|An experiment creates a new universe
One of the most important things to remember about
physics is that Nature looks different depending on the distance or
energy scale being looked at. Physical constants
like the speed of light and Planck's constant have values that tell
us the size or energy where the the observable physics begins to change
substantially, and a different way of describing the physics mathematically
is called for.
The first example is the speed
In a physical system where all the velocities that matter are much
much less than the speed of light, the system can usually be described
very well by ordinary Newtonian physics.
When some important velocity in the system begins to approach the speed
of light, the Newtonian description doesn't fit so well any more, and
the system has to be described in fully relativistic
terms using the mathematics of Einstein's theory of special relativity.
The most important physical constant uncovered in
the 20th century is Planck's constant
which tells us about the distance or momentum scale where classical
physics stops making sense and a quantum
description becomes necessary. (The unit labeled eV is called an electron-volt,
it is the amount of work one needs to do to move one electron across
one volt of electric potential. This is a standard unit for measuring
particle physics energy scales. You'll see more of it on this web site.)
Planck's constant, in the form of the de Broglie wavelength,
tells us when the wave/particle duality of quantum physics becomes measurable
in a physical object. The de Broglie wavelength of a particle of momentum
In quantum particle-wave duality, if the size of an object of momentum
p is smaller than its de Broglie wavelength, then quantum wave interference
will be measurable enough so that classical physics will fail to be
a good description of the object's behavior.
Planck's constant is a very very small number. The de Broglie
wavelength of something like a piece of cheese in the fridge would very
very tiny. The cheese would have to be subatomic size before quantum
cheese effects would take over -- and then it wouldn't be identifiable
as cheese any longer.
Planck's constant combined
with the mass and electric
charge of an electron gives us another important number in physics
called the Bohr radius
which tells us the average size of a hydrogen
atom. The Bohr radius describes the distance scale where atomic
physics, using nonrelativistic quantum mechanics
in a classical electromagnetic field, is the best way to describe the
Elementary particle physics
In elementary particle physics, electromagnetism, the
strong and weak nuclear forces are described by a combination of relativity
and quantum mechanics, called relativistic quantum field theory. The
important numbers for comparing these three forces are called coupling
constants, whose size measures the strength of the respective force.
For electromagnetism, the coupling constant is called the fine
structure constant a and
is formed by the electron charge, Planck's constant and the speed of
Notice this constant ends up being just a plain number,
with no units associated with it. That is what is meant by a dimensionless
The combination of Planck's constant
with the speed of light and the electron
charge means this coupling constant is telling us about the quantum
relativistic physics of electromagnetism, that is, it tells us
something about electromagnetism at distance scales where quantum mechanics
and special relativity are both important to the physics at the same
There are also dimensionless coupling constants for the
strong and weak nuclear interactions. The table below compares their
relative strengths and ranges.
|Strong nuclear force
|Weak nuclear force
The weak nuclear force isn't actually that weak when measured
by aW, but it has
the shortest range, because the gauge bosons are very heavy and have
short lifetimes, so they can't travel very far without decaying into
lighter particles. The strong nuclear force binds quarks into neutrons,
protons and other hadrons, and binds protons and neutrons into the nuclei
of atoms, but because of quark confinement, the strong force has a very
small range as well.
Spontaneous symmetry breaking
Physicists originally had a lot of trouble reconciling
relativistic quantum field theory with the weak
interaction that is responsible, for example, for what is called
beta decay of neutron into proton, electron
and neutrino. The very short range of weak interaction suggested that
the gauge boson the mediated the force must be very heavy. But quantum
relativistic gauge field theories only seemed to make sense if the gauge
boson had zero mass.
The paradox was resolved by the discovery that a special
type of coupling to a particle called the Higgs
could make the weak interaction gauge bosons able to become very heavy
without destroying the symmetries that make the quantum theory mathematically
consistent. This interaction between the gauge bosons and Higgs particles
is called spontaneous symmetry breaking,
which is a misnomer because the symmetry of the theory is still there,
it's just hidden in the interactions of the theory.
Spontaneous symmetry occurs at some energy scale determined
by the quantum interactions of the Higgs particle with itself, and this
scale in turn determines the mass of the gauge boson. If the scale of
symmetry breaking is very large, then it takes a very large particle
accelerator to find evidence of the effect. In 1983, this theory was
confirmed by the direct observation of the heavy gauge bosons in the
powerful particle accelerator at CERN
in Geneva. The masses of the three weak interaction gauge bosons are
now known to be
Running coupling constants
Assigning a coupling strength to each force is tricky,
however, because of the quantum relativistic effect known as the running
coupling constant. In quantum relativistic field theory, the
calculation of a simple particle interaction, say, an electron interacting
with another electron by exchanging a photon, is complicated by an infinite
series of possible virtual particle interactions in a cloud
of quantum relativistic fluctuations.
That cloud of quantum relativistic fluctuations changes
the measured value of the coupling constant and makes it depend on the
energy scale at which one is trying to measure it.
The electromagnetic coupling constant increases
with energy. The strong and weak nuclear coupling constants decrease
with energy. The strong force in particular exhibits a property called
asymptotic freedom. The force that binds quarks together into a proton
gets stronger at lower energy but becomes negligible at very high energies.
That's why, in very high energy scattering experiments, the quarks inside
a proton scatter almost like free particles.
A unified theory
The three running coupling constants wind up having the
same strength at some very high energy scale, much higher than the weak
interaction scale of about 80 GeV. That fact, and some nifty
mathematics concerning particle multiplets
in group theory convinced physicists that there should be some
energy scale where these three forces all have the same
strength and where all the different types of particles fit into
the same mathematical theory in one unified group. This type of elementary
particle theory is called a Grand Unified Theory
or GUT for short.
The three gauge groups of the Standard Model of known elementary
particle physics are SU(3)xSU(2)xU(1).
In a Grand Unified Theory, these three groups all fit into a single
unified group with a unified set of gauge bosons whose number is determined
by the properties of the unified group. The most studied theories have
been SU(5) and SO(10).
The same process of spontaneous symmetry breaking that makes the weak
bosons massive at a scale of 80 GeV is invoked by physicists to make
most of the unified gauge bosons massive at a much higher scale.
When physicists look for a mass
scale where the three known running coupling constants run into
a single value necessary for a Grand Unified Theory, they find a very
high mass scale of
This mass scale is far too high to be reached by particle accelerators
in the near or distant future.
But there is a way to test Grand Unified Theories without
probing that mass scale directly. The weak interaction was discovered
because of beta decay, where a neutron decays into a proton, and electron
and a neutrino. In a Grand Unified Theory, something like beta decay
can happen to a proton. Even a small rate of proton
decay would be disastrous and very noticeable, because the stability
of the proton is the basis for the stability of all known matter in
the Universe. So far, no evidence of proton decay has been observed
in experiments set up to detect it.
What about gravity?
The natural constant that describes the measured strength
of the gravitational force is called Newton's constant. This is the
constant that appears in Newton's law for the gravitation force between
two objects (written here in its generalization to higher dimensions,
where d is the dimension of spacetime)
Newton's constant is very different from the speed of light and Planck's
constant, because the units depend on the number of spacetime dimensions
Gravity feels like a strong force at the macroscopic distance
scales where humans experience it, but gravity is a very very weak force
from a microscopic point of view. For example, the equivalent of the
fine structure constant for an electron and a proton interacting according
to Newton's law is
The gravitational radius
of an object of mass M is a distance scale made from Newton's
constant and the speed of light
When the size of an object approaches its gravitational radius, the
object can collapse into a black hole. This gives a natural length scale
where we expect the system to be described by the Einstein equations
rather than by Newtonian physics.
The natural length scale at which quantum
gravity should become important is called the Planck
length, made from Newton's constant (in four dimensions), the
speed of light and Planck's constant.
In string theory, the set of physical quantum states usually
contains a graviton that gives rise to gravitational interactions. Therefore,
it has been widely assumed that the natural distance scale of string
theory should be the Planck scale. However string theories contain many
duality symmetries that connect a string
theory at one distance scale to a different string theory at a different
scale. So the idea of a distance scale itself is not as firm and reliable
in string theory as it it normally is in quantum field theory.
String theory is supposed to contain the physics of the
quantum behavior of gravity. This implies a very subtle and rich structure
where the idea of distance itself is shifting and obscure.