A new deck of 52 cards usually has two jokers. Likewise
there are two jokers that bedevil physics -- zero and infinity. They
represent powerful adversaries at either end of the realm of numbers
that we use in modern science. Yet, zero and infinity are two sides
of the same coin -- equal and opposite, yin and yang. "Multiply zero
by anything and you get zero. Multiply infinity by anything and you
get infinity. Dividing a number by zero yields infinity; dividing a
number by infinity yields zero. Adding zero to a number leaves the
number unchanged. Adding a number to infinity leaves infinity
unchanged." Yet, the biggest questions in science, philosophy, and
religion are about nothingness and eternity, the void and the infinite,
zero and infinity.
Zero is behind all of the big puzzles in
physics. In thermodynamics a zero became an uncrossable barrier: the
coldest temperature possible. In Einstein's theory of general
relativity, a zero became a black hole, a monstrous star that
swallows entire suns and can lead us into new worlds. The infinite
density of the black hole represents a division by zero. The big bang
creation from the void is a division by zero. In quantum mechanics, the
infinite energy of the vacuum is a division by zero and is responsible
for a bizarre source of energy -- a phantom force exerted by
nothing at all. Yet dividing by zero destroys the fabric of mathematics
and the framework of logic -- and threatens to undermine the very basis of
science.
The biggest challenge to todays physicists is how to
reconcile general relativity and quantum mechanics. However, these
two pillars of modern science were bound to be incompatible. "The
universe of general relativity is a smooth rubber sheet. It is
continuous and flowing, never sharp, never pointy. Quantum
mechanics, on the other hand, describes a jerky and discontinuous
universe. What the two theories have in common -- and what they clash
over -- is zero." "The infinite zero of a black hole -- mass crammed
into zero space, curving space infinitely -- punches a hole in the
smooth rubber sheet. The equations of general relativity cannot deal
with the sharpness of zero. In a black hole, space and time are
meaningless."
"Quantum mechanics has a similar problem, a problem
related to the zero-point energy. The laws of quantum mechanics
treat particles such as the electron as points; that is, they take up no
space at all. The electron is a zero-dimensional object, and its
very zerolike nature ensures that scientists don't even know the
electron's mass or charge." But, how could physicists not know
something that has been measured? The answer lies with zero.
According to the rules of quantum mechanics, the zero-dimensional
electron has infinite mass and infinite charge. As with the zero-point
energy of the quantum vacuum, "scientists learned to ignore the
infinite mass and charge of the electron. They do this by not going all
the way to zero distance from the electron when they calculate the
electron's true mass and charge; they stop short of zero at an arbitrary
distance. Once a scientist chooses a suitably close distance, all
the calculations using the "true" mass and charge agree with one
another." This is known as renormalization -- the physicist Dr. Richard
Feynman called it "a dippy process."
The leading approach to
unifying quantum theory and general relativity is string
theory. In string theory each elemental particle is composed of
a single string and all strings are identical. The "stuff" of all
matter and all forces is the same. Differences between the
particles arise because their respective strings undergo different
resonant vibrational patterns -- giving them unique fingerprints.
Hence, what appear to be different elementary particles are actually
different notes on a fundamental string. In string theory zero
has been banished from the universe; there is no such thing as zero
distance or zero time. Hence, all the infinity problems of quantum
mechanics are solved.
But, there is a price that we must pay to
banish zero and infinity. The size of a typical string in
string theory is the Planck length, i.e., about 10^{-33}
centimeters. This is over a thousand trillion times smaller that what
the most advanced particle detection equipment can observe. Are these
unifying theories, that describe the centers of black holes and explain
the singularity of the big bang, becoming so far removed from
experiment that we will never be able to determine their correctness?
The models of the universe that string theorists and cosmologists
develop might be mathematically precise, beautiful and consistent and
might appear to explain the nature of the universe -- and yet be utterly
wrong. Scientific models/theories, philosophies, and religions will
continue to exist and be refined. However, because of zero and
infinity, we can never have "proof". All that science can know is that
the cosmos was spawned from nothing, and will return to the nothing from
whence it came.
References for quotes and further background:
Charles Seife, Zero: The Biography of a Dangerous Idea, NY:
Viking, 2000, pp.191-209: Brian Green, The Elegant Universe:
Superstrings, Hidden Dimensions, and the Quest for the Ultimate
Theory, NY: Vintage Books, 1999.
William C. Gough
, Mar 2002
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