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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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