The Sagnac Effect Falsifies Special Relativity Theory

Transcription

1 The Sagna Effet Falsifies Speial Relativity Theory Ramzi Suleiman,2,3, a). Triangle Researh & Development Center, PO-Box 267, Kfar Qari, 30075, Israel. 2. Department of Psyhology, University of Haifa, Abba Khoushy Avenue 99, Haifa, , Israel. 3. Department of Philosophy, Al Quds University, East Jerusalem and Abu Dies, P.O.B. 5000, Palestine. Abstrat It is believed that the Sagna effet does not ontradit Speial Relativity theory beause it is manifest in non-inertial rotational motion; therefore, it should be treated in the framework of General Relativity theory. However, several well-designed studies have onviningly shown that a Sagna Effet idential to the one manifest in rotational uniform motion is also manifest in transverse uniform motion. This result should have been suffiient to falsify Speial Relativity theory. In the present artile, we offer theoretial support to the experimental results by eluidating the notion that the dynamis of transverse and rotational types of motion are ompletely equivalent. Sine the transverse Sagna effet ontradits Speial Relativity theory, it follows that the rotational Sagna effet ontradits Speial Relativity theory as well. In addition, we show that our reently proposed Information Relativity theory, in whih we abandoned the onstany of the veloity of light axiom, theoretially aounts for the Sagna effet. Key words: Sagna effet, Speial Relativity, Information Relativity, Systems equivalene, GPS. a) suleiman@psy.haifa.a.il I. Introdution The Sagna effet, alled after its disoverer in 93 [], has been repliated in many experiments (for reviews see [2-5]). It is well known that the Sagna effet has ruial appliations in navigation [2, 3, 6] and in fiber opti gyrosopes (FOGs) [7-]. In the Sagna effet, two light beams sent lokwise and ounterlokwise around a losed path on a rotating disk take different time intervals 2 v l to travel the path. For a irular path of radius R, the differene an also be represented as t = 2, where v = ω R is the speed of the irular motion and l=2πr is the irumferene of the irle. Today, FOGs have beome highly sensitive detetors for measuring rotational motion in navigation [2, 6, 0, ]. In the GPS system, the speed of light relative to a rotating frame is orreted by ± ω r, where ω is the radial veloity of the rotating frame and r is the rotation radios. A plus/minus sign

2 is used depending on whether the rotating frame is approahing the light soure or departing from it, respetively. It is laimed that the Sagna effet does not ontradit Speial Relativity theory, sine it is manifest in rotational motion, whih is onsidered an aelerated motion (.f., [2-4]); thus, the effet should be treated in the framework of General Relativity (.f., [5-6]). Despite the abovementioned laim, a orretion for Speial Relativity's time dilation is still implemented in GPS system (alongside with a rotational Sagna orretion)! More importantly, the findings of well-designed experiments ([7-9], see also [20-2]) ontradit the aforementioned laim by demonstrating, unambiguously, that the effet manifest in rotational motion, whih is idential to Sagna effet, is also manifest in transverse uniform motion. The manifestation of a Sagna effet in the latter type of motion should have raised very serious doubts about the validity of Speial Relativity's seond axiom. However, given its entral plae in all physis, the aforementioned axiom ontinues to be an "untouhable" exeption that defies falsifiation. II. On the equivalene between transverse and rotational dynamis In this artile, we give further support to the experimental refutation of Speial Relativity by restating that the theoretial desriptions of the dynamis of transverse and rotational systems are idential, implying that the two types of motion are ompletely equivalent. In systems sienes (.f., [22-23]), the equivalene of two dynamial systems implies that their mathematial desriptions must be indistinguishable. On the one hand, the dynamis of a transversely moving body is ompletely desribed by the variables t (time), x (distane), v (transverse veloity), m (mass), F (Fore), and their interdependenies, as formulated by the laws of transverse motion (see left-side olumn in Table ). On the other hand, the dynamis of a rotating body is ompletely desribed by the variables t (time), θ (angular position), w (angular veloity), I (radial inertia), τ (torque), and their interdependenies, as formulated by the laws of rotational motion (see middle olumn in Table ). A short inspetion of the table reveals that the two sets of equations are equivalent. A general representation of the two systems is depited in the right-side olumn of Table. Confronted with the set of equations appearing in the right-side olumn of the table, we will have no way of knowing whether the system's parameters {p i } and their interdependenies represent a system in transverse or rotational motion (Q.E.D). Note that in the table, we did not speify that the parameter p should represent position; that the parameter p 2 should represent veloity, and so forth. This is beause any physial, biologial, or other dynami system with the same set of parameters {p i } and the same interdependenies desribed in the right-side olumn of Table is equivalent to the two systems of motion disussed here. If the reader is onvined that, in general, the transverse and rotational systems are ompletely equivalent, then the equivalene between the speial ases of uniform motion with onstant veloities v and w, respetively, follows as a orollary. It follows immediately that the laim that the rotational Sagna effet does not ontradit Speial Relativity is a false laim. 2

3 Table Dynamial equations of transverse and rotational systems Translational Radial General p i system parameter i x - Transverse position θ - Angular position p v = dx - Transverse veloity a = dv - transverse aeleration dθ ω= - Angular veloity p 2 = dp dω α= - Angular aeleration p 3 = dp 2 M - Mass I - Radial inertia p 4 F= ma - Newton s seond law τ = I α - Newton s seond law p 5 = p 4 p 3 W= Fdx Transverse work W = τ dθ Angular Work p 6 p 5 dp E= 2 mv2 - Transverse kineti energy E= 2 I ω2 - Angular kineti energy p 7 = 2 p 4 p Another, indiret support for our laim that the Sagna effet ontradits Speial Relativity theory is the fat that the Sagna effet an be derived theoretially from our reently proposed Information Relativity theory (.f., [24-25]) in whih we abandoned the seond axiom of Einstein's Speial Relativity. For a transversely moving detetor with veloity v relative to light soure, the theory presribes that the time duration, as measured by the detetor, of an event with duration Δt taking plae at the light soure, is given by the following Doppler-like formula: Δt = ± v Δt () Where the "+" sign applies when the detetor approahes the light soure and the "-" applies when it is moving away from the light soure. For a path of length l, we have: Δt = l. Substitution in eq. yields: Δt = ± v l = l ± v (2) The differene between the arrival times of two light beams propagating in opposite diretions along the same path is given by: ΔT = ( v - + v ) l = (+v) ( v) ( v)(+ v) l = ( v)(+ v) = 2 v 2 2 (3) 3

4 The above result is idential to the formula whih desribes the rotational and transverse Sagna effet (see [7-8]). III. Summary and onlusions It is ommonly aepted that the manifestation of the Sagna effet in rotational motion does not ontradit Speial relativity, sine the latter applies only to transverse uniform motion and not to rotational motion, whih involves aeleration. The fat that a Sagna Effet, idential to the one manifest in rotational motion, was also deteted in transverse uniform motion [7-20] strongly refutes Speial Relativity Theory. However, given the entral role of the theory's seond axiom in all physis, the above-mentioned results onerning the existene of a Sagna effet in transverse uniform motion has been until now widely negleted. In the present paper, we provided further support to the experimental refutation of Speial Relativity by showing theoretially that the transverse and rotational types of motion are ompletely equivalent dynamial systems. In priniple, we eluidated the fat that when the set of equations desribing the interdependenies between the variables of a rotational (or transverse) dynami system are written using a set of uninformative symbols {p i }, i =,2, n, then we will have no way of knowing whether the system's parameters {p i } and their interdependenies desribe a transverse or a rotational motion. Aordingly, it follows that both the rotational and transverse types of Sagna effets ontradit Speial Relativity. If we aept the priniple that theories are falsified by ontraditory empirial evidene [26-27], then Speial Relativity's seond axiom must be abandoned, no matter how dramati the onsequenes might be. Referenes [] Sagna, M. G. C. R. Aad. Si. 57, , 93. [2] Ashby, N. Relativity in Rotating Frames, Springer, [3] Post, E. J. Rev. Modern Phys. 39, (967). [4] Anderson, R., Bilger, H. R., Stedman, G. E. "Sagna" effet: A entury of Earth-rotated interferometers. Amerian Journal of Physis, 62,, , 994. [5] Malykin, G. B. Earlier studies of the Sagna effet. Phys.-Usp., 40 37, 997. [6] Ashby, N. Relativity and the Global Positioning System. Physis Today, 4-47, May, [7] Chow, W.W. et al. The ring laser gyro. Reviews of Modern Physis, 57 (), 6-04, 985. [8] Vali, V., & Shorthill, R. Appl. Opt. 6, 290, 977. [9] Leeb, W., Shiffner, G., & Sheiterer, E. Appl. Opt. 8, 293, 979. [0] Lefevre, H. The Fiber-Opti Gyrosope. Arteh House: Boston, 993. [] Burns, W. K. Fiber Rotation Sensing, Aademi Press, Boston, 994. [2]. Malykin, G. B. The Sagna effet: orret and inorret explanations. Phys.-Usp., 43, 229, [3] Landau, L., Lifshitz, E. The Classial Theory of Fields, 4 th. Ed. Pergamon: New York, 997. [4] Logunov, A. A., & Chugreev, Y. V. Speial theory of relativity and the Sagna effet, Sov. Phys. Usp., 3 86, 988. [5] Ashtekar, A., & Magnon, A. The Sagna effet in general relativity. J. Math. Phys., 6, 34, 975. [6] Vigier, J. P. New non-zero photon mass interpretation of the Sagna effet as diret experimental justifiation of the Langevin paradox. Physis Letters A 234, 75-85, 997. [7] Wang, R, Zheng, Y., Yao, A., & Langley, D. Modified Sagna experiment for measuring traveltime differene between ounter-propagating light beams in a uniformly moving fiber. Physis Letters A, ,

5 [8] Wang, R., Zheng, Yi, & Yao, A. Generalized Sagna effet. Phys. Rev. Lett., 93 (4), 4390 (3 pages), [9] Ghosal, S. K., & Sarker, M. Cosmologially preferred frame, linear Sagna effet and absolute synhrony, Pro. Physial Interpretation of Relativity Theory Meeting (VI) (Supplementary papers), Imperial College, London, pp , 998. [20] Wang, R. First-order fiber-interferometri experiments for ruial test of light-speed Constany. Galilean Eletrodynamis, 6 (2), 23-30, [2] Gezari, D. Y., Experimental basis for speial relativity in the photon setor. arxiv: , [22] Kalman, R. Mathematial desription of linear dynamial systems. J.S.I.A.M. Control, (2), (963). [23] Ogata, K. System dynamis, Prentie Hall, 4th. edition (2003). [24] Suleiman, R. Information relativity theory solves the twin paradox symmetrially, Physis Essays, 29, (206). [25] Suleiman, R. Information Relativity: The speial and general theory. DOI: 0.340/RG [26] Popper, K. Conjeture and refutation. London: Routledge (963). [27] Sauer, T. Einstein and the early theory of superondutivity. Arhive for History of Exat Sienes, 6, 59 2(2007). 5