Fractions Are Hard?

by Ed Whelan

 I don’t usually spend my spare time reviewing and correcting mathematical calculations by physicists, but I think yesterday evening was an exception.

In the course of an interesting reflection in the Wall Street Journal yesterday on the recent experiment appearing to show that neutrinos travel faster than the speed of light, Michio Kaku, a professor of theoretical physics at City College of New York, wrote:

Physicists fired a beam of neutrinos (exotic, ghost-like particles that can penetrate even the densest of materials) from Switzerland to Italy, over a distance of 454 miles. Much to their amazement, after analyzing 15,000 neutrinos, they found that they traveled faster than the speed of light—one 60-billionth of a second faster, to be precise. In a billionth of a second, a beam of light travels about one foot. So a difference of 60 feet was quite astonishing.

If Professor Kaku means that the neutrinos arrived “one 60-billionth of a second” faster (i.e., sooner) than a light beam would, then the difference between the neutrinos and the light beam would be only 1/60 of one foot (or 1/5 of an inch). But from reports that the neutrinos did indeed appear to beat a light beam by 60 feet, it would appear that Professor Kaku meant to write that the neutrinos were “60 billionths of a second faster” (or, if you prefer, “60 one-billionths of a second faster”). In other words, it appears that he put the 60 in the denominator when it belongs in the numerator of the fraction.

(I have sent an e-mail inquiry to Professor Kaku.)

UPDATE: By e-mail, Professor Kaku has acknowledged the error.