[FOM] Abdul Lorenz on Kieu

martin@eipye.com martin at eipye.com
Thu Apr 22 11:52:23 EDT 2004

1 - I still keep my point of view about the physical meaning of the
squared Diophantine operator D^2. A physical Hamiltonian in Quantum
Mechanics has dependence only on the second power of the momentum
operator: p^2.  However, as the D^2 operator involves arbitrary powers of
the number operator, say n^k;  this means D^2 contains terms that go as
p^(2k)!!! In consequence, D^2 can not be interpreted as a Hamiltonian
describing any physical system, nor the D^2 eigenvalues represent
energies. Therefore, D^2 can not be reproduced in the laboratory.

2.- The transition process, described by Kieu's algorithm, for passing
from an oscillator Hamiltonian to the D^2 operator in a not well defined
time T,  has to deal with all the decoherence processes that result from the
interaction of the measurement and control apparatus to the coherent
states. Decoherence would destroy the coherent state in a finite time.
These effects are not taken into account in any way into Kieu's analysis,
reflecting that one is assuming a completely ideal system, where a
coherent state is to be conserved in time. A real experiment has to take
into account that there always be dissipation and/or scattering processes
that produce decoherence. Since decoherence grows in time, one can not
extend the time T arbitrarily.

3.- Regarding the required precision  one has to reach to determine
whether there is a zero "energy"  level in the D^2 spectrum, Kieu has
argue that it should be enough to reach a Delta E smaller than
the space among the first two levels. In principle, given by a integer
number multiplied by some constant that gives the dimensions of energy to
the spectrum. But knowing this spacing is equivalent to know in advance
the spectrum of D^2, and so, whether there is a solution to the
Diophantine equation!!!

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