integrates to f^3 and so on.

Of course, this all assumes zero vacuum coherence, that the ZPE is totally random. You can get an effect if the vacuum coherence is different on the two sides. But that is NOT the Casimir force! That is something entirely new that only I have predicted.

Therefore, there is something deeply wrong about the mode-counting argument to get the virtual photon Casimir force

~ (pi/24)hc/a^2 for two plates separated by distance a.

* These considerations do not apply to Ian Peterson's Van Der Waal's force argument!

Original message from Hal:

"Jack,
 
In several of your recent postings you say that the flat-space, quantum physics Casimir model that we quantum physicists use (that does not take into account w = -1 implications of dark energy on the microscopic scale) has been overtaken by the discovery of dark energy.  Indeed, you use this claim to (a) criticize the Casimir model and (b) come up with a "dark energy" model for Shoulders' charge cluster phenomenon ("dark energy in a bottle," you call it). 
 
When I point out that Casimir, Milonni, I, et al. use the quantum vacuum fluctuation Casimir-type model to advantage (and, BTW, get the right answer for Casimir attraction between parallel plates!) you point out that it is a false model in a flat space that does not take into account the recent GR cosmology concepts and therefore is flawed ("Casimir's greatest blunder," you call it!).
 
Specifically, you argue that the ZPE radiation pressure modeling that uses w = 1/3 vacuum radiation pressure forces (as in the 1988 Phys. Rev A paper by Milonni et al., "Radiation pressure from the vacuum: Physical interpretation of the Casimir force") must be set aside in favor of the use of the w = -1 repulsion vacuum forces. 
 
Here is my challenge to your line of logic.  Forget the Shoulders' model for the moment, and simply show how your line of logic involving the w = -1 repulsion vacuum force leads to the known attractive Casimir force between parallel plates, which has been precisely measured and accounted for on the basis of the quantum physicists' use of the w = 1/3 vacuum forces.  It would seem that you insist that instead the w = -1 repulsive force is the important force on this level, previously neglected, so please show how to derive the attractive Casimir force by your counter-claim with its opposite-sign vacuum force.
 
In summary, we see how Casimir's positive-radiation-pressure "blunder" model leads to agreement with experiment; we don't see how your opposite-sign dark-energy w = -1 repulsion force model would lead to the observed attraction.  Please show this.  If you can show this for the  standard parallel plate Casimir Effect, then consideration of its use for more exotic geometries (e.g., Shoulders' charge cluster phenomenon) would be warranted.  If not .....  
 
Collegially,
Hal"