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Uncertainty Principle
Name: John
Status: other
Age: 20s
Location: N/A
Country: N/A
Date: 2000-2001
Question:
Often I've heard people use the Heisenberg Uncertainty
Principle to explain why soup temperature can't be accurately measured
because the thermometer itself adds or subtracts to/from the
temperature,
or that surveys can never receive truly accurate results because the
participating peoples' answers are affected by the survey itself.
However, as stated in Dr. Bart Kosko's book, "Fuzzy Thinking," I think
that the HUP is misused in these circumstances. Am I (and Dr Kosko)
right
in this assumption, or are these variants of the principle that are
acceptable?
Replies:
You are correct. Your suspicion that these pattently false attributes to the
Heisenberg Uncertainty Principle arise from an ignorance of the HUP about
the size of a red giant star.
The HUP states that the uncertainty in a particle's momentum multiplied
times the uncertainty in its position, both being measured simultaneously,
is of the order of
h, where in m.k.s. units Planck's constant: h= 6.63x10^ -34
JouleHz^-1=[ Kg* (m/s)]*(m). We say, "of the order of" because in some
formulations angular frequency is used instead of Hz^ -1, in which case "h"
is divided by 2*pi. This quantity is called "h-bar" because the symbol is an
"h" with a bar through it. The value of "h-bar" = 1.05x10^ -34 Joule*sec.
which is not a conceptual difference. There is an analogous uncertainty
relation between the uncertainty in the simultaneous measurement of the
energy and time, which is dimensionally equivalent [Joule*sec]. Planck's
constant is a very small number!!
As a result, this mutual uncertainty is of consequence for momenta,
distances, energies, and times of the order of atomic dimensions and less.
For macroscopic objects, say, the uncertainty in position of a 1 Kg mass
moving at 1 m/sec. is about 10^ -34 meters -- inconsequential.
Of course, an even more popular object for such ignorant statements is
Einstein's Theory of Relativity.
Vince Calder
You guys are right. The uncertainty principle places a lower limit on
the *product* of the uncertainties of two simultaneous measurements on
the same system, and not just any two measurements, but specifically
measurements of "incompatible" [my word, not a technical term] observables.
It's hard to give a good everyday explanation of what makes observables
incompatible, because the measurement uncertainty is peculiar to
quantum mechanics, and normally it is completely ignorable in everyday
situations -- particularly those involving soup. Examples of pairs of
incompatible observables are (energy, time) and (position, momentum).
The reason for the measurement uncertainty is, however, analogous to
the reason for measurement uncertainties in everyday situations. The
crux of the idea -- that the act of making a measurement changes the
system -- is common to both cases. The difference is that in everyday
situations, you could, in principle, achieve an arbitrarily small
measurement uncertainty (e.g., use a very small thermometer in a huge
bowl of soup). But in situations to which the uncertainty principle
applies, it says "This is how good a measurement can possibly be."
Tim Mooney
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Update: June 2012
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