The Doppler Factor and Quantum Electrodynamics Basics in Laser-Driven Light Sailing

Transcription

1 International Letters of Cemistry, Pysics and Astronomy Online: ISSN: , Vol. 19, pp doi: / 013 SciPress Ltd., Switzerland Te Doppler Factor and Quantum Electrodynamics Basics in Laser-Driven Ligt Sailing Gabriel James Tambunga 916 S. Deli Street, Piladelpia, PA 19147, U.S.A. address: ABSTRACT Basic concepts in Quantum Electrodynamics (QED) and te doppler factor were applied to laser-driven ligt sailing, were tis combination was not considered before. QED indicates tat a reflection is an absorption and an emission of discreet energy, and te doppler factor indicates a cange in velocity of a reflector would result in te reflector observing a cange in wavelengt from a source. Applying tese concepts results in te reflectors available discrete energy states not being filled, after te reflector canges its velocity. Canges in te apparatus of te laser-driven ligt sail and canges in te current understanding of te transfer of momentum from ligt to matter for effective laser-driven ligt sailing are suggested. Keywords: Quantum Electrodynamics; Doppler Factor; Laser-Driven Ligt Sailing 1. INTRODUCTION In 1966 it was teorized tat space traveling was possible by te use of lasers [1]. Tis idea was re-enforced by furter calculations [,3] and remains a possibility [4]. Tis idea is based on te source, te laser, aving a constant wavelengt wile te reflector results in a cange in momentum after a reflection; te cange in momentum of a reflector can result in a doppler sift, were te reflector, from te reflectors perspective, would view a larger wavelengt, or decrease in frequency, of te lasers potons. Te doppler sift was previously considered [5,6]. However, Quantum Electrodynamics indicates a reflection is two events, an absorption and emission of a poton, were te energy tat is absorbed and emitted is discreet [7,8]; and an absorption of a poton is based on available energy states of an atom [9-11], or for a reflector for tis paper. Tis implies te reflector may not reflect te lasers emissions if te cange in momentum of te reflector results in wavelengts tat are too low in energy, from te reflectors perspective, for te available energy states, of te reflector, wic are used in reflection. Laser cooling considered tis by using lasers of increasing frequencies to slow down particles. Tat is, wen a particle is approacing a source, te particles view te lasers emissions as iger in energy, so te laser must ave a lower energy emission so te particles SciPress applies te CC-BY 4.0 license to works we publis: ttps://creativecommons.org/licenses/by/4.0/

2 International Letters of Cemistry, Pysics and Astronomy Vol discreet available energy states can be filled for a reflection to occur; and after te reflection, to slow te slower particle furter, te lasers emissions would need to be sligtly increased but still lower in energy, as compared to te particle at te same moving reference frame as te source, for anoter reflection to occur [1,13]. In tis paper te doppler effect of a reflection will be discussed wit te consideration tat te reflectors available energy states will be uncanging from te perspective of te reflector. Te results of tis paper will suggest canges in te apparatus for laser travel in space.. ABSOPTION AND EMISSION Te source, or laser, for interstellar laser travel would need to cange so te reflector can view te frequency of te potons, from te source, to be consistent if te source is to continually provide momentum to te reflector. If te reflector requires frequency f r, ten te source frequency would be wic is acquired from te doppler factor f r f s f o, (a) were β = v/c, f s is te frequency from te source and f o is te observed frequency. Equation (a) represents te frequency relationsips for te absorption part of te reflection. For absorption, te energy of te poton is temporarily stored in te atoms/molecules, leaving no excess energy for te reflector to be in motion. For an emission tere is a drop in energy state, of te atoms/molecules, wic is equal to te energy of te emission, were again tere is no excess energy for te reflector to be in motion., 3. CONSERVATION OF ENERGY Considering only te energy, tere would be no motion resulting from te absorption or emission from te reflectors perspective. However, te energy from te source, from te sources perspective, is not equal to te energy from te reflector. Tat is, te frequency from te reflector would be f r. (b) Toug energy is conserved from te reflectors perspective, te source would view a loss of Er, (c)

3 1 Volume 19 from te energy emitted and received, were E r = f r. To determine were te loss of energy went to, te momentum of te potons will be considered. Using te relations p = /λ and c = λf, te momentum from te source is r, (d) te momentum te reflector sees is /λ r, and from te sources perspective, te reflector emits r. (e) Considering parallel vectors, as te vectors are in opposite directions te resultant vector would be r, (f) pointing in te direction of te source poton. Tis implies te energy can be transferred to motion from te sources perspective. However, for te conservation of energy to be conserved, kinetic energy resulting from a reflection occurs as a result of te doppler sift from te sources perspective and not a direct excange of energy between poton and reflector. 4. CONSERVATION OF MOMENTUM For te conservation of momentum to be conserved tere are two viewpoints tat will be considered Viewpoint One Te first viewpoint is te current belief tat tere is a transfer of momentum from te potons to te reflector upon absorption [9-11], were te reflectors momentum would be /λ r in its iger energy state, from te reflectors perspective. From tis same perspective, recoil of te reflector, after emission, would cange te momentum to /λ r, as te momentum acquired from te recoil is equal to te momentum of te emitted poton. Furter, as te emission and recoil would appen at te same time, te momentum of te returning poton, from te sources perspective, would be were: ' ' r,

4 International Letters of Cemistry, Pysics and Astronomy Vol and m is te mass of te reflector. Te momentum of te reflector, from te sources perspective, would ten be r ' ' Comparing te increase in momentum from te reflectors perspective to te sources perspective yields r r r ' ' Tat is, despite velocity of te reflector or wavelengt of te poton from te source, te momentum would not go beyond /λ r. Simple spreadseet calculations indicate r r ' ' for all values of velocity, v, or source wavelengt. Similarly, comparing te energy gain of te reflector, /mλ r, after recoil from te reflectors perspective, to te poton energy before and after reflection, from te sources perspective, yields r m E r ' ' for all values of velocity, v, or source frequency after simple spreadseet calculations. From tis viewpoint, conservation of momentum and energy are not always conserved. 4.. Viewpoint Two Te second viewpoint as not been considered before, to te autors knowledge. Tat is, momentum is absorbed into te energy state of te atoms/molecules, and does not transfer to te atom/molecules distinctly from te energy; te emitted vector from te reflector canges te speed and direction of te universe, from te reflectors perspective, if te vector leaving te reflector is not identical to te absorbed vector, were te absorbed vector originates from a moving source; and te energy lost from te sources perspective is equal to te energy gained in te reflectors perspective, and vice versa for a mirror slowing down due to laser emissions. From tis viewpoint, te momentum and kinetic energy of te reflector, after a reflection, are results of a doppler sift, from te sources perspective; tereby, conserving energy and momentum. r r E r 5. CONCLUSION Equations (a) to (f) can be applied to a reflector moving away from a source, to increase its energy and momentum, and a reflector moving toward a source, to decrease its energy and momentum; were te sign of te velocity is positive if te reflector is moving in te direction of te sources emissions and negative if moving towards. Te equations also imply tat a

5 14 Volume 19 monocromatic source may not be adequate for a reflector intended to increase or decrease in velocity, as te reflector would see different wavelengts tan te source emits after a cange in te reflectors velocity. Te source potons would need to cange in wavelengt and/or te reflector must be capable of reflecting multiple wavelengts, possibly beyond te visible spectrum. Tese equations and te second viewpoint are not consistent wit current beliefs [6,10], but can be easily proven or disproven, wic is beyond tis teoretical introduction presented in tis paper. However, if a reflector can be designed to maintain an adiabatic excited energy state for a measurable time, ten an increase in te velocity of te reflector would be at about alf tis time according to te first viewpoint, or at about tis time according to te second viewpoint. References [1] G. Marx, Nature 11 (1966) -3. [] J. L. Redding, Nature 13 (1967) [3] J. F. L. Simmons, C. R. Mcinnes, Am. J. Pysics 61 (1993) [4] Y. K. Bae, Pysics Procedia 38 (01) [5] A. Macleod, ttp://arxiv.org/abs/pysics/ (004) pages. [6] C. R. Mcinnes, Solar Sailing: Tecnology, Dynamics and Mission Applications, Springer-Verlag, London, (004). [7] M. Fox, Quantum Optics, An Introduction, Oxford University Press, New York, (006). [8] V. B. Berestetskii, L. P. Pitaevskii, Quantum Electrodynamics, Elsevier, Burlington, MA, (198), ed. : vol. 4. [9] G. S. Summy, B. Lomann, W. R. MacGillivray, M. C. Standage, Z. Pys. D. 30 (1994) [10] G. S. Summy, W. R. MacGillivray, M. C. Standage, J. Pys. B: At. Mol. Opt. Pys. 9 (1996) [11] G. S. Summy, B. T. H. Varcoe, W. R. MacGillivray, M. C. Standage, J. Pys. B: At. Mol. Opt. Pys. 30 (1997) L541-L549. [1] T. W. Hansc, A. L. Scawlow, Optics Communication 13 (1975) [13] W. D. Pillips, H. Metcalf, Pysics Review Letters 48 (198) ( Received 9 August 013; accepted 0 September 013 )