Download Issue number 120 - fall 2006

Phys13news
Department of Physics & Astronomy
University of Waterloo
Waterloo, Ontario, Canada
N2L 3G1
Fall 2006
Number 120
The Planck satellite
2
Phys13News 120
Cover
Artist’s impression of the Planck satellite, scheduled for launch next year.
Planck will build on WMAP’s success, improving the measurement of
CMB polarization in particular. [Images
courtesy ESA http://www.esa.int/
esa-mmg/mmg.pl]
From the Editor
Contents
Watching the Very End of the Big Bang . . . . . . . . . . . . . . .
3
James discusses the science behind
this year’s Nobel prize for physics.
– James E. Taylor
The Physics of the Violin . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fall 2006
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In this issue we have a fantastic article on watching the Big
Bang by a new UW Physics & Astronomy professor, James
E. Taylor. This is very topical as it discusses the cosmic microwave background (CMB) radiation, for which John Mather
and George Smoot were awarded this year’s Nobel Prize in
physics. This article also provides the fantastic picture for this
issue’s cover: the Planck satellite, which will provide follow-up
measurements on the CMB radiation.
We also have two articles by UW undergraduate students.
The first is by Chris Saayman on the physics of violins and the
second is by Sonia Markes on the famous EPR paradox.
Following these articles is a report from Robbie Henderson
on the CUPC which he, along with seven other UW physics
students, attended earlier this year.
Finally, we have our usual SIN BIN column (now from Rohan instead of myself) and amusements from Tony Anderson (a
crossword this issue) and some prof-quotes collected by George
McBirnie.
As always, I look forward to receiving feedback on the content of this issue and suggestions for (or even contributions of)
future articles. Please let me know what you like and dislike
and topics you would like to see explored in future issues.
Chris O’Donovan is the editor of Phys13news and can be reached at [email protected].
Chris combines his two favourite
pastimes. – Christopher Saayman
Outside the Classical Comfort Zone . . . . . . . . . . . . . . . . . . . 10
Sonia examines the famous EPR “paradox”
and what Einstein called “spooky action at a
distance.” – Sonia Markes
Canadian Undergraduate Physics Conference 2006 . . . . 12
Robbie tells us about this year’s conference in New Brunswick. – Robbie D. E. Henderson
The SIN Bin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
This month’s SIN bin column
presents a new problem and gives a
solution to the previous issue’s problem. – Rohan Jayasundera
Mostly Relativistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Tony challenges us with a crossword. – Tony
Anderson
Prof Quotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
George serves up a selection of his favourite quotations. – George McBirnie
Phys13News is published four times a year by the Department of Physics & Astronomy at the University of Waterloo.
Our policy is to publish anything relevant to high school and
first-year university physics, or of interest to high school
physics teachers and their senior students. Letters, ideas
and articles of general interest with respect to physics are
welcome by the editor. You can reach the editor by email
at [email protected]. Alternatively, you
can send correspondence to:
Paper: Phys13News
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Editor: Chris O’Donovan
M. Balogh
R. Epp
Editorial Board:
M. Ghezelbash
R. Hill
Publisher: J. McDonnell
Printing: UW Graphics
R. Jayasundera
R. Thompson
F. Wilhelm
D. Yevick
Fall 2006
Phys13News 120
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Watching the Very End of the Big Bang
James E. Taylor
recent Nobel prize for the discoveries of the COBE satellite and spectacular new data from the Wilkinson Microwave Anisotropy Probe (WMAP) mark the culmination of four
decades of dedicated experimental work on the cosmic microwave background. The picture of the Universe that emerges
is (to paraphrase J.B.S. Haldane) “queerer than we might have
supposed” [1].
A
Introduction
At 9 a.m. on Friday, December 8th of this year, the Royal
Swedish Academy of Sciences gathered in Aula Magna, the
Great Lecture Hall of Stockholm University, to hear two astronomers describe how they first detected, some 17 years ago
now, a relic glow from the Big Bang spread out across the whole
sky. Nobel Prizes are unusual in Astronomy; in the 106 years
the prize for Physics has been awarded, only 15 of the 178 recipients have been Astronomers or Astrophysicists [2]. The longterm trend is encouraging, however – of the 8 prizes awarded for
astrophysical topics, all but one (Hess, 1936, for the discovery
of cosmic rays) were awarded in the last 40 years. Five of the
8 have been awarded in the last 30 years, and 2 of 8 in the last
5 years. At this rate, one might expect astrophysics to take over
the competition completely within a decade. (Proving, perhaps,
how dangerous it is to extrapolate from a small number of data
points!)
There can be no question that this year’s prize recognizes
one of the most important scientific discoveries of the past century. John Mather of NASA’s Goddard Space Flight Center
and George Smoot of the University of California, Berkeley
were the principal investigators in charge of two instruments
on board NASA’s Cosmic Background Explorer (COBE) satellite [Figure 1]. COBE was first launched in November 1989,
more than a decade after its initial conception. Over the next
few years, Mather’s instrument measured the energy spectrum
of the microwave background, confirming that it is a blackbody
spectrum, the theoretical form predicted for radiation in thermal equilibrium with matter at a single temperature – in this
case, 2.725◦ above absolute zero. Smoot’s instrument looked for
minute variations in the temperature of the background across
the sky, and finally found them, even though they were only
1/30,000 of a degree kelvin in amplitude. Together these two
results confirmed the hot Big Bang model for the origin of the
Universe and gave us our first view of the fluctuations from
which galaxies, stars, planets and people arose, as they appeared
13 billion years ago when the Universe was still in its infancy.
The Long Road from Bell Labs to WMAP
As with most scientific discoveries, the spectacular results produced by COBE and its successor WMAP were built on many
years of hard theoretical and experimental work, including some
carried out here in Canada. In 1934, following on the heels
of Hubble’s discovery of universal expansion, Richard Tolman
considered the behaviour of thermal radiation in an expanding
universe. He showed explicitly that a blackbody spectrum pro-
Figure 1: An artist’s impression of COBE, NASA’s first
microwave satellite.
Launched in 1989, the satellite
was about the size of a large moving van.
[Image
courtesy GSFC/NASA http://map.gsfc.nasa.gov/m ig/
990295/990295.html]
duced at early times would conserve its characteristic shape during the expansion, while being red-shifted to lower temperatures. By the late 40s, proponents of the Big Bang model were
predicting that such a relic background, with a temperature of
around 5◦ kelvin (5 degrees above absolute zero), should fill the
present-day universe. There was even observational evidence
for a thermal background of a few degrees, from observations
of excited spectral lines produced by the interstellar molecule
CN (by McKellar, in 1941), but the significance of these results
was ignored for two decades.
Then in 1963, Arno Penzias and Robert Wilson, two young
physicists working at Bell Labs in New Jersey, came across an
unexplained and persistent noise source during their experimental attempts at microwave communication with an orbiting satellite [3]. Using a large horn-shaped microwave antenna, they determined that the source was constant in time and did not seem
to come from any particular direction on the sky. After trying everything they could think of to get rid of noise sources in
their system (including shooing away pigeons who had roosted
in their microwave horn, and cleaning out the resulting “white
dielectric”), they were preparing to give up and bury the news
of their mysterious detection at the end of a long technical paper about the antenna. Then, on a fateful flight home from a
meeting, Penzias sat next to an astronomer who told him about
the work underway at Princeton, in the astrophysics group of
Robert Dicke [4]. Dicke had independently predicted the existence of a microwave background filling the sky and was in
the midst of building an antenna to detect it when he learnt
of Penzias and Wilson’s discovery. After comparing notes, the
two groups published companion articles in The Astrophysical
Journal [5,6], one announcing the discovery of the cosmic microwave background (CMB) and the other explaining its astrophysical significance. The detection provided strong evidence
for the hot Big Bang model, and won Penzias and Wilson the
1978 Nobel Prize in Physics.
Given the smoothness and uniformity of the background
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Fall 2006
Figure 3: Fluctuations in the cosmic microwave background,
as reconstructed from WMAP data. Observations at five different wavelengths have been combined to minimize contamination from foreground sources like our galaxy. Red spots
are 200◦ µK hotter than the 2.725◦ K average, while dark blue
spots are 200◦ µK cooler. [Image courtesy the WMAP Science
Team – see http://lambda.gsfc.nasa.gov/product/
map/current/m images.cfm]
Figure 2: In the early 1990s NASA’s COBE satellite finally detected fluctuations in the CMB. The lower oval is
an all-sky map in galactic coordinates, showing the fluctuations as well as “foreground” contamination from our galaxy,
along the plane of its disk. Following on COBE’s success,
ground and balloon-based experiments tried to measure fluctuations in the CMB on smaller angular scales. This upper
insert shows how three years of data from a series of balloon
flights in Saskatoon gave a much more detailed picture of one
patch of the sky. [Image courtesy the Saskatoon experiment
page: http://cosmology.princeton.edu/cosmology/
saskatoon/sask intro.html]
detected by Penzias and Wilson, one might wonder when and
how the diverse structures seen in the present-day universe first
formed. Unfortunately, microwaves are strongly absorbed by
water vapour in the Earth’s atmosphere, making it impossible to
study the CMB in detail from conventional sites at sea level. Between 1965 and 2006, many different experiments have tried to
get as high above the atmosphere as possible, to search for small
variations in the temperature of the CMB from one direction
in space to another. Successive experiments moved from using high-altitude microwave telescopes, to balloon and rocketborne detectors, to satellites orbiting completely out of the
Earth’s atmosphere. In the early 1990s, the COBE satellite finally detected fluctuations on an angular scale of 7◦ and larger
[7], a discovery leading to this year’s Nobel prize. The success
of COBE re- energized the field, and soon the search was on
for fluctuations on scales of a degree or less [8]. These hold
a particular importance in the physics of the early universe, as
explained below. The Canadian prairies being an ideal source
of cold, dry air, a number of high-altitude balloon experiments
were launched from Saskatoon between 1993 and 1995, giving the city a place of honour on many a cosmologist’s plot [9]
[Figure 2].
These many decades of work have culminated in two major
satellite projects, WMAP and Planck. WMAP, the Wilkinson
Microwave Anisotropy Probe, was conceived of and built by a
fairly small team of scientists, including UBC professor Mark
Halpern. It orbits out at Lagrange point 2 (L2), a sort of parking
spot where the gravitational forces from the Sun and the Earth
partly cancel out. The satellite’s twin microwave telescopes sit
back-to-back, scanning two separate patches on the sky simultaneously and recording the temperature difference between them
[10]. For the past four years now, this steady stream of data
has mapped out the CMB fluctuations in unprecedented detail
[Figure 3].
Acoustic Ripples on the Sky
So why all the excitement over a rather noisy map of the microwave sky? First, it’s worth noting that the CMB radiation
comes to us from as far away as light can travel directly; in that
sense, it represents an image of the “edge” of the Universe. It is
an edge more in time than in space; many things happened in the
Universe before the time of the CMB, but we will never be able
to observe them directly using electromagnetic radiation. This
is for the same reason that we can’t see inside the Sun – winding
the clock back to earlier and earlier times, the radiation now in
the microwave background gets hotter and hotter. By a redshift
of 1100, 380,000 years after the Big Bang and around the time
the CMB photons are emitted (or, technically speaking, around
the time they last scatter off free electrons – thus the term “last
scattering” for this epoch), the temperature of the background
radiation reaches 3000◦ K, only a bit cooler than the surface of
the Sun. At this point the ambient heat in the universe is enough
to keep it ionized, and an ionized plasma of sufficient depth is
opaque to light.
The fluctuations in this all-sky plasma screen correspond to
spots where it is slightly hotter or slightly cooler. On large
scales, the hot and cold spots indicate regions of greater or
smaller gravitational potential – over-dense or under-dense
patches of the universe. As explained in the Theory of Relativity, photons climbing out of gravitational potentials are redshifted and thus less energetic, or “cooler,” while photons from
regions of reduced potential are blue-shifted, and thus “hotter.”
Thus potential fluctuations over large volumes of space produce
the CMB temperature fluctuations across large patches of the
sky.
The origin of the underlying potential fluctuations on these
very large scales is a bit mysterious, however. Consider the sit-
Fall 2006
Phys13News 120
uation back at the time of last scattering. Since only 380,000
years have elapsed since the Big Bang, signals can only have
travelled 380,000 light years out from any given point in the universe. A fluctuation of this physical size, out at the “edge” of the
universe, appears to cover about a degree on the sky as we see it
from the Earth today. Angular scales larger than this correspond
to volumes that cannot have communicated with themselves to
establish a common temperature by the time of last scattering.
How then do we explain coherent fluctuations on angular scales
larger than a few degrees?
The answer to this riddle is a process called inflation, by
which the universe is believed to have expanded faster than the
speed of light during a very early period, well before the time of
last scattering. Inflation would have taken small-scale quantum
fluctuations from the very early universe and blown them up
to huge spatial scales, producing the patterns we see today on
the largest angular scales in the CMB. The theory of inflation,
long viewed with scepticism, is on a much firmer footing since
WMAP detected coherent patterns in both temperature and polarization on these large scales.
On smaller angular scales, simple gas physics also contributes to the fluctuations. Small acoustic ripples propagating
through a plasma can alternately compress it, making it hotter, or expand it, making it cooler. Acoustic waves propagate
at some sound speed cs less than the speed of light, so by the
time of last scattering tls , 380,000 years after the Big Bang,
they could only have propagated across regions smaller than
lac = cs tls = 380, 000 light-years. On scales much larger
than this, the effects of acoustic oscillations coming from many
different directions should average out. Considering the amplitude of the temperature fluctuations in the CMB as a function
of angular scale on the sky, one would expect some feature at
the angular scale corresponding to lac , marking the onset of the
acoustic regime.
Sure enough, plots of the amplitude of fluctuations in the
CMB as a function of angular scale show a large peak at a scale
of ∼ 1◦ [Figure 4]. This “first peak” marks the scale on which
large regions have been compressed for the first time by a single pressure wave; on smaller scales waves will have had time to
oscillate once, twice, or more, leading to a whole set of smaller
peaks at fractions of the basic scale. Figure 4 shows the final
spectrum of fluctuations as a function of angular scale, as measured by WMAP during the first three years of its flight.
Cosmology: A Set of Fundamental Numbers?
The final “power spectrum” of fluctuation amplitude versus angular scale derived by CMB experiments like WMAP [Figure
4] may seem a bit dry and technical, but it conceals a whole
set of juicy physical measurements. The angular scale of the
first peak, which is set by the sound speed and the age of the
universe at the time of last scattering, as explained previously,
marks out a fixed physical length scale at redshift 1100. By
measuring the angle this scale subtends on the sky, we can determine the overall geometry of the universe – whether it is flat (or
Euclidian), such that parallel lines never meet, or closed (such
that parallel lines converge), or open (such that parallel lines
diverge) [Figure 5]. The latest WMAP measurements suggest
that our universe is flat, at least to within the measurement errors of ∼5%. The height of the “plateau” in the power spectrum
5
Figure 4: The angular power spectrum of the cosmic microwave
background, as measured by the WMAP satellite (black points)
and various ground or balloon-based experiments (coloured
points). The angular power spectrum measures the variation in
the temperature of the background when measured over distinct
patches of various sizes, as a function of patch size. The main
peak in the power spectrum shows that the background varies
most on ∼ 1◦ scales. The thin grey curve shows the theoretical prediction from the cosmological model that best fits the
data. The pink envelope shows the range of scatter expected
around this best-fit model when it is observed from a particular location in space, such as our solar system. [Image from
Hinshaw et al. 2006 [11] – see http://lambda.gsfc.nasa.
gov/product/map/current/m images.cfm]
on scales larger than the first peak also tells us whether the universe is dominated by matter, by radiation or by something else.
The relative height of the first three peaks tell us how much of
the matter is normal (or “baryonic”) matter, and how much is
the mysterious “dark matter,” since dark matter doesn’t interact
with light, and thus behaves differently around the time of last
scattering.
Taken together, these different features of the CMB power
spectrum have greatly increased our confidence in the current
model of the universe. They have confirmed earlier estimates
of the fundamental cosmological parameters, such as the presentday matter density, that were based on galaxy properties, distances in the universe and the clustering of matter, and they
have also reduced the errors on many of these estimates dramatically. The final picture we are left with is a rather odd
one, however. It seems that the universe is flat, and thus that
it must have the exact energy density needed to maintain this
geometry. The energy content is divided up into a very strange
mixture of components, however – a small fraction of radiation
and neutrinos, 4% normal matter, 22% dark matter, and 74% ...
something else. Because of the way it behaves, we know that
this last component can be neither matter nor radiation. It is
sometimes called “dark energy,” for lack of a better term, but
we have no real idea what it is. Measuring the fractional contribution of the different components so accurately – the numbers
quoted above are good to a few percent – represents a huge triumph for the current generation of cosmologists. But why our
universe consists of these different components, and why in this
ratio, remains a mystery.
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Phys13News 120
Fall 2006
References
[1] http://en.wikipedia.org/wiki/Haldane’s Law
[2] http://nobelprize.org/nobel prizes/physics
[3] The details of this account are from Barbara Ryden: Introduction to Cosmology, 2003 (Addison Wesley - San Francisco), p.148 ff. , and from Bennett et al.: The Cosmic Perspective, 2007 (Addison Wesley - San Francisco), p.691
Figure 5: Since the largest acoustic modes seen in the CMB
have a fixed physical size, their apparent angular size tells us
about the geometry, or equivalently the energy density, of the
universe – whether it is closed (Ω > 1), open (Ω < 1), or flat
(Ω = 1) and thus whether light rays diverge faster than, slower
than, or at the usual Euclidian rate. The detection of the peak
in the angular power spectrum at roughly 1◦ by WMAP and an
earlier balloon experiment named BOOMERANG indicate that
the universe is flat, at least to within a few percent. [Images
courtesy NASA/GSFC and the WMAP Team – http://map.
gsfc.nasa.gov/m uni/uni 101bb2.html ]
The Future
Ultimately, physics is the study of what the universe is made
of and how it works. As such, it seems appropriate that the
field’s greatest prize be awarded to an experiment that helped
determine the composition and nature of the universe on the
largest scales. The universe at the time of last scattering was
much simpler than it is now, and it is precisely this simplicity that makes observations of the CMB such a powerful tool
for cosmology. In particular, the detailed shape of the fluctuation power spectrum provides many independent tests of the
cosmological model. From its analysis we are left with precise
measurements of the age and composition of the universe, but
no deep understanding of why it is the way it is. In that sense,
the situation is similar to particle physics where the “Standard
Model” classifies the known fundamental particles, without really explaining their origin.
We have not yet finished analysing the microwave background. Planck, the second of the next-generation CMB experiments, is scheduled for launch in 2008 [see the cover of this
issue and the caption on page 2]. It will provide much more
detailed measurements than WMAP of the polarization of the
microwave background, and this in turn may produce definite
proof of the reality of inflation and possibly even an indication
of the energy scale on which it occurs. Planck and other polarization experiments will also give us a clearer picture of what
has happened in the universe since the time of last scattering, as
foreground sources between us and the last-scattering surface
can also generate polarization in the CMB. In the longer term,
however, we will have to design radically different experiments
to explore the fundamental question of why our universe is what
it is.
James Taylor is a new faculty member in the Department of
Physics & Astronomy at the University of Waterloo. He can be
reached at [email protected].
[4] Other notable members of Dicke’s group include Jim Peebles and David Wilkinson. Peebles, one of Canada’s greatest astrophysicists, was born in Winnipeg and graduated
from the University of Manitoba in 1958. He is now the
Albert Einstein Professor of Science Emeritus at Princeton
University. David Wilkinson, also a professor at Princeton
during his lifetime, was a founding member of the MAP
satellite project. After his death in 2002, MAP was renamed
WMAP in his memory.
[5] Penzias, A. A., & Wilson, R. W. 1965: A Measurement of Excess Antenna Temperature at
4080 Mc/s, The Astrophysical Journal vol. 142,
p.419
(http://adsabs.harvard.edu/cgi-bin/
nph-bib query?bibcode=1965ApJ...142..419P)
[6] Dicke, R. H., Peebles, P.J.E., Roll, P.G. & Wilkinson, D.T. 1965:
Cosmic Black-Body Radiation,
The Astrophysical Journal vol. 142, p.414 (http:
//adsabs.harvard.edu/cgi-bin/nph-bib query?
bibcode=1965ApJ...142..414D)
[7] An angular scale of 7◦ on the sky is about three-quarters
of the width of your hand, when held at arm’s length with
the fingers together. There are 816 independent patches of
this diameter on the sky, so if you spent a minute looking at
each one it would take 13.5 hours to survey the whole sky.
[8] An angular scale of 1◦ on the sky is slightly less than the
width of one finger, held at arm’s length. It is also about
twice the angular size of the moon. There are 40,000 independent patches of this diameter on the sky, so if you spent a
minute looking at each one it would take a month (working
non-stop) to survey the whole sky.
[9] Eventually, the balloonists moved their launch sites from
the wintery Canadian prairies to Antarctica. They claim this
had something to do with circumpolar winds, but my own
suspicion is that they found the Antarctic climate a bit less
harsh.
[10] NASA has animations of the satellite orbit and the
scan strategy at: http://map.gsfc.nasa.gov/m or/
mr media2.html (along with many other great animations).
[11] Hinshaw et al. 2006: Three-year Wilkinson Microwave
Anisotropy Probe (WMAP) Observations: Temperature
Analysis, The Astrophysical Journal (submitted) (http:
//arxiv.org/abs/astro-ph/0603451)
[12] Many thanks to Sara Brooks & Kate Taylor for advice and
a careful reading of this article.
Fall 2006
Phys13News 120
The Physics of the Violin
Christopher Saayman
he violin is a bowed four stringed instrument and the principal member of the family of instruments which superseded
the viols from about 1700. Earlier versions of the violin can be
traced back to the 9th Century, possibly to Asia. Many Kings
and Queens were required to learn how to play the violin, and
some of the greatest composers wrote music only for the violin. Despite its long history, research continues in the area of
violin making. In this report, the history of the violin will be
outlined, along with its evolution as a musical instrument. The
physics behind the violin, with special attention to acoustics,
is discussed. Finally, advances in violin production are mentioned, along with technique.
T
Introduction
What is it that captivates us when we listen to music? Is it the
instrument, or the musician? Webster’s dictionary defines music as “the art and science of combining vocal or instrumental sounds or tones in varying melody, harmony, rhythm, and
timbre, especially so far as to form structurally complete and
emotionally expressive compositions”. It also defines a musician as “one who is skilled in music, especially a professional
performer of music.” It takes a performer to skillfully manipulate an instrument to produce music that captivates us. Music is
thought to predate language (and certainly predates the written
word). It varies between countries and even regions and it can
reflect a society’s way of life. The violin is predominantly used
in the orchestra and in chamber music. Its range is from the
G below middle C, upwards for more than three and a half octaves. The violin itself has evolved over the past several hundred
years, and several changes in style as well physical appearance
have been made. Recently, modern research has been applied
to violin production, with the hope of improving sound quality
to create modern instruments similar to a Stradivarius, the most
famous of all violins; some of the difficulties with this lie in the
fact that few performers who own one are willing to let it be
taken apart for scientific research!
History of Sound
Music has always been an important part of human history.
It has been around for countless years and has evolved with
us. The first musical instruments were made out of stone and
bones. In Egypt there is proof that strings and bows were used
in an early version of the harp. Pythagoras discovered the basics of music theory, when he noticed certain frequencies produced unique harmonics. During the past 500 years, many great
thinkers worked in the field of music, which was considered a
science until relatively recently, when it became exclusively an
art. Galileo described the oscillating pendulum and thus also described vibrations of strings. Hooke determined the relationship
between force and oscillatory motion. Fourier and Lagrange
put the production of sound on a mathematical level. Savart
(from the Bio-Savart Law) is perhaps most noted for his application of physics to violin acoustics in his paper Treatise on the
7
Construction of Bowed String Instruments. In the early 1900’s,
Helmholtz, Rayleigh and Savart developed modern acoustics.
With the advent of analogue and digital electronics, the science
and art of music have once again melded, and the communication between musician and scientist is bringing forth new ideas
every day.
History of the Violin
Invented in its modern form
sometime in the middle of the
16th century, the violin evolved
from several types of stringed
instruments, most notably the
lute. Before this, the stringed
family of viol were mainly
used. It is thought that Andra Amati was hired by a noble
family to create an instrument
Figure 1: A violin by
that street musicians could play,
the famous violin-maker,
while at the same time good
Stradivari. [photo courtesy
enough for nobility to use. He
of Wikipedia]
founded the Cremona school of
violin makers around this time, whose pupils included Stradivari and Guarneri, two of the most famous violin makers in
history. Not since their time have violins been so beautifully
crafted. Even now their violins are sought after, some valued
at more than $1 million. The oldest surviving violin was made
by Amati in 1564. The most famous violin is the Le Messiah,
crafted by Stradivari in 1716, and is rumoured never to have
been played. (See Figure 1 ) There is a famous story of three
violin making families in Italy. One put up a sign saying they
had the best violins in the city. The next, not to be outdone, put
up a sign saying they have the best violins in the country. The
third, the Stradivari family, put up a sign saying they have the
best violins on the block.
Introduction to the Basics of Music
The musical scale is divided into semitones, which together
make an octave. There are 12 semitones per octave, which begins and ends on the same musical letter, but 8 notes higher. The
basic letters of a musical scale are ABCDEFG. Between each of
these there are one or two semi-notes. Semi-notes are denoted
by a sharp (# ), which raises the note one semi-tone, or a flat ([),
which lowers the note a semi-tone. Take for example the note
D. If we want to raise this note by a semi-tone we put # after it,
so D# . If we want to lower D by a semi-tone, we add a flat ([),
and get D[. The mathematics behind musical scales is simple.
Each octave is a simple ratio of harmonics. Two notes played
an octave apart will have a frequency ratio of 2:1. Harmonics
typically sound pleasing to our ear. (Incidentally, most casino
cash games make the set of harmonics known as the C-Major
cord, which is shown to be the most pleasing to the human ear.)
Not all instruments are tuned to the same note. The violin is a
four stringed musical instrument tuned in fifths (discussed below), played with a bow and held between the shoulder and the
chin. A violin is a “concert C” instrument, meaning a C played
on the violin matches with the piano and the flute. A trombone
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on the other hand, is concert E flat. The violin and trombone
are unique because they do not have any frets or set valves. It is
therefore possible to play an unlimited number of notes within
their ranges. As a consequence of this, vibrato, most popular
amongst singers, can be applied to violins. Vibrato varies the
pitch of a note slightly, and thus can make sound waves seem to
emanate from different points in the room, making a piece livelier. A violinist can also change the violin harmonics by moving
the bow closer or further to the bridge. Bringing the bow closer
will increase the harmonics that are produced, moving it further
will produce richer tones.
The Physics of Sound
A sound wave is an air vibration that travels outward from its
source as a spherical shell. As the wave moves along, it compresses air in front of it, and expands air behind it. Our ears can
detect this pressure difference, and our brain interprets this as
sound. Sound waves are technically longitudinal waves, though
we often represent them as transverse (or side-to-side) waves.
Doing so enables us to visualize their frequency and wavelength
more easily. The human ear can detect sound waves with a frequency as low as 25Hz, and as high as 20, 000 Hz. At certain
frequencies, it is even possible to discriminate two tones only
2 Hz apart. When a violin is played, the strings oscillate with
a given frequency, causing the air around it to respond with the
same frequency. In general, strings have natural modes of oscillations. The first mode is called the fundamental frequency,
and all other harmonics are integer multiples of it. Harmonics
can be created on the violin by lightly touching the string with a
finger, at specific locations. Resonance occurs when the string
oscillates near, or at a harmonic. In music, frequency ratios of
the harmonics that are integer values are most pleasing to the
ear. For example, a perfect fifth contains notes with a frequency
ratio 2:3, while a perfect fourth has ratios 3:4. The “perfect
fifth” differs from the “augmented fifth” or “diminished fifth”,
while “the fifth” corresponds to the interval it spans across the
musical scale.
Parts of the Violin
There are several parts to the violin that need to be assembled.
At each step the violin maker
must make sure each component is properly aligned. Even
a slight misalignment will result in an off-sounding violin.
The bodies of the violin are typically made from aged maple
wood or Norway spruce. Modern experiments show the natuFigure 2: The parts of a
ral frequency of wood is around
typical violin. [photo cour440 Hz, which is the standard
tesy of Wikipedia]
tuning note in orchestras. The
fingerboard is made of ebony
for support, and the bridge is made of hardwood. Perhaps the
most carefully-chosen type of wood is used for the sound post.
Resting between the top and the bottom of the instrument, and
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(a) y
kink
string
A
x
B
bow
envelope of string’s motion
(b) vA
stick
t
(c) vA
skip
Figure 3: Idealized Helmholz motion. Rosin is used to increase
the friction between the bow and the strings.
off to the right side, it is perhaps the most important piece of the
violin. The French call it the soul of the violin. Even a slight
alteration in position or tightness, can result in drastic changes
to the sound. The holes in the violin are called f-holes and they
serve to amplify the sound waves of the strings (See Figure 2).
Before synthetic fibres were introduced, the strings were made
from sheep gut wrapped tightly around steel, and, depending
on quality, dipped in silver. Even the glue and varnish are chosen carefully by the violin maker, as each can have a distinctive
affect on the overall performance of the instrument.
The Physics of the Violin
Although the bow and the string are the parts that make contact
when playing, very little sound comes from the strings. The
main source of sound is from the body of the instrument. The
strings pass over the bridge, which is attached to the body. The
vibrations travel through the hollow body, causing the wood,
and thus the air, to expand and contract, producing a much
louder sound. The sound post serves to make the violin asymmetrical, in terms of acoustics. It effectively cancels out the
vibrations from the right side of the bridge, letting the left side
vibrate freely. If the sound post were not there, the waves would
interfere with each other, and considerably less sound would be
produced. The bass bow, located just over the G-string, also
causes the violin to become asymmetrical, in the lower frequency region. Even with these two aids, the violin is still a
terribly inefficient instrument, converting less than 1 percent of
the work done by a performer into sound. The rest is transformed into heat and interference patterns. Typically, the most
resonance is found near C# on the G string; it is possible to feel
the vibrations through the violin.
Most violinists will tell you the older a violin is, the better it
generally is. Whether this is based on science, or on judgment,
is still up for debate, but current research has been able to uncover a few details. It seems that when a violin is played for a
long period of time, its characteristics seem to change slightly.
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A violin that has not been played will not have any change in
its tones. This could be because of water vapour that is absorbed by the wood over the years, making the violin heavier,
and causing the body to respond in different ways. Also, the
edges around the violin called the purfling strips tend to loosen
over time due to the glue. This may cause an alteration of tone.
Another explanation for this theory is that older violins are better, simply because they were not mass produced as they are
now. Many violins are produced in factories, and even some
department stores sell them.
The Bow
The physics of the bow is well understood. It was developed
mathematically by Helmholtz. He investigated the path a piece
of grain took attached to a string, as he moved the bow across
the string. He found that the displacement vs. time graph of this
was a “zig-zag” of two straight lines. (See Figure 3) This can
be explained by friction. When the bow is moving, it has sliding
friction, and when (momentarily) stopped, it has static friction.
The change from one to the other is discontinuous; the zig-zag
shape of the graph is when the player changes directions of the
bow. The bow is coated with rosin, which increases the friction
between the bow and strings.
Room Acoustics
Up until 1895, opera and concert hall designs were mostly a
work of art. Then Wallace Sabine from Harvard began looking
into quantifying different characteristics of acoustics, and found
certain relationships that could be used to build a better theatre.
He then applied his knowledge to build the first scientificallyinspired music hall, the Boston Symphony Hall, in 1900.
Wallace founded the field of room acoustics. This looks
at several factors including echoes, large structures, resonances,
creep, sound focusing, and reverberation time. Each affects how
the audience will hear a piece of music. Echoes occur when the
shape of the stage is such that the waves bounce off the walls
and reach the audience slightly after the original wave. Large
structures, such as balconies can cause diffraction of the sound
waves, leading to a different pitch heard by audience members
in different parts of the hall. Resonance is a major concern
in smaller rooms, where the length of the room may only be
a few wavelengths long (for lower frequencies, we can have
wavelengths on the order of meters). Creep is sound travelling
around the perimeter of domes, and is often referred to as the
“library effect.” Sound focusing occurs on concave surfaces,
where sound reflections tend to interfere constructively at foci.
Lastly, reverberation time is defined as the length of time it takes
for a given material to absorb most of a sound wave. It is proportional to the size of the room, since the bigger the room, the
longer sound waves will take to reach the absorbing surfaces.
Concert halls have the additional challenge of designing a hall
with the audience members’ clothes in mind. Average absorption can increase by several factors, depending on frequency.
Currently, the three most accepted shapes for acoustic orchestral buildings are rectangles, fans, and horseshoes.
9
Current Research
In the last 50 years a new
group of violin makers have
emerged, with the goal of taking a more scientific approach.
Hutchins founded the Catgut
Society of America, which investigates acoustic properties of
the violin. She was joined by
Saunders and Schelling, from
Figure 4: An electric violin
Bell Laboratories. These peomanufactured by Vector
ple are still active in acoustic reInstruments of Nova Scotia
search and continue to strive towith a mass of less than
wards making even better vio400 g. [photo courtesy
lins. One of the major contribuVector Instruments http:
tions they have made to the field
//vectorinstruments.
is to aid violin makers in decidcom]
ing when the thickness of the
violin body is just right. Traditionally this was done by “tapping” the body, to listen for the
right “tones.” Now they can hook up a machine resembling an
oscilloscope to determine the thickness they need. Research
into producing a better violin has come a long way in the past
100 years, but there is still much that can be done. Another
new invention is the electric violin, Figure 4 . Most companies
will claim that the quality of sound from an upper-end model is
comparable to that of a professional violin; however, few professional violinists are fully convinced. An alternative to this,
is adding a microphone to a violin. Wireless microphones can
be used in performances when a violinist wants the freedom to
stroll around.
Conclusion
The violin has brought joy to millions of musicians and music lovers for hundreds of years. Several improvements have
been made, mainly in response to current preferences. The
great age of violin-makers is long gone; however, modern researchers have tried to replicate the sound, using oscilloscopes
and advanced methods of “tapping.” The acoustical properties
of concert halls have improved dramatically in the last 100 years
and have made concerts more enjoyable. The future of producing violins is exciting and promises to offer new techniques and
styles, enticing audiences and musicians alike.
Chris Saayman is a third year undergraduate student in the Department of Physics & Astronomy at the University of Waterloo.
He can be reached at [email protected].
References
[1] ”The Physics of Sound” (Readings from Scientific American 1978. W.H Freeman et al.
[2] ”The Physics of the Violin” 1962, C. Hutchins
[3] ”The Physics of the Bowed String” 1974, J. Schelleng
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[4] ”Acoustics and Vibrational Physics” 1996, Stephens. London Edward Arnold Publishers Ltd.
[5] ”The Physics of Sound” 1982, R. Berg and D Stork.
Prentice-Hall Ltd.
[6] ”The Science and Applications of Acoustics: Second Edition” Raichel, Spring Ltd.
[7] Conversations with Dr. Vanderkooy, Dept. of Physics & Astronomy, University of Waterloo.
[8] ”The Violin Site” http:://www.theviolinsite.com/
[9] ”Wikipeida” http://en.wikipedia.org/wiki/Violin
[10] ”Wikipeida” http://en.wikipedia.org/wiki/Perfect fifth
[11] ”Physics for Scientists and Engineers, 5th edition” Serway
[12] ”Science and the Stradivarius” Physics World April 2000
[13] Websters New Twentieth Century Dictionary, Second Ed.
Outside the Classical Comfort Zone
Sonia Markes
“I can, if the worse come to worst, still realize that God
may have created a world in which there are no natural laws.
In short, chaos. But that there should be statistical laws with
definite solutions, i.e., laws that compel God to throw dice in
each individual case, I find highly disagreeable.”[1]
It is no secret that Albert Einstein did not believe in quantum mechanics. But Neils Bohr did. It is said that he once told
Einstein to “stop telling God what to do.” Both men were brilliant scientists who were each responsible for major advancements in modern physics, but it is their difference in opinion
that makes this pair legendary. In fact, much of quantum mechanics developed because of the directly opposing views of
these two great minds, including the concept of non-locality. It
all began, as good science often does, with a question: Can the
quantum-mechanical description of physical reality be considered complete?
Background
Before we can explore this question, we need to set out the facts
about quantum mechanics that we will need for this discussion.
All the information that quantum mechanics can tell us about a
system is contained in the wavefunction. Wavefunctions can be
represented as linear combinations of the eigenfunctions of an
operator that corresponds to an observable. Arguably, the most
significant difference between classical mechanics and quantum
mechanics is the commutivity, or lack thereof, between some
of these operators. This non-commutivity gives us many key
features of quantum mechanics. One of these key features is
the Uncertainty Principle. The Uncertainty Principle states that
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between any two non-commuting operators, there exists a minimum value of the product of the standard deviations of the measurements of the two quantities. As a consequence of this relation, there is a maximum amount of information that can be obtained at the same time about two observable quantities whose
corresponding operators do not commute. Another property of
a pair of non-commuting operators is that there is no set of linearly independent functions in the Hilbert space (the space of
wavefunctions) that are simultaneously eigenfunctions of each
of the two operators. Another concept we will need in our exploration of the EPR paradox is intrinsic angular momentum,
more commonly referred to as spin. Every fundamental particle
that has been observed to date has a precise value of spin. Spin
can take either half integer or integer multiples of Planck’s constant, ~, a quanta of angular momentum. For instance a photon
has total spin 1 and an electron has total spin 21 , in units of ~.
Though quantum mechanical spin is not the same as classical
spin, it can be treated as such when interpreting the physics.
Spin is conserved, much in the way that angular momentum is.
For example in a two particle system with a total spin 0, if one
particle is measured to have a spin of positive one half in the
z direction (we call this spin up) then the second particle will
have a spin of negative one half in the z direction (we call this
spin down). One thing to keep in mind during this discussion is
that quantum mechanics contradicts classical intuition. In classical mechanics there was never a difficulty in interpreting what
the mathematical formalism of the theory was telling us about
the physical situation. This is because we can see many of the
phenomena classical mechanics describes, and because classical mechanics is deterministic. For example, if the position of a
ball is known as a function of time, then we can also determine
its momentum (both linear and angular), acceleration, energy,
and every other physical quantity that describes the system at
any instant in time or for all time. However, with quantum mechanics, things are not so clear. There are no trajectories. What
makes it difficult is that the nature of the theory is probabilistic, and therefore it does not possess the same kind of ‘classic
causality.’
Einstein’s Argument
In 1935, Boris Podolsky, Nathan Rosen, and, of course, Albert
Einstein, published a paper[2] with the conclusion that quantum
mechanics was not complete. They did not define completeness,
but rather declared a necessary condition of completeness. “Every element of the physical reality must have a counterpart in the
physical theory” where the condition for physical reality is the
following statement: “If, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal
to unity) the value of a physical quantity, then there exists an
element of physical reality corresponding to this physical quantity.” I would like to break this down into two separate criteria.
1) Observation should not disturb the system. 2) Predictions
should be deterministic. Now consider two physical quantities
such that their corresponding operators do not commute. They
explain that the more that is known about one of the physical
quantities, the less that is known about the other. This argument
hinges on Heisenberg’s Uncertainty Principle. Another way to
look at it is that since they do not have simultaneous eigenfunctions, we cannot determine values for both physical quantities
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Phys13News 120
at the same time. By the above definitions, it suggests that only
one of the physical quantities has physical reality at any given
time (assuming the quantum mechanical description to be complete). Then, logically, either quantum mechanical description
is not complete or physical quantities corresponding to noncommuting operators cannot be real at the same time. Einstein,
Podolsky, and Rosen then set out to show that the second option
is false. Consider two particles (particle One and particle Two)
and two physical quantities (call them A and B) that are correlated between the two particles. Also, the operator corresponding to measuring quantity A of particle One does not commute
with the operator corresponding to measuring quantity B of particle One. Likewise for particle Two. The two particles are then
separated by a very large distance. Measure quantity A of particle One and quantity B of particle Two. Then, because of the
correlation between the quantities, we know the quantity A of
particle Two and the quantity B of particle One. By the criteria for physical reality, it would seem that physical reality can
be attributed to both physical quantities even though their associated operators are non-commutative. This is a contradiction.
Thus, the conclusion is that quantum mechanics is incomplete.
Bohr’s Rebuttal
There are two major complaints that Bohr had with Einstein,[3]
Podolsky and Rosen’s case. His first criticism was of their criterion for reality. He stated that their formulation of the criterion
for reality was brought about by a classical mindset. Bohr suggested that quantum mechanics brought about “...the necessity
of a final renunciation of the classical idea of causality and a
radical revision of our attitude towards the problem of physical reality.” Trying to interpret a physical situation within the
framework of quantum mechanics without ‘renunciation’ and
‘revision’ would lead to interpretations that would not match the
physical situation. His second criticism was that they had neglected the connection between the particle being measured and
the measuring apparatus. An apparatus can measure in one basis composed of eigenfunctions or another, but not both simultaneously. We, as observers, cannot control, predict, or know
the interaction between the measuring apparatus and the thing
we want to measure. Putting these two criticisms together we
can get a clear picture of why Einstein, Podolsky and Rosen’s
argument fails. We do not arbitrarily pick the physically real
quantities that then negate the reality of other quantities, but
experiments, and more specifically, experimental set-ups and
processes determine what can be measured. What in a classical
light, appears to be arbitrary, is simply our choices as observers
as to how we put together the experiment, thereby choosing
what we want to observe. This gives a picture of a system where
particles and measuring apparatus are all within the system, and
not separable. However, we still do not know what is ‘real.’
Bohm’s View: Today’s EPR
David Bohm proposed an alternate thought experiment.[4,5]
Consider a system of two spin- 12 particles with zero total spin.
The wave function is the singlet state
1
Ψ = √ (↑↓ − ↓↑) .
2
11
Say the particles are separated in such a way that the spins are
not disturbed. Once they are very far apart, we measure one
of the components of the spin of one of the particles. By conservation of spin (i.e. angular momentum), we can determine
what that component of spin is for the other particle. When
viewed with a classical way of thinking, there is no paradox. In
fact, there is nothing interesting here at all. Each particle has a
definite spin that can be broken down into three definite components at all times. But in quantum mechanics, this is not the
case. Particles do not have definite spin until someone takes a
measurement. The components cannot all be known at the same
time as they have non-commuting operators. For example, say
we measure the z-component of the spin of the first particle. We
then know the z-component of the spin of the second particle to
be the opposite value. Then say we measure the x-component
of the spin of the second particle. Classically, because both the
particles have definite spin in all three components at all times,
we would know the x-component of the spin of the first particle. But if we then measure the z-component of the spin of
the first particle, we do not necessarily get the same result as
when we measured it before. We interpret this to mean that a
measurement on either particle disturbs both particles because
neither have definite spin in any direction until one is measured.
This can be generalized for any two non-commuting operators.
This means that if we have a pair of non-commuting operators,
the observable quantities associated with those operators do not
have definite values until measured. In classical mechanics, observable quantities have definite values at all times. This is a
key difference between classical and quantum mechanics and it
should be emphasized that this difference comes out of the difference between commuting and non-commuting quantities; in
classical mechanics, all quantities commute whereas in quantum mechanics, there are non-commuting quantities. Indeed,
it is the fact that the operators do not commute that gives the
paradigm shift from classical to quantum thinking.
Conclusion
Bohr quickly showed that the original argument provided by
Einstein, Podolsky and Rosen did not in fact give rise to a paradox when viewed without classical assumptions. It should have
ended there. However, Bohm’s continued exploration of the
subject revealed an even greater insight into the nature of quantum mechanics. It was in fact the opposite of what Einstein
wanted, a theory filled with ‘spooky action at a distance’ preventing systems from ever truly being separated. It is interesting to note that the legacy of the EPR paper has little to nothing
to do with what Einstein, Podolsky, and Rosen set out to show;
namely, that quantum mechanics is incomplete. Its legacy is in
having brought non-locality to the forefront of the study and interpretation of quantum mechanics. In addition to the insight
that has been gained into the nature of the quantum mechanical world, work on the EPR paradox also gave rise to Bell’s
Inequalities, hidden variable theories (for example, Pilot Wave
Theory), and is utilized in every aspect of quantum information
theory, quantum computing, quantum teleportation, quantum
encryption and quantum gravity. But the original question of
whether or not quantum mechanics is complete remains unanswered. To this day, it is a question that scientists work on and
likely will continue to for years to come.
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Phys13News 120
Sonia Markes is a third year undergraduate student in the Department of Physics & Astronomy at the University of Waterloo.
She can be reached at [email protected].
References
[1] A. Calaprice “The New Quotable Einstein” (Princeton University Press, Princeton 2005.)
[2] A. Einstein, B. Podolsky and N. Rosen “Can quantum mechanical description of physical reality be considered complete?” Phys. Rev. 47, pp 777-780, 1935.
[3] N. Bohr “Can quantum mechanical description of physical
reality be considered complete?” Phys. Rev. 48, pp 696702, 1935.
[4] D. Bohm and Y. Aharonov “Discussion of Experimental
Proof for the Paradox of Einstein, Rosen and Podolsky”
Phys. Rev. 108, pp 1070-1076, 1957.
[5] D. Bohm “Quantum Theory” (Prentice-Hall, Engelwood
Cliffs 1951.) Reprinted by Dover Publications 1989.
Canadian Undergraduate Physics Conference 2006
Fall 2006
Hamilton to Fredericton.
The kids with the poster tubes were a dead giveaway. It turned
out that McMaster had sent their crowd on the same flight I
had chosen, and I got chatting with them during my stopover in
Montréal. It was a big crowd, at that: fifteen students, which
comprised about 9 per cent of the 170 delegates. Already it was
nice meeting other young researchers and hearing about what
they were doing.
I must, firstly, congratulate the organising committee on
their wonderful choice of venue. The Crowne Plaza Lord Beaverbrook hotel was really quite grand. Although there may have
been ongoing construction, and the occasional bit of debris landing on some poor unsuspecting delegate, all in all, it was a very
classy place for a bunch of young physicists to hang out for a
conference. Those five brilliant days went something like this.
Friday:
Even before arriving at the hotel – before, even, leaving Fredericton airport – fraternising ensued in a most lively fashion.
After settling in, a healthy group of about twenty of us went
out searching for a place to get some dinner. This was more
difficult than it might sound. Putting the minor detail aside of
having consensus on location, the mere fact that there was such
a large group meant also that we had to find a place with sufficient space. We managed, and even arrived back to the hotel
in time for the single official event on Friday: the ever important ‘meet-and-greet.’ I won’t even try to repeat all the nerdy
conversations that went on.
Robbie D. E. Henderson
Having seen nothing of
the world of physics outside that of my own
university, being in my
fourth year I decided
it was about time to
get out there and see
what the rest of the
country’s undergraduate
physicists were up to.
I recently attended the
Canadian Undergraduate
Physics Conference, this
year hosted by the University of New Brunswick. I’ll say this much:
it was the most incredible five days of my university life, and a most
enriching social experience. Let me tell you
a little bit about my first
CUPC.
Despite the fact that
I knew no undergraduate physicists at any other
university, it was quite
straightforward to find
them on my journey from
Saturday:
Figure 1: The Waterloo contingent to the 2006 CUPC conference. Each of these eight students
made a presentation.
On this first day of actual physics, the conference began with a
morning talk by Dr. Bob Romer, former editor of the American
Journal of Physics. As an excellent speaker, he kept our attention with both humour and very useful anecdotes. After the first
round of student talks and some lunch, we attended a talk by
Dr. Bruce Balcom on MRI. More student talks ensued, with my
own, on “The Stellar Mass Content of Distant Galaxy Groups,”
being slated in the last timeslot of the day. As it turned out I
was the first of the Waterloo group to deliver their talk. This
happened to be my very first on any sort of scale such as this,
but despite the fact that I was apprehensive the entire afternoon,
it went pretty well.
A group of us enjoyed
a nice dinner at a Greek
restaurant nearby, where
all of us, composed of students of Carleton, Regina,
Victoria, as well as Waterloo, got to know each other.
After all this, of course
the opening day would not
be complete without some
sort of large-scale social
Figure 2: The Waterloo continevent. The event so chosen
gent to the 2006 CUPC conferwas an evening pub crawl,
ence enjoys a night out.
and was certainly an excellent way to observe some of the night life that nearby Fredericton had to offer. There just so happened to be an Irish pub right
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Phys13News 120
there at the hotel, which was among the four venues planned;
however, for some reason they decided to make it the second
stop. One would expect it to be much easier to leave it till last
in order to make it easier to get back to the rooms at the end of
the night. As it turned out, a great deal of people wandered off
track and decided to take over a dance club for the remainder
of the evening. Some interesting stories came out of this, but
perhaps they should be left back in Fredericton...
Sunday:
The morning began with
a three-hour run of student talks.
This, perhaps, was not the greatest
idea, as there were many
still recuperating from the
previous evening.
Just
for the record, I made it
for the 9am start time,
partly to offer support to
some new friends fortuFigure 3: On Sunday the UW
nate to have their talks
physics students went out with
scheduled for that mornwith Jan Kycia, a UW physics
ing. Among those giving
professor that also attended the
talks this day was our own
CUPC conference.
Andrew Louca, who spoke
on “Characterising Noise in Quantum Circuits,” the second of
the Waterloo gang to deliver their talk. Third and fourth in line,
respectively, were Patrick McVeigh, presenting “Localisation
of Neural Sources in Magnetoencephalography,” and Joseph
Petrus who gave his talk on “The use of Microwaves to Manipulate Rydberg Atom Energy Levels.”
After a brief break, a guest speaker, Dr. Alain Haché, gave a
rather interesting primer on the physics of hockey. After lunch,
most of the students not scheduled for talks presented their posters.
There were a number of them, and I made an effort to browse
through all of them. Some were quite impressive, and I got a
number of new ideas on design. As far as I remember, no one
from Waterloo gave a poster.
Later in the evening, a rather large group of us from Waterloo, Carleton, Regina, Victoria, St. Mary’s, and Calgary went
out in search of a reputable Caribbean place for dinner. We were
quite disappointed when we discovered it was closed that day,
and settled instead for a grill across the street. It turned out quite
nice, actually, and we all enjoyed it very much. The evening
also included a tour of the University of New Brunswick’s facilities.
Monday:
Crêpes are an excellent way to start the day, which is exactly
what a compilation of students from McMaster, Waterloo, St.
Mary’s, and I did on this final day of the conference. I tell you,
for such a seemingly small place, downtown Fredericton sure
had a great many interesting places at which to eat.
Four of those from Waterloo delivered their talks on this
day, beginning with Peter Watson and “takin’ care of bismuth:
determination of high energy neutron spectra via bismuth activation in the TNF.” Next up was Paul McGrath, on “The Ge-
13
ometry of Gravitational Radiation,” followed by Mark Ilton and
“Frustrated Quantum Magnets.” Lastly, but most certainly not
least (not that there was a least), Kate Ross delivered her talk on
“Small Dose Segments vs. Noise in Intensity Modulated Radiation Therapy.”
Having attended each of the talks from Waterloo students,
all friends of mine, I must say that all of them delivered their
presentations splendidly.
A graduate fair took place in the afternoon, which was tremendously useful. We all chatted, mingled, and inquired for a
couple of hours before changing into our glad rags for the evertraditional evening banquet.
I was quite surprised at how well put-together the banquet
was. Not only was the meal delectable, but the speakers were
brilliant. Not a head had dropped as Drs. Ben Newling and Dennis Tokaryk kept everyone entertained with their clever presentation on “Life on Both Sides of the Podium: Learning Physics
from the Teacher and Student Perspective.” This was, in fact,
one of the best talks I have been to. This is not even to mention
the invigorating intra- and inter-table conversations. We all sort
of mingled afterwards in rather boisterous clumps in various
rooms of the hotel, much to the dismay of the staff.
Tuesday:
Saying goodbye to newfound friends is never easy, and as such,
this day of departure was bittersweet to be sure. Mark and I
got up early to join the girls from Regina and Carleton for some
breakfast before they had to leave. The advantage of both having a later flight and getting up early was it allowed for some
free time to roam about Fredericton and do some exploring by
the riverbank. This was on purpose: after all, it would have been
a terrible shame to not take advantage of a visit to the Maritimes.
It was also my first trip out east, and I’ll definitely go back again
sometime.
On the plane ride home, I happened to be on the flight with
all the kids from Western. I actually hadn’t come across them
during the conference, so it was great to get a chance to chat
with them and find out what physics and astronomy were like
over there, both the people and program. The trip home was, all
in all, quite pleasant, despite the fact that this conference had
come to an end.
In conclusion...
What struck me most at this conference was finally realising
how many fellow undergraduate astronomers there were out
there (as well as physicists, of course, but then again I’m biased), and how stimulating it was to talk to them about their research. In addition to this, never before have I met so many new
friends in such a short amount of time. This trip was definitely
worth the academic turmoil I had upon my return to school.
Well, another year, another CUPC; I decided to finally take
advantage this time. And for all who read this who have not
been before, next year you should, too, if you have the opportunity. I know I’ll be at Simon Fraser University in Vancouver.
Robbie Henderson is a 4th year Honours Physics student at the
University of Waterloo. He can be reached at rdehende@ sciborg.uwaterloo.ca.
14
Phys13News 120
Fall 2006
Turning Point
The SIN Bin
Rohan Jayasundera
Starting point
v(km)
2(km)
SIN BIN # 119
vt
5 km
Block m2 is in contact with block
m1 as shown in the diagram. When
m1
a horizontal force F~ = 30 N is applied to m2 , block m1 will move in a
θ
F
m2
vertical plane. While m2 will move
in a horizontal plane. If m1 = 5 kg,
and m2 = 3 kg, θ = 30◦ and all
surfaces are smooth (frictionless), find the acceleration of m1 .
Answer in m/s2 .
#
SIN BIN 118 – Solution
Two students are canoeing on a river. While heading upstream
they accidentally drop an empty bottle overboard. They then
continue paddling for 60 minutes, reaching a point 2.0 km farther upstream. At this point they realize that the bottle is missing and, driven by ecological awareness, they turn around and
head downstream. They catch up with and retrieve the bottle
(which has been moving along with the current) 5.0 km downstream from the turn-around point. Assuming a constant paddling effort throughout, find how fast is the river flowing in
km/hr.
Let’s assume the water is flowing downstream at some speed
v measured by some one standing on shore. Hence relative to
this person the river flows at a speed of v km/hr. Since the
person is standing on Earth, we can say that the speed of the
river or the speed of “water” relative to earth is v. In short vR,E
(velocity of river relative to earth) is v.
Now if the river were not flowingm, the students would have
been able to paddle in both directions of the river with relative
ease, at some speed V . However, since the river is flowing the
speed at which they can travel upstream will be V − v. This is
due to the fact they have to overcome the “water current”. The
speed at which they would travel downstream will be V + v.
Now, according to the question, they travel for 60 minutes or 1
hour up stream reaching a point which is 2.0 km away from the
2
starting point. Therefore can say that V − v = distance
time = 1
V − v = 2.
(1)
During this time the bottle that falls overboard would have travelled a distance x = vt = v(km/hr)(1 hr) = vkm down stream.
This is when the students realize that the bottle is missing.
Starting point
2(km)
v(km)
At this stage the distance between the bottle and the canoe
is (2 + v) km. Now if the students turn back and paddle down
stream they will be moving at (V + v) km/hr. Say they catch
up with the bottle in “t” hours. During this time “t” the canoe
would have moved 5 km (according to the question).
(V + v)t = 5
(2)
The distance the bottle travelled during this time is vt =
5(2 + v)
vt = 5 − (2 + v) = 3 − v
(3)
now we have created 3 equations with 3 unknowns.
From (1), (2) and (3)
2t +
6t
=5
t+1
2t2 + 3t − 5
=
0
(2t + 5)(t − 1)
=
0
This quadratic produces a positive “t” of t = 1 and a negative “t” value which we neglect.
Hence substituting this back to equation #3, we get v = 1.5
km/hr.
Rohan Jayasundera is a Lecturer in the Department of Physics
& Astronomy at the University of Waterloo. He can be reached
at [email protected].
2007 Sir Isaac Newton Prize Exam
May 3, 2007
The SIN exam is an annual prize exam that is run by the
Department of Physics & Astronomy at the University
of Waterloo. It is administered by high school physics
teachers across Ontario and around the world. On Thursday, May 3, 2007 the 39th SIN Exam will be held. The
exam is administered by high school physics teachers or
counselors who can order exams through the SIN web
site; the deadline for ordering is Friday, April 13th .
Each year several SIN Scholarships are offered to our
incoming first year physics students who are proceeding
toward an Honours Physics degree at the University of
Waterloo on the basis of the SIN Exam results. These
scholarships can pay the student up to $4,000 over the
course of their time at the University of Waterloo. We
also give book prizes to the top students writing the exam
regardless of whether or not they study physics at the University of Waterloo.
For more information and a promotional poster contact
us at
web: http://sin.uwaterloo.ca
email: [email protected]
fax: 519-746-8115
telephone: 519-885-1211x63556
paper: The SIN Exam
Department of Physics & Astronomy
University of Waterloo
200 University Ave. W.
Waterloo, ON, Canada N2L 3G1
Fall 2006
Phys13News 120
Mostly Relativistic
1
Tony Anderson
8
Once you have solved the puzzle, use the letters corresponding to the various Greek symbols in the grid (in the usual order:
left to right, top row first) to form the names of five famous
“relativistic” scientists:
α(7 letters); β(7); γ(8); δ(9); (9).
Submit these five names (not the crossword) to Rohan for a
chance to win a book prize and certificate.
A draw for a book prize will be made from all correct entries
received before the first of February.
15
3 ε
2
ε
γ
9
δ
10
15
11
Down
1: (With 4 across). “Diane, Tim toil”
for this temporal relativistic effect.
(4,8)
4: See 1 across.
8: Washroom. (2)
9: Underwriters’ Association. (2)
11: Linked with 1 across by Einstein.
(5)
14: This fully is craftily. (3)
15: Preposition. (2)
16: Over this is too much! (4)
17: See 43 across.
21: Lives of a cat? (4)
22: (With 13 down). “Tonal concert night” reduces one dimension.
(6,11)
24: In this is sitting for business. (7)
25: See 20 down.
26: See 1 down.
30: Uncooked. (3)
33: “Rotating via” this was explained in the General Theory of
Relativity. (11)
37: That is to say. (2)
38: See 26 down.
42: Brazilian city. (3)
43: (With 17 across). “Girly heat”
gives an astronomical distance. (5,4)
45: Strangely uneven. (3)
47: Very small. (3)
49: Of the Universe. (6)
51: Lanthanum. (2)
52: “Her tea” gives luminiferous
medium. (6)
53: Needed in an election. (6)
55: “Any suite, Milt” for events at
the same time. (12)
1: (With 26 across). “Raw toxin
pad” gives this age asymmetry. (4,7)
2: Internal Combustion. (2)
3: Particles used to confirm 1 and 4
across. (5)
5: Loaded. (5)
6: Conjunction. (2)
7: New Testament. (2)
10: Beers. (4)
11: This state is a branch of physics.
(5)
12: Buddy. (3)
13: See 22 across.
15: This rod connects. (3)
18: Seventh Greek letter. (3)
19: Applied Health Sciences. (3)
20: (With 25 across). Equivalent to
lots of energy according to Einstein.
(4,4)
23: General Motors. (2)
26: (With 38 across). “Poor cupid in tar” changes energy into mass.
(4,10)
27: Could be bronze or stone. (3)
28: Rural Route. (2)
29: Alcoholics Anonymous. (2)
31: Prefix for 10-18. (4)
32: Animal garden. (3)
34: Victorian Order. (2)
35: Identification. (2)
36: Trade Union. (2)
38: Writer in verse. (4)
39: Rugby league. (2)
40: Lazy. (4)
41: Loud. (5)
44: Initially, a music store. (3)
46: Feathered missile. (4)
47: Backward toothed cutting tool.
(3)
48: Early English. (2)
49: Companion of Honour. (2)
50: Strontium. (2)
54: Tellurium. (2)
γ
21
24
ε
26
27 β
This contest is open to all readers of Phys 13 News, and submissions from students are especially welcomed. The solution
and winner’s name will be given in the next issue of the magazine. Please include your full name, affiliation and address with
your solution.
Paper: Rohan Jayasundera
Department of Physics & Astronomy
University of Waterloo
Waterloo ON N2L 3G1
Fax: 519-746-8115 (marked: attention of Rohan).
E-mail: [email protected]
γ
37
12
δ
α
28
δ
β
34
35
17
α
23
α
25 β
30
β
19
20 α
γ
32 α
δ
δ
40 γ
44
45
50 ε
49
52
55
7
ε
31
36 γ
6
14
18
39
43 ε
48
γ
α
22
29
38
ε
13
δ
42
47 β
5 α
16
33 δ
Across
4 δ
41 γ
46
51 β
53
β
δ
ε
54
ε
Prof Quotes
George McBirnie
A compilation of recent memorable quotations taken from
actual physics lectures at the University of Waterloo.
“Please don’t tell the math profs that analogy.”
–Forrest, PHYS 252
“Whoever invented vector product... I know it was that Greek
guy, Vectorgus.”
–Forrest, PHYS 252
Prof, after drawing a square: “This is infinite, even though it
looks finite.”
–Ha, PHYS 441A
“It’s good that you asked though. Whatever you asked.”
–Thompson, Phys 434 (Quantum Physics 3)
“Engineers use j instead of i because i is used for current. I like
it for this reason and because it stands for Jim.”
–(Jim) Martin, Phys 252 (Electricity and Magnetism 1)
George is a third year undergraduate student in the Department
of Physics & Astronomy at the University of Waterloo. He has
been collecting prof-quotes for years and plans on eventually
publishing a book. He can be reached at [email protected].
16
Phys13News 120
Fall 2006
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