Parameterized Special Theory of Relativity (PSTR)

Transcription

1 Apeiron, Vol. 19, No., April Parameterized Speial Theory of Relativity (PSTR) Florentin Smarandahe University of New Mexio Gallup, NM 87301, USA We have parameterized Einstein s thought experiment with atomi loks, supposing that we knew neither if the spae and time are relative or absolute, nor if the speed of light was ultimate speed or not. We have obtained a Parameterized Speial Theory of Relativity (PSTR) (198). Our PSTR generalized not only Einstein s Speial Theory of Relativity, but also our Absolute Theory of Relativity, and introdued three more possible Relativities to be studied in the future. After the 011 CERN s superluminal neutrino experiments, we reall our ideas and invite researhers to deepen the study of PSTR, ATR, and hek the three new mathematially emerged Relativities 4.3, 4.4, and 4.5. Keywords: Speial Theory of Relativity, Absolute Theory of Relativity, Parameterized Relativity, Thought Experiments 01 C. Roy Keys In.

2 Apeiron, Vol. 19, No., April Einstein s Thought Experiment with the Light Cloks. There are two idential loks, one is plaed aboard of a roket, whih travels at a onstant speed v relative to the earth, and the seond one is on earth. In the roket, a light pulse is emitted by a soure from A to a mirror B that reflets it bak to A where it is deteted. The roket s movement and the light pulse s movement are orthogonal. There is an observer in the roket (the astronaut) and an observer on the earth. The trajetory of light pulse (and impliitly the distane traveled by the light pulse), the elapsed time it needs to travel this distane, and the speed of the light pulse at whih is travels are pereived differently by the two observers {depending on the theories used see below in this book}. Aording to the astronaut: Fig. 1 B A d d t ' (1) where: t ' = time interval, as measured by the astronaut, for the light to follow the path of distane d ; d = distane; 01 C. Roy Keys In.

3 = speed of light. Apeiron, Vol. 19, No., April Aording to the observer on earth: Fig. B A s A B l l l v t () s = AB = BA (3) d = BB (4) l = AB = B A (5) t = time interval as measured by the observer on earth. And where using the Pythagoras Theorem in the right triangle ABB, one has vt s d l d (6) 01 C. Roy Keys In.

4 but s t Apeiron, Vol. 19, No., April , whene vt t d (7) Squaring and omputing for t one gets: d 1 t v 1 Whene Einstein gets the following time dilation: where t t'. t t ' v 1 (8) (9). Parameterized Speial Theory of Relativity (PSTR) In a more general ase when we don t know the speed x of the light as seen by the observer on earth, nor the relationship between t ' and t, we get: 01 C. Roy Keys In.

5 Apeiron, Vol. 19, No., April But d t' vt d x t, therefore: (10) xt t' vt (11) Or x t t' v t Dividing the whole equality by whih is the PSTR Equation. (1) t we obtain: t' x v t (13) 3. PSTR Elapsed Time Ratio (Parameter). We now substitute in (10) for a general ase t ' (0, ) t (14) where is the PSTR Elapsed Time Ratio. Therefore we split the Speial Theory of Relativity (STR) in the below ways. 01 C. Roy Keys In.

6 Apeiron, Vol. 19, No., April PSTR Extends STR, ATR, and Introdues Three More Relativities. v If [1]), sine replaing x by, one has t' v t, t or, i.e. Lorentz s fator, we get the STR (see v t', t' v t 1 [0,1] as in the STR. 4..If =1, we get our Absolute Theory of Relativity (see []) in the partiular ase when the two trajetory speed vetors are perpendiular, i.e. x v = v. 01 C. Roy Keys In.

7 0 4.3.If Apeiron, Vol. 19, No., April v 1, the time dilation is inreased with respet to that of the STR, therefore the speed x as seen by the observer on earth is dereased (beomes subluminal) while in STR it is. v 4.4.If 1there is still time dilation, but less 1 than STR s time dilation, yet the speed x as seen by the observer on earth beomes superluminal (yet less than in our Absolute Theory of Relativity). About superluminal veloities see [3] and [4]. t' t ) 4.5.If >1, we get an opposite time dilation (i.e. with respet to the STR (instead of t' t ), and the speed x as seen by the observer on earth inreases even more than in our ATR. Further Researh The reader might be interested in studying these new Relativities mathematially resulted from the above 4.3, 4.4, and 4.5 ases. Referenes [1] Einstein, A., Zur Eletrodynamik bewegter Körper, Annalen der Physik, Vol. 17, pp , 1905; 01 C. Roy Keys In.

8 Apeiron, Vol. 19, No., April 01 1 [] Smarandahe, F., Absolute Theory of Relativity & Parameterized Speial Theory of Relativity & Noninertial Multirelativity, Somipress, 9 p., 198. [3] Smarandahe, F., There is No Speed Barrier in the Universe, mss., Lieul Pedagogi Rm. Vlea, Physis Prof. Elena Albu,197; [4] Rabounski, D., A blind pilot: who is super-luminal observer? Progress in Physis, Vol., C. Roy Keys In.