Suppose somehow the Earth's rotation gradually and imperceptibly slowed down to the point that one half always faced the sun, while the other half always faced away. What would be some ramifications of this new state of things on Earth?
In theory, it is possible for the Earth to rotate such that one side always faces the Sun, while the other side always facesaway. This concept is known as "sidereal day" or "daylight saving time." However, in practice this scenario appears extremely unlikely, as a rapid slowing of the Earth's rotation would result in severe consequences for our planet's geological stability.

For example, if the Earth were to slow down by just 1 second per century, it would cause massive tides along the coastlines due to the changing orientation of the Earth's spin axis relative to the orbit of the Moon around the Earth. Additionally, the movement of the Earth's continents and oceans might become erratic, leading to unpredictable weather patterns, earthquakes, and sea level rises.

It is also worth noting that humans do not currently have any mechanism capable of implementing gradual and imperceptible changes to the Earth's rotation. Any attempts at implementing such a system would likely require advanced technologies and decades of research and development.