Proposal of atomic clock in motion: Time in moving clock

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1 Proposal of aomic clock in moion: Time in moving clock Masanori Sao Honda Elecronics Co., d., 0 Oyamazuka, Oiwa-cho, Toyohashi, ichi , Japan msao@honda-el.co.jp bsrac: The ime in an aomic clock in moion is discussed using he analogy of a sing around sound source. Sing around frequency is modified according o he moion of he sing around sound source, using he orenz ransformaion equaion. Thus, if we use he sing around frequency as a reference, we can define he reference ime. We propose ha he ime delay of an aomic clock in moion be derived using he sing around mehod. In his leer, we show ha ime is defined by a combinaion of ligh speed and moion. PCS numbers: p Key words: omic clock in moion, orenz ransformaion, Michelson-Morley experimen, special relaiviy, sing around 1. INTRODUCTION The derivaion of he orenz ransformaion equaion was clearly described by Feynman e al. [1]. The Doppler shif equaion was observed o be differen beween acousic wave and ligh, hus we deermined he reason for his difference []. We poined ou ha he frequency of a sound source should be modified according o is moion. We proposed a sing around sound source whose frequency changes wih is velociy, as is suggesed by he orenz ransformaion equaion. We discussed he reference frequency of a moving sound source wih respec o he orenz ransformaion equaion. The sing around sound source moving in air exhibis a decrease in frequency. If he modified frequency is used as a reference frequency, he ime delay in a moving frame can be explained []. We also proposed a number of feasible experimens [3, 4]. These experimens are concerned wih signaling by quanum enanglemen [3] and inerference [4], and may provide for anoher inerpreaion of special relaiviy. We clearly accep he heory of special relaiviy. However, a his sage, we are no saisfied wih 1

2 is curren inerpreaion, because invesigaing phenomena using is curren inerpreaion is difficul. We believe ha special relaiviy can be defined in a simpler manner. In his sudy, o define he ime delay in moion, we propose a use of he analogy of a sing around sound source in moion.. TOMIC COCK IN MOTION. nalogy of sing around sound source in moion In acousic waves, for he measuremen of sound speed, no only inerference bu also he sing around mehod is used. The sing around mehod uses wo pairs of ransmiers and receivers as shown in Fig. 1, where a pulsed signal is ransmied by ransmier 1 and deeced by deecor. fer is deecion, he pulsed signal is amplified by amplifier, and a new pulsed signal is ransmied by ransmier, deeced by deecor 1, ransmied again by ransmier 1, and so on. The frequency of he sing around sound source was deermined on he basis of he repeiion of pulsed acousic waves, and deeced using he frequency couner. Transmier 1 Receiver Going pah R Pulsed sound mplifier 1 mplifier Reurning pah T Receiver 1 Transmier Frequency couner Fig. 1 Sing around sound source a res. Now le us consider he frequency modificaion according o he moion of he sing around sound source. Here, we show ha he frequency of he sing around sound soured is defined by he raveling ime of he pulsed sound beween a ransmier and a receiver. ccording o he moion of he sing around sound source, he raveling disance of he pulsed sound is increased. Therefore, he moion of he sing around sound source in air decreases he sing around frequency. The frequency modificaion according o he moion of he sound source depends on he relaionship beween he sound direcion and he moion direcion of he sound source. If he sing around sound source moves ransverse o he sing around direcion, i.e., θ = π/, where θ is he angle beween he sound direcion and he moion direcion of he sound source shown in Fig., we obain ( c = + v. 1 ) ( 1)

3 Thus, c 0 1 = = = (1), c v v 1 c v 1 c where c is he sound speed, 1 is he ime when a pulsed sound arrives a posiion R, is he pah beween a ransmier and a receiver when he sing around sound source is a res, and v is he velociy of he sing around sound source, 0 = /c is he reference ime a res, whereas 1 is ha in moion. The represenaion of he modified frequency is similar o ha of he orenz ransformaion. θ = π/ = 0 v 1 Going pah = c 1 R = 1 T Reurning pah = c 1 = 1 Fig. Sound pah of he sing around sound source in moion. The direcion of moion is ransverse o he direcion of sound, i.e., θ = π/. Sing around frequency can be deermined. I is because he going and reurning pahs are equal. 3

4 If he sing around sound source moves parallel o he sound direcion, he sing around frequency canno be deermined, because he going and reurning raveling imes of he sound are differen. Figure 3 shows ha a θ = 0, he going ime is = and he reurning ime 3 is c v 3 = ; hus, is no equal o 3. Therefore, we canno define he sing around frequency. The c v + sing around frequency has a resonance whose sharpness depends on he velociy v and angle θ. The resonance condiion is θ = π/, and he larger he velociy v, he sharper he resonance. c v = 0 = = 0 = R R T = = + 3 = = + 3 T v 3 c 3 Fig. 3 Sound pah of sing around sound source in moion. The direcion of moion is parallel o he direcion of sound. Going ime is he period ha pulsed sound ransmied from is received by R, going pah is c. We obain he equaion c = + v. Reurning ime 3 is he period ha pulsed sound ransmied from T (a he ime ) is received by R (a he ime = + 3 ). Reurning pah is c 3, we obain he equaion c 3 = - v 3, 3 is no equal o. 4

5 s menioned above, he sing around frequency is defined as he frequency of repeiions. The frequency of repeiions is used as a fundamenal (reference) frequency which can be used o define ime. We noe here he analogy beween he sing around sound source and he aomic clock, in ha he reference frequency is deermined on he basis of he velociy of he moion v as he represenaion of he orenz ransformaion. We propose ha he reference ime, which is defined by he fundamenal frequency, of he aomic clock is similar o he frequency definiion mechanism of he sing around sound source. B. omic clock in moion There are similariies beween he sing around sound source and he aomic clock. We can apply he concep of he sing around sound source o he aomic clock. The reference ime of he aomic R 1 P θ v R Fig. 4 Sound direcion and he direcion of source moion. cousic waves are irradiaed from poin sound source P for all direcions. The inensiy of sing around frequency is proporional o sinθ, for example, a θ = π/ reflecion poins are on he circle π, a θ = 0 reflecion poins are only R 1 and R. Resonance condiion is θ = π/, i.e., on his condiion going ime and reurning ime is equal, hen sing around frequencies can be defined, whose frequency is represened by orenz ransformaion. ccording o he analogy of sing around sound source, we can define he ime of aomic clock in moion. clock in moion can be deermined on he basis of he fligh ime of phoons. The phoon in he aom in moion ravels a longer disance han he aom a res. e us consider he elecromagneic phenomenon in an aom. This phenomenon occurs hrough a phoon. e us discuss he fligh ime of a phoon in an aomic clock. s menioned above, we assume ha informaion is ransmied hrough phoon; he ime of he aomic clock is hen defined by he fligh ime of he phoon. Phoons in an aomic clock in moion have o ravel a longer disance han hose in an aomic clock a res. If he aomic clock moves a he velociy v, he phoons ravel differen disances according o he direcion of fligh. Phoons in an aomic clock a res are emied in all 5

6 direcions and have he same raveling disance independen of heir direcions. However, in moion, he ravel disance of he phoons depends on heir direcion. Figure 4 shows he probabiliy of phoon arrival, where θ is he direcion beween he aomic clock moion and he raveling phoon. The probabiliy of phoon arrival depends on sinθ. θ =π/, as menioned in secion., we obain ( c = + v ; hus, equaion (), which is similar o equaion (1), is 1 ) ( 1) 0 1 = = = (), c v c v v 1 1 c c where c is ligh he speed, 1 is he ime when a phoon arrives a posiion R, is he phoon pah in he aomic clock a res, and v is he velociy of he aomic clock in moion, 0 = /c is he reference ime in he aomic clock a res, whereas 1 is he reference ime in he aomic clock in moion. The probabiliy of phoon arrival is proporional o sinθ, and he mos frequen case is a θ = π/. This indicaes ha he probabiliy ha a phoon moves parallel or aniparallel o he aom moion is very low. θ = π/, we obain a high probabiliy. 3. DISCUSSION We discuss elecromagneic phenomena, for example, he radiaion of an aomic clock. Elecromagneic phenomena occur hrough phoons, i.e., hey are exchanges of phoons. ccording o equaion (), he phoon pah is geomerically expanded when he aomic clock is in moion. (Here, is for an aom radius.) Therefore, i akes more ime in he aomic clock in moion han in he aomic clock a res. We assume ha he exchanges of phoons occur resonanly. I is because only he phoon moving ransversely o he aom moion direcion can be modified as shown in equaion (). The phoon moving parallel o he aom moion direcion canno paricipae in elecromagneic phenomena, because he resonan frequency canno be deermined. Of course he resonan exchange of phoons is a highly speculaive hypohesis, however large amoun of experimenal daa show ha equaion () is enirely accurae, indicaing ha hese daa are in accordance wih he hypohesis. The represenaion of phoon exchange as well as ha of resonance, is ambiguous. Tesing he hypohesis by experimen is no feasible; however, simple geomerical represenaion is aracive. We can direcly derive he orenz ransformaion equaion for ime delay geomerically, which is differen from he convenional echnique. The convenional echnique of deriving he orenz ransformaion equaion is shown in he appendix. 4. CONCUSION In his leer, we showed ha ime is a combinaion of ligh speed and moion. We discussed he 6

7 ime in he aomic clock in moion, using he analogy of he sing around sound source. The sing around frequency is modified according o he moion of he sing around sound source, using he orenz ransformaion equaion. If we use he sing around frequency as he reference, we can define he reference ime. We propose ha he ime delay of he aomic clock in moion be derived using he sing around mehod. References 1) R. P. Feynman, R. B. eighon, and M. Sands, The Feynman ecures on Physics Vol. 3 (ddison Wesley, Reading, M, 1965). ) M. Sao, "Doppler shif of acousic waves and orenz ransformaion," IEICE, [Ulrasonic], US004-9, (in Japanese). 3) M. Sao, "Proposed experimen of local momenum ransfer in Young's double sli," quan-ph/ ) M. Sao, "Proposed experimen on he coninuiy of quanum enanglemen," quan-ph/ ) M. Sao, "Proposal of Signaling by Inerference Conrol of Delayed-Choice Experimenal Seup," quan-ph/ ppendix: Derivaion of orenz ransformaion equaion From he resuls of he Michelson-Morley experimen, 1 = + 3 was confirmed, where 1 and are represened by equaions (1) and () respecively. Therefore, he disance is assumed o shrink. is he disance measured verically o he moion direcion, and is he disance measured parallel o he moion direcion, c v = +, c v c + v v = 1. (.1) c This is he orenz ransformaion equaion for disance. 7