Notes on Relativity and Cosmology - Physics Department, UCSB

110 CHAPTER 4. MINKOWSKIAN GEOMETRY
In the direction of the boost, this plane of simultaneity acts just like the
lines of simultaneity that we have been drawing. However, in the direction
perpendicular to the boost direction, the boosted plane of simultaneity is not
tilted. This is the statement that simultaneity is not affected in this direction.
Now, let’s put this all together. I also want to display the moving observer’s
idea of “right and left,” so I have drawn the plane of events that the moving
observer finds to be straight to her right or to her left (and not at all in front
of or behind her). Here, the observer is moving across the paper, so her “right
and left” are more or less into and out of the paper.