Hiding in the Mirror (32 page)

Tesseract:
A
four-dimensional version of a three-dimensional cube. The “faces”
of this hypercube comprise eight different three-dimensional cubes.
Torus:
A donut-shaped object, with a hole
in the center. One can produce such an object by taking a flat piece
of paper and pasting together two opposite edges, and then the
other two opposite edges. Alternatively, one can simply lay the
paper flat and merely “identify” the two edges, so that for example,
whenever an object heads off the right edge of the paper it would
appear coming in from the left edge. In the language of topology, a
torus therefore is topologically distinct from a flat piece of
paper, in that it has a hole, but geometrically it can still be
considered flat.
Uncertainty principle:
One
of the fundamental principles of quantum mechanics that implies
there are certain combinations of quantities associated with any
object that can never be measured exactly. For example, both the
position and the momentum (see
momentum
) of
an object cannot be known together with absolute accuracy. As one
measures the position of an object more and more accurately, the
uncertainty in knowledge about its momentum will increase. Since
this minimum combined uncertainty in position and momentum is,
however, very small, the effect of the uncertainty principle is not
usually directly observed on scales much larger than the size of
atoms.

Unitarity:
A
fundamental mathematical property of nature that essentially says
that probabilities do not change over time. Simply put, it implies
that when one considers all of the different possibilities that may
arise when one particle interacts with another, and sums up the
different probabilities, they will add up to unity.

Vacuum energy:
The
energy associated with empty space, containing no matter or
radiation. While common sense says that this energy should be zero,
the laws of quantum mechanics and relativity together imply that
empty space is full of a swarm of “virtual particles” that pop in
and out of existence on a timescale so short we cannot observe them
directly. When we try to calculate what the contribution of these
particles might be to the energy of empty space, we come up with a
very large number—indeed, far larger than anything we measure
today. We currently do not understand why this prediction is
incorrect. At the same time, any such energy, if it exists, is
gravitationally repulsive, and could cause the observed expansion
of the universe to accelerate. This is what we observe today in the
universe on large scales.

Virtual particles:
The
laws of quantum mechanics and special relativity together imply
that elementary particles and their antiparticles can spontaneously
appear together out of empty space, exist for a short time, and
then annihilate again, leaving nothing but empty space. As long as
they do so for periods so short that we cannot measure them
directly, their existence is ensured by the uncertainty principle.
While virtual particles cannot be directly observed, their indirect
effects can be observed, and predictions agree well with
observations.

Vortex rings:
A ring,
like a smoke ring, that is stable and can move about, maintaining
its form even as it moves through some background medium like
air.

Warped space:
This has,
alas, nothing to do with
Star Trek
. Rather,
it is a term that has been used to describe certain
extra-dimensional theories with possibly large extra dimensions. In
these theories the geometry (and hence the strength of gravity) in
the three spatial dimensions we experience is not separated from
the existence of the higher dimension(s), but is rather a function
of where you are located in the higher dimension(s). In this case,
it is possible not only for all familiar particles and
nongravitational forces to be confined on our three-dimensional
space, but also for gravity to be effectively restricted to lie in
our space, leaving the higher dimensions thus far undetected, but
in fact allowing the possibility of their detection in new high
energy accelerators such as the large hadron collider, and also
allowing a possible new approach to the hierarchy problem.
Wavelength:
For any periodic wave, with
peaks and crests, the distance between successive peaks is called
the wavelength of the wave.
Weak scale:
This is the energy (or length) scale at which the weak interaction,
responsible for the nuclear reactions inside the sun, for example,
becomes of roughly comparable order in strength as the
electromagnetic interaction, and which the mathematical symmetry
between these two forces of nature, which is spontaneously broken
at large scales, becomes manifest.

Yang-Mills theory:
This
represents a wide class of physical theories that are
generalizations of electromagnetism, in which the particles that
play the role of photons in electromagnetism, which are neutral,
are instead charged, and also can have a mass, and therefore have
more complicated interactions with one another and with other
particles than photons do. Both the weak force and the strong force
are described by Yang-Mills theories.