July 17, 2010
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Heisenberg's Uncertainty Principle ought to be considered here as a possible limitation for such experiments. Or, to put it another way, how did the researchers avoid that?
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I suspect because it isn't influencing anything they are interested in measuring to an important extent. As near as I can make out (IANAP, IJPOOTV) they are measuring the energy transitions in a hydrogen atom where a muon has replaced the electron. Recall the Bohr model of the hydrogen atom. That treats the proton as a point charge, which is an approximation. My guess is that they are using quantum mechanics to calculate how spreading the charge of a proton over space (its charge density, aka its size) should affect the energy transition levels. And then measure those. The problem is, the energy transition levels are solidly nailed down by the Rydberg constant (as mentioned in one of the articles). And take a look at what it is built up from in the wikipedia article. Those constants are precise out to multiple decimal places, way more than the four or so that we thought we knew the proton's size to. Looked at from that perspective, this isn't a 4% error, this is a 6 orders of magnitude miss. I exaggerate. And someone has probably made a mistake in a calculation somewhere. But still...
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Oh, and the uncertainty principle will affect the measurement of an energy transition. In this case, you trade off a precise knowledge of the energy of a transition with (if I recall correctly) knowing how long it took to occur.
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Well, I don't even play a physicist on TV but I'm willing to have a go... We know that the Moon does not orbit the Earth. In truth the Moon and the Earth both orbit their combined center of mass. So as the moon goes around in an orbit the earth also gyrates, just as your hand moves while swinging a ball on a string. The upshot is that the moon has a lower orbit (seen from outside the system) than it would if it were orbiting something that didn't yield as much. Now, they switched the puny electron for a fat old muon (the moon) which, because of its bigger mass slightly displaces the single proton (the earth) as it orbits, and thus has a lower than expected orbit (in either energy state) and hence less energy is released when changing states, and hence a wrong size result. Q.E.D. Also, if you buy any of that faux physics I have a model plane and a treadmill I could sell you...
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Does this treadmill have Mel Gibson's face on it?
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I've checked around the house, but I don't have a tape or a ruler that goes small enough, so I can't give you any definitive decision on the issue. As far as physics goes, I'm still stuck on that wave/particle business. *wave or particle* *Coke or Pepsi*