Dear Andrei and colleagues,
I believe that Landauer taught us an essential fact about information -
that it is always physical. He wrote that information �is represented by
engraving on a stone tablet, a spin, a charge, a hole in a punched card,
a mark on paper, or some other equivalent.� Every physical thing that
exists, at every scale of the universe, is composed of physical quanta,
whether light photons, protons and electrons, or the compound objects
made of constituent quanta, like molecules, cells, animals, or stars.
And, every physical quantum contains energy.
So that when information is exchanged between two objects, as in a
measurement, there must be at least one physical quantum transferred,
and energy also. Landauer�s description of information implies a
particular physical arrangement of constituents, such as a pencil mark
at some location on a piece of paper. Or, in terms of the prototypical
quantum measuring apparatus, a single bit of information is encoded in
the energy state of a simple bi-level atom. If the atom�s physical
configuration is a single electron in its excited state, we would refer
to the information bit as set to one. If the electron is in its ground
level in the atom, we symbolize the information state as zero. I would
emphasize that this single bit of information is encoded by an energy
difference. That�s always the case also in practical memory devices
incorporated into computers and such. They also encode bits of
information as distinct energy states.
I�m sure, as you say, Andrei, that we must definitively specify
information by a precise mathematical formulation, if we expect to make
any progress. But, I think the Shannon and von Neumann formulas are not
sufficiently general. They only describe the information content of an
ensemble of identically prepared objects. That�s entirely adequate for
the statistical results of real quantum experiments, or, say, for the
train of electrical pulses in a telegraph signal, but they do not
describe an individual bit of information.
There is no single entropy bit, since entropy is a collective property
of the entire ensemble. I think that to completely describe information,
we must also be able to formally depict a single bit of information,
and, I believe that general formula will rely on the energy content of
the physical object.
Cordially,
Michael Devereux
_______________________________________________
fis mailing list
fis@listas.unizar.es
http://webmail.unizar.es/mailman/listinfo/fis
Received on Sat Jun 10 22:12:09 2006
