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Cosmic Adventure 5.1 Relative Motion in Special Relativity

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The classical equations of relative motion are translated by the theory of Special Relativity into relativistic equations. The origin of the Lorentz factor recapitulated.

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Cosmic Adventure 5.1 Relative Motion in Special Relativity

1. 1. © ABCC Australia 2015 new-physics.com FROM GALILEAN TO EINSTEINIAN Cosmic Adventure 5.1
2. 2. © ABCC Australia 2015 new-physics.com what is wrong with them? They are not valid when the speed of light is considered You know what is wrong with your equations?
3. 3. © ABCC Australia 2015 new-physics.com System x: 𝑥′ = 𝑥 − 𝑣𝑡 𝑦′ = 𝑦 𝑧′ = 𝑧 𝑡′ = 𝑡 System x’: 𝑥 = 𝑥′ + 𝑣𝑡 𝑦 = 𝑦′ 𝑧 = 𝑧′ 𝑡 = 𝑡′ Because in between frames, you should have light speeding along No Light Involved
4. 4. © ABCC Australia 2015 new-physics.com To take the speed of light into consideration, you need to have a Lorentz transformation with the Lorentz factor! 𝛾 = 1 1 − 𝑣2 𝑐2
5. 5. © ABCC Australia 2015 new-physics.com
6. 6. © ABCC Australia 2015 new-physics.com 𝑥′′ = 𝑥′ − 𝑣𝑡 1 − 𝑣2 𝑐2 𝑡′′ = 𝑡′ − 𝑣𝑥′/𝑐2 1 − 𝑣2 𝑐2 𝑥′ = 𝑥′′ + 𝑣𝑡 1 − 𝑣2 𝑐2 𝑡′ = 𝑡′′ + 𝑣𝑥′′/𝑐2 1 − 𝑣2 𝑐2 Relativistic Equations
7. 7. © ABCC Australia 2015 new-physics.com 𝛾 = 1 1 − 𝑣2 𝑐2 Where did you this funky Lorentz factor come from?
8. 8. © ABCC Australia 2015 new-physics.com Normally I would not tell where I get these equations. But for this competition, I have to do so because Angela already knew it.
9. 9. © ABCC Australia 2015 new-physics.com BeamB Beam A Viewer Light Path Geometry [at Rest] on plan These equations came from Michelson’s concept of the experiment itself. In the absence of aether wind, the two lights will recombine at the viewer in sync. No fringe will be observed.
10. 10. © ABCC Australia 2015 new-physics.com BeamB Beam A Viewer Light Path Geometry According to Michelson According to Michelson, the two lights will pursue different paths due to the influence of the aether wind.
11. 11. © ABCC Australia 2015 new-physics.com Michelson’s Working Equation 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝐵𝑒𝑎𝑚 𝐴 = 2𝑙 𝑜 𝑐 1 − 𝑣2/𝑐2 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝐵𝑒𝑎𝑚 𝐵 = 2𝑙 𝑜 𝑐 1 − 𝑣2/𝑐2 In the experiment there are two durations of time for the two beams.
12. 12. © ABCC Australia 2015 new-physics.com The ratio between the Times of the Beams 𝑇𝑖𝑚𝑒 𝑓𝑜𝑟 𝐵𝑒𝑎𝑚 𝐴 𝑇𝑖𝑚𝑒 𝑓𝑜𝑟 𝐵𝑒𝑎𝑚 𝐵 = 2𝑙 𝑜 𝑐 1 − 𝑣2/𝑐2 ÷ 2𝑙 𝑜 𝑐 1 − 𝑣2/𝑐2 = 2𝑙 𝑜 𝑐 1 − 𝑣2/𝑐2 × 𝑐 1 − 𝑣2/𝑐2 2𝑙 𝑜 = 1 1 − 𝑣2/𝑐2 1 1 − 𝑣2/𝑐2
13. 13. © ABCC Australia 2015 new-physics.com This factor was later brought up by Albert Lorentz in his postulate of time dilation to explain the experiment. I got inspired and made use of it in my theory. In its turn, the factor accounts for failure of the Michelson-Morley experiment to produce the desired results. 1 1 − 𝑣2/𝑐2
14. 14. © ABCC Australia 2015 new-physics.com Looking at your equations, it is obvious the major variable is the relative velocity 𝑣. What if both systems are at rest? 𝑥′′ = 𝑥′ − 𝑣𝑡 1 − 𝑣2 𝑐2 𝑡′′ = 𝑡′ − 𝑣𝑥′/𝑐2 1 − 𝑣2 𝑐2 Relativistic Equations
15. 15. © ABCC Australia 2015 new-physics.com Then 𝑣 will become zero and the equations will revert to the starting point. 𝑥′′ = 𝑥′ − 𝑣𝑡 1 − 𝑣2 𝑐2 → 𝑥′ 𝑡′′ = 𝑡′ − 𝑣𝑥′/𝑐2 1 − 𝑣2 𝑐2 = 𝑡′
16. 16. © ABCC Australia 2015 new-physics.com What about when the observer and the object are at rest and are separated by a distance s? They are not moving, so 𝑣 is again 0. 0’ 𝑥′ P 𝑥′′ 0’’ P 𝑠
17. 17. © ABCC Australia 2015 new-physics.com VISONIC TRANSFORM WITHOUT MOTION To be continued on Cosmic Adventure 5.2