- Summary
- What exactly does the non interaction theorem asserts?

At the end of appendix C (concerning the non-interaction theorem of classical relativistic hamiltonian systems) of the book "Classical Relativistic Many-Body Dynamics" by Trump and Schieve it is stated that

"It follows that Currie's equation (C.21), and subsequently the assertion of vanishing acceleration in eq. (C.43), is valid only over an infinitesimal duration of time. Likewise, the conclusion that the world line is straight is valid only over an infinitesimal length of the particle trajectory in spacetime. This conclusion, however, is precisely what had been assumed in both eq. (C.36) and (C.50). It is simply the statement that any particle moves locally as a free particle, which is the foundation of all of kinematics. Likewise, any one-dimensional curve in a metric space is, to lowest order, straight. 8 The no interaction theorem makes no statement at all about the acceleration over finite lengths of the world line"

If this correct? if so, what's the meaning of the non-interaction theorem?

"It follows that Currie's equation (C.21), and subsequently the assertion of vanishing acceleration in eq. (C.43), is valid only over an infinitesimal duration of time. Likewise, the conclusion that the world line is straight is valid only over an infinitesimal length of the particle trajectory in spacetime. This conclusion, however, is precisely what had been assumed in both eq. (C.36) and (C.50). It is simply the statement that any particle moves locally as a free particle, which is the foundation of all of kinematics. Likewise, any one-dimensional curve in a metric space is, to lowest order, straight. 8 The no interaction theorem makes no statement at all about the acceleration over finite lengths of the world line"

If this correct? if so, what's the meaning of the non-interaction theorem?