All of this weird uncertainty doesn’t seem to bother us in everyday life. Why not? Once again, it’s all a matter of scale.
Heisenberg showed that the product of the uncertainties of conjugate pairs of observables can be about as small as Planck’s constant, but no smaller. But since Planck’s constant itself is extremely small compared to the energies, masses, and sizes that we usually deal with, the precision with which we can know both the position and velocity of ordinary objects is good enough that we never get close to the limits. Even the speck of dust we used in our example above has so much mass that for all practical purposes we can narrow down its location and speed as precisely as we would ever want to, and still not violate the uncertainty principle.
Specifically, that tiny speck of dust can be located very precisely and also be virtually motionless, apparently violating the uncertainty principle. Imagine locating the position of the dust speck to a region much smaller than the wavelength of visible light. Heisenberg’s uncertainty principle tells us that minimum momentum could not be zero. If we use Heisenberg’s relation to calculate its minimum possible momentum, however, we would find that it would move less than the diameter of an atom in 100,000 years! Even for the most patient of physicists, this is too slow to ever be measured in the laboratory.
QUANTUM LEAP
Recall that for macroscopic scales, where classical physics is more than sufficient to describe the world around us, it is safe to simply assume that Planck’s constant is zero. If we make this substitution into Heisenberg’s uncertainty relation, we see straight away that there is no longer any theoretical limit to the precision with which we can simultaneously measure position and momentum, or energy and time.
Similarly, we don’t see pumpkins, planets, or other macroscopic masses appearing and disappearing suddenly—also because Planck’s constant is so small. Our dust particle could possibly appear out of nothing, but because even its mass (and therefore energy) is relatively large relative to the quantum realm, it would have to disappear again in an unimaginably short time to slip by under the uncertainty principle.
So once again, the startling weirdness that arises in quantum physics is, for all intents and purposes, confined to microscopic scales. Only in the realm of atoms and subatomic particles does the seesaw of uncertainty produce significant effects. The reason for this is the same as the reason little girls on playground swings don’t detect discrete energy levels, and we don’t observe interference effects for flying potatoes. Energy steps and wavelengths on the order of Planck’s tiny constant make the effects too small to observe. The product of the uncertainties has a minimum value, about the size of Planck’s constant, so we couldn’t get close to the minimum for even the tiniest visible particles.
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