Since the Euler-Lagrange equation is homogeneous, the equation of motion of a system of particles or a field is independent of the scale of the Lagrangian. That is, we can multiply the Lagrangian by any constant and arrive at the same equation of motion. But does the scale of Lagrangian or the action integral ever have any absolute meaning? Suppose we have two fields A and B with respective free field action integrals S_A and S_B. The action for the full system would be of the form S_A + S_B + S_interaction. But how do I know this is correct? Since kS_B, where k is a constant, is an equivalent free-field action for field B, the correct full action might be S_A + kS_B + S_interaction. Is the determination of k a purely empirical question? Or are there theoretical considerations which could narrow the possible values of k?