You maybe right, although it's hard to do a useful calculation. If you imagine an N2 molecule localized (to it's own diameter) in the left nostril of Leonardo on his death bed 501 years ago, and you treat is as one massive particle (i.e. ignore degrees of freedom other than center-of-mass motion) then you can estimate that the uncertainty of its position will expand at 140m/s. So the uncertainty in it's position will exceed the mean-free-path (68e-9 m) in 500 nanoseconds; which I think is rough estimate of how long you could track a single molecule. Brent On 4/3/2020 12:42 PM, James Propp wrote:
Interesting point! One certainly can't "tag" a nitrogen atom and see where it ends up later. Nonetheless, my understanding is that the classical approximation to quantum physics is sufficiently close (and the natural decay of nitrogen nuclei sufficiently slow) that nitrogen atoms have a well-defined identity over human time-scales (even though nitrogen MOLECULES don't because of chemical processes). Am I wrong?
Jim
On Fri, Apr 3, 2020 at 3:03 PM Brent Meeker via math-fun <math-fun@mailman.xmission.com <mailto:math-fun@mailman.xmission.com>> wrote:
That raises the question of how big does something have to be in order to retain its identity over 500yrs? All nitrogen molecules are identical and their location spreads out per Schroedinger's equation so that one is indistinguishable from others whose wave-functions overlap. We can refer to a pen or a chair that Leonardo used, but not to an atom he breathed. Exactly, how objects gain and keep their classical character is part of the interpretation problem of quantum measurement.
Brent
On 4/3/2020 5:07 AM, Éric Angelini wrote: > ... Where did Leonardo (or X) sign the molecule he breathed? > Is your question purely statistic? > Best, > É. > > > >> Le 3 avril 2020 à 13:49, James Propp <jamespropp@gmail.com <mailto:jamespropp@gmail.com>> a écrit : >> >> >> There's a popular science writing trope about how every breath you take >> contains atoms that were once breathed by X [or, for extra piquancy, in X's >> dying breath]. I think the one I saw in the late 1960s had X = Archimedes. >> >> My first question is, do any of you remember a specific source from the >> 1900s? (At >> https://www.newscientist.com/article/mg15020308-500-the-last-word/ someone >> writes "Is it true that every time we take a breath of air or swallow a >> mouthful of water, we consume some of the atoms breathed or swallowed by >> Leonardo da Vinci (as I read in a children’s science book in 1960)?" but >> doesn't mention the source.) >> >> My second question is, what's the best writeup of this that you know? I >> just borrowed (in e-book form) Sam Kean's recent book "Caesar's Last >> Breath", which I'm guessing will do a decent job of explaining the science. >> >> My third question is, how far back does this sort of observation go? Does >> it have an attributable original source? (Maybe Kean addresses this; it's a >> pretty thick book.) >> >> If the history of science has a subfield treating history of science >> popularization, and people do PhD's in it, maybe someone has tracked this >> trope in all its incarnations, showing how the choice of who gets to play >> the role of X reflects underlying cultural assumptions about significance >> and worth. >> >> Jim Propp >> _______________________________________________ >> math-fun mailing list >> math-fun@mailman.xmission.com <mailto:math-fun@mailman.xmission.com> >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com <mailto:math-fun@mailman.xmission.com> > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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