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than I was!” Much later he reportedly gave another reason for not
acknowledging the possibility of a new particle: “Pure cowardice.”
Dirac’s “prediction,” even if reluctant, was a remarkable
milestone. It was the first time that, purely on the basis of theoretical
notions arising from mathematics, a new particle was predicted.
Think about that.
Maxwell had “postdicted” the existence of light as a result of his
unification of electricity and magnetism. Le Verrier had predicted
the existence of Neptune by using observations of anomalies in the
orbit of Uranus. But here was a prediction of a new basic feature of
the universe based purely on theoretical arguments about nature at
its most fundamental scales, with no direct experimental motivation
in advance. It may have seemed like a matter of faith, but it wasn’t—
after all, the proposer didn’t actually believe it—and while like faith it
proposed an unobserved reality, unlike faith it proposed a reality that
could be tested, and it could have been wrong.
The discovery of relativity by Einstein revolutionized our ideas of
space and time, and the discoveries by Schrödinger and Heisenberg
of the laws of quantum mechanics revolutionized our picture of
atoms. Dirac’s first combination of the two provided a new window
on the hidden nature of matter at much smaller scales. It heralded
the beginning of the modern era in particle physics, setting a trend
that has continued for almost a century.
First, if the Dirac equation was applied more generally to other
particles, and there was no reason to believe it shouldn’t be, then not
only would electrons have “antiparticles,” as they later became
known, so would all the other known particles in nature.
Antimatter has become the stuff of science fiction. Starships such
as the USS Enterprise in Star Trek are invariably powered by
antimatter, and the possibility of an antimatter bomb was the silliest
part of the plot in the recent mystery thriller Angels & Demons. But
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antimatter is real. Not only was the positron discovered in cosmic
rays, but antiprotons and antineutrons were discovered later as well.
At a fundamental level, antimatter is not so strange. Positrons are
just like electrons, after all, only with the opposite charge. They do
not, as many people think, fall “up” in a gravitational field. Matter
and antimatter can interact and completely annihilate into pure
radiation, which seems sinister. But particle-antiparticle annihilation
is just one in a host of new possible interactions of elementary
particles that can occur once we enter the subatomic realm.
Moreover, one would need a large amount of antimatter to actually
annihilate enough matter to even light a lightbulb with the energy
produced.
Ultimately, that is why antimatter is strange. It is strange because
the universe we live in is full of matter, and not antimatter. A
universe made of antimatter would seem identical to ours. And a
universe made of equal amounts of matter and antimatter—which
would surely seem the most sensible universe to begin with—would,
unless something happened in the meantime, be boring because the
matter and antimatter would have long ago annihilated each other
and the universe would now contain nothing but radiation.
Why our world is full of matter and not antimatter remains one
of the most interesting issues in modern physics. But recognizing
that the real reason why antimatter is strange is simply because you
never encounter it once caused me to suggest the following analogy.
Antimatter is strange in the same sense that Belgians are strange.
They are certainly not intrinsically strange, but if you ever ask in a
big auditorium full of people, as I have, for the Belgians to raise their
hands, almost no one ever does.
Except when I lectured in Belgium, as I did recently, and where I
learned my analogy was not appreciated.
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C h a p t e r 8
A W R I N K L E I N T I M E
For you are a mist that appears for a little time and then
vanishes.
—JAMES 4:14
Each hidden connection in nature revealed by science since
the time of Galileo has led physics in new and unexpected directions.
The unification of electricity and magnetism revealed the hidden
nature of light. Unifying light with Galileo’s laws of motion revealed
the hidden connections between space and time embodied in
relativity. The unification of light and matter revealed the strange
quantum universe. And the unification of quantum mechanics and
relativity revealed the existence of antiparticles.
Dirac’s discovery of antiparticles came as a result of his “guessing”
the correct equation to describe the relativistic quantum interactions
of electrons with electromagnetic fields. He had little physical
intuition to back it up, which is one reason why Dirac himself and
others were initially so skeptical of his result. Clarifying the physical
imperative for antimatter came through the work of one of the most
important physicists of the latter half of the twentieth century,
Richard Feynman.
Feynman could not have been more different from Dirac. While
Dirac was taciturn in the extreme, Feynman was gregarious and a
charming storyteller. While Dirac rarely, if ever, intentionally joked,
Feynman was a prankster who openly enjoyed every aspect of life.
While Dirac was too shy to meet women, Feynman, after the death
ͣ͜͝
of his first wife, sought out female companions of every sort. Yet,
physics breeds strange bedfellows, and Feynman and Dirac will
forever be intellectually linked—once again by light. Together they
helped complete the description of the long-sought quantum theory
of radiation.
Coming a generation after Dirac, Feynman was in awe of him and
spoke of him as one of his physics heroes. Therefore, appropriately, a
short 1939 paper that Dirac wrote, in which he suggested a new
approach to quantum mechanics, would inspire the work that
ultimately won Feynman a Nobel Prize.
Heisenberg and Schrödinger had explained how systems behave
quantum mechanically starting with some initial state of the system
and calculating how it evolves over time. But, once again, light
provides the key to another way to think about quantum systems.
We are accustomed to thinking of light as always going in straight
lines. But it doesn’t. This is manifest when you view a mirage on a
long straight highway on a hot day. The road looks wet way up
ahead because light from the sky refracts, bending as it crosses the
many successive layers of warm air near the surface of the road, until
it heads back up to your eye.
The French mathematician Pierre de Fermat showed in 1650
another way to understand this phenomenon. Light travels faster in
warmer, less dense air than it does in colder air. Because the warmest
air is near the surfac
e, the light takes less time to get to your eye if it
travels down near the ground and then returns up to your eye than it
would if it came directly in a straight line to your eye. Fermat
formulated a principle, called the Principle of Least Time, which says
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that, to determine the ultimate trajectory of any light ray, you simply
need to examine all possible paths from A to B and find the one that
takes the least time.
This makes it sound as if light has intentionality, and I resisted the
temptation to say light considers all paths and chooses the one that
takes the least time because I fully expect that Deepak Chopra would
later quote me as implying that light has consciousness. Light does
not have consciousness, but the mathematical result makes it appear
as if light chooses the shortest distance.
Now, recall that in quantum mechanics, light rays and electrons
do not act as if they take a single trajectory to go from one place to
another—they take all possible trajectories at the same time. Each
trajectory has a specific probability of being measured, and the
classical, least time, trajectory has the largest probability of all.
In 1939, Dirac suggested a way of calculating all such probabilities
and summing them to determine the quantum mechanical
likelihood that a particle that starts out at A will end up at B. Richard
Feynman, as a graduate student, after learning about Dirac’s paper at
a beer party, mathematically derived a specific example
demonstrating that this idea worked. By taking Dirac’s hint as a
starting point, Feynman derived results that were identical to those
that one would derive using the Schrödinger or Heisenberg pictures,
at least in simple cases. More important, Feynman could use this
new “sum over paths” formula to handle quantum systems that
couldn’t easily be described or analyzed by the other methods.
Eventually Feynman refined his mathematical technique to help
push forward Dirac’s relativistic equation for the quantum behavior
of electrons and to produce a fully consistent quantum mechanical
theory of the interaction between electrons and light. For that work,
establishing the theory known as quantum electrodynamics (QED),
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he shared the Nobel Prize in 1965 with Julian Schwinger and Sin-
Itiro Tomonaga.
Even before completing this work, however, Feynman described
an intuitive physical reason why relativity, when combined with
quantum mechanics, requires the existence of antiparticles.
Consider an electron moving along on a possible “quantum”
trajectory. What does this mean? An electron takes all possible
trajectories between two points as long as I am not measuring it
while it travels. Among these are trajectories that are classically not
allowed because they would violate rules such as the limitation that
objects cannot travel faster than light (arising from relativity). Now
the Heisenberg uncertainty principle says that even if I try to
measure the electron along its trajectory over some short time
interval, some intrinsic uncertainty in the velocity of the electron
remains that can never be overcome. Thus even if I measure the
trajectory at various points, I cannot rule out some weird
nonclassical behavior during these intervals. Now, imagine the
trajectory shown below:
For the short time in the middle of the time interval shown the
electron is traveling faster than the speed of light.
But Einstein tells us that time is relative, and different observers
will measure different intervals between events. And if a particle is
traveling faster than light in one reference frame, in another
reference frame it will appear to be traveling backward in time, as
shown below (this is one of the reasons relativity restricts all
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observed particles to travel at speeds less than or equal to the speed
of light:
Feynman recognized that in the latter frame this would look like
an electron moving forward in time for a little while, then moving
backward in time, then moving forward in time. But what does an
electron moving backward in time appear like? Since the electron is
negatively charged, a negative charge moving backward in time to
the right is equivalent to a positive charge moving forward in time to
the left. Thus, the picture is equivalent to the following:
In this picture one starts with an electron moving forward in
time, and then sometime later an electron and a particle that appears
like an electron but has the opposite charge suddenly appear out of
empty space, and the positively charged particle moves to the left,
again forward in time, until it encounters the original electron and
the two annihilate, leaving only one electron left over to continue
moving.
All of this happens on a timescale that cannot be observed
directly, for if it could be, then this strange behavior, violating the
tenets of relativity, would be impossible. Nevertheless, you can be
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assured that inside the paper in the book you are now reading, or
behind the screen of your ebook, these kinds of processes are
happening all the time.
Nevertheless, if such a trajectory is possible in the invisible
quantum world, then antiparticles must exist in the visible world—
particles identical to known particles but with opposite electric
charge (which appear in the equations of this theory as if they were
particles going backward in time). This also makes it possible for
particle-antiparticle pairs to spontaneously appear out of empty
space, as long as they annihilate in a time period quickly enough so
that their brief existence cannot be measured.
With this line of reasoning, not only did Feynman give a physical
argument for the existence of antiparticles required by the
unification of relativity and quantum mechanics, he also
demonstrated that at any time we cannot say that only one or two
particles are in some region. A potentially infinite number of
“virtual” particle-antiparticle pairs—pairs of particles whose
existence is so fleeting that they cannot be directly observed—can be
appearing and disappearing spontaneously on timescales so short
that we cannot measure them.
This picture sounds so outrageous that you should be
incredulous. After all, if we cannot measure these virtual particles
directly, how can we claim that they exist?
The answer is that while we cannot detect the effects of these
virtual particle-antiparticle pairs directly, we can indirectly infer
their presence because they can indirectly affect the properties of
systems we can observe.
The theory in which these virtual particles are incorporated,
along with the electromagnetic interactions of electrons and
positrons, called quantum electrodynamics, is the best scientific
theory we have so far. Predictions based on the theory have been
͝͝͞
compared with observations, and they agree to more than t
en
decimal places. In no other area of science can this level of accuracy
be obtained in the comparison between observation and prediction,
based on the direct applications of fundamental principles on the
most basic scales we can describe.
But the agreement between theory and observation is only
possible if the effects of virtual particles are included. Indeed, the
very phenomenon of virtual particles implies that, in quantum
theory, forces between particles are always conveyed by the
exchange of virtual particles, in a way I shall now describe.
In quantum electrodynamics, electromagnetic interactions occur
by the absorption or emission of the quanta of electromagnetism,
namely photons. Following Feynman, we can diagram this
interaction as an electron emitting a wavy “virtual” photon (γ) and
changing direction:
Then, the electric interaction between two electrons can be
diagrammed as:
In this case, the electrons interact with each other by exchanging
a virtual photon, one that is spontaneously emitted by the electron
͟͝͝
on the left and absorbed by the other in so short a time that the
photon cannot be observed. The two electrons repel each other and
move apart after the interaction.
This also explains why electromagnetism is a long-range force.
The Heisenberg uncertainty principle tells us that if we measure a
system for some time interval, then there is an associated uncertainty
in the measured energy of the system. Moreover, as the time interval
gets bigger, the associated uncertainty in energy gets smaller.
Because the photon is massless, a virtual massless photon, using
Einstein’s relation between mass and energy, can carry an arbitrarily
small amount of energy when it is created. This means that it can
travel an arbitrarily long time—and therefore an arbitrarily long
distance—before being absorbed, and it will still be protected by the
uncertainty principle, as the energy it can carry is so small that no
visible violation of the conservation of energy will occur. Thus, an
electron on Earth can emit a virtual photon that could travel to
Alpha Centauri, four light-years away, and that photon can still
produce a force on an electron there that absorbs it. If the photon
Lawrence Krauss - The Greatest Story Ever Told--So Far Page 11
