A Special Kind of Casimir Plates for Making Exotic Matter

A special kind of Casimir plates for making exotic matter

Abstract

Herein a process of suitable extraction of energy from vacuum is introduced. By following Ridgely’s idea[1], it is proposed some molecular fine-scale plates. Then some properties of them are considered. In fact Casimir effect is viewed in engineering manner. The introduced plates may be applied for support of traversable wormholes (TWs) & warp drives (WDs).

Introduction

Herein the basic idea is the introduction of flat Casimir plates in nano scale however changing for engineering reasons, (e.g circle, washer) always remain parallel to themselves. Herein it is followed Ridgely who proposed an approach leading to creating macroscopic amounts of exotic matter (EM) [1]. People who work in field know existence of EM or in other words negative energy (NE) is “almost” necessary for TWs & WDs. The word “almost” is because there is comment about violation of weak energy condition (WEC) with no need to EM such as creation & control of massive scalar or massless scalar [2,3,4,5,6,7,8], nutrino[9,10,11], Brans-Dicke (BD)[12], & so on fields[13,14]. But they don’t seem to delete engineering problems which an advanced civilization [15] must do for creation , stabilization & control of TWs or WDs completely. Herein it is shown nano scale plates may be useful. Also some properties are imputed to plates and scene. At last conclusion is if we have enough plates, proper configurations may give us suffician amount of NE.

Fundamental assumptions:

It can be briefly mentioned results of [1]: For two parallel perfect conducting square plates we have:

L2c π 2 U (r) = h casimir − 720r 3 (1)

− ∂U (r) − L2c π 2 → F(r) = = h r<

2 2 − L chπ U1 = 3 720r1 (3)

2 2 − L chπ U 2 = 3 720r2 (4)

2 −π 2 1 1 ∆U = U 2 −U1 = hcL ( 3 − 3 ) 720 r2 r1 (5)

2 π 2 1 1 W12 = hcL ( 3 − 3 ) 720 r2 r1 (6)

W∞ = Lim(W12) r1 →∞

(7)

L2c π 2 − L2c π 2 W = h →U = h ∞ 720r 3 ∞ 720r 3 (8)

as a result it can be mentioned if zero point field (ZPF) performs positive work in a localized region of spacetime then NE density of the system arises. By the way, there is no difference between inertial properties of EM & common matter.

Properties of suitable Casimir plates:

Let’s assume a pair of flat structures (plates) which are composed of some conductive quantums. For our purposes a few properties of plates & condition are desired:

A: The shape of plates should be square or rectangular or circular. Square is because easy calculation but circular is for more output of collection (fig 1). As reader knows circle is the extreme area in a flat plate. By the way due to U ∝ L2 increasing the area is very important.

B: According to [16] dependence of Casimir energy to mass is described by:

∞ 1 2 2 2 ε = dttd Ln(1− e−2 t +µ a ) (d +1) d +1 ∫ ad +1 2d +1π 2 Γ( ) 0 2

(9)

d µa +1 1 ∞ 1 = −2( ) 2 K (2µan) d +1 ∑ d d 4π a +1 +1 n=1 n 2 2 (10)

λ−2 = ω 2 − k 2 µ 2 (11)

here µ denotes mass for the scalar field. So less massive quantums (molecules or atoms) , more output of collection.

C: The “plates” should be as much as possible “flat” & a proper topology must be available. So molecules should be as much as possible tiny in particular if there are a few of them.

D: The plates should be light because zero point energy should be extracted more and more & a little of it should move the plates.

E: The plates should be as much as possible thin because more volume of vacuum need to be covered and dug

F: Evidently more conductive plates is better & superconductivity should be considered.

G: All factors leading to friction should be diminished to all forces be conservative. Less wasting is more needed.

H: According to [16] there is a contrary dependence between Casimir force & growing temperature:

−1 d d k n=∞ 2κ F Τ = n ∫ d ∑ 2κ na 2β (2π ) n=−∞ e −1

(12)

1 2 2 2 κ n = [k + (2πn β ) ] (13)

β =1 kT (14)

So temperature of the surrounding should be low.

Can we extract NE from vacuum?

The calculations show with a reachable number of plates it can be produced sufficient NE (dependent to elegance of operation from ~ hundreds to bilions number of plates & distance between them from pico- meters to nano-meters) we can produce needed EM at least for the case reported in[17]. The calculations are under consideration & will be published in my next letter.

[1] C.T.Ridgely , “A macroscopic approach to creating exotic matter”[arXiv:physics/0010027] [2] D.N.Vollick,” Maintaining a wormhole with a scalar field” [arXiv:gr- qc/9806071] [3] C.Barcelo , M.Visser, “Traversable wormholes from massless conformally coupled scalar fields”[arXiv:gr-qc/9908029] [4] S.W.Kim , S.P.Kim, “The traversable wormhole with classical scalar fields”[arXiv:gr-qc/9907012] [5] A.A.Popov, S.V.Sushkov,” Vacuum polarization of a scalar field in wormhole spacetimes”[arXiv:gr-qc/0009028] [6] C.Barcelo, M.Visser,” Scalar fields, energy condition, and traversable wormholes”[arXiv:gr-qc/0003025] [7] C.Armendariz-Picon,”On a class of stable, traversable Lorentzian wormholes in classical general relativity”[arXiv:gr-qc/0201027] [8] V.Khatsymovsky,” Towards possibility of self-maintained vacuum traversible wormhole”[arXiv:gr-qc/9612013] [9] V.Khatsymovsky,”Can neutrino vacuum support the wormhole?”[arXiv:gr-qc/9707052] [10] S.Krasnikov, ”A traversable wormhole”[arXiv:gr-qc/9909016] [11] S.Krasnikov, ”Toward a traversable wormhole”[arXiv:gr- qc/0003092] [12] L.A.Anchordoqui, S.P.Bergliaffa, D.F.Torres,”Brans-Dicke wormholes in nonvacuum spacetime”[arXiv:gr-qc/9610070] [13] L.A.Anchordoqui, “Wormholes in spacetime with torsion”[arXiv:gr- qc/9612056] [14] A.Wang, P.S.Letelier, “Bubbles and wormholes: analytic models”[arXiv:gr-qc/9506004] [15] M.Morris, K.Thorne, “Wormholes in spacetime and their use for interstellar travel: a tool for teaching general relativity” Am.J.Phys.56,395 (1988) I think above papers can’t be used in the lab. For example neutrino & scalar particles are so much unreachable. If we can produce them & make their vacuums in a reasonable time, we’ve done a great work! But I seem from all proposed approaches, this paper and its extended versions that are ready to submit in Lanl archive is best experimentally for present technology. [16] K.A.Milton, “The Casimir effect: physical manifestations of zero- point energy” (World Scientific , 2001) [17] S.Krasnikov, “The quantum inequalities do not forbid spacetime shortcuts”[arXiv:gr-qc/0207057] the below papers are recommended to review: [18] M.Visser, S.Kar, N.Dadhich, “Traversable wormholes with arbitrarily small energy condition violations”[arXiv:gr-qc/0301003] [19] F.Loup, D.Waite, E.Halerewicz Jr, “Reduced total energy requrements for a modified Alcubierre warp drive spacetime”[arXiv:gr- qc/0107097] [20] C.Van Den Broeck, “A ‘warp drive’ with more reasonable total energy requirements”[arXiv:gr-qc/9905084] [21] [email protected] URL:www.mansouryar.com

fig1a fig1b