Assuming a pole moving from left to right at a constant speed. According to Lorentz length contraction, will the leading end of the pole contract towards the trailing end of the pole, case (a) shown, or case (b) the trailing end towards the leading end or case (c) both ends of the pole will contract at equally amount towards the middle of the pole?
Is the contraction in the pole homogeneous or not? And if not what is the asymmetry?
The pole appears to contract equally along its length, so your answer c) is the correct one. You should be able to guess that from your diagrams- if c) were not the answer then some sections of the pole would have contracted more than others.
Length contraction is an effect caused by the relativity of simultaneity. It is a property of spacetime, not of objects as such.
Suppose you have two points in space that are at rest relative to each other a distance d apart. If you measure the distance in any other frame in which the points are moving along the line that joins them you get a shorter value for d. The reason is that in the other frame simultaneous measurements of the positions of the two points are actually measurements at two separate moments in the rest frame. The position of the leading point is measured before the trailing point, which gives the trailing point a chance to move ahead before it is measured, so the recorded gap between the two points is shortened.
So you see that length contraction affects space itself, not just objects within it.
