Re: The mathematics of effective perfection

From: scerir (
Date: Sun Nov 26 2000 - 10:45:18 MST

Eliezer S. Yudkowsky wrote:
The second type of perpetual motion machine,
the quantum, notes that state-vector reduction
again reduces the volume of phase space.
A large volume of phase space, describing
the probability amplitude that an electron
is present at all points of space, collapses
into a single point which describes the electron
as being present at a single point in space.
State-vector reduction takes zillions of possible
superposed Universes and annihilates all but one of them.
Thus, it may be possible to build a quantum perpetual
motion machine in which the amplitudes "cold states"
tend to add up while the amplitudes of "hot states"
cancel out; effectively, this dumps waste heat into
a superposed state that gets blipped out of existence
when the quantum collapse occurs.

Since measurement on a quantum system seems to be
an irreversible process one would say that, performing
such a measurement, the entropy should increase
(John von Neumann,the projection postulate, about 1930).
But the entropy change occuring, without measurement,
in an isolated quantum system and the entropy change due
to measurement are, of course, different (in the later
case some amount of information can be obtained).
So, how this information gain must be paid for?
And, If we look for the entropy change when the unitary
evolution of a quantum system is interrupted by a
"sequence" of measurements, how does entropy change?
"Repeated" measurements, with same result, on a quantum
system, reiterate resettings of the evolving wave function.
It brings about even an impediment of the evolution, when
the temporal separation of the detections is reduced, and
the interaction approaches to "continuous" measurement.
Well, the answer seems to be that: "repeated" measurements
on a quantum system tends to decrease the entropy
of this quantum system; a "continuous" measurement
on a quantum system tends to reduce the entropy to zero.
Of course it is somewhat counter-intutive that "repeated"
measurements decrease the entropy of a quantum system.
This "Zeno" effect is, perhaps, suggesting another
perpetual motion weird machine!

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