Quantum states of a field partitioned by an accelerated frame

The discrete Minkowski Bessel mode technology is developed. This development includes (i) the eigenvalue spectrum, (ii) the phase-space integral formulation of the quantized Klein-Gordon (KG) field in accelerated frames with a finite bottom ($b>\mathrm{}0\mathrm{}$), and (iii) the procedure for making the transition to bottomless ($b=0\mathrm{}$) frames. This technology is used to show that the Rindler vacuum state of an acceleration-partitioned real KG field is perpendicular not only to the Minkowski vacuum state, but also to every quantum state associated with a "detector" accelerating through what initially was the Minkowski vacuum. In fact, every element of the Hilbert space containing the Rindler vacuum is perpendicular to the Hilbert space containing the Minkowski vacuum.