  There is a longstanding debate about the zero-point term in the Johnson noise
voltage of a resistor. This term originates from a quantum-theoretical
treatment of the Fluctuation-Dissipation Theorem (FDT). Is the zero-point term
really there, or is it only an experimental artefact, due to the uncertainty
principle, for phase-sensitive amplifiers? Could it be removed by
renormalization of theories? We discuss some historical measurement schemes
that do not lead to the effect predicted by the FDT, and we analyse new
features that emerge when the consequences of the zero-point term are measured
via the mean energy and force in a capacitor shunting the resistor. If these
measurements verify the existence of a zero-point term in the noise, then two
types of perpetual motion machines can be constructed. Further investigation
with the same approach shows that, in the quantum limit, the Johnson-Nyquist
formula is also invalid under general conditions even though it is valid for a
resistor-antenna system. Therefore we conclude that and a satisfactory quantum
theory of the Johnson noise, the Fluctuation-Dissipation Theorem, must, as a
minimum, include also the measurement system used to evaluate the observed
quantities. Issues concerning the zero-point term may also have implications
for phenomena in advanced nanotechnology.
