our sector of it) abhors infinities much the same way as it was thought
that nature abhorred a vacuum. As a result, no particle with a finite mass
can travel at the speed of light—for then the denominator in the above
equation would be 0, and the mass m would be infinite. This does not
prevent light from traveling at the speed of light, for photons, the parti-
cles of light, are massless—they have no rest mass.
Enter the Tachyon?
Einstein’s theory also showed that infinite energy would be required to
enable a particle with nonzero mass to move at the speed of light. How-
ever, a closer look at the above equation—which was derived for objects in
our universe—reveals a potential counterpart of Dirac’s antielectron. If v
is greater than c, the denominator requires us to take the square root of a
negative number, resulting in an imaginary number. The rules govern-
ing the arithmetic of imaginary numbers dictate that the result of di-
viding a real number by an imaginary number is an imaginary number,
so if it were possible to accelerate an object beyond the speed of light, the
mass of the object would become imaginary. Objects with imaginary
masses traveling faster than the speed of light are called tachyons—from
the Greek word for “speed.” No messengers from the other side of infin-
ity have yet been detected in our universe—but absence of evidence is not
evidence of absence. Tachyons have such a bad reputation in contempo-
rary physics that a theory that allows them is said to have an instability,^6
but they have not been totally ruled out. While there is no way to envision
how a tachyon that “slowed down” to speeds less than that of light could
suddenly become a particle with real mass, some particles known to exist
do change character; there are three different species of neutrinos, and
they change species as they travel. Bizarre as the notion of a particle
changing its species appears, it is the only current explanation for what is
referred to as the solar neutrino deficit problem. Decades of collecting
neutrinos resulted in only one-third the expected number of neutrinos;
the only way to account for this is to assume that neutrinos actually
change species in f light, as the neutrino collectors could detect only a
single species of neutrino.
String Theory
Earlier in this chapter we referred to John Archibald Wheeler’s remark,
“Why these equations?” An equally valid, and perhaps more down- to-
this-universe question, is “Why these particles?” Why are the particles
140 How Math Explains the World