equations?”^4 Unsaid, but implied, was “Why not other equations?” Why
does the universe in which we live support Einstein’s equations in general
relativity and Maxwell’s equations in electromagnetism, but not some other
set of equations? Tegmark proposes a possible answer: the multiverse sup-
ports all possible (consistent) sets of equations; it just does so in different
sectors, and we happen to be living in the Einstein-Maxwell sector.
One of the great debates that raged in physics for centuries is the nature
of light—is it a wave or is it a particle? The answer to this, that it’s both,
would not be fully appreciated until the twentieth century, but in the
middle of the nineteenth century Maxwell’s equations, which described
electromagnetic behavior, appeared to give the nod to waves, as the equa-
tions led to solutions that were obviously wavelike. Nonetheless, a prob-
lem still remained: waves were thought to need a medium in which to
propagate. Water waves need water (or some other liquid) and sound
waves need air (or some other substance to transmit the alternating rar-
efactions and compressions that constitute waves). The medium in which
electromagnetic waves were believed to propagate was the exquisitely
named luminiferous aether. With such a lovely appellation, it was a pity
that experiments initially conducted by Albert Michelson and Edward
Morley in 1887, and which continue up to the present day, have demon-
strated to an extraordinarily high degree of precision that there is no such
thing as luminiferous aether. The Michelson-Morley result led quickly to
the Lorentz transformations, which expressed the relationships between
distance and time in a coordinate frame moving at constant velocity with
respect to another frame, and these transformations helped Einstein for-
mulate special relativity, best known for the formula Emc^2. However,
Einstein also managed to derive the following expression for mass as a
function of its velocity
m 0
m =
1( / ) − vc^2
Here m 0 is the mass of the object at rest, and m is its mass when it is
moving with velocity v.^5 It is easy to see that when v is greater than 0 but
less than c, the denominator is less than 1, and so the mass m is greater
than the rest mass m 0. Equally easy to see is that as v gets closer to c, the
denominator approaches 0, and m gets larger and larger: when v is 90
percent of the speed of light, the mass has more than doubled; when v is
99 percent of the speed, the mass has increased by a factor of 7; and when
v is 99.99 percent of the speed of light, the mass is more than 70 times
what it was at rest.
As we noted above, our universe (or the physicists currently populating
Space and Time: Is That All There Is? 139