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

by Why Are We Here (pdf)

  in space with a certain magnitude (and is called a vector field in

  physics for this reason), is not sufficient. The electric field must be

  replaced by a field described by a mathematical object called a

  ͤ͢͝

  matrix—not to be confused with anything having to do with Keanu

  Reeves.

  Yang and Mills explored the mathematics behind this new and

  more complex type of gauge symmetry, which today we call either a

  non-abelian

  gauge

  symmetry—arising

  from

  a

  particular

  mathematical property of matrices that makes multiplying them

  different from multiplying numbers—or, in deference to Yang and

  Mills, a Yang-Mills symmetry.

  Yang and Mills’s article appears at first glance to be an abstract—

  or purely speculative—mathematical exploration of the implications

  of a guess about the possible form of a new interaction, motivated by

  the observation of gauge symmetry in electromagnetism.

  Nevertheless, it was not an exercise in pure mathematics. The paper

  tried to explore possible observable consequences of the hypothesis

  to see if it might relate to the real world. Unfortunately the

  mathematics was sufficiently complicated such that the possible

  observable signatures were not so obvious.

  One thing was clear, however. If the new “gauge fields” were to

  account for and thus cancel out the effects of separate isotopic spin

  transformations made in distant locations, the fields would have to

  be massless. This is equivalent to saying that only because photons

  are massless can the force they transmit between particles be

  arbitrarily long-range. To return to my chessboard analogy, you need

  a single rulebook to tell you how to properly move over the entire

  board if I have previously changed the colors of the board randomly

  from place to place. But having massive gauge fields, which cannot

  be exchanged over arbitrarily long distances, is equivalent to having

  a rulebook that tells you how to compensate for changing colors

  only on nearby squares around your starting point. But this would

  not allow you to move pieces across the board to distant locations.

  ͤͣ͝

  In short, a gauge symmetry such as that in electromagnetism, or

  in the more esoteric Yang-Mills proposal, only works if the new

  fields required by the symmetry are massless. Amid all the

  mathematical complexity, this one fact is inviolate.

  But we have observed in nature no long-range forces involving

  the exchange of massless particles other than electromagnetism and

  gravity. Nuclear interactions are short-range—they only apply over

  the size of the nucleus.

  This obvious problem was not lost on Yang and Mills, who

  recognized it and, frankly, punted. They proposed that somehow

  their new particles could become massive when they interacted with

  the nucleus. When they tried to estimate masses from first

  principles, they found the theory was too mathematically

  complicated to allow them to make reasonable estimates. All they

  knew was that empirically the mass of the new gauge particles would

  have to be greater than that of pions in order to have avoided

  detection in then-existing experiments.

  Such a willingness to throw their hands in the air might have

  seemed either lazy or unprofessional, but Yang and Mills knew, as

  Yukawa had known before them, that no one had been able to write

  down a sensible quantum field theory of a particle like the photon,

  but one that, unlike the photon, had a mass. So it didn’t seem

  worthwhile at the time to try to solve all the problems of quantum

  field theory at once. Instead, with less irreverence than Jonathan

  Swift, they merely presented their paper as a modest proposal, to

  spur the imagination of their colleagues.

  Wolfgang Pauli, however, would have none of it. While he had

  thought of some related ideas a year earlier, he had discarded them.

  Moreover, he felt that all this talk about quantum uncertainties in

  estimating masses was a red herring. If there was to be a new gauge

  symmetry in nature associated with isotopic spin and governing

  ͤͤ͝

  nuclear forces, the new Yang-Mills particles, like the photon, would

  have to be massless.

  For these reasons, among others, the Yang-Mills paper made far

  less of a stir at the time than the later Yang and Lee opus. To most

  physicists it was an interesting curiosity at best, and the discovery of

  parity violation seemed much more exciting.

  But not to Julian Schwinger, who was no ordinary physicist. A

  child prodigy who had graduated from university by the age of

  eighteen, he received his PhD by the age of twenty-one. Perhaps no

  two physicists could have been as different as he and Richard

  Feynman, who shared the Nobel Prize in 1965 for their separate but

  equivalent work developing the theory of quantum electrodynamics.

  Schwinger was refined, formal, and brilliant. Feynman was brilliant,

  casual, and certainly not refined. Feynman relied often on intuition

  and guesswork, building on prodigious mathematical skill and

  experience. Schwinger’s mathematical skill was every bit Feynman’s

  equal, but Schwinger worked in an orderly fashion, manipulating

  complicated mathematical expressions with an ease not possible for

  ordinary mortals. He joked about Feynman diagrams, which

  Feynman had developed to make what had previously been

  perilously laborious calculations in quantum field theory

  manageable, saying, “Like the silicon chips of more recent years, the

  Feynman diagram was bringing computation to the masses.” Both of

  them shared one characteristic, however. They marched to the beat

  of a different drummer . . . in opposite directions.

  Schwinger took the Yang-Mills idea seriously. The mathematical

  beauty must have appealed to him. In 1957, the same year that parity

  violation was discovered, Schwinger made a bold and seemingly

  highly unlikely suggestion that the weak interaction responsible for

  the decay of neutrons into protons, electrons, and neutrinos might

  benefit from the possibility of Yang-Mills fields, but in a new and

  ͤͥ͝

  remarkable way. He proposed that the observed gauge symmetry of

  electromagnetism might simply be one part of a larger gauge

  symmetry in which new gauge particles might mediate the weak

  interaction that caused neutrons to decay.

  An obvious objection to this kind of unification is that the weak

  interaction is far weaker than electromagnetism. Schwinger had an

  answer for this. If somehow the new gauge particles were very heavy,

  almost one hundred times heavier than protons and neutrons, then

  the interaction they might mediate would be of much shorter range

  than even the size of a nucleus, or even a single proton or neutron.

  In this case, one could work out that the probability that this

  interaction would cause a neutron to decay would be small. Thus, if

  the range of the weak interaction was small, these new fields, the
<
br />   strength of whose intrinsic coupling to electrons and protons on

  small scales could be comparable to the strength of

  electromagnetism, could nevertheless, on the scale of nuclei and

  larger, appear to be much, much weaker.

  Put more bluntly, Schwinger proposed the outrageous idea that

  electromagnetism and the weak interaction were part of a single

  Yang-Mills theory, in spite of the remarkable and obvious

  differences between them. He thought that perhaps the photon

  could be the neutral member of a Yang-Mills-type set of three gauge

  particles required by treating isotopic spin as a gauge symmetry, with

  the charged versions conveying the weak interaction and being

  responsible for mediating the decay of neutrons. Why the charged

  particles would have a huge mass while the photon was massless, he

  had no idea. But, as I have often said, lack of understanding is neither

  evidence for God, nor evidence that one is necessarily wrong. It just

  is evidence of lack of understanding.

  Schwinger was not only a brilliant physicist but a brilliant teacher

  and mentor. While Feynman had few successful students, probably

  ͥ͜͝

  because none of them could keep up with him, Schwinger seemed to

  have a knack for guiding brilliant PhD students. In his life he

  supervised more than seventy PhDs, and four of his students later

  won the Nobel Prize.

  Schwinger was sufficiently interested in relating the weak

  interaction to electromagnetism that he encouraged one of his

  dozen graduate students at Harvard at the time to explore the issue.

  Sheldon Glashow graduated in 1958 with a thesis on the subject and

  continued to explore the issue for the next few years as a National

  Science Foundation postdoctoral researcher in Copenhagen. In his

  Nobel lecture twenty years later, Glashow indicated that he and

  Schwinger had planned to write a manuscript on the subject after

  Glashow graduated, but one of them lost the first draft of the

  manuscript, and they never got back to it.

  Glashow was no clone of Schwinger’s. Refined and brilliant, yes,

  but also brash, playful, and boisterous, Glashow did research that

  was not characterized by mathematical acrobatics, but rather by a

  keen focus on physical puzzles and exploring new possible

  symmetries of nature that might resolve them.

  When I was a young graduate student in physics at MIT, I was

  initially drawn to deep mathematical questions in physics and had

  written my admissions essay for my PhD application on just this

  subject. Within a few years I found myself depressed by the nature of

  the mathematical investigations I was pursuing. I met Glashow at a

  summer school for PhD students in Scotland and became friends

  with both him and his family—a friendship that continued to

  blossom when we later became colleagues at Harvard. The year after

  we met, he spent a sabbatical year at MIT. During this important

  time for me, when I was considering alternatives, he said to me,

  “There’s physics, and there’s formalism, and you have to know the

  difference.” Implicit in this advice was the suggestion that I should

  ͥ͝͝

  pursue physics. When I saw the fun he was having, it became easier

  to consider joining in.

  I soon realized that for me to make progress in physics I needed

  to work on questions driven primarily by physical issues, not ones

  driven primarily by mathematical issues. The only way I could do

  that would be to keep in touch with ongoing experiments—and new

  experimental results. By watching Shelly and how he did physics, I

  realized that he had an uncanny ability to know which experiments

  were interesting, and which results might be significant or might

  point toward something new. Part of this was undoubtedly innate,

  but part was based on a lifetime of keeping in touch with what was

  happening on the ground. Physics is an empirical science, and we

  lose touch with that at our peril.

  In Copenhagen, Glashow realized that if he wanted to properly

  implement Schwinger’s proposal to connect the weak interaction

  with the electromagnetic interaction, then simply making the

  photon be the neutral member of a triplet of gauge particles, with

  the charged members becoming massive by some as yet unknown

  miracle, wouldn’t fly. This couldn’t explain the proper nature of the

  weak interaction, in particular the strange fact that the weak

  interaction seemed to apply only to left-handed electrons (and

  neutrinos), whereas electromagnetic interactions don’t depend on

  whether the electrons are left- or right-handed.

  The only solution to this problem would be if another neutral

  gauge particle existed—in addition to the photon—which itself

  coupled to only left-handed particles. But clearly the new neutral

  particle would also have to be heavy since the interactions it

  mediated would have to be weak as well.

  Glashow’s ideas were reported to the physics community by

  Murray Gell-Mann at the 1960 Rochester meeting, as Gell-Mann

  had by then recruited Glashow to Caltech to work in Gell-Mann’s

  ͥ͝͞

  group. Glashow’s paper on the subject, submitted in 1960, appeared

  in 1961 in print. Yet, no sudden stampede occurred in response.

  After all, two fundamental problems remained with Glashow’s

  proposal. The first was the long-familiar problem of how one could

  have the different masses of the particles needed to convey the

  different forces, when gauge symmetries required all the gauge

  particles to be massless. Glashow simply stated in the introduction of

  his paper, following in a long line of such hubris, “It is a stumbling

  block we must overlook.”

  The second problem was more subtle, but from an experimental

  perspective equally severe. Neutron decay, pion decay, and muon

  decay, if they were indeed mediated by some new particles

  conveying the weak force, all appeared to require only the exchange

  of new charged particles. No weak interaction had been observed

  that would require the exchange of a new neutral particle. If such a

  new neutral particle did exist, calculations at the time suggested it

  would allow the other known heavier mesons that decayed into two

  or three pions (and were responsible for the original confusion that

  led to the discovery of parity violation) to decay much more rapidly

  than they were observed to decay.

  For these reasons, Glashow’s proposal drifted into the

  background as physicists became entranced with the new particle

  zoo that was emerging out of accelerators, and the concomitant

  opportunity for new discoveries. Yet several of the key theoretical

  ingredients needed to complete a revolution in fundamental physics

  were in place, but it was far from obvious at the time. That within

  slightly more than a decade after Glashow’s paper was published all

  of the known forces in nature save gravity would be unveiled and

  understood would have seemed like pure fantasy at the time.

  And symmetry would be the key.

  ͝
ͥ͟

  C h a p t e r 1 4

  C O L D,

  S TA R K

  R E A L I T Y:

  B R E A K I N G

  B A D

  O R

  B E AU T I F U L ?

  From whose womb has come the ice? And the frost of heaven,

  who has given it birth?

  —JOB 38:29

  It is easy to pity the poor protagonists in Plato’s cave, who may

  understand everything there is to know about the shadows on the

  wall, except that they are shadows. But appearances can be

  deceiving. What if the world around us is just a similar shadow of

  reality?

  Imagine, for example, that you wake up one cold winter morning

  and look out your window, and the view is completely obscured by

  beautiful ice crystals, forming strange patterns on the glass. It might

  look like this:

  Photograph by Helen Filatova

  The beauty of the image is striking at least in part because of the

  remarkable order on small scales lurking within the obvious

  randomness on large scales. Ice crystals have grown gorgeous

  treelike patterns, starting in random directions and bumping into

  ͥ͝͠

  each other at odd angles. The dichotomy between small-scale order

  and large-scale randomness suggests that the universe would look

  very different to tiny physicists or mathematicians confined to live

  on the spine of one of the ice crystals in the image.

  One direction in space, corresponding to the direction along the

  spine of the ice crystal, would be special. The natural world would

  appear to be oriented around that axis. Moreover, given the crystal

  lattice structure, electric forces along the spine would appear to be

  quite different from the forces perpendicular to it: the forces would

  behave as if they were different forces.

  If the physicist or mathematician living on the crystal was clever,

  or, like the mathematician in Plato’s cave, lucky enough to leave the

  crystal, it would soon become clear that the special direction that

  governed the physics of the world they were used to was an illusion.

  They would find, or surmise, that other crystals could point in many

  other directions. Ultimately if they could observe the window from

  the outside on large enough scales, the underlying symmetry of

  nature under rotations in all directions, reflected in the growth of the

  crystals in all directions, would become manifest.