What condition allows for a 1/2 inch relative movement of the tie plate to the crosstie?

The condition that allows for a 1/2 inch relative movement of the tie plate to the crosstie is when the tie is split or impaired. In the context of railroad ties, a split or impaired tie can lose its structural integrity, causing a lack of stability and allowing for movement between the tie plate and the crosstie.

This relative movement occurs because the tie is not able to effectively hold the tie plate in place as it would under normal, unstocked conditions. When a tie is compromised, the forces acting on it during train operations—such as vibrations and dynamic loading—can cause the attached components (like the tie plate) to shift or move independently of the crosstie itself.

The other choices either relate to conditions where the ties are intact and functioning properly or do not relate specifically to the context of movement caused by damage or impairment. Thus, the understanding that movement is largely due to impairment highlights the importance of regular inspection and maintenance of railway ties to ensure safe operation and limit such movements.