  Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac
in 1949, the instant form and the front form can be interpolated by introducing
an interpolation angle between the ordinary time $t$ and the light-front time
$(t+z/c)/\sqrt{2}$. Using this method, we introduce the interpolating
scattering amplitude that links the corresponding time-ordered amplitudes
between the two forms of dynamics and provide the physical meaning of the
kinematic transformations as they allow the invariance of each individual
time-ordered amplitude for an arbitrary interpolation angle. In particular, it
exhibits that the longitudinal boost is kinematical only in the front form
dynamics, or the light-front dynamics (LFD), but not in any other interpolation
angle dynamics. It also shows that the disappearance of the connected
contributions to the current arising from the vacuum occurs when the
interpolation angle is taken to yield the LFD. Since it doesn't require the
infinite momentum frame (IMF) to show this disappearance and the proof is
independent of reference frames, it resolves the confusion between the LFD and
the IMF. The well-known utility of IMF usually discussed in the instant form
dynamics is now also extended to any other interpolation angle dynamics using
our interpolating scattering amplitudes.
