The Possibility of FTL Space Travel by using the Quantum Tunneling Effect through the Light Barrier

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1 ISSN: The Possibility of FTL Spae Travel by using the Quantum Tunneling Effet through the Light Barrier Musha T Advaned Si-Teh Researh Organization, , Namiki, Kanazawa-Ku, Yokohama 65, Japan Corresponding author: Musha T, Advaned Si-Teh Researh Organization, , Namiki, Kanazawa-Ku, Yokohama 65, Japan, Tel: ; takaaki.musyha@gmail.om Reeived: April, 17; Aepted: May 1, 17; Published: May 15, 17 Abstrat In normal physis, nothing an move faster than the speed of light, beause Einstein's theory of relativity forbids it. However, some physiists have proposed a model of faster-than-light (FTL) travel, formulated in the ontext of Lorentzian manifolds, whih are used in general relativity to onstrut spae-time models, alled a wormhole and an Alubierre s warp drive. Warp drive works by distorting the fabri of the spaetime, ontrating spaetime in front of the spaeship and expanding it behind to reate a warp ontinuum bubble between the two spaetime distortions in front of and behind the raft. However, it has been shown that the total integrated energy density needed to maintain the warp metri is physially unattainable. In this artile, the author presents another possibility of a FTL travel method whih applies the tunneling effet through the light barrier aused by the manipulation of ZPF field surrounding the spaeship. Keywords: Warp drive; Tunneling effet; FTL travel; Tahyon; ZPF field Introdution Some physiists have proposed a model of faster-than-light (FTL) travel, formulated in the ontext of Lorentzian manifolds, whih are used in general relativity to onstrut spae-time ontinuum models [1]. In normal physis, nothing an move faster than the speed of light. Einstein's theory of relativity forbids it. There are two exeptions to this rule however. The first is what's ommonly alled a worm hole, a bridge onneting two different parts of spae []. A ship rossing this bridge would move at below light speed, but still arrive before a beam of light that would have had to go the long way around. Warp drives are the seond and more appealing option. A ship an't move through spae faster than the speed of light. But with enough energy, spae itself an move faster than the speed of light. The most renowned theory is the Alubierre drive, whih is possible to irumvent the problem by suitably warping spae-time []. The Mexian physiist Mique Alubierre originally developed the idea in the 199's, named an Alubierre warp drive whih would reate a bubble of energy behind the ship and a lak of energy in front of the ship, like a giant osmi wave a spae ship ould surf. That partiular setion of spae an travel faster than the speed of light in the surrounding spae, and anything on or in that bubble will aelerate with it. Finazzi Citation: Musha T. The Possibility of FTL Spae Travel by using the Quantum Tunneling Effet through the Light Barrier. J Spae Explor. 17;6(1): Trade Siene In. 1

2 May17 et al. propose reating this bubble of spae-time by using a massive amount of "exoti matter," or dark energy [4], but how this bubble would be reated is still a mystery and they give no knowledge as to how a warp bubble might atually be established. Aording to their alulations, it would take a huge amount of energy to reate the bubble, and then inreasing amounts of energy to ontain the highly repulsive dark energy. Another method is based on general relativity whih permits the travel of an objet at a greater veloity than that of light by bending the spae-time itself. If spae-time is warped properly, the veloity of traveling objet does not exeed the speed of light, but it appears to be moving faster than light to observers in normal spae-time. If ertain quantum inequalities onjetures by Ford and Roman hold, it was shown by Pfenning and Ford [5] that the energy requirement for some warp drives beame the energy equivalent of 1 64 kg to transport a small spaeship aross our galaxy. The author proposed in his paper that there is a possibility of light partiles whih an penetrate through the light barrier by the violent aeleration [6], whih suggests that eletron neutrinos travels in a spae in a FTL mode as onfirmed many experiments. Reently, a group of physiists have been working to measure the neutrinos generated from a partile aelerator at CERN. This group disovered neutrinos arriving faster than would have been expeted and they appear to be traveling faster than the speed of light itself, but they draw no definitive onlusions [7,8]. In this artile, the author presents an advaned theory that the spaeship an be traveled at FTL speed by applying the theory of tunneling effet through the light barrier. Possibility of Tunneling Through the Light Barrier From the wave funtion for the partile given by i H t, (1) the wave equation for an aelerating partile an be desribed as [9] p i 4 ma p m, () where is a wave funtion of the partile, is a Plank onstant divided by, p is its momentum, is a light speed, H is a Hamiltonian given by H 4 p m, and a is a proper aeleration given by p mat, where m is a proper mass. From Eq. (), we have the solution given by [9] C exp i p p m m log( p p m ) ma, () where C is an arbitrary onstant.

3 May17 From whih, we obtain (subluminal speed: v ) m v 1 v C exp i log( m) a v v, (4) (superluminal speed: v ) m v C exp a v 1 v log( m ) v, (5) where m is an absolute value of the imaginary mass and v is a veloity of the superluminal partile. FIG.1. shows the wave funtion for the highly-aelerated partile, whih shows the possibility of tunneling through the light barrier. We onsider the light barrier as a potential barrier, the probability of a partile to tunnel through the light barrier an be estimated aording to the WKB approximation shown as [1]. T m exp a 1 1 log( m ) log 1 1, (6) where v / and T is a probability to beome FTL state. FIG.1. Wave funtion for the highly aelerated elementary partile.

4 May17 Supposing that m m, the probability of a spaeship omposed of N elementary partiles to plunge into a FTL state an be roughly estimated as follows when we let ; T N k 1 mk exp a m log( mk) exp N a log( m). (7) Thus it an be seen that violent aeleration makes possible for the spaeship to tunnel through the light barrier as shown in FIG.. FIG.. Quantum tunneling through the light barrier by manipulating ZPF field. However, it an be estimated from Eq. (7) that enormous aeleration over 6 m ) is required for the spaeship with the proper mass of 1 tons to plunge into a FTL state, whih annot be attained by the onventional propulsion systems. 1 ( /se Aeleration generated by the manipulation of the ut-off frequeny of ZPF spetrum By the Puthoff s theory on zero-point-flutuation (ZPF) field [11], the rest mass of the pion orresponding to ZPF field an be given by m, (8) where represents a damping onstant for Zitterbewegung osillations. 4

5 May17 d As the fore ating on the mass of the body an be desribed by f (mv), then we have f m a v m. Under dt dt the ondition that f, we have a v m dm dt, then enormous aeleration an be produed when the utoff frequeny of ZPF spetrum is redued to be zero around the spaeship from Eq. (8) shown as follows; d a v m d dt m v d 1 v / 1 v / dt 1, (9) where is an upper frequeny of ZPF spetrum and v /. From Eqs. (7) and (9), the probability to tunnel through the light barrier is given by T exp N 1 4 log. (1) When we let / t t, where /, then we have / t m p Eq. (1), the probability to tunnel the light barrier of the spaeship beomes. By inserting them into T exp N 1 4 t log. (11) Supposing that. 1 and 1., t in Eq. (11), the tunneling probability of the spaeship with the mass of 1 tons, that an plunge into FTL state versus the utoff frequeny of ZPF field an be shown in FIG.. From whih, it is possible to travel at the FTL state if we an derease the mass of the spaeraft by the manipulation of ZPF field around the spae ship. FIG.. Possibility to tunnel the light barrier vs. the ZPF utoff frequeny. 5

6 May17 Possibility to manipulate ZPF field around the spaeship If the wave energy emitted by a spaeship in the form of beam interats with vauum eletromagneti zero-point field (ZPF), it perturbs ZPF and dereases zero-point radiation pressure, the zero-point radiation pressure in the rear viinity of spaeship ating upon spaeship. For dereasing ZPF energy, we an utilize negative energy radiation. There are two main approahes to generate negative energy, whih are the Casimir effet and the squeezed vauum. The seond way to obtain negative energy is to squeeze quantum vauum by ultrahigh intensity lasers. By reduing the energy below the zero-point flutuation of vauum, the vauum beomes squeezed, resulting in negative energy. Davis and Puthoff [1] proposed a method by use of an ultrahigh intensity laser oupled with fast moving mirrors. By their method, negative energy an be generated by an array of ultra-intensity lasers using an ultra-fast rotating mirror system to reate the squeezed state of the eletromagneti field, both pulses (positive and negative) are equal in time interval release. Rapidly rotating mirrors in this setup would serve the purpose of separating the positive and negative energy, if the beams hit the mirror at a very shallow angle. Another method would be to superimpose photons upon eah other in order to reate a beam of negative energy proposed by Pfenning [1], the way to squeeze light would be to manufature extremely light ontaining train of pulses and ombine them together to reate squeezed state. For the squeezed vauum state, the density is given by E sinh r[sinh r os r os r os( L )], (1) where numbers. L is the volume of a large box with the length L and r is the squeeze parameter related to the expetation of photon By utilizing these methods, negative energy have just beome available. This suggests that one might oneivably surround a spaeship with a bubble of highly energy-depleted (negative energy) vauum, whih makes possible to derease the mass of the spaeraft to indue violent aeleration, whih makes possible to jump into a FTL mode by quantum tunneling effet as shown in FIG. 4. FIG. 4. Aeleration indued by the manipulation of ZPF field. 6

7 May17 FTL travel of the spaeship in a tahyoni state From the bosoni string world-sheet ation given by 1 S 4 d g g ab a X b X, (1) the spetrum of bosoni strings ontains a tahyoni mode for open strings [14] shown as 1 1 m,,,,, (14) whih allows the existene of negative energy, that leads to the instability of the vauum. This means that the tahyon is an unstable partile, whih is allowed to appear for a short period of time in empty spae and the FTL state of a spaeship maintained within a short period of time. From the unertainty relation for the tahyon shown as follows [15], we an estimate the distane of the spaeship in a FTL state; p t v v. (15) From whih, the differene of momentum before and after penetrating light barrier is m v m v p. (16) v / 1 1 v / If v, then v / v / m m 1, thus Eq. (16) beomes m 1 p, (17) when we suppose m m. From Eq. (15), the traveling distane of the spae ship in a FTL state beomes L v t ( v v ) p v m ( v v) 1 1. (18) 7

8 May17 In the ase when 1 L 1 and v / v is negligibly small, the traveling distane of FTL travel an be roughly estimated by, (19) from Eq. (8), whih alulation result is shown in FIG. 5. FIG. 5. Traveling distane of the spaeship in a FTL state vs. ZPF frequeny around the spaeship. From FIG.. the radial frequeny to plunge into FTL state for the spaeship with the mass of 1 tons an be estimated to be about Hz, then the spaeship an travel in a FTL state with a distane of m from Eq. (19), whih is beyond the distane to the near-by galaxies. Thus, it is shown that tunneling FTL travel an be possible if negative energy an be utilized whih is also used for the onstrution of worm holes [16]. The total negative energy required to anel the positive ZPF field surrounding the spaeship an be roughly estimated by 4R E 4.11 d 41 (J), () if we let 4 R 5m,whih is a radius of the negative energy surrounding the spae ship, 1. 1 s and / 1 4 /s. As the equivalent mass of whih beomes kg, then it is required about a half of the Earth s mass to transport a small spaeship between galaxies. However, is muh lower value, we don t need so muh negative energy. Thus, we suppose that there is some sort of quantum tunneling that might allow a subliminal partile to beome a superluminal partile, it is onsidered that we ould tunnel through suh a light barrier using quantum effet to attain superluminal veloities for spae travel. 8

9 May17 Conlusion In this paper, the author presents an advaned theory that the spaeship an be traveled at superluminal speed by applying the Puthoff s theory on ZPF field. From the theoretial analysis, it an be seen that the FTL travel an be ahieved by the quantum tunneling effet indued by the manipulation of the ZPF spetrum surrounding the spaeship. REFERENCES 1. Benett GL, Forward RL, Frisbee RH. Report on the NASA/JPL workshop on advaned quantum/relativity theory propulsion. Proeeding of the 1st AIAA/ASME/SAE/ASEE Joint Propulsion Conferene, San Diego, CA. 1995:1-.. Forward RL. Spae warps: A review of one form of propulsionless transport. J Br Interplanet So. 1989;4:5:4.. Alubierre M. The warp drive: Hyper-fast travel within general relativity, Class. Quantum Grav. 1994;11:L7-L Finazzi S, Liberati S, Barelo C. Semilassial instability of dynamial warp drive. Phys Rev D. 9;79: Pfenning J, Ford LH. The unphysial nature of warp drive, lass. Quant Grav. 1997;14: Musha T. Possible existene of faster-than-light phenomena for highly aelerated elementary partiles. Speulations Si Tehnol. 1998;1: MLaughlin B. Neutrinos and the speed of light-a primer on the CERN Study; Adam T, Agafonova N, Aleksandrov A, et al. Measurement of the neutrino veloity with the OPERA detetor in the CNGS beam. High Energy Physis-Experiment; Musha T. Superluminal effet for quantum omputation that utilizes tunneling photons. Phys Essays. 5;18(4): Frenh AP, Taylor EF. An introdution to quantum physis. The M.I.T Introdutory Physis Series, MIT Press; Puthoff HE. Gravity as a zero-point-flutuation fore. Phys Rev A. 1998;9(5): Davis EW, Puthoff HE. Experimental onepts for generating negative energy in the laboratory, in proeedings of spae tehnology and appliations international forum (STAIF-6), El-Genk MS, editor. AIP Conferene Proeedings, Melville, New York; 6:16-7p. 1. Pfenning MJ. Quantum inequality restritions on negative energy densities in urved spaetimes. General Relativity and Quantum Cosmology; Szabo RJ. An introdution to string theory and D-brane dynamis, Imperial College Press, London; Park M, Park Y. On the foundation of the relativisti dynamis with the tahyon. IL Nuov Cimento. 1996;111(11): Ford LH, Roman TA. Negative energy, wormholes and warp drive. Sientifi Amerian. ;8: