Einstein Relatively Easy

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"The special theory of relativity is nothing but a contradiction-free amalgamation of the results of Maxwell-Lorentz electrodynamics and those of classical mechanics."

Einstein [January 1920] Fundamentals and Methods of the Theory of Relativity

 

In 1905, Albert Einstein published the theory of Special Relativity, which explains how to interpret motion between different Inertial Frame of References.

This theory can be seen as a synthesis of both the Newton's laws of motion and the Maxwell's electromagnetism equations.

It takes place in a new pseudo-flat four-dimensional spacetime, the  Minkowski's Space-Time, in which the space and time absolute invariants Δd and Δt from the classical Newtonian mechanics are replaced by these two new invariants[1]:

  • c = speed of light in vacuum; its exact value is 299792458 metres per second (approximately 3.00×108 m/s)
  • Δs = √(c2Δt2 - Δd2) = spacetime interval

 

From the law of conservation of momentum, Einstein was also able to derive in this new context the equivalence between mass and energy, the famous E = mc2 equation. See Introduction to Four-momentum vector and E = mc2 for this last point.

 

[1] A quantity is invariant in special relativity if it has the same value in all inertial frames. The speed of light in a vacuum remains the univeral constant, whereas space shrinks and time slows down when two observers are uniformly speeding either toward or away from each other. Space and time are different in each reference frame.

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"Pas plus de cinq ou six semaines s'écoulèrent entre la conception de l'idée de la relativité restreinte et la rédaction de l'article correspondant."
Einstein à Carl Seelig, 11 Mars 1952

"N'importe quel étudiant dans les rues de Göttigen en connaît plus qu'Einstein sur les géométries à 4 dimensions. Et pourtant ce fut Einstein qui accomplit le travail, et non les mathématiciens."
David Hilbert

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