Here's the plan for the proposed system of FTL communication.
A huge pole made of the strongest solid in existence (or whatever solid would work best for this scenario, if no solid exists that would allow for it then assume the pole is made of indestructible Unobtanium) stretches between two space stations on the endpoints of the pole.
The two endpoints are 54.6 million kilometers away from each other (the distance from Earth to Mars), so communication is on a large delay (13 minutes and 48 seconds).
Here's how we get around this:
At Endpoint Two, the end of the pole is suspended in front of a button. The pole is pushed by the station of Endpoint One back and forth to telegraph out a message.
The theory goes that by pushing the pole, the movement of the pole affects the whole pole simultaneously, allowing information to be transferred faster than the speed of light.
Is this in any way plausible as a method of FTL communication? Assume whatever resources and means required are available, and that if need be the pole can be made of indestructible materials.