The Physics of Finding Osama bin Laden (As Mis-Reported on NPR)

Over in Scientopia, Janet notes an interesting mis-statement from NPR, where Dina Temple-Raston said of the now-dead terrorist:

[O]ne intelligence officials told us that nothing with an electron actually passed close to him, which in a way is one of the ways they actually caught him.

As Janet notes, this would be quite a feat, given that electrons are a key component of ordinary matter. But for the sake of silly physics blogging, let’s take this seriously for a moment. Suppose that Osama bin Laden really could make himself utterly devoid of electrons: would that be a good way to hide?

To answer this, let’s think about some of the physics involved. If bin Laden were totally electron-free, that give him a large positive charge, of one electron charge unit per proton in his body. These positive charges would attract the negative charges in nearby matter, and repel the positive charges. The resulting polarization turns nearby objects into electric dipoles, which leads to a force drawing those objects toward him. This is the process whereby you can stick balloons to the ceiling by rubbing them on your head first– the rubbing transfers some electrons from one object to the other, and the now-charge balloon polarizes atoms and molecules in the ceiling, creating a force that keeps the balloon in place.

Given that, how much force would an electron-free Osama exert on his surroundings?

For the purposes of this silly calculation, let’s say Osama has a mass of 100 kg– that’s almost certainly too big, but not by more than a factor of two, so the different doesn’t matter. What would his positive charge be after he got rid of all his electrons?

Well, humans are mostly water, so as an easy approximation, let’s ask how many molecules there are in 100 kg of water. Water consists of one oxygen, with a mass of 16 atomic mass units (on average), and two hydrogens with a mass of one atomic unit each. An atomic mass unit is 1.7×10-27kg, so electron-free Osama would contain roughly 3.3×1027 electron-less water molecules (What’s holding them together, you ask? Pure fanatical nastiness. Just roll with it, OK?). Each of these molecules contains ten protons (eight for the oxygen, one for each hydrogen) for a total charge of 5.3×109 Coulombs.

So, how much force does this exert on a nearby object, say a Navy SEAL sneaking around the compound? Well, the equation for the force between a charge q and a polarizable particle, lifted from my notes for first-year E&M, looks like this:


The force depends on the distance between the centers of the objects, r, and the polarizability of the second object α, plus a bunch of constants. Plugging in the numbers, you find that for the charge calculated above, and the polarizability of water (from this page that I Googled up), the force is 0.73 N for a separation of 1m.

“That’s less than one Newton,” you say, “and a Newton is the weight of a 100-gram object (an apple, say), which is pretty insignificant.”

True enough. Except that’s the force on a single water molecule. To estimate the total force, you’d need to multiply by the number of water molecules in a Navy SEAL, which would be roughly the same as the number of water molecules in Osama, namely 3.3×1027. Which means the total force would be around 2.4×1027N, or something like a hundred thousand times greater than the gravitational force keeping the Earth in orbit around the Sun.

But, of course, that’s the force between electron-free Osama and a SEAL a meter away, and if they get that close, he’s dead, anyway. But the force drops off very rapidly with distance– as 1/r5— so maybe a more distant SEAL wouldn’t notice it so readily. So, how far away would the searchers need to be for the force to be an all-but-undetectable 1N?

You can get the answer by setting F=1 and solving the above equation for r, and it comes out to roughly 300,000m. So, as long as nobody looking for him came within 300km, this might not be a problem. Other than, you know, all the objects that started out 1m away crashing inwards at relativistic speeds due to the huge electric polarization force.

So, you know, probably not the most effective strategy for an international fugitive. The best bet would be to keep anything containing electronics away, though even that obviously wasn’t foolproof…

9 thoughts on “The Physics of Finding Osama bin Laden (As Mis-Reported on NPR)

  1. This is the cutest, weird thing I’ve seen yet about the Osama (“Usama”?) takedown. BTW, with no electrons, wouldn’t his nuclei rush away from each other first? Reminds me of my union joke: the company made workers go through charging screens, because they didn’t want unionized workers.

    I heard that the SEAL team was used instead of bombing the compound, mostly so they could get DNA. Rush’s seeming, fawning praise for Obama may have been sarcastic, but indeed the first plan was to use B-2 bombers to flatten the thing, then Obama’s close team said “we want the DNA.” We can only hope that convinces some of the “deathers” who don’t believe OBL was taken out, citing e.g. the burial at sea leaving no hard evidence, claims he died a few years ago, etc.

  2. A B2 was not used because a 2000 lb pound bomb makes a big mess and Bin Laden was 1 km from the Pakistani equivalent of West Point.

    I do like John Novak’s suggestion. And here everyone thought Bin Laden was on dialysis. Instead it was some kind of dileptonisis.

  3. Clearly, he simply replaced all his electrons with negative muons.

    Making him roughly 1/200th his original size, which is why he was so hard to find…

    Gives new meaning to the term “Mini-Me.”

  4. I disagree with the force calculation at a distance of 1 meter. The linear polarizability formula doesn’t apply if the electric field is greater than what’s needed to field-ionize the molecules.

    But you wouldn’t need to use detect him via his force: you could detect electronless Osama him from the giant plasma discharge created in the air around him by his electrical field. Which would quickly destroy the building he was hiding in.

    I don’t know how Osama would maintain his electronless state in the presence of that discharge, but, hey, details.

    Heck, I’d guess (I didn’t work out the numbers) the electrical field at the surface of his body would be enough to pull pairs out of the vacuum.

  5. Well, here’s about how using information technology to find Osama really worked:
    “Geographers Had Calculated 89% Chance That Osama Was in Abbottabad”
    by Sara Reardon on 2 May 2011, 5:56 PM | Permanent Link
    Did anyone notice “up there”? Maybe, they did find him.

    PS, a friend of mine named Abbott (may or not be relation to the Brit who founded city) got a kick out of the city’s name. “… named after Major James Abbott who founded the town and district in January 1853 after the annexation of the Punjab.” – Wikipedia

  6. Most amusing, Chad, but you missed the line I found most interesting in one of the early reports. “Thanks to sophisticated satellite monitoring, U.S. forces knew they’d likely find bin Laden’s family on the second and third floors of one of the buildings on the property” [from an AP story in our paper]. I’d be impressed if Google didn’t already show the image quality available in the private sector. Sounds like they were watching people on the balcony. From space.

    @1 and @4:
    The problem with a 2000 lb bomb is not only plausible deniability (how many times have you seen reports about “civilians” killed by a bombing that we said targeted terrorists), but also everything else that would be destroyed. Six years of data from his computer and other files, like his Rolodex? Priceless.

    The headline disagrees with the article, which says they predicted he was in a different town and only gave that 3-sig-fig probability for a 300 km radius that included the entire northern region of Pakistan. Now pull up Google’s satellite photos and try to find the correct “large” compound within 1 km of that specific training center. I tried, and the first one I found (and later also saw in a media report) was a mile from where he actually was. There are larger compounds than his, and most are also in among small homes. They appear to have no zoning laws in Pakistan, so the rich just build walls wherever they happen to put up a house.

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