# “Spacetime tells matter how to move; matter tells spacetime how to curve” and acceleration in flat space-time? [closed]

John Wheeler stated "Spacetime tells matter how to move; matter tells spacetime how to curve."

Does this contradict with the assumption that mass can be accelerated in flat space-time (see i.e. this thread Acceleration in special relativity)

• Why would it contradict? Gravity is not the only thing that can accelerate a body. There are real forces in addition to gravity. – CuriousOne Apr 1 '16 at 9:02
• Beside gravity (mass) energy can accelerate a body. According to STR E=mc^2. So does energy curve space-time ? – ralf htp Apr 1 '16 at 9:05
• Energy doesn't accelerate bodies. Force accelerates bodies. The formula is incomplete and as is, false. – CuriousOne Apr 1 '16 at 9:09
• forces base on energy: difference of energy niveaus is the cause - force is the effect (i.e. free fall (potential energy)) – ralf htp Apr 1 '16 at 9:15
• That's just one type of force. Forces are what accelerates bodies and it's forces that quantify the amount and direction of acceleration. Energy is an observer dependent quantity and always undetermined up to a constant. – CuriousOne Apr 1 '16 at 13:57

But suppose someone has sneaked up and attached a small rocket to my back and turned it on. If I now release an object I will see it accelerate away from me because I am still being accelerated by the rocket but the released object isn't. That means my proper acceleration is non-zero. A non-zero proper acceleration is what we normally think of as acceleration when doing calculations with Newtonian mechanics. The result of a non-zero proper acceleration is that we feel a force given by $F=ma$.