  The quantum noise in a linear amplifier is shown to be thermal noise. The
theory of linear amplifiers is applied first to the simplest, single or double
oscillator model of an amplifier, and then to linear model of an amplifier with
continuous fields and input and outputs. Finally it is shown that the thermal
noise emitted by black holes first demonstrated by Hawking, and of dumb holes
(sonic and other analogs to black holes), arises from the same analysis as for
linear amplifiers. The amplifier noise of black holes acting as amplifiers on
the quantum fields living in the spacetime surrounding the black hole is the
radiation discovered by Hawking. For any amplifier, that quantum noise is
completely characterized by the attributes of the system regarded as a
classical amplifier, and arises out of those classical amplification factors
and the commutation relations of quantum mechanics.
