Sch J Appl Sci Res 2018 Scholar Journal of Applied Sciences Volume 1: 9 and

Mathematical Proof of Concept: Celalettin-Field Quantum Observation Tunnel; A Quantum Communication Countermeasure

Metin Celalettin1* 1College of Engineering & Science, Victoria University, Ballarat Road, Footscray, Horace King1 Australia

Abstract Article Information

The ‘Celalettin-Field Quantum Observation Tunnel’ (COT) is a Article Type: Research speculative structure produced in an ensemble of Orbital Angular Article Number: SJASR202 Momentum (OAM) polarized outer ‘s’ shell , whereby an Received Date: 29 November, 2018 incoming , depolarizes ‘s’ shell electrons as it burrows through Accepted Date: 05 December, 2018 the ensemble, creating a tunnel. The depolarized particles when Published Date: 13 December, 2018 viewed as a single quantum system can theoretically be used to acquire information on the incoming photon which in effect, measures it *Corresponding author: Metin Celalettin, College of satisfying the criterion for ‘quantum observation’. Enabling equations Engineering & Science, Victoria University, Ballarat are discussed which describe the behaviour of the photon / Road, Footscray, Australia. Email: metin.celalettin(at)live. interactions in the tunnel, the medium in which the tunnel is produced, vu.edu.au and the information the medium acquires on the photon as it tunnels through. The Schrodinger wave equation, Mathieu differential equation, Citation: Celalettin M, King H (2018) Mathematical Proof Lagrangian QED equation and the Lorentz quantum parameter of Concept: Celalettin-Field Quantum Observation Tunnel; (OAM coupling) simultaneously describe the COT phenomenon. This A Quantum Communication Countermeasure. Sch J Appl study proposes the COT as a quantum communication countermeasure, Sci Res Vol: 1, Issu: 9 (06-10). be it a quantum or spy satellite utilizing quantum computing. Military quantum communications, , Copyright: © 2018 Celalettin M. This is an open-access Keywords: article distributed under the terms of the Creative Commons Quantum radar, Spy satellites. Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the Introduction original author and source are credited. Quantum communications operate unaffected by extant signal countermeasures [1]. Using a quantum radar as an example, where as in the past, electromagnetic waves from a conventional radar would additionrebound offto aother jet and jet return borne to stealththe radar, capabilities, fighter jets plasma had options stealth to counter clouds aresuch highly attacks researched by absorbing and consist or reflecting of ionised the atoms electromagnetic which trap electrons, waves. In radar, the entangled are not as affected by electromagnetic absorptionpreventing themas the from photons returning are not to drawna conventional to ionized radar. atoms In ina quantum the way electrons are. Information is acquired by monitoring the retained idler photon (γIdler) [2]. religious and philosophical debate, with the most widely accepted The cause of quantum observation is a topic of global scientific, interpretation states that when a photon’s spin, OAM or frequency is measuredscientific understandingthen the entangled being photon the ‘Copenhagen in a superposition interpretation’. collapses Thisto a a quantum radar, or spy satellite harnessing quantum communications wouldsingle position.inhibit its Introducingability to function quantum [3]. observation into the function of This study introduces quantum observation to cause , to military quantum communications devices. In a quantum radar, its entangled signaller photon (γsig) is observed via a proposed www.innovationinfo.org

‘Celalettin-Field Quantum Observation Tunnel’ (COT). At Achieving these aforementioned objectives would theoretically keep the jet stealthily in the presence of a jets to remain stealth in the presence of a quantum radar. quantum radar. The capability to enshroud a supersonic jet AEquation proposed 11 Polarized the proposed Electron COT Cloudwould (Pe.Cloud) enable stealth is required fighter with a plasma stealth cloud already exists [5], and Lockheed Martin already have a patent on a military grade quantum would leave an ensemble of depolarized electrons as it attemptsto enshroud to reach the jetand to rebound provide off a mediumthe jet. When for which viewed γsig, as Conceptradar [12,13]. by the production of the COT through the medium enabled Celalettin-Field Quantum Observation Tunnel bya single OAM quantumcoupling system,between information the entangled on γsigphoton is acquiredand the produced in the proposed Pe.Cloud. OAM coupling is of depolarized electrons in the Pe.Cloud. This is discussed In Figure 2, the proposed COT is illustrated as being furtherpolarized in electronsdetail. in the presence of an electric field, made ensemble of depolarized electrons. When considered as proposed to be caused by the tunnelling γsig, leaving an Literature Review monitoring the density of the Pe.Cloud or imaging the COT; a The aerodynamic complications that the Soviet Sputnik a single quantum system, the γsig could be measured [8], program encountered and those that the U.S are tirelessly This study investigates a phenomenon that is expected form of quantum observation [14-20]. to take place within fractions of a millionth of a second prior jet with an airborne ionized chemical plasma cloud are all avoidedtrying to [4-6]. overcome This is because by enshrouding the Pe.Cloud a supersonic is not an on-board fighter the depolarized COT electrons, into their initial Pe.Cloud. continueto the fighter style. jet’s on-board electromagnet repolarizing canisters. Rather, it polarizes local outer ‘s’ shell electrons; thereplasma, is norno isrequirement it deployed tovia entrap a continuous electrons flow beamed via on board from Mathematical Proof of Concept a conventional radar, but rather, treat local photon-photon The mathematical proof of concept does not attempt quantum entanglement via a COT. to reconcile quantum equations with classical physical The COT would be caused by a high energy photon tunnelling into the Pe.Cloud, namely a scalar quantum electrodynamics (QED) Lagrangian operation with OAM coupling. This is the crux of the idea behind the COT as enables the interaction between the photon and the OAM polarized electrons in the Pe.Cloud in order to allow a COT to be produced [7]. The COT exists when considering the intrinsic OAM’s of all affected depolarized electrons as a single quantum system whereby the individual depolarized electrons cannot be described independently of each other. intrinsic OAM of Pe.Cloud’s electrons tunnelling through theThe Pe.Cloud, γsig’s size and would the bePe.Cloud evidenced density by depolarizingwould increase the as the photons scatter the electrons during tunnelling; essentially enabling the Pe.Cloud to be provided with quantum observation requirement, and therefore would Figure 1: Plasma stealth cloud. causeinformation quantum on thedecoherence γsig. This betweensatisfies Wernerthe quantum Heisenberg’s radar’s entangled photon’s, subsequently inhibiting its function [8]. used to absorb electromagnetic radiation is illustrated. The plasmaIn Figure stealth 1, cloud an extantis made plasma of ionized stealth atoms cloud which currently attract the electrons beamed from a conventional radar [9-10]. This plasma stealth cloud would have no effect on a quantum radar, as photons would not interact with ionized atoms and the γsig, would penetrate the plasma stealth cloud striking the Therejet [2,11]. are two objectives of this research: • To mathematically investigate quantum observation via a proposed COT • Ascertain whether a Pe.Cloud can be engineered to inhibit

Figure 2: Celalettin-Field Quantum Observation Tunnel (COT). a quantum radar’s ability to detect a stealth fighter jet Sch J Appl Sci Res 2018 07 www.innovationinfo.org equations to formulate an equation for the COT. Rather, The wave function for quantum entanglement is an ensemble of parent equations have been manipulated to describe the behavior of photonic and electric behavior 1 φφ− with regards to the functionality of a military quantum expressed Ψ= [23]: (,eαα eii + ge , ) communications devices such as a quantum radar, and once 2 ensembled, these equations as a system enable the COT to (2) introduce quantum decoherence to the entangled photons utilized by a quantum radar. Therefore, no COT equation Where:The quantum αe = eigenvalues, mechanical operatore = γsig, g used = γidler to operate on the wave function for the purpose of the COT is the Hamiltonian, run simultaneously under typical military capabilities, and for which solutions for time independent quantum equations is formulated, however there are five equations that when applied1. The scalar to the quantumCOT, it is enabledelectrodynamics [21]. These (QED) equations Lagrangian are: exist as eigenvalues [24]. Quantum observation has also been operation with OAM coupling at Equation 10, which thedefined state by of Wernerthe observable Heisenberg changes as ‘sampling and the observer the observable’ can no [8,25]. Therefore, if the observer can sample the state, then polarized electrons in the Pe.Cloud in order to allow a enables the interaction between γsig and the OAM COT to be produced [7]. longerRubidium be factored isotope out 87 [26]. (Rb87) atoms have a complete shell 2. The Klein-Gordon Equation 13, which proposes that when with one electron in its outer shell are passed through a structure plus one electron in its outer ‘s’ shell [27]. If atoms a COT via both Compton scattering and OAM coupling and isa γsig the of conduit sufficient in energythis circumstance enters a Pe.Cloud, for the it will Lagrangian produce thenon-homogenous, randomly opposite vertical spin magnetic states of field, their their outer polarizations s electrons are aligned upwards and downwards [28,29]. This is due to 3. formulationThe wave function being usedfor quantum in a quantum entanglement setting [22] at Equation states through a cavity, the two quantum states 1, which described the entangled photons employed [27]. When sending Rb87 atoms in a superposition of two in quantum communications as and mathematically quantum decoherence by OAM coupling within a polarized Rb87shift phases atomic causing gas chamber quantum as opposed decoherence to pumping [23]. Observing quantum entangled Rb87 atoms into a microwave cavity is therefore a 4. The Boltzmann equation for a plasma at Equation 3, to describes γsig. plausible experiment. accommodate the density of the environment in which the photon-electron interactions will occur in the presence of Plasma stealth clouds rely on the density of ionized atoms

electromagnetic energy from conventional to entrap requiredan electric to field. acquire The information density of the on Pe.Cloud it. is paramount asto manyaffect radarsthe reflection, transmitted absorption electrons and as possibletransmission [9, 30]. of Thethe as depending on the size of γsig, enough medium is 5. needs to be high energy enough to depolarize electrons in the The quantum parameter χ in units of Schwinger Pe.Cloudproposed to Pe.Cloud produce needs the COT to beto causedense quantum enough, observation,and the γsig whichacceleration is why asthe ≡ Lagrangian m, at Equation formulation 8. If it of is the greater scalar than and and protect the jet from quantum radar detection [1]. Given spinor1, then in it anis electrondetermined reservoir that γsig is relevant has a quantum as under nature,special the Boltzmann equation for a plasma to accommodate the conditions later mentioned, this equation is appropriate. density of the environment in which the photon-electron 6. Time. Whilst not an equation, the power output of the electromagnet it known and the COT will only exist for in equation (3): interactions will occur in the presence of an electric field as the amount of time it takes for the electromagnet to re- e(φφ 2− 1)/k BeT (3) polarize the OAM’s of the depolarized electrons. nee(φφ21) = ne( ) Therefore, the new learning is not that there is a new Where: n mathematical formulation, but rather that the correct e e of the plasma, and kB equations are present, running simultaneously under the function. = electron number density, T = temperature correct condition to enable the production of a COT. = Boltzmann constant and φ = work Derivations 2 In addition,1 thee electron radius (re) is given by: Here the Schrodinger equation is introduced as the T = (4) fundamental equation of physics for describing quantum e 2 4πε 0 mce mechanical behavior which is the physics which describes −15 (5) quantum entanglement; the fundamental phenomena rme = 2.8*10 underlying a quantum radar:

0 ∂ ^ free space i ψ () tHt= Ψ () (1) Where: e = , m = mass, ε = permittivity of ∂ As such, the average spacing between Rb87 atoms in an t experimental Pe.Cloud would need to be <4.94nm, given

Sch J Appl Sci Res 2018 08 www.innovationinfo.org the atomic radius of Rb87 is 4.94nm. This would be dense describe electrons in terms of a scalar due to Faraday’s Law enough to tunnel deep enough into the Pe.Cloud, indicated scalar formulation of QED in a plasma. It is not possible to viaenough the photoelectric for a 400nm γsig effect to viaproduce Compton a COT scattering if it is high when energy not [36]. So therefore magnetic vector potential is included absorbed [31]: throughof Induction, the inclusion unless a ofmagnetic an electromagnet, vector potential enabling is included the use of this equation. The electromagnet is required to be high = −ϕ (6) energy enough to OAM polarize the electrons that enables Kmax hf the Lagrangian scalar formulation to investigate the required kinetic energy of the laser to cause the COT. Thus, the scalar QED plasma Lagrangian required for a photonWhere: which K =denotes Kinetic the energy minimum of the energy signaler required entangled to Pe.Cloud is given by the Lagrangian formalization for scalars movephoton, a delocalised h = Planck electron constant, as per f = frequencyEinstein’s work of the on incident photon equation [33]: / electron interaction. 1 * µµ LsQED =[( ∂+µµieA ) Φ ][( ∂− ieA ) Φ ] there will be enough energy in the Pe.Cloud for it to produce 2 (10) If the quantum radar’s γsig were 200nm, at Equation (4) 11µ −M2* ΦΦ− FFv 2 16π µv a COT [32]. photons are given by: The quantum entangled Idler (e) and Signaller (g) 1 iiφφ− conjugate, and where the electromagnetic strength is given Ψ=(,eαα e + ge , ) (7) by:Where: Φ = charged scalar field, Φ∗ = its complex 2 (11) We begin with the Schrodinger wave function equation: Fµvv=∂ AA µµ −∂ v 8π 2 m ∇2 Ψ+(EV −) Ψ=0 (8) h2 Where: Aµ = vector potential of particles is derived from the Lagrange equations, where the InEuler-Lagrange Lagrangian mechanics, equation thedescribes trajectory the ofmotion an ensemble for the Where: E = energy,2 V = potential energy 1 du x = > 1 (9) m ds scalarδδ fieldLL [33,37]: = ∂ **µ δδΦ() ∂Φµ The quantum parameter χ in units of Schwinger (12) thisacceleration research as will ≡ m.consider If it is greater the Lagrangian than 1, the formulation particle motion of the scalarin the and electromagnetic spinor in an electron field has reservoir a quantum [33]. nature, hence Gordon equation: The Euler-Lagrange equation (12), yields the Klein- 2 2 22 (13) mass. [−∂ +M ] Φ = [ − e A + 2 ieA .] ∂ Φ Where: s = proper time of the particle and m = particle Equation (9) considers a plasma, and in particular the

2 2 Lagrangian mechanics is a label given to a situation where Where:Further, ∂ the ≡ ∂µ∂µ,Dirac A/ ≡AµAµ,Klein-Gordon A·∂ ≡ Aµ∂µ.equation reduces to thephotoelectric Lagrange attributesclassical ofequation γsig interacting is applicable with ato Pe.Cloud. certain the Mathieu ordinary differential equation under special conditions. formulation will be considered to ‘exist with’ ( ): The special conditions are: quantum mechanical situations. In this study the Lagrangian OAM coupling equation, and • • The motion for the Pe.Cloud is in the presence of an • Schrodinger equation [34].

• electromagneticThe required electric field charge of the electromagnet to required to depolarize atomic Rb87 outer ‘s’ shell electrons polarize the Pe.Cloud is known haveThe been behavior derived of atomicat equation Rb87 (14). and theAn γsig’sensemble energy of • polarized atomic Rb87 is governed by the Lorentz invariant parameters which consist of both classical and quantum, for The γsig tunnels through the Pe.Cloud, depolarizing which equation (9) is the quantum parameter [35]. electrons in its wake via Compton scattering [22] energy enters a Pe.Cloud, it will produce a COT via both Considering the electron motion in a quantum parameter ComptonThis equation scattering proposes and OAM that whencoupling. a γsig The of sufficientPe.Cloud can then be imaged and the COT is proposed to acquire re-visits Raicher et al.’s construction of the Lagrangian (χ > 1), QED describes the γsig emission process. This study information on the γsig’s size / frequency and the Pe.Cloud’s Sch J Appl Sci Res 2018 09 www.innovationinfo.org change in density which would prove that the depolarized 16. Decoherence and the transition from quantum to classical—revisited. Quantum Decoherence, Springer pp: 1-31. Zurek WH (2006) through the proposed COT as discussed. 17. Optical spin-to-orbital angular electrons have been pushed aside during γsig’s tunnelling momentum conversion in inhomogeneous anisotropic media. Physical Conclusion ReviewMarrucci Letters L, Manzo 96: 163905C, Paparo. D (2006) The mathematical proof of concept that a Pe.Cloud 18. Optical angular momentum and atoms. Phil . causing quantum decoherence via a proposed COT is Franke-Arnold S (2017) mathematically feasible. Calibration of said variables will be 19. Trans R Soc A 375 pp: 20150435Spin and orbital angular momenta of electromagnetic waves in free space. 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Citation: Celalettin M, King H (2018) Mathematical Proof of Concept: Celalettin-Field Quantum Observation Tunnel; A Quantum Communication Countermeasure. Sch J Appl Sci Res Vol: 1, Issu: 9 (06-10).

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