An improvement of the accuracy of Fizeau s experiment

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This would make it possible to compare the experimental results with the theoretical predictions of Relativity or of another theory, such as neo-newtonian mechanics.

1 An improvement of the accuracy of Fizeau s experiment o.serret@free.fr Abstract: The purpose is to improve the precision of the measurements of the experiment of Fizeau by replacing the medium liquid water in translation by solid glass in rotation. This would make it possible to compare the experimental results with the theoretical predictions of Relativity or of another theory, such as neo-newtonian mechanics. Résumé : L objet est d améliorer la précision des mesures de l expérience de Fizeau en remplaçant le médium eau liquide en translation par du verre solide en rotation. Cela permettrait de comparer les résultats expérimentaux avec les prédictions théoriques de la Relativité ou d une autre théorie, comme la mécanique néo-newtonienne. Keywords: Fizeau, experiment, water in motion, disk in rotation, Relativity, Neo-Newtonian Mechanics. - o O o 1. Introduction Fizeau realized his experiment with water in motion to try to decide among the different theories of aether [1]. His results served Einstein to reinforce his theory of Relativity [2]. This experiment [3] shows that the Newtonian addition of speeds does not work. On the other hand, according to the experimenters, the measures seem very variable [4] in spite of the modern means; why? 2. Measurement, uncertainty and new experiment Depending on the medium, the water in Fizeau's experience, the speed of light varies. From this difference in speed of light, it is possible to create luminous interferences with an alternation of light lines and dark lines, the Fringe Shift (FS). By measuring this FS, we can deduce the variation in the speed of light. And by putting the water in motion, the FS varies, one can thus deduce the law of addition of velocities (see Fig.1). Figure 1: Experimental and Theoretical Fringe Shift GSJ April 1st, 2018 O. Serret 17

$With current laser technology, the wavelength of the light wave is stable and accurately known; the same is true of refractive indices.$

2 With current laser technology, the wavelength of the light wave is stable and accurately known; the same is true of refractive indices. On the other hand, the uncertainty of measurement on moving water (see Fig.2) generates different types of uncertainty as describe hereafter: the systematic errors are dominated by our flow rate measurement. A more careful calibration should thus be performed in order to improve the accuracy. Then, the factor of about 1.16 due to the shape of the velocity profile should be measured for our system. A final source of uncertainty is the determination of the actual length ( ). In practice, the flow makes a right-angle turn at each end of the pipes. The velocity distribution is affected up and downstream on length scales presumably on the order of the pipe diameter d. This implies a correction of order dl (i.e., on the percent level) but, again, an accurate estimation is difficult. [5] Figure 2: uncertainty on water motion This is why it is proposed here to change the medium, replacing water with glass. The water in rectilinear motion is replaced by a rotating glass disk (Fig. 3). GSJ April 1st, 2018 O. Serret 27

It is assumed that only the velocity component parallel to the light axis will intervene in the light propagation velocity.

Theoretical results Depending on the theory tested, we obtain different results.

neo-newtonian mechanics (*) * Note: Neo-Newtonian mechanics is Newtonian mechanics without the principle of equivalence, that is to

3 It is assumed that only the velocity component parallel to the light axis will intervene in the light propagation velocity. Figure 3: Improved Experience with a Rotating Glass Disc 3. Theoretical results Depending on the theory tested, we obtain different results. Look (see Table 1) - the traditional Newtonian mechanics - the aether theory according to Fizeau - the theory of Relativity - the neo-newtonian mechanics (*) * Note: Neo-Newtonian mechanics is Newtonian mechanics without the principle of equivalence, that is to say with a gravitational mass different from the inert mass (of a gamma factor). Theory Formula Réf Newtonian 2 (1) Aether (2) Relativity Neo-Newtonian (3) See formulas [6] hereafter Table 1: the different theoretical formulas GSJ April 1st, 2018 O. Serret 37

With this experience, it should be easy to discriminate these two theories. 4.

4 (4.a-b) From the following experimental data, we obtain the following theoretical results as shown in Figure 4. Figure 4: theoretical results Neo-Newtonian theory gives results 25% lower than those predicted by the theory of Relativity. With this experience, it should be easy to discriminate these two theories. 4. Conclusion It would be interesting for a laboratory to realize this experiment with a solid transparent medium in rotation, if only to reinforce, or not, the theory of Relativity. GSJ April 1st, 2018 O. Serret 47

5 5. References 1. Weinstein G., Albert Einstein and the Fizeau 1851 Water Tube Experiment, Arxiv (2012), 2. Einstein A., Relativity the Special and General theory, pages (1920), 3. Fizeau H., Hypothèses relatives à l éther lumineux, Académie des Sciences (1851), 4. Maers A. &, The Fizeau Experiment: Experimental Investigations of the Relativistic Doppler Effect, ARP page 306 (2013), 5. Lahaye T., Labastie P. and Mathevet R., Fizeau s Aether-Drag Experiment in the Undergraduate Laboratory, AM J PHYS, 80, pp (2012), DOI: Serret O., Velocity Addition Demonstrated from the Conservation of Linear Momenta, an Alternative Expression, Journal of Modern Physics, 6, (2015), Appendix 1: Conversion FS = Fringe Shift By hypothesis, δ = optical path length difference n = refractive index u = light celerity difference 6. APPENDIX!" $ % & (A.1) $ 2' (A.2) ( ) * + ) * (A.3.a-b) (A.4) Then!", -. ) ) * * + (A.5)!",) -. * * +.* (A.6)!",) 2. * -. ) (A.7)!",.2 -. ) (A.8) GSJ April 1st, 2018 O. Serret 57

6 Appendix 2: Disc and Velocity Figure 5: Disc and Velocity ; <=>9? : (A.10.a-b-c) Then sin: (A.11) sin: ; & (A.12) D 5sin: & (A.13) EF (A.14) And ' 2 D cos: & (A.15) GSJ April 1st, 2018 O. Serret 67

7 Appendix 3: Application 8: & 8: IJ; 9 3 K+: IJ; M : & + 9 +K+9 N (A.20.a-b-c) Then M : & : IJ; : & + 9 N : IJ; + 9 N (A.21) (A.22) 8: & sin : & + 9 N 8: & sin: &.cos 9 N +cos: &.sin 9 N 1+cotg: & (A.23) (A.24) (A.25) : & R47S 2 1 (A.26) Numerical application If n=1.52 for λ=532 nm, then : & 41 and : IJ; 86 With a disc of 1.3 meter of perimeter (Ø=0.42 m) and a rotational velocity of 50 turns, it would give w =50 ms (or 180 kms) and L=0.31 m GSJ April 1st, 2018 O. Serret 77

Velocity Addition Demonstrated from the Conservation of Linear Momenta, an Alternative Expression

Journal of Modern Physics, 015, 6, 719-78 Published Online May 015 in SciRes http://wwwscirporg/journal/jmp http://dxdoiorg/10436/jmp01566077 Velocity Addition Demonstrated from the Conservation of Linear