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

ABSTRACT

Is it possible to demonstrate the velocity addition without using a variable time (as it is done in theory of relativity)? The topic of this paper is to propose and demonstrate an alternative expres-sion based on the conservation of linear momenta. The method proposed here is to start from a physical object (and not from a mathematical point), i.e. from an object with a mass. And the hy-pothesis is inertial mass to be different from gravitational mass. Then, when impulses are added, we get an expression of the velocity addition itself. When numerical predictions are compared with experimental results, the differences are lower than the measures uncertainty. And these numerical results are much close to those predicts by the theory of relativity, nevertheless with a little difference at high velocities. If this demonstration and this expression were validated, it would allow giving an alternative explanation to some experiments and nature observations as Doppler Effect on light celerity. But first, it would be necessary to get from laboratories more precise experimental results, in order to validate or not this hypothesis of the sum of linear momenta with a Variable Inertial Mass.

Is it possible to demonstrate the velocity addition without using a variable time (as it is done in theory of relativity)? The topic of this paper is to propose and demonstrate an alternative expres-sion based on the conservation of linear momenta. The method proposed here is to start from a physical object (and not from a mathematical point), i.e. from an object with a mass. And the hy-pothesis is inertial mass to be different from gravitational mass. Then, when impulses are added, we get an expression of the velocity addition itself. When numerical predictions are compared with experimental results, the differences are lower than the measures uncertainty. And these numerical results are much close to those predicts by the theory of relativity, nevertheless with a little difference at high velocities. If this demonstration and this expression were validated, it would allow giving an alternative explanation to some experiments and nature observations as Doppler Effect on light celerity. But first, it would be necessary to get from laboratories more precise experimental results, in order to validate or not this hypothesis of the sum of linear momenta with a Variable Inertial Mass.

KEYWORDS

Velocity Addition, Variable Time, Variable Inertial Mass, Relativity, Light Celerity, Impulse, Linear Momentum, Kinetic Energy, Fizeau’s Experiment

Velocity Addition, Variable Time, Variable Inertial Mass, Relativity, Light Celerity, Impulse, Linear Momentum, Kinetic Energy, Fizeau’s Experiment

Cite this paper

Serret, O. (2015) Velocity Addition Demonstrated from the Conservation of Linear Momenta, an Alternative Expression.*Journal of Modern Physics*, **6**, 719-728. doi: 10.4236/jmp.2015.66077.

Serret, O. (2015) Velocity Addition Demonstrated from the Conservation of Linear Momenta, an Alternative Expression.

References

[1] Bonnet-Bidaud, J.-M. (2008) Astrophysician at CEA (Commissariat a l’Energie Atomique). Les preuves etaient fausses.

http://www.cieletespace.fr/evenement/relativit-les-preuves-taient-fausses

[2] Wikipedia, History of Special Relativity.

http://en.wikipedia.org/wiki/History_of_special_relativity

[3] Einstein, A. (1979) La relativite, from Edition Payot.

[4] Serret, O. (2015) Journal of Modern Physics, 6, 252-259.

http://dx.doi.org/10.4236/jmp.2015.63030

[5] Serret, O. (2012) Mass of Inertia and Kinetic Energy.

http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/4113

[6] Serres, M. and Farouki, N. (1997) Le Tresor-Dictionnaire des Sciences. Ed. Flammarion, 1037.

[7] Landau, L.D. and Lifshitz, E.M. (1960) Mechanics. Pergamon Press, Oxford, 4-6.

[8] Noether’s Theorem.

http://en.wikipedia.org/wiki/Noether%27s_theorem

[9] Lahaye, T., Labastie, P. and Mathevet, R. (2012) Fizeau’s “Aether-Drag” Experiment in the Undergraduate Laboratory.

http://arxiv.org/abs/1201.0501

[10] Fizeau, H. Hypotheses relatives a l’ether lumineux.

http://www.orgonelab.org/EtherDrift/Fizeau1851.pdf

[1] Bonnet-Bidaud, J.-M. (2008) Astrophysician at CEA (Commissariat a l’Energie Atomique). Les preuves etaient fausses.

http://www.cieletespace.fr/evenement/relativit-les-preuves-taient-fausses

[2] Wikipedia, History of Special Relativity.

http://en.wikipedia.org/wiki/History_of_special_relativity

[3] Einstein, A. (1979) La relativite, from Edition Payot.

[4] Serret, O. (2015) Journal of Modern Physics, 6, 252-259.

http://dx.doi.org/10.4236/jmp.2015.63030

[5] Serret, O. (2012) Mass of Inertia and Kinetic Energy.

http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/4113

[6] Serres, M. and Farouki, N. (1997) Le Tresor-Dictionnaire des Sciences. Ed. Flammarion, 1037.

[7] Landau, L.D. and Lifshitz, E.M. (1960) Mechanics. Pergamon Press, Oxford, 4-6.

[8] Noether’s Theorem.

http://en.wikipedia.org/wiki/Noether%27s_theorem

[9] Lahaye, T., Labastie, P. and Mathevet, R. (2012) Fizeau’s “Aether-Drag” Experiment in the Undergraduate Laboratory.

http://arxiv.org/abs/1201.0501

[10] Fizeau, H. Hypotheses relatives a l’ether lumineux.

http://www.orgonelab.org/EtherDrift/Fizeau1851.pdf