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Is Low Power Warp Drive Possible? Breaking the Space‐Time S>ffness Barrier Jack SarfaB adastra1@me.com ISEP San Francisco, CA 94133 • All conven>onal forms of spacecraO propulsion are unlikely to mo>vate large‐scale private capital because the >me scales for interstellar travel even to the nearest exo‐ planet are simply too long for prac>cal commerce, the habitat problems are likely to be too difficult, and the cost in our declining world economy on the brink of financial if not environmental collapse in 2011 appear to be too great. • Recent discoveries in the slowing of the speed of light in Bose‐Einstein condensates and the nega>ve electric permiBvity and magne>c permeability in metamaterials suggests a low power specula>ve possibility for warp drive based on Einstein’s orthodox field equa>on for gravity coupled to the electromagne>c field. • Suppose, for example, that the speed of light can be slowed to 3 cm/sec keeping the magne>c response close to 1 with a non‐propaga>ng near‐ field low frequency nega>ve dielectric response suscep>bility. Therefore, since c scales as the inverse square root of the product of the electric and magne>c suscep>bilites, yielding a dimensionless amplifica>on of the repulsive an>‐ gravity field of perhaps as much as order of the cube of the electric suscep>bility ~ 1060. This would break the space‐>me s>ffness barrier to low power warp‐wormhole technology. This conjecture is en>rely new and needs further inves>ga>on. Einstein’s Gravity Field Equa>on 8π G Gσν + 4 Tσν = 0 c Maxwell’s Unifica>on 1 c = εµ 2 Cons>tui>ve Equa>ons ε = ε vac (1+ χ E ) µ = µvac (1+ χ B ) Einstein’s Eq Inside Material 2 Gσν + 8π G ( ε vac µvac (1+ χ E ) (1+ χ B )) Tσν = 0 Electromagne>c Field Source Tensor Electromagne>c Field Stress Tensor Nonlinear Material Electrodynamics Metamaterials Near Fields • However, what is required for prac>cal low power warp drive is not propaga>ng radia>on, but a new kind of metamaterial, filled with very low frequency off‐mass‐shell non‐ propaga>ng near field virtual photons that are Bose‐Einstein condensed into macro‐quantum coherent Glauber states of sharp phase and uncertain number. It may be possible to generate them from the aforemen>oned strong EM field nonlineari>es. Near Field Metamaterial Suscep>bility  χ ω , k  0 ( ) ω →0  ω ≠ck Capacitor Filled With Metamaterial TσνEM ⎛ 1 2 ε χ E − ⎜ 2 vac E → ⎜ B→0 χ B →0 ⎜ 0 ⎜⎝ 0 −ε vac 1 χ E Ei E j − ε vac χ E E 2 2 ⎞ ⎟ ⎟ ⎟ ⎟⎠ Low Power Warping Space‐Time ⎛ G00 ⎜ ⎜⎝ Gi 0 G0i Gij ⎛ 1 − ε vac χ E E 2 ⎞ ⎜ 2 2 2 ⎟ + 8π ( ε vac µvac ) χ EG ⎜ ⎟⎠ ⎜ 0 ⎜⎝ 0 1 −ε vac χ E Ei E j − ε vac χ E E 2 2 ⎞ ⎟ ⎟ ~0 ⎟ ⎟⎠ Warp Drive Newtonian Limit p⎞ ⎛ ∇ φ − 4π G ⎜ ρ + 3 2 ⎟ ~ 0 ⎝ c ⎠ 2 1 2 2 2 2 3 ∇ φ − 12π ( ε vac µvac ) χ E (1+ χ B ) Gε vac E ~ 0 2 c Ultra‐Low Power Warp Drive? ? 2 1 2 2 2 κχ E3 (1+ χ B ) ( ε vac µvac )Gε vac E 2 3 2 ∇ φ−e 12π ( ε vac µvac ) χ E (1+ χ B ) Gε vac E ~ 0 2 c Energy is Conserved U i + Win + Qin = U f + Wout + Qout Ui > 0 Uf < 0 Wout + Qout > Win + Qin > 0 How Much Energy? • The mass of the Earth is ~ 1025 kgm (1042 Joules). Therefore, we would not need imprac>cally large electric fields to neutralize the Earth’s gravity around the ship if we could achieve large resonances in the low frequency dielectric suscep>bility response func>ons of metamaterials. The amplifica>on scales as the cube of the suscep>bility , so if we only want to store say one Joule total in the slowly varying near electric fields of the metamaterial capacitor, we need a resonance of (1014)3 . Therefore, . Consequently, the required index of refrac>on in the non‐ radia>ive near field ELF range that scales as the reciprocal square root of the suscep>bility is ~ 107 i.e., a metamaterial speed of light ~ 30 meters/sec. Instant space communica>ons using nonlocal quantum entanglement? • Jacques Vallee emphasized the importance of trying to overcome the light barrier for star ship technology with quantum entanglement in the first mee>ng of the joint DARPA‐NASA 100 Year Star Ship workshop in January 2011 in Marin County. MIT physics historian David Kaiser describes how this idea came about and objec>ons to it in his book “How The Hippies Saved Physics” (W.W. Norton, New York, 2011). Mainstream opinion is that the direct use of quantum entanglement as a C3 command, control, and communica>on channel without a light‐speed limited signal “key” is fundamentally impossible because of the linearity of observable operators and the unitarity of quantum state >me evolu>on between strong measurements. My 1978 Concept Reborn? Antony Valen>ni wrote • “It is argued that immense physical resources ‐ for nonlocal communica7on, espionage, and exponen7ally‐fast computa7on ‐ are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present 7me. It is suggested that 'non‐quantum' or nonequilibrium ma@er might exist today in the form of relic par7cles from the early universe. We describe how such ma@er could be detected and put to prac7cal use. Nonequilibrium ma@er could be used to send instantaneous signals, to violate the uncertainty principle, to dis7nguish non‐orthogonal quantum states without disturbing them, to eavesdrop on quantum key distribu7on, and to outpace quantum computa7on (solving NP‐ complete problems in polynomial 7me).” Coherent State Sender Entangled With A Single Qubit Receiver Nonorthogonal Sender Coherent States Give Signal Nonlocality 1 2 2 − α + β − 2α * β α β =e 2 ≠ δ (α − β ) ( ) Entangled Density Matrix ρ AB 1⎛ α A 0 B = A, B B, A = ⎜ 2⎝+ α A 0 B 0 B B A 1 α +β A β +β A 1 A B B 1 1 B B β ⎞ ⎟ 0 A α⎠ A The Nonlocal Entanglement Signal { P (1)B = Tr 1 B B 1 ρ AB } 1 = 1+ α β 2 ( 2 A ) Viola>on of Born Probability Rule { P ( 0 )B = Tr 0 B B 0 ρ AB } P ( 0 )B + P (1)B = 1+ α β 1 = 1+ α β 2 ( 2 A >1 2 A ) = P (1) B