Fictitious forces, fictitious fields, fictitious masses? – on how to deal with the socalled inertial forces

The concept of fictitious forces has been in use in physics since the early days of mechanics. The best known is the centrifugal force. Fictitious forces are still used by many authors today, while others reject them. The idea of fictitious or inertial forces dates back to a time when there were no fields, when interactions still had to be described as action-at-a-distance effects. With the advent of electromagnetism, the field concept entered physics and gravitation could be described in a more modern way. We discuss the consequences for the fictitious forces from the perspective of a field theory. We point out an important difference between the centrifugal force and the inertial force during linear acceleration. In the first case, the third time derivative of the position is different from zero, in the second it is not. In the first case the law of momentum conservation (Newton’s second law) is violated, in the second it is not.