Einstein Relatively Easy

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I have recenly registered to a physics forum website https://www.physicsforums.com/, where i was paying  special interest to Special and General Relativity category.

A few days ago, there was a discussion about the interval transformations under Lorentz transformations.

Some contributors/moderators there don't seem to believe that the space and time coordinate differences Δx or Δt do transform under Lorentz transformations (which is obvious due to the linearity of the transformation) or that these intervals could even  be used to demonstrate the length contraction or time dilation phenomena, simply showing that they don't understand even the basis and real signification of the Lorentz transformation!

The proof of it can be found in any basic course on relativity, and is used by Einstein himself in chapter 12 of his book Relativity  (1920) to derive the time dilation and space contraction between inertial referentials in relative uniform movement.

Below a copy of my contribution in the thread, which has been questionned by a moderator: i would not change a simple word of it!

 

This discussion is linked to this article The Lorentz transformations Part III - Measuring-Rods and Clocks in motion, in which we derive the equations of the length contraction and time dilation from the Lorentz transformation (even though presented in a slightly different manner).

 

 

 

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"Five or six weeks elapsed between the conception of the idea for the special theory of relativity and the completion of the relevant publication" Einstein to Carl Seeling on March 11, 1952

"Every boy in the streets of Göttingen understands more about four-dimensional geometry than Einstein. Yet, in spite of that, Einstein did the work and not the mathematicians."
David Hilbert

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