How do we know if a particle is moving or not?

Question

if there is only one particle in the universe, how do we know if it is moving or not? We don't have any other object to track the distance between the two, then is it possible to determine the position of such particle?

Answer 1

We can only say a body at motion relative to any other body(may be static). Now if there is no body in the vicinity of body you cannot really state if the body is moving or not. Motion is a relativistic term thus to claim a body is moving you need a frame of reference, but it is not in the case of rotational motion it is only true for translational motion. In case of rotational motion you need not to have any frame of reference, as you can observe it simply.

Answer 2

Your question assumes that either a body is moving or it is not. That is simply wrong. There is no absolute motion, only relative motion. The consequence is that you must define a frame of reference against which you can specify a body's position and its state of motion. Relative to the room in which I am sitting, I am not moving, but relative to a passing aeroplane I am moving- It is not a question of whether I am moving or not moving in any absolute sense, since I am simultaneously moving with respect to the plane and not moving with respect to the room.

To return to your isolated particle in space, it is not moving with respect to its own rest frame, but it is moving with respect to any other frame you would like to specify that is not its rest frame. Of course, if there were truly only a single particle, then specifying other rest frames would be a very abstract idea- you would have nothing to relate them to apart from the particle itself.