I don't think about the Planck length at all when I'm thinking about relativity problems. It's a quantum mechanical concept and isn't needed in a discussion about classical physics. I don't know how to fit the Planck length into this discussion.Yeah, you are speaking of the length of the planckmeters in between the atoms (what atoms excist in) is decreasing compared to the stationary frame, right?
I'm using units of distance and time such that c=1. With this choice of units, the slope of those lines is 1/v, where v is the velocity of the train. The slope of the blue line is v. (The angle between the blue line and the x axis should be the same as the angle between the two parallel lines and the t axis).I wonder, is the slope of the two parallell lines changing by an angle defined by the speed, and the point B' is always at the same place? Is there any way of calculating where this point, or what angle the line, is supposed to be, in a defined speed? Assuming this is the normal way of showing contraction(and time dialation and relative mass increase I suppose after reading your text).
The parallel lines are parallel to a moving observer's time axis. The blue line is parallel to a moving observer's space axis.