One sure way to unmask pseudoscientific arguments is to check the numbers. Pseudoscientists attempt to exploit the general science illiteracy of the public, making what sounds on the surface as plausible arguments ostensibly based on established scientific principles. But they often sweep the quantitative implications of their claims under the rug and when you put in the numbers, you can quickly prove many such claims to be bogus.

I gave one striking example in my Skeptical Briefs column of June, 1999 (available here) that bears repeating.

Physicist Harold Puthoff and others have argued that an inexhaustible supply of “free energy” might someday be extracted from the vacuum—given a sufficient investment in their research, of course. I took the equation for the stored energy between two plates, which appears in Puthoff’s papers and has been verified empirically, and put in some numbers. I calculated that two highly polished metal plates 200 kilometers by 200 kilometers on a side separated by one micron (a millionth of a meter) have enough potential energy to light a 100-Watt light bulb for one second. If we were to stumble upon 30 million or so of these structures out in space, we could hook them up to our light bulb and keep it lit for a year. Unfortunately, astronomers have not yet observed such structures in the space near Earth where they might be utilized.

In another example, I was recently contacted by The History Channel to possibly appear in a program they planned on The Philadelphia Experiment (see here). This legend has appeared in several books. As the story goes, in 1943 the U.S. Navy was conducting experiments in the Philadelphia Naval Yards on making ships invisible when a destroyer was accidentally teleported to Norfolk, Virginia and back.

The destroyer, USS Eldridge, was supposedly fitted with an electromagnetic generator designed to bend light around the ship. Now, light is made of electrically neutral photons, which are not deflected by electromagnetic fields. However, Einstein’s “unified field theory,” was supposedly applied, with Uncle Al himself said to be a participant. As near as I can tell, the generator was to produce a gravitational field great enough to bend the light.

Of course, the bending of light by gravity was one of the triumphant predictions of Einstein’s earlier general theory of relativity that has been successfully tested during total solar eclipses. (Einstein never succeeded in developing his unified theory.) General relativity is perfectly quantitative, so let’s put in the numbers. The angular deflection is proportional to the mass of the gravitating body and inversely proportion to the impact parameter (distance to center at closest approach) and amounts to 1.75 seconds of arc for a light ray just grazing the surface. The gravitational deflection of a light ray around an object with the mass of the Eldridge (1,240 tons) with an impact parameter of, say, 100 meters would be 3×10-16 arc seconds, hardly enough to make it invisible. If the role of the electromagnetic generator were to somehow produce the equivalence of a large gravitating mass, then for a one-degree deflection that mass would have to be over a trillion-trillion tons.

This, however, is not the end of the story. According to reports, on October 28, 1943 the Eldridge vanished from Philadelphia and simultaneously appeared 600 km away at the U.S. Naval base at Norfolk. After a few minutes it vanished again and reappeared in Philadelphia.

The Navy and ship crew denied the whole story, but that is, of course, a cover up according to proponents, who claim the event was an accidental case of “teleportation,” so familiar to us all from Star Trek.

Here again we can make a quantitative estimate of what would be involved. This year is the hundredth anniversary of what science writers call “Einstein’s famous equation,” E=mc2 (they all have a macro for this in their word processors). The famous equation presumably makes it physically possible to convert mass into energy, propagate the energy through space, and then convert it back to mass some distance away. Well, if you set m equal to the mass of the Eldridge and multiply it by c2, after putting in some conversion factors you obtain the energy equivalent of 20 million one-megaton hydrogen bombs. I think this effect might have been noticed.

I invite the reader to make another calculation: What is the total number of bits of information that would have to be transmitted in order to exactly reconstruct the Eldridge in Norfolk, and again back in Philadelphia?

As is always the case with pseudoscientific cons, the various terms and concepts that are being exploited can be found in legitimate scientific literature. In this case, we can read about “quantum teleportation,” experiments in which an unknown quantum state is destroyed at one point in space and recreated at another distant point using a quantum effect known as “entanglement.”

Here information is transmitted, not matter—just as in any ordinary electromagnetic communication. The fact that it is quantum information, measured in “qubits” rather than bits holds the promise of future higher information communication. But that technology is still well in the future and hardly conceivable in 1943.

Information cannot be sent by quantum teleportation to some arbitrary location, but to a prepared receiver. Basically you start with two particles, such as photons, in an entangled state. You send one photon to the sender and the other to the receiver. The sender then combines her photon with another in an unknown quantum state and performs a measurement on the resulting state. Since measurements “collapse” quantum states, the result is a classical, disentangled state. The sender then transmits a classical signal in that state to the receiver. The receiver combines that signal with his entangled photon to reconstruct the original, unknown quantum state.

Note that the signal is not transmitted faster than the speed of light. This is not a case of so-called “nonlocal” communication via the Einstein-Podolsky-Rosen effect, which is provably impossible. Somehow it seems rather unlikely that the accidental quantum teleportation of a ship and crew took place in Philadelphia back in 1943