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Cosmic Adventure 5.3 Frames in Motion in Relativity


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The Einstein way of transforming time and location by the Lorentz factor, marking the departure from Newtonian physics. But why is it so is not explained.

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Cosmic Adventure 5.3 Frames in Motion in Relativity

  1. 1. Β© ABCC Australia 2015 FRAMES IN MOTION Cosmic Adventure 5.3
  2. 2. Β© ABCC Australia 2015 Motion in Special Theory of Relativity In the Special Theory of Relativity, we deal with two observers, each in his own reference system. The first observer stays in rest while the other is on the move.
  3. 3. Β© ABCC Australia 2015 π‘₯β€² = π‘₯β€²β€² + 𝑣𝑑 π‘₯β€²β€² = π‘₯β€² βˆ’ 𝑣𝑑 The classical equations for two systems’ positions related to each other. 𝑂′′ is on the move at velocity 𝑣. 𝑠 = 𝑣𝑑 π‘₯β€²β€² π‘₯β€² 𝑂′ 𝑃𝑂′′
  4. 4. Β© ABCC Australia 2015 𝑠 = 𝑣𝑑 0’ π‘₯β€² P System 1 Primed (β€˜) π‘₯β€²β€² 0’’ P System 2 Primed (β€˜β€™) Two Static Reference Systems We start off with two reference systems A and B which are at the same location together. They are in line with each other, but for clarity, we split them into two. System B is moving away from the stationary system A at a speed 𝑣 which becomes their relative speed.
  5. 5. Β© ABCC Australia 2015 System x: π‘₯β€² = π‘₯ βˆ’ 𝑣𝑑 𝑦′ = 𝑦 𝑧′ = 𝑧 𝑑′ = 𝑑 System x’: π‘₯ = π‘₯β€² + 𝑣𝑑 𝑦 = 𝑦′ 𝑧 = 𝑧′ 𝑑 = 𝑑′ The trouble with these equations is that the speed of light is not considered. No Light Involved
  6. 6. Β© ABCC Australia 2015 Lorentz Factor To change them into a form adaptable to the finite speed of light is by the method of coordinate transformation according to the postulates of Special Relativity. This is done by introducing the Lorentz factor: 𝛾 = 1 1 βˆ’ 𝑣2 𝑐2 𝛾 = 1 1 βˆ’ 𝑣2 𝑐2
  7. 7. Β© ABCC Australia 2015 π‘₯β€²β€² = π‘₯β€² βˆ’ 𝑣𝑑 1 βˆ’ 𝑣2 𝑐2 𝑑′′ = 𝑑′ βˆ’ 𝑣π‘₯β€²/𝑐2 1 βˆ’ 𝑣2 𝑐2 π‘₯β€² = π‘₯β€²β€² + 𝑣𝑑 1 βˆ’ 𝑣2 𝑐2 𝑑′ = 𝑑′′ + 𝑣π‘₯β€²β€²/𝑐2 1 βˆ’ 𝑣2 𝑐2 This Lorentz factor is the crucial element in most of equations and operations of my theory. It is mysterious and powerful.
  8. 8. Β© ABCC Australia 2015 𝑠 = 𝑣𝑑 0’ π‘₯β€² P System 1 Primed (β€˜) π‘₯β€²β€² 0’’ P System 2 Primed (β€˜β€™) Two Static Reference Systems For example, in calculating the Lorentz factor when the relative velocity is one- hundredth of that of light: 𝑣 = 𝑐 100 = 0.01𝑐
  9. 9. Β© ABCC Australia 2015 Examples of Valuating 𝜸 at Low Velocity For low velocity such as 𝑣 = 0.01𝑐: 1 βˆ’ 𝑣2 𝑐2 β†’ 1 βˆ’ 0.012 𝑐2 𝑐2 = 1 βˆ’ 0.001 = 0.995 = 0.9975 π‘₯β€²β€² = π‘₯β€² βˆ’ 0.9975𝑑 0.9975 𝑑′′ = 𝑑′ βˆ’ 0.9975π‘₯β€²/𝑐2 0.9975 Since 0.9975 is close to unity, there is not much change to the equations.
  10. 10. Β© ABCC Australia 2015 Example of 𝜸 at High Velocity For high velocity such as 𝑣 = 0.9𝑐: 1 βˆ’ 𝑣2 𝑐2 β†’ 1 βˆ’ 0.92 𝑐2 𝑐2 = 1 βˆ’ 0.81 = 0.19 = 0.4359 π‘₯β€²β€² = π‘₯β€² βˆ’ 0.4359𝑑 0.4359 𝑑′′ = 𝑑′ βˆ’ 0.4359π‘₯β€²/𝑐2 0.4359 Since 0.4359 is comparatively small, it is able to impart significant changes to the equations.
  11. 11. Β© ABCC Australia 2015 So the effects of Relativity will become noticeable at very high speed – at least somewhere close to that of light.
  12. 12. Β© ABCC Australia 2015 The origin of the equations is not clear and the mathematical operations are not that straight forward either. However the idea sounds good and innovative. So we cannot pass our judgements at this moment until we have the presentation from Angela as well.
  13. 13. Β© ABCC Australia 2015 OBJECTS IN MOTION IN VISONICS To be continued on Cosmic Adventure 5.4