Please correct me if I am wrong, but it is my understanding of Special Relativity that the faster a particle moves the more force it requires to accellorate - laymans terms: becomes more massive. I had a post earlier where I tried to present this in the framework of an "atomic pop gun". I was told that I did not understand the conservation of energy, so I will ask my question and its basic level to try to find out where my understanding derails. If a particle is pushed in one direction to the a velocity close to the speed of light, the object that is accelorating the particle will be pushed back as if the particle was more massive than it's at rest mass. This would be the conservation of energy, wouldn't it? If both the particle and the object were allowed to travel for a period of time and then the particle was stoped by the object so that both the particle and the object were at rest relative to each other, where would be the center of mass for the particle/object? Since the particle was traveling at relativenistic speeds and became more "massive" and the conservation of energy would state that the center of mass would remain the same during this event. However, once the particle/object stopped, the center of mass would move towards the object since the particle is nolonger as massive. This is my thinking...as the particle and the object are traveling in different directions, the object is traveling as if the particle was more massive. When the object "stops" the particle, the particle will pull the object back as if it were more massive until it come to rest. For example: accelleration takes 1 sec, both the particle and object travel in opposite directions for 10 secs and then the object exserts a force on the particle to stop it which takes 1 second. The deacceloration of 1 sec will move the object back the distance the acceloration for 1 second moved it away. However, the 10 seconds of travel with no forces being applied would have moved the object farther away than what would have been expected if the particle did not travel at relativnistic speeds. So when the particle/object are at rest following this process, the center of mass is different then when the process began. At the conclusion of this process, it appears to violate the conservation of energy, but it also appears to me with my understanding that this is the only way to follow the law of conservation of energy when the forces are applied while using Special Relativity in this scenerio. Any suggestions on where my thought process/understanding is going astray? Thank you!