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Lorentz Transformation and Lorentz Contraction

This text explores the analytical significance of Lorentz transformation and contraction, pioneered by Nobel Laureate Hendrik Lorentz in 1902. The discussion begins with the concept of the ether as a medium for electromagnetic phenomena, raising questions about its nature and properties. Lorentz's work laid the foundation for modern physics, particularly the idea of spacetime intervals and the invariance of the speed of light, leading to essential concepts such as time dilation and length contraction. The interplay between geometry and physics is emphasized, showcasing the profound impact of Lorentz's concepts on our understanding of the universe.

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Lorentz Transformation and Lorentz Contraction

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  1. Lorentz Transformation and Lorentz Contraction The analytical centerpiece

  2. Hendrik Lorentz • Nobel Prize, 1902 • 1902 < 1905!

  3. From Noble lecture 1902: Permit me now to draw your attention to the ether. Since we learnt to consider this as the transmitter not only of optical but also of electromagnetic phenomena, the problem of its nature became more pressing than ever. Must we imagine the ether as an elastic medium of very low density, composed of atoms which are very small compared with ordinary ones? Is it perhaps an incompressible, frictionless fluid, which moves in accordance with the equations of hydrodynamics, and in which therefore there may be various turbulent motions? Or must we think of it as a kind of jelly, half liquid, half solid?

  4. Clearly, we should be nearer the answers to these questions if it were possible to experiment on the ether in the same way as on liquid or gaseous matter. If we could enclose a certain quantity of this medium in a vessel and compress it by the action of a piston, or let it flow into another vessel, we should already have achieved a great deal. That would mean displacing the ether by means of a body set in motion. Unfortunately, all the experiments undertaken on these lines have been unsuccessful; the ether always slips through our fingers.

  5. Having reached this point, we can consider the ether as a substance of a completely distinctive nature, completely different from all ponderable matter. With regard to its inner constitution, in the present state of our knowledge it is very difficult for us to give an adequate picture of it.

  6. Lorentz transformation

  7. Review • Spacetime interval • Invariant by definition • Definition? • Time read by inertial clock present at both events • Invariant speed of light implies

  8. t t´ x´ x s t´, x´ t, x ?

  9. y y´ x´  x Euclidean space

  10. t t´ x´ x Minkowski space

  11. Minkowski Euclidean

  12. Euclidean Minkowski Physics implies geometry

  13. Euclidean geometry Hyperbolic geometry

  14. t t´ A x´ x Time dilation?

  15. t t t´ t´ x´ x´ B x x C Length contraction

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