From: Damien Broderick (d.broderick@english.unimelb.edu.au)
Date: Tue Apr 30 2002 - 02:16:41 MDT
http://www.cosmiverse.com/news/science/science04290204.html
"Exact uncertainty" brought to quantum world April 29, 2002 8:00 CDT
Michael Hall, a theoretical physicist at Australian National University's
Institute of Advanced Studies, set out to improve Heisenberg's uncertainty
principle.
Hall supposed that quantum systems can be broken down into two parts. The
first part can, in principle, be measured exactly. The second part is a
quantum part, measured by probabilities of differing values. It is fuzzy
and cannot be measured precisely. Hall set out to quantify the second part
more exactly. Exact uncertainty sounds like a contradiction in terms, but
it governs the quantum world, according to Hall.
To quantify quantum uncertainty, Hall borrowed a mathematical tool
developed by British statistician Ronald Fisher in 1925. Fisher quantified
differences between human populations by sampling a few members of each.
His calculations gave an uncertainty in results. Hall realized that making
measurements on quantum particles was mathematically similar to Fisher's
statistics.
Hall's resulting looks like Heisenberg's original relation, but Hall has
an equation rather than an inequality. This is "a far stronger relation,"
Hall told New Scientist. The result of Hall's equation gives exact
uncertainty in the measurements of position and momentum.
Hall and Marcel Reginatto, of the Physical-Technical Institute in
Braunschweig, Germany, have already put the new equation to work. They have
derived the basics of quantum mechanics from the new, stronger relation.
Schrödinger equation, which describes the behavior of quantum-mechanical
wave functions, has also been put to the test. Their paper was published in
Journal of Physics A this month.
"I find it remarkable that the Schrödinger equation no longer has to be
god-given," Wolfgang Schleich told New Scientist. He added that one still
had to make the assumption that there is some quantum uncertainty, but this
is much simpler than assuming Schrödinger 's equation. Schleich studies at
the University of Ulm.
Hall's new formulation could have practical applications. Hall told New
Scientist that the new formula implies a tight relationship between
uncertainty and energy which makes it easier to understand why systems, in
quantum mechanics, have a minimum kinetic energy even when no forces are
acting. "There's a kind of quantum kinetic energy that comes from the
uncertainty," Hall says.
Also, the new uncertainty equation makes it possible to estimate the
minimum energy within a given quantum system. This is useful in complicated
systems, such as atoms with many orbiting electrons.
Source: New Scientist
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