How do convergent boundary plates move?
according to modern plate tectonics the two convergent plates are being pushed by convection currents in the mantle that are creating new crust at the divergent boundaries.
The evidence for plate tectonics includes observations of new crust being formed at mid ocean ridges. The new crust comes to surface and pushes the older crust away from the mid ocean ridges. The new crust becomes part of the plate that the crust is attached to.
The mid Atlantic ridge is pushing the North American plate Westward. The mid Pacific ridge is pushing part of the Pacific plate Eastward. Where the plates meet is the convergent boundary. The Pacific plate being heavier and thinner is pushed under the North American plate. This creates earthquakes at the convergent boundary as well as volcanos where the melted ocean sediments come back up to the surface as magma.