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Circle and Ellipse
This is how Einstein's Lorentz boost works. If we label the horizontal and vertical axes as the longitudinal and time-like axes, the circle becomes an ellipse in a different Lorentz frame.
If you are not convinced, use Dirac's light-cone variables. According to special relativity,
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z2 - t2 = constant .
It is matter of simple algebra to write this expression as
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(t + z) (t - z) = constant.
If the variable (t + z) becomes expanded, (t - z) must be contracted.
When I include this circle/ellipse picture, I am talking about Einstein, and also about Paul A. M. Dirac.