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Final Project

This final project discusses the theory of relativity and specifically focuses on the Twin Paradox and rocket acceleration. It delves into the calculation of time, velocity, and distance from both the rocket's and Earth's views. The derivation of formulas for acceleration and the relationship between Earth's time and the rocket's time is explored. The use of hyperbolic functions and the Lorentz transformation is also included.

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Final Project

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  1. Final Project Theory of Relativity Xavi Wang

  2. math problem

  3. problem 13 & 14 Twin Paradox: A rocket sets off from earth to a galaxy L light years away. If it accelerates with a constant acceleration a, show the time it takes from the rocket`s view and a man on earth`s view.

  4. Problem 10: Derive the relationship of accelerations in rocket`s view and earth`s view. a quick review • Problem 11: • Derive the formula of velocity and distance of uniform acceleration motion in the earth`s view.

  5. Acceleration is only constant in rocket`s view,a` Time,velocity and distance discussed so far are all in the earth`s view

  6. Go through the process of solving distance:

  7. In problem 13,x(t)=L.It could then be solved that the time is Time from the earth`s view

  8. First go to Problem 14: Derive the relationship between the earth`s time and the rocket`s time.

  9. Recall Lorentz Transformation • Derive:

  10. A new knowledge: Hyperbolic function arcsinh

  11. It turns out that the solution to problem 14:

  12. Head back to problem 13: We have

  13. Plug in:

  14. More about Hyperbolic function: After simplification:

  15. The final Answers: Problem 13 : • Problem 14: time on rocket time relationship

  16. Twin Paradox example: If L=10 light years, a=10m\s^2, t`=3 years, t=11 years The twin accelerating experienced less time

  17. Space-Time Diagram

  18. ct/m galaxy light Twin on earth Twin on rocket earth x/m light

  19. The endThank youThank youThank youThank you

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