According to our current understanding of physics, an object cannot move solely in time without any movement in space. In the context of spacetime, which is the framework used to describe the fabric of the universe, objects with mass or energy are bound by the concept of four-dimensional spacetime, where movement involves changes in both space and time coordinates.
In spacetime, we perceive motion as a combination of movement through space and the progression of time. All objects with mass or energy are constantly moving through time, experiencing the flow of time at a constant rate. However, for an object to move in space, it must also have a velocity or change its position relative to other objects.
If we consider the concept of "rest" in space, it means that an object is not moving relative to its surrounding environment. In this case, the object would still be experiencing the passage of time, but it would not be changing its spatial position.
It's worth mentioning that there are phenomena in physics, such as time dilation, where the perception of time can be altered depending on the relative motion between observers or gravitational fields. For example, an object moving at speeds close to the speed of light or in the presence of strong gravitational fields can experience time passing differently compared to a relatively stationary observer. However, even in these cases, the object still has a velocity and is moving through both space and time.
To summarize, in the framework of our current understanding, an object cannot move exclusively in time without any movement in space.