Robert McNees Brown University

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• Robert McNeesBrown University
• (Alum, National Science Bowl 91)

Department of Energy National Science Bowl 2007
Yes, that was the first one. Some of you
were born that year.
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Outline

1. The System of the World
2. The Early 20th Century Quantum Mechanics and
   Special Relativity
3. General Relativity Curvature and Motion
4. The Standard Model of Particle Physics
5. Faint Supernovae and Glowing Black Holes
6. String Theory

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The System of the World
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Isaac Newton
1. 2. with 3.For every
action there is an equal and opposite reaction.
And, of course, he inventedthe Calculus, did
pioneeringwork in Optics, etc
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Newtonian Gravity
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Electricity and Magnetism
William Gilbert and the Scientific Method

• Observed attraction and repulsion between poles
  of a magnet
• Produced static electricity by rubbing amber
• Concluded that Electricity and Magnetism were
  distinct.

It wasnt what he did. It was how he did it!
In the discovery of secret things, and in the
investigation of hidden causes, stronger reasons
are obtained from sure experiments and
demonstrated arguments than from probable
conjectures and the opinions of philosophical
speculators. - De Magnete (1600)
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Electricity and Magnetism
Hans Oersted Electric Current produces a
magnetic effect!

• Michael Faraday
• Electromagnetic Induction A changing
  magnetic field induces a current.
• Suspected that Electricity and Magnetism were
  wave phenomenon, related to light, propagate
  at finite speed
• Electrical experiments gave him huge
  sideburns.

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Electricity and Magnetism
James Clerk Maxwell made theconnection b/t
electricity andmagnetism in a beautiful set
ofequations
UNIFICATION - Phenomena that appear to be
unrelated turn out to be aspects of a single,
underlying cause.
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The Early 20th Century Quantum Mechanics
and Special Relativity
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Blackbody Radiation

• A blackbody radiates based on its
• Temperature, not its composition.
• Radiated energy peaks at a specific frequency.
• Drops off at higher frequencies.

Classical physics couldnt come up with the right
curve. The physics was saying that the black body
should emit more and more at higher
frequencies The Ultraviolet Catastrophe!
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Max Planck
Perhaps energy must be radiated in indivisible
units
This assumption leads to the correct result for a
blackbody
Fits the data beautifully! It depends on a new
constant, called Plancks Constanth 6.6 x
10-34 Joule-seconds
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Einstein and the Photoelectric Effect
Shining light on a metal can produce a current!
Energy ofelectrons depends on frequency of
light, not intensity.
Einstein suggested that the electrons all
havethe same energy because they receive it in
whole packets, or quanta, from the light.
Quanta are real!
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The Bohr Hydrogen Atom

• An electron can only orbit the nucleus at
  certain fixed radii.
• The orbits are stable. Other orbits are not
  allowed.
• Electrons jumping from one orbit to another
  release quanta of light.
• Each orbit only has room for a certain
  number of electrons.

Bohrs model correctly predicts the spectral
lines for Hydrogen.
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De Broglie, Schrodinger, and Heisenberg
Suggested that electrons can also behave like
waves. In fact, any particle can. This was
verified in electron diffraction experiments.
Erwin Schrodinger developed a quantum mechanical
model of the electron that treatsit like a wave.
Werner Heisenberg developed a quantummechanical
model of the electron that treatsit like a
particle.
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The Uncertainty Principle
Heisenberg noticed something important. You can
treat the electron like a particle, but there is
an inherentuncertainty that goes along with that.
The more precisely you try to say where it is,
the lessprecisely you can measure its momentum,
and vice-versa. As he put it
we cannot know, as a matter of principle,the
present in all of its details.
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1905 A Big Year for Einstein

• 1905 was a busy year for
• Einstein.
• He established the reality of quanta.
• He explained Brownian motion.
• He laid down the founda-tions of Special
  Relativity.

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Special Relativity
Consider these three observations, all accepted
by physicists at the end of the 19th century.

• The laws of physics are the same for a stationary
  observer and an observer moving at constant
  speed.
• Galileos rule for adding velocities is
  correct.
• Light travels at a finite speed, which is a
  consequence of physical laws described by
  Maxwells equations.

Any two of these are mutually consistent. But if
you take all Three together, you get
contradictions.
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Lorentz Transformations
Einstein said that Galileos rule for adding
velocities must be wrong.Transformations between
frames of reference have to preserve thespeed of
light.
Consider two observers moving at relative
velocity v. The first one uses coordinates
(x,t), and the second uses coordinates (x,t).
Not consistent with Maxwells equations.
Consistent with Maxwells equations.
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Time Dilation
The Lorentz transformations have some pretty
weird consequences.For instance, if I see a
clock moving with speed v, it looks like it
isticking too slow!
This has been verified in lots of experiments,
with fantastic precision.

• Measured in atomic clocks that are sent around
  the world on a plane.
• Measured in the lab directly, as a relativistic
  Doppler shift.

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Length Contraction
An observer who sees an object moving with a
velocity v perceives thatobjects length as
being contracted. It is a small but real effect
v 0.87c
v 0.999c
v 0.99c
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Special Relativity is not intuitive, but it is
true. It has been verified in numerous
experiments.Phenomena like length contraction
and timedilation are physical effects, as real
as anythingelse we experience. But Einstein
still felt like something was missing.
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General Relativity
Matter tells space how to curve, and curved
space tells matter how to move.
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Some Problems with Newtonian Gravity
The orbit of Mercury precesses about 1.5 degrees
each century. Influence of other planets account
for all but 0.1 degree of this. This excess is
not explained by Newtonian gravity.
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Some Problems with Newtonian Gravity
Why are inertial mass and gravitational mass the
same thing?
And what is gravity, anyway? What causes it?
Newton says that it just happens, and it is
instantaneous. Action at a distance?
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General Relativity!
Einstein The structure of spacetimeis
influenced by matter and energy

• Matter and Energy curve spacetime.
• The curvature of spacetime is what causes
  gravity.
• Objects follow geodesics the straightest
  lines on a curved surface.

Curved Spaces
Curved Time?
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There are a lot of cleverways of
representingcurved spaces. The artistM.C.
Escher used themin many of his drawings,like
this one. This drawing representsa
two-dimensional spacewith constant
negativecurvature.
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Consequences and Tests of General Relativity

• Curvature of spacetime is larger closer to the
  sun.
• Larger curvature means that GR is more
  important.
• Corrections to Newton from GR are more
  important for Mercury than for the other
  planets.

Mercury
Sun
Earth
General Relativity accounts for the precession
of Mercurys orbit.
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Consequences and Tests of General Relativity
Changes in the curvature - and the effect of
gravity propagateat the speed of light. Not
instantaneous.
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Gravitational Bending of Light
Path that light follows (a geodesic) bends due
tothe suns gravity. A smallbut measurable
effect.
Gravitational Lensing This is an image of a
distant quasar. Thegravitational effect of a
galaxy betweenus and the quasar results in four
images.
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Redshift of Light Due to Gravity
Light loses energy as it overcomes gravity,
justlike a ball thrown in the air loses kinetic
energy.

• This effect was measured in 1959 by Pound and
  Rebka, in a three story tower in Jefferson Lab
  at Harvard.
• This effect is essential in Cosmology. It helps
  us piece together what the universe looked like
  along the trajectory of a photon.

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The Standard Modelof Particle Physics
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SR QM QFT
When you combine Quantum Mechanics with Special
Relativity,the result is called Quantum Field
Theory. It is the frameworkthat we use to
describe the physics of elementary particles.
What is a field?
Fields exist everywhere. Sometimes these fields
are constant.Excitations bumps and wiggles in
the fields are what wethink of as particles.
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Propagation
A particles is an excitation of a field. The way
it moves or propagates follows the rules of
Special Relativity.
t
The excitation can propagate into this region
the future is t gt 0.
This is where the excitationis right now t 0.
y
The excitation could havewound up where it is
nowby starting off somewherein here the past
is t lt 0.
x
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Interactions
Particles can absorb and emit other particles.
There are rules thatgovern the ways this can
happen.
Forces between two particles are due to one
particle emitting an intermediate particle,
which is then absorbed by a second particle.
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Virtual Particles
We are interested in Quantum field theory. The
Uncertaintyprinciple tells us that a particle
and its anti-particle can popinto existence.
They cant stick around for long, but they
havereal consequences
In a QFT we have to considerall the ways the
particles mightinteract. There are usually
aninfinite number of things to keeptrack of!
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The Building Blocks
QFT is a framework a set of rules we can use to
describe particles. There are a lot of possible
QFTs. The StandardModel is a specific QFT that
describes the real world. It con-tains many
different kinds of fields.
The Fermions that make up matter are arranged in
threegenerations. Everything about particles in
a column is thesame except for their mass.
FirstGeneration
SecondGeneration
ThirdGeneration
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The Fundamental Forces (Well, except gravity)
In the standard model forces are due to the
exchange of particles called vector bosons.
Three forces of this type have been
identifiedElectromagnetism, the Weak Nuclear
force, and the Strong Nuclear Force. The first
two are really one force the Electroweak force.

1. Electromagnetism Mediated by the exchange of
   photons.
2. Weak Force Responsible for some forms of
   nucleardecay. Mediated by three vector bosons
   W, W-, and Z. Only left-handed quarks and
   left-handed leptons experience this force!
3. Strong Force Binds quarks together into baryons
   (like the proton and neutron) and mesons (like
   the pion). Mediated by massless vector bosons
   called gluons.

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Tests and Predictions of the Standard Model
The Standard Model makes numerous predictions.
Here are a few of them

1. Anomalous magnetic moment of the
   electronpredicted value0.0011596521594(230)obs
   erved value 0.0011596521884(43)
2. Predicts the existence of the Top
   quark.Discovered in 1995 at Fermilab.
3. Predicts the W and Z bosons. Discovered in 1983.

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Some (Big) Open Questions

1. Why do particles have mass?Most particle
   physicists assume that a particle known as the
   Higgs Boson is responsible. Weanticipate that it
   will be found soon.
2. Why dont we see any antimatter outside of the
   lab?Seems weird, right? We dont know why
   natureshould prefer matter over anti-matter.
3. Why are there three families of particles?We
   dont know for sure. Any ideas?

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The Large Hadron Collider (LHC)
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Faint Supernovae and Glowing Black Holes
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The Expanding Universe
In 1929 Edwin Hubble reported that the Universe
was expanding.Everything seemed to be moving
away from everything else. Themore distant
galaxies seemed to be receding faster than
thecloser ones.
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Hubble Expansion
C
A
C
B
A
A long time ago, galaxiesB and C were far, far
awayfrom galaxy A (thats us). Now, their
distances from A-as measured on the surfaceof
the globe- have increased.
B
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The Big Bang
What if we follow the expansion back in time?
Things must have been very hot and dense.
We can only go back so far. Eventually the
physics breaks down! The Big Bang refers to the
initial event or period from which theuniverse
(as we currently understand it) emerged. It is an
expansion, but not into anything. It is an
expansion of space and time itself.
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Well what about the future?

• Until very recently we assumed that one of two
  things would
• happen to the expansion of the universe
• Gravity stops the expansion. The Universe
  collapses in a fiery Big Crunch.
• Gravity slows down the expansion, but does not
  stop it. The Universe goes out with a cold and
  lonely Big Whimper.
• The poet Robert Frost had already figured this
  out in 1923.

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The Cosmological Constant
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Einstein had added an extra term to his
equations, called the cosmo-logical constant. He
needed this term to describe a universe that
wasstatic. But since the universe is expanding,
he could get rid of it!
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And then, 70 years later
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Faint supernova?
In the late 90s twogroups of astronomerswere
observing distantsupernovae. The type Ia SN
arethought to be goodstandard candles. Weknow
how bright theyshould be, so we canfigure out
how faraway they are.
They found somethingtotally unexpected.
Thesupernova were too dim.
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The Accelerating Universe
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Dark Energy
The data is telling us that 70 of the stuff in
the universe is amysterious force that we call
Dark Energy. It does the oppositeof what gravity
is supposed to do it makes space want to
ex-pand instead of contract.
(And another 20 is Dark Matter we dont know
what that is either.)
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Not so fast, Dr. Einstein!
That term Einstein wanted to drop from his
equations theCosmological Constant seems to
be the best candidate forDark Energy!
My Bad!
So, whats on the next slide? Do we predict the
cosmological constant with amazing accuracy?
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The Cosmological Constant is an example of a
question ourtheories cant answer. A naïve
application of QFT the ruleswe use for the
Standard Model makes a prediction. It just
happens to be super-wrong.
Not bad! Only off by about 120 orders of
magnitude. Thats a factorof 10000000000000000000
0000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000
000.
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What went wrong?
We asked our theory a question it didnt know how
to answer, so it gave us a nonsense result. To
get the right answer we willprobably need a
framework that combines the principles ofGeneral
Relativity and Quantum Mechanics. We call it
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Speaking of Quantum Gravity
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Black Holes
Predicted in context of Newtonian gravity by John
Mitchell in1784, then by Laplace in 1796. Based
on escape velocity.
Modern view based on Relativity gravity the
curvature ofspace becomes so strong that
nothing can escape a region.The boundary of this
region is the Event Horizon.
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How Do We Detect Them?
We observe the things around them. Gas spiraling
in is heatedto millions of degrees, emitting
x-rays and other forms of rad-iation, as well as
energetic jets of particles.
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We detect them by seeing things around them gas
and stuff spirals in and radiates.
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Nothing Can Escape
We think of this as a defining characteristic of
Black Holes. But
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Glowing Black Holes?
In the 1970s the British physicistStephen
Hawking realized thatBlack Holes actually
radiate. Sure, the stuff that falls into
them Is hot and emits radiation. But the Black
Holes are also Glowing on their own! This is a
consequence of quantummechanics, and his
predictionsshow up no matter what routeyou take
to describing the physicsof Black Holes.
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In 2003 I had a chance to have dinner with
Stephen Hawking. I wasnt sure how to break the
ice. So I asked him the following question
Which are you more proud of your
groundbreaking work on singularity theorems, or
your appearance on the Simpsons?
What do you think he said?
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Where did all the info go?
There is a problem with Black Holes one we
still dont know how to resolve. What happens to
the stuff that falls in? We assume that Quantum
Mechanics is something really fun-damental. But
the idea that something can disappear into
theBlack Hole poses a big problem. This is
called the Information Paradox. It is a problem
because,without access to the info that
disappeared, one of the centralassumptions of
Quantum Mechanics seems to break down.
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What Is Inside a Black Hole?
A lot of strange things happen. A freely falling
observer would not notice that they crossed the
Horizon. Much later, however, the force of
gravity would be so much stronger at their feet
than at their head that the difference what we
call a tidal force would rip them apart.
Eventually they would reach a region where
gravity is so violentlystrong that everything we
know about physics breaks down. Whathappens
here? No one is sure.
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Its kind of like the old maps drawn by sailors.
Sailors havepretty vivid imaginations. They
might see a pod of whalesfrom a distance, and
not recognize it for what it was. So theywould
come up with an explanation for what they were
seeing the curves of a sea serpent. Then they
would draw some sort of sea monster on their
maps. You cant blame them. They knew they saw
something. Saying Arr! Check out yon
sea-serpent! sounds a lot better than Idont
know what happens in a Black Hole. Knowing
which questions you can or cannot answer is just
asimportant as the answers themselves. Right
now, what we know about General Relativity and
Quantum Mechanics is notcapable of probing too
far into a Black Hole. Maybe a theory ofQuantum
Gravity could tell us more. Anything else is a
storytold by a sailor.
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String Theory
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Ive given you two examples of problems at the
intersectionof Gravity and Quantum Mechanics.
Physicists have beenworking for many years to
try and devise a quantum modelof gravity.There
are a few different approaches out there. They
are allmodels frameworks that may lead to a
theory, but dontmake many concrete predictions
yet. The model I work on is called String
Theory. It is based on theidea that, in addition
to the point particles used in QFT, weshould
also consider extended, one dimensional objects.
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The Origins of String Theory
Originally proposed as a model of the strong
nuclear force. Lost out to QCD (Quantum
Chromodynamics).
String Tension ConstantForce Tension x
SeparationRestoring Force grows with distance.
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The idea is simple. All the particles we see are
actually excitations of very, very small
strings. They are so small that they look like
point particles.
Instead of having lots of different kinds of
particles, we have two kinds of strings open
and closed. The different sorts of wiggles
excitations of these strings correspondto all
the particles and forces we observe.
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Strings interact by joining and splitting.
Anyother interaction is inconsistent with
quantummechanics.
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String theory requires depending on who you ask
10 or 11spacetime dimensions. Thats a high
price to pay, but we geta model of quantum
gravity for our trouble. Think of an extrasphere
attached to every point in space.
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The extra dimensions tend to curl up in shapes
called Calabi-Yau manifolds. They are 6
dimensional shapes with specialproperties. The
details of the shape have an impact onfeatures
of the theory like the number of generations
ofparticles we see in the Standard Model.
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The simplicity of nature is not to be measured
by thatof our conceptions. Infinitely varied in
its effects, natureis simple only in its causes,
and its economy consists inproducing a great
number of phenomena, often verycomplicated, by
means of a small number of generallaws. -
Pierre Simon LaPlace Exposition du Systeme du
Monde (On the System of the World)