Transcript slides - Latsis Symposium 2013

Exact, Broken, and
Approximate Symmetries
A. Zee
University of California
Santa Barbara, CA
6513
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Symmetries: a lifelong love of many theoretical
physicists
Just a few highlights: the golden moments
“Perfection” in the laws of physics, not in the solution
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Chadwick’s discovery
of the small number ~ 0.00137
[ mass difference of neutron and proton /mass of
neutron]
led Heisenberg to open a window into internal
space.
Previously, symmetries of space and time
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Spacetime or Internal
Exact or Broken
Global or Gauged
The “profound” gauge symmetries of physics now
understood to be a redundancy in the description.
For instance, the freedom to change spacetime
coordinates
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At one time, people argued that there is something
unseemly about exact global internal symmetries.
If isospin were exact, to leave the action unchanged,
we would have to rotate the proton and the neutron by the same
amount throughout the universe.
Now, within QCD, we know that isospin is not exact, and “merely” due
to the fact that the up and down quark masses (whatever the
mechanism responsible for them; their ratio is not
particularly close to 1) happen to be much smaller than the QCD
energy scale.
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Poster child of the profound impact of one area of physics on
another
Yang-Mills theory (1954) massless gauge bosons
--- rendered massive
--- confined
--- ???
(taken from a talk in 2011 “Superconductivity at 100”)
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Concepts in one area of theoretical physics migrating to
another:
a glorious history
Now that the Higgs particle(s) have been discovered,
Ginzburg-Landau (1950)
Will we have the analog of BCS (1957)?
The universal versus the specific in theoretical physics
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Search for the Universal
Fermat: Least time principle
Euler-Lagrange: Action principle
What do we “gain”?
Dirac-Feynman path integral formulation of quantum mechanics
offers the most natural path to quantum field theory
The action principle permeates modern theoretical physics
Hilbert almost beat Einstein to the punch!
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That Ginzburg-Landau holds the key to the
electroweak
interaction seems obvious now, but that is in the
glare of
hindsight, an instance of staircase wit.
Could a bright young guy in 1954, 55, 56, or even 57 have
seen
the relevance of Meissner and Ginzburg-Landau to the
dilemma
facing Yang-Mills theory?
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What lessons, if any, can we learn?
My former “boss” (twice over!) Bob Schrieffer (26 in 1957) told me
that when he gave his talk at the University of Chicago, the old guys,
in particular Wentzel (59 in 1957), gave him a hard time, but Nambu
(36 in 1957) the youngster saw the profound implications.
The deep concept behind all this --- spontaneous
symmetry breaking --- dating back to Heisenberg
and ferromagnets, was first recognized as such in
this context by Nambu.
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Transporting the concepts from one physical
problem to another
The method of analogy in theoretical physics
A possible example:
The cosmological constant paradox (the most humongous
discrepancy between expectation, dogma, and observation
in theoretical physics today)
(See my talks at Dirac’s 80th, Yang’s 85th, and
Gell-Mann’s 80th)
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Two naturalness problems in physics:
The cosmological constant problem & the Higgs mass
We may have lost the right to talk about naturalness
Another possible analogy for the cosmological constant
paradox:
A civilization on a very large planet with a thick cloud cover
Physics could have developed to a high level. With new
technology the rate of ships disappearing over the horizon,
postulated by some eminent theorists to be mathematically zero,
was finally measured to be tiny but not zero. But using the
known physics, people are unable to calculate this rate. …….
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What if ?
Suppose superconductivity had not been
discovered. (Perhaps refrigeration technology is
particularly poor in this civilization.). What would
have happened to electroweak unification?
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I think that with Heisenberg’s idea of spontaneous symmetry already
fermenting for decades, some theorist would sooner or later ask what
would happen in a gauge theory. (Indeed, many people did!)
In fact, Higgs’ first paper (received 27 July 1964) did not mention
superconductivity at all, but his second (received 31 August 1964)
did, (and was written in “modern language”.)
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Some history
Higgs’ first paper mentioned two confusing papers: one by
Klein and Lee showing that Goldstone’s theorem could be
avoided in a non-relativistic theory because an additional
vector
becomes available, and a subsequent paper by Gilbert
arguing against Klein and Lee showing that such a vector is
absent in relativistic theories.
Higgs pointed out that in gauge theories, gauge fixing
introduced this vector.
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More history
Anderson’s paper (received 8 November 1962) starts the
abstract by saying “Schwinger has pointed out that the
Yang-Mills vector boson ….. does not necessarily have zero
mass, if …..”. He talks about Sakurai’s 1961 attempt to use
Yang-Mills for the strong interaction.
Anderson concludes: “…considering the superconducting
analog,…the way is now open for a degenerate vacuum
theory of the Nambu type without any difficulties involving
either zero-mass Yang-Mills gauge bosons or zero-mass
Goldstone bosons. These two types of bosons seem
capable of ‘canceling each other out’ and leaving finite mass
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bosons only.”
Private Higgs
Observe that the rich and the powerful
do not share chauffeurs
Strikes me as strange if the top quark and the electron have
to
share the same Higgs
Various papers with Porto, Bentov, Yuan, and others;
many implications for LHC phenomenology and a “natural”
candidate for dark matter
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Stubble in Occam’s
razor
Ironically, the more unknown parameters a
particle theory model has, the more wriggle room
and the more difficult it is to eliminate it.
Curse of the free parameters
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The Einstein-Hilbert action contains only one
parameter G (in fact two, also Λ!)
which was already known to Newton.
A priori, no reason that it should be so.
Suppose it had contained 17 previously unknown
parameters instead. Then, in 1915, progress in
physics would not have been nearly so dramatic.
Experimentalists would have been kept busy for
years, possibly decades, measuring these
parameters.
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Not true that there were no numbers in particle physics
to be explained, as some people said.
The CKM and the neutrino mixing matrices are the two most
expensive matrices since linear algebra was invented.
It may well be that these numbers are different in the next village
in the landscape, but it is not known where one can buy a bus
ticket to the next village to verify this rumor.
Hard to imagine how neutrino mixing angles could affect galaxy
formation the way the cosmological constant can.
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Neutrino mixing
Tetrahedral group T, double cover T’, etc etc etc
Mixing presumably has to do with the deep mystery
of why three families (Feynman: “If you want to be
king…..”)
vast literature, many many authors: E. Ma, ……, BenTov & Zee,
Hartman & Zee (Frobenius groups), ……
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Dream of replicating Heisenberg’s and Gell-Mann’s
successes have not come to pass. Ratio of masses
and transition amplitudes not O(1).
Family symmetry: continuous (e.g. SO(3), SU(3)), gauged, discrete
Early literature: for example Wilczek and Zee (1977, 1978),
many others….
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Impose a symmetry on the action,
and hope to “fix” the physics
Einstein invented this way of doing theoretical physics
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From my book Fearful Symmetry (Magische Symmetrie
in the German speaking world)
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Einstein’s schema (some would say possibly
a bad influence on theoretical physics)
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Has the “traditional use” of symmetry in particle
physics been exhausted?
Again, the roadmap for possible new avenues
may be provided by condensed matter physics.
Quantum Hall fluid: a new kind of order
topological rather than Ginzburg-Landau
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For example, the long distance physics of certain
classes of quantum Hall fluids is described by
Order is not characterized by a local field,
but rather by fractional spin, statistics, and
ground state degeneracy on genus g surfaces, all
determined by the matrix K.
Also, chiral spin liquid
(Wen, Wilczek, & Zee, …)
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Thus far, perhaps disappointingly, this has not
been turned into a major new paradigm for
particle physics the way Ginzburg-Landau has
been.
The central role of symmetry in modern
theoretical physics
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Symmetry as a reflection of the human mind?
Physicists in love with their own Creation!
what physicists are capable of understanding
Jean-Léon Gérome
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END
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END
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Superconductivity at 100:
some reflections
A. Zee
Institute for Theoretical Physics
University of California
Santa Barbara, CA
Invited talk at the meeting of the American Physical Society, May 1, 2011
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Ginzburg-Landau (1950), Bardeen-Cooper-Schrieffer (1957)
Energy of constant magnetic field in superconductor scales
faster
than volume since
Meissner-Ochensfeld effect (1933)
=> “Higgs mechanism” (1963-64)
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Concepts in one area of theoretical physics migrating to
another:
a glorious history
Some examples
Diffraction: water wave => sound wave, electromagnetic
wave, quantum wave
Eigenfrequency: Vibrating string => quantization
Spontaneous symmetry breaking: spin wave in ferromagnet
=> pion as Nambu-Goldstone boson
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I end with an extremely lame concluding remark
The next great idea in particle physics
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What does the order parameter have to do with a
field?
Quantum fields as highly singular operators.
“Don’t mess with fields!”
Shackles of Feynman diagrams
Students were taught quantum field theory as sums of
perturbative
diagrams (as late as early 1970s or perhaps even now in
some places)
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Would non-relativistic conclusions hold in a
relativistic context?
In hindsight, it is clear that the addition of time does not
change anything essential, but only in hindsight!
Indeed, Higgs’ first paper was in response to some confusion
on this issue. See later.
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What does free energy have to do with the action of
a relativistic theory?
Both functionals of fields (order parameters)
But the way we learn about free energy, all tied up with
mysterious concepts like temperature and entropy, would
have prevented us from seeing the connection.
Lesson is to look for similar objects from different areas of
physics?
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What does the London penetration length have to do
with the mass of a Yang-Mills gauge boson?
Compton wavelength (1922)
Conceivably, someone could have seen the connection, but it
would have taken a stroke of genius.
As far as I know, nobody suggested anything remotely like
that.
Even Landau, who straddled condensed matter and particle
physics, did not see the connection.
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Qualitative understanding of mixing matrices
***
Tled.
Itor.
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