In analogy with the ultimate speed c, there is an ultimate acceleration β, nobody's acceleration can exceed this limit β, in the solar system, β=2.961520e+10(m/s2). Because this ultimate acceleration is large, any effect related to β will become easy to test, including quantum gravity tests. In this paper, an approach is put forward to connect the ultimate acceleration with quantum theory, as an application, this relativistic model gives out the sunspot cycle to be 10.38 years due to the ultimate acceleration. The same approach is applied to earthquake problems in Japanese islands. About 10% of the world's active volcanoes are found in Japan, which lies in a zone of extreme crustal instability. As many as 1500 earthquakes are recorded yearly, major earthquakes occur infrequently. The calculation indicates that the beat period of the earth's shell corresponding to the wind 50m/s over Japanese islands to be 1 year. Coupling with the strongest mean wind of 50m/s at the altitude of 10km (200hPa) over Japan islands, the local Earth shell sensitive to the wind is at the depth about 10km. The height of Mount Fuji of 3776(m) make an increase in the local coupling constant C as viewing the Japanese islands as a wall on the sea to resist the winds.