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- #1

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- #2

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- #3

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Have a look at my PF Insights

https://www.physicsforums.com/insights/spacetime-diagrams-light-clocks/

https://www.physicsforums.com/insights/relativity-rotated-graph-paper/

The diagonals of an observer's light-clock diamonds mark off the tickmarks along an observer's time and space axes.

The area of these diamonds is a Lorentz invariant. Under a boost, the light-like directions are preserved and (since the determinant equals one) the area is preserved. The stretching and shrinking along the light-like directions are the Doppler factors (the eigenvalues of the boost).

https://www.physicsforums.com/insights/spacetime-diagrams-light-clocks/

https://www.physicsforums.com/insights/relativity-rotated-graph-paper/

The diagonals of an observer's light-clock diamonds mark off the tickmarks along an observer's time and space axes.

The area of these diamonds is a Lorentz invariant. Under a boost, the light-like directions are preserved and (since the determinant equals one) the area is preserved. The stretching and shrinking along the light-like directions are the Doppler factors (the eigenvalues of the boost).

- #6

- 97

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I see, the pictures were very helpful. Thanks!

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For a graphical illustration of this very straight-forward way to explain the right "scaling" of the axes of different inertial observers, see Fig. 1.1 on p9 of

https://th.physik.uni-frankfurt.de/~hees/pf-faq/srt.pdf

One should clarify this issue by the clear statement that you must forget your Euclidean geometry of the plane completely and substitute it by Minkowskian geometry, where indeed the "unit circles" must be substituted by the unit hyperbolae ##(c t)^2-x^2=\pm 1## of constant unit proper time or unit distance, respectively.

For an alternative depiction of space time, based on the use of "light-cone coordinates", see @robphy 's Insight articles, quoted in #5.

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