Lawrence Krauss - The Greatest Story Ever Told--So Far

by Why Are We Here (pdf)

  that the particle/top is spinning about the direction of motion, the

  particle is said to be right-handed. If you put your left hand out and

  do the same thing, a left-handed particle would be spinning

  clockwise to match the direction of your left-curled hand:

  Just as viewing your left hand in a mirror will make it look like a

  right hand, if you see a spinning arrow in the mirror, its direction of

  motion will be flipped, so that if the arrow is moving away from you

  in the real world, it will be moving toward you in the mirror, but the

  spin will not be flipped. Thus, in the mirror a left-handed particle

  will turn into a right-handed particle. (And so, if the poor souls in

  Plato’s cave had had mirrors, they might have felt less strange about

  the shadows of arrows flipping direction.)

  This working picture of left-handed particles is not exact, because

  if you think about it, you can also turn a left-handed particle into a

  right-handed particle by simply moving faster than the particle. In a

  frame in which a person at rest observes the particle zipping by, it

  may be moving to the left. But if you hop in a rocket and head off to

  the left and pass by that particle, then relative to you, it is moving to

  the right. As a result, only for particles that are massless—and are

  therefore moving at the speed of light—is the above description

  exact. For, if a particle is moving at the speed of light, nothing can

  move fast enough to pass the particle. Mathematically, the definition

  of left-handed has to take this effect into account, but this

  complication need not concern us any more here.

  Electrons can spin in either direction, but what the V-A

  interaction implies mathematically is that only those moving

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  electrons whose currents are left-handed can “feel” the weak force

  and participate in neutron decay. Right-handed currents don’t feel

  the force.

  What is more amazing is that neutrinos only feel the weak force,

  and no other force. As far as we can tell, neutrinos are only left-

  handed. It is not just that only one sort of neutrino current engages

  in the weak interaction. In all the experimental observations so far,

  there are no right-handed neutrinos—perhaps the most explicit

  demonstration of the violation of parity in nature.

  The seeming silliness of this nomenclature was underscored to

  me years ago when I was watching a Star Trek: Deep Space Nine

  episode, during which a science officer on the space station discovers

  something wrong with the laws of probability in a gaming casino.

  She sends a neutrino beam through the facility, and the neutrinos

  are observed to be coming out only left-handed. Clearly something

  was wrong.

  Except that is the way it really is.

  What is wrong with nature? How come, for at least one of the

  fundamental forces, left is different from right? And why should

  neutrinos be so special? The simple answer to these questions is that

  we don’t yet know, even though our very existence, which derives

  from the nature of the known forces, ultimately depends on it. That

  is one reason we are trying to find out. The elucidation of a new

  force led to a new puzzle, and like most puzzles in science, it

  ultimately provided the key that would lead physicists down a new

  path of discovery. Learning that nature lacked the left-right

  symmetry that everyone had assumed was fundamental led

  physicists to reexamine how symmetries are manifested in the world,

  and more important, how they are not.

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  C h a p t e r 1 3

  E N D L E S S

  F O R M S

  M O S T

  B E AU T I F U L :

  S Y M M E T RY

  S T R I K E S B A C K

  Now faith is the substance of things hoped for, the evidence of

  things not seen.

  —HEBREWS 11:1

  Borrowing from Pauli, we can say Mother Nature is a weak

  left-hander. With the shocking realization that nature distinguishes

  left from right, physics itself took a strange left turn down a road

  with no familiar guideposts. The beautiful order of the periodic table

  governing phenomena on atomic scales gave way to the mystery of

  the nucleus and the inscrutable nature of the forces that governed it.

  Gone were the seemingly simple days of light, motion,

  electromagnetism,

  gravity,

  and

  quantum

  mechanics.

  The

  spectacularly successful theory of quantum electrodynamics, which

  had previously occupied the forefront of physics, seemed to be

  replaced by a confusing world of exotic phenomena associated with

  the other two newly discovered weak and strong nuclear forces that

  governed the heart of matter. Their effects and properties could not

  easily be isolated, despite that one force was thousands of times

  stronger than the other. The world of fundamental particles

  appeared to be ever more complicated, and the situation was getting

  more confusing with each passing year.

  • • •

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  If the discovery of parity violation created shadows of confusion by

  demonstrating that nature had completely unexpected preferences,

  the first rays of light arose from the realization that other nuclear

  quantities, which on the surface seemed quite different, might, when

  viewed from a fundamental perspective, be not so different at all.

  Perhaps the most important discovery in nuclear physics was that

  protons and neutrons could convert into each other, as Yukawa had

  speculated years earlier. This was the basis of the emerging

  understanding of the weak interaction. But most physicists felt that it

  was also the key to understanding the strong force that appeared to

  hold nuclei together.

  Two years before his revolutionary work with T.-D. Lee, exposing

  the demise of the sacred left-right symmetry of nature, C.-N. Yang

  had concentrated his efforts on trying to understand how a different

  type of symmetry, borrowed from quantum electrodynamics, might

  reveal an otherwise hidden beauty inside the nucleus. Perhaps, as

  Galileo discovered regarding the basis of motion, the most obvious

  things we observe about nature are also the things that most

  effectively mask its fundamental properties.

  What had slowly become clear, not only from the progress in

  understanding neutron decay and other weak effects in nuclei, but

  also from looking at strong nuclear collisions, was that the obvious

  distinction between protons and neutrons—the proton is charged

  and the neutron is neutral—might, as far as the underlying physics

  governing the nucleus is concerned, be irrelevant. Or at least as

  irrelevant as the apparent distinction between a falling feather and a

  falling rock is to our understanding of the underlying physics of

  gravity and falling objects.

  First off, the weak force could convert protons into neutrons.

  More important, when one examined the rates of other, stronger

  nuclear reactions involving proton or
neutron collisions, replacing

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  neutrons by protons and vice versa didn’t significantly change the

  results.

  In 1932, the year the neutron was discovered, Heisenberg had

  suggested that the neutron and proton might be just two states of the

  same particle, and he invented a parameter he called isotopic spin to

  distinguish them. After all, their masses are almost the same, and

  light-stable nuclei contain equal numbers of them. Following this,

  and after the recognition by the distinguished nuclear physicists

  Benedict Cassen, Edward Condon, Gregory Breit, and Eugene

  Feenberg that nuclear reactions seemed to be largely blind to

  distinguishing protons and neutrons, the brilliant mathematical

  physicist Eugene Wigner suggested that isotopic spin was

  “conserved” in nuclear reactions—implying an underlying symmetry

  governing the nuclear forces between protons and neutrons.

  (Wigner had earlier developed rules demonstrating how symmetries

  in atomic systems ultimately allowed a complete classification of

  atomic states and the transitions between them, for which he later

  won the Nobel Prize.)

  Earlier, when discussing electromagnetism, I noted that the net

  electric charge doesn’t change during electromagnetic interactions—

  i.e., electric charge is conserved—because of an underlying symmetry

  between positive and negative charges. The underlying connection

  between conservation laws and symmetries is far broader and far

  deeper than this one example. The deep and unexpected relationship

  between conservation laws and symmetries of nature has been the

  single most important guiding principle in physics in the past

  century.

  In spite of its importance, the precise mathematical relationship

  between conservation laws and symmetries was only made explicit

  in 1915 by the remarkable German mathematician Emmy Noether.

  Sadly, although she was one of the most important mathematicians

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  in the early twentieth century, Noether worked without an official

  position or pay for much of her career.

  Noether had two strikes against her. First, she was a woman,

  which made obtaining education and employment during her early

  career difficult, and second, she was Jewish, which ultimately ended

  her academic career in Germany and resulted in her exile to the

  United States shortly before she died. She managed to attend the

  University of Erlangen as one of 2 female students out of 986, but

  even then she was only allowed to audit classes after receiving

  special permission from individual professors. Nevertheless, she

  passed the graduation exam and later studied at the famed

  University of Göttingen for a short period before returning to

  Erlangen to complete her PhD thesis. After working for seven years

  at Erlangen as an instructor without pay, she was invited in 1915 to

  return to Göttingen by the famed mathematician David Hilbert.

  Historians and philosophers among the faculty, however, blocked

  her appointment. As one member protested, “What will our soldiers

  think when they return to the university and find that they are

  required to learn at the feet of a woman?” In a retort that eternally

  reinforced my admiration for Hilbert, beyond that for his

  remarkable talent as a mathematician, he replied, “I do not see that

  the sex of the candidate is an argument against her admission as a

  Privatdozent. After all, we are a university, not a bathhouse.”

  Hilbert was overruled, however, and while Noether spent the next

  seventeen years teaching at Göttingen, she was not paid until 1923,

  and in spite of her remarkable contributions to many areas of

  mathematics—so many and so deep that she is often considered one

  of the great mathematicians of the twentieth century—she was never

  promoted to the position of professor.

  Nevertheless, in 1915, shortly after arriving at Göttingen, she

  proved a theorem that is now known as Noether’s theorem, which

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  all graduate students in physics learn, or should learn, if they are to

  call themselves physicists.

  • • •

  Returning once again to electromagnetism, the relationship between

  the arbitrary distinction between positive and negative (had

  Benjamin Franklin had a better understanding of nature when he

  defined positive charge, electrons would today probably be labeled as

  having positive, not negative, charge) and the conservation of

  electric charge—namely, that the total charge in a system before and

  after any physical reaction doesn’t change—is not at all obvious. It is

  in fact a consequence of Noether’s theorem, which states that for

  every fundamental symmetry of nature—namely for every

  transformation under which the laws of nature appear unchanged—

  some associated physical quantity is conserved. In other words, some

  physical quantity doesn’t change over time as physical systems

  evolve. Thus:

  • The conservation of electric charge reflects that the laws of

  nature don’t change if the sign of all electric charges is changed.

  • The conservation of energy reflects that the laws of nature don’t

  change with time.

  • The conservation of momentum reflects that the laws of nature

  don’t change from place to place.

  • The conservation of angular momentum reflects that the laws

  of nature don’t depend on which direction a system is rotated.

  Hence, the claimed conservation of isotopic spin in nuclear

  reactions is a reflection of the experimentally verified claim that

  nuclear interactions remain roughly the same if all protons are

  changed into neutrons and vice versa. It is reflected as well in the

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  world of our experience, in that for light elements, at least, the

  number of protons and neutrons in the nucleus is roughly the same.

  In 1954, Yang, and his collaborator at the time, Robert Mills, went

  one important step further, once again thinking about light.

  Electromagnetism and quantum electrodynamics do not just have

  the simple symmetry that tells us that there is no fundamental

  difference between negative charge and positive charge, and that the

  label is arbitrary. As I described at length earlier, a much more subtle

  symmetry is at work as well, one that ultimately determines the

  complete form of electrodynamics.

  Gauge symmetry in electromagnetism tells us that we can change

  the definition of positive and negative charge locally without

  changing the physics, as long as there is a field, in this case the

  electromagnetic field, that can account for any such local alterations

  to ensure that the long-range forces between charges are

  independent of this relabeling. The consequence of this in quantum

  electrodynamics is the existence of a massless particle, the photon,

  which is the quantum of the electromagnetic field, and which

  conveys the force between distant particles.

  In this sense, that gauge invariance is a symmetry of nature

  ensures that electroma
gnetism has precisely the form it has. The

  interactions between charged particles and light are prescribed by

  this symmetry.

  Yang and Mills then asked what would happen if one extended

  the symmetry that implies that we could interchange neutrons and

  protons everywhere without changing the physics, into a symmetry

  that allows us to change what we label as “neutron” and “proton”

  differently from place to place. Clearly by analogy with quantum

  electrodynamics, some new field would be required to account for

  and neutralize the effect of these arbitrarily varying labels from place

  to place. If this field is a quantum field, then could the particles

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  associated with this field somehow play a role in, or even completely

  determine, the nature of the nuclear forces between protons and

  neutrons?

  These were fascinating questions, and to their credit Yang and

  Mills didn’t merely ask them, they tried to determine the answers by

  exploring specifically what the mathematical implications of such a

  new type of gauge symmetry associated with isotopic spin

  conservation would be.

  It became clear immediately that things would get much more

  complicated. In quantum electrodynamics, merely switching the sign

  of charges between electrons and positrons does not change the

  magnitude of the net charge on each particle. However, relabeling

  the particles in the nucleus replaces a neutral neutron with a

  positively charged proton. Therefore whatever new field must be

  introduced in order to cancel out the effect of such a local

  transformation so that the underlying physics is unchanged must

  itself be charged. But if the field is itself charged, then, unlike

  photons—which, being neutral, don’t themselves interact directly

  with other photons—this new field would also have to interact with

  itself.

  Introducing the need for a new charged generalization of the

  electromagnetic field makes the mathematics governing the theory

  much more complex. In the first place, to account for all such

  isotopic spin transformations one would need not just one such field

  but three fields, one positively charged, one negatively charged, and

  one neutral. This means that a single field at each point in space, like

  the electromagnetic field in QED, which points in a certain direction