Download From the Big Bang to String Theory

Robert McNees
Brown University
(Alum, National Science Bowl `91*)
* Yes, that was the first one.
Some of you were born that
year.
Department of Energy
National Science Bowl
2007
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
The System of the World
Isaac Newton


dv
1. F  0 
0
dt
 d p


2. F 
with p  m v
dt
3.`For every action there is an
equal and opposite reaction.’
And, of course, he invented
the Calculus, did pioneering
work in Optics, etc…
Newtonian Gravity
Mm
F G 2
r
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 wasn’t 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)
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.
Electricity and Magnetism
James Clerk Maxwell made the
connection b/t electricity and
magnetism in a beautiful set of
equations
UNIFICATION - Phenomena that appear to
be unrelated turn out to be aspects of a
single, underlying cause.
th
20
The Early
Century:
Quantum Mechanics and
Special Relativity
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 couldn’t 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!
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 `Planck’s Constant’
h = 6.6 x 10-34 Joule-seconds
Einstein and the Photoelectric Effect
Shining light on a metal can produce a current! Energy of
electrons depends on frequency of light, not intensity.
Current
Einstein suggested that the electrons all have
the same energy because they receive it in
whole packets, or quanta, from the light.
Quanta are real!
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.
Bohr’s model correctly predicts
the spectral lines for Hydrogen.
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 treats
it like a wave.
Werner Heisenberg developed a quantum
mechanical model of the electron that treats
it like a particle.
The Uncertainty Principle
Heisenberg noticed something important. You can treat
the electron like a particle, but there is an inherent
uncertainty that goes along with that.
The more precisely you try to say where it is, the less
precisely you can measure its momentum, and viceversa. As he put it:
“we cannot know, as a matter of principle,
the present in all of its details.”
1905: A Big Year for Einstein
1905 was a busy year for
Einstein.
1. He established the reality
of quanta.
2. He explained Brownian
motion.
3. He laid down the foundations of Special Relativity.
Special Relativity
Consider these three observations, all accepted by physicists
at the end of the 19th century.
1. The laws of physics are the same for
a stationary observer and an
observer moving at constant speed.
2. Galileo’s rule for adding velocities
is correct.
3. Light travels at a finite speed, which
is a consequence of physical laws
described by Maxwell’s equations.
Any two of these are mutually consistent. But if you take all
Three together, you get contradictions.
Lorentz Transformations
Einstein said that Galileo’s rule for adding velocities must be wrong.
Transformations between frames of reference have to preserve the
speed of light.
Consider two observers moving at relative velocity v. The first one
uses coordinates (x,t), and the second uses coordinates (x’,t’).
Galileo: x  x  v t
Einstein: x 
x  vt
v2
1 2
c
t  t
vx
2
c
t 
v2
1 2
c
Space and time are no
longer separate concepts:
Not consistent with
Maxwell’s equations.
t
Consistent with
Maxwell’s equations.
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 is
ticking too slow!
t 
t0
2
v
1 2
c
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.
Length Contraction
An observer who sees an object moving with a velocity v perceives that
object’s length as being contracted. It is a small but real effect
2
v
L  L 1  2
c
v = 0.87c
v = 0.99c
v = 0.999c
Special Relativity is not intuitive, but it is true.
It has been verified in numerous experiments.
Phenomena like length contraction and time
dilation are physical effects, as real as anything
else we experience.
But Einstein still felt like something was missing.
General Relativity
“Matter tells space how to curve, and
curved space tells matter how to move.”
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.
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?
General Relativity!
Einstein: The structure of spacetime
is 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?
There are a lot of clever
ways of representing
curved spaces. The artist
M.C. Escher used them
in many of his drawings,
like this one.
This drawing represents
a two-dimensional space
with constant negative
curvature.
Consequences and Tests of General Relativity
•Curvature of spacetime
is larger closer to the sun.
Mercury
Sun
Earth
•Larger curvature means
that GR is more important.
•Corrections to Newton from
GR are more important for
Mercury than for the other
planets.
General Relativity accounts for the
precession of Mercury’s orbit.
Consequences and Tests of General Relativity
Changes in the curvature - and the effect of gravity – propagate
at the speed of light. Not instantaneous.
Gravitational Bending of Light
Path that light follows (a
geodesic) bends due to
the sun’s gravity. A small
but measurable effect.
Gravitational Lensing
This is an image of a distant quasar. The
gravitational effect of a galaxy between
us and the quasar results in four images.
Redshift of Light Due to Gravity
Light loses energy as it
overcomes gravity, just
like 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.
The Standard Model
of Particle Physics
SR + QM = QFT
When you combine Quantum Mechanics with Special Relativity,
the result is called `Quantum Field Theory’. It is the framework
that 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 we
think of as particles.
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 > 0.
This is where the excitation
is right now: t = 0.
y
x
The excitation could have
wound up where it is now
by starting off somewhere
in here: the `past’ is t < 0.
Interactions
Particles can absorb and emit other particles. There are rules that
govern 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.
Virtual Particles
We are interested in Quantum field theory. The Uncertainty
principle tells us that a particle and its anti-particle can pop
into existence. They can’t stick around for long, but they have
real consequences:
In a QFT we have to consider
all the ways the particles might
interact. There are usually an
infinite number of things to keep
track of!
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 Standard
Model is a specific QFT that describes the real world. It contains many different kinds of fields.
The Fermions that make up matter are arranged in three
generations. Everything about particles in a column is the
same except for their mass.
First
Generation
Second
Generation
Third
Generation
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 identified:
Electromagnetism, 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 nuclear
decay. 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.
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 electron:
predicted value:0.0011596521594(230)
observed 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.
Some (Big) Open Questions
1.Why do particles have mass?
Most particle physicists assume that a particle
known as the Higgs Boson is responsible. We
anticipate that it will be found soon.
2.Why don’t we see any antimatter outside
of the lab?
Seems weird, right? We don’t know why nature
should prefer matter over anti-matter.
3.Why are there three families of particles?
We don’t know for sure. Any ideas?
The Large Hadron Collider (LHC)
Faint Supernovae and
Glowing Black Holes
The Expanding Universe
In 1929 Edwin Hubble reported that the Universe was expanding.
Everything seemed to be moving away from everything else. The
more distant galaxies seemed to be receding faster than the
closer ones.
Hubble Expansion
C
A
C
B
A
A long time ago, galaxies
B and C were far, far away
from galaxy A (that’s us).
Now, their distances from A
-as measured on the surface
of the globe- have increased.
B
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 the
universe (as we currently understand it) emerged. It is an
expansion, but not into anything. It is an expansion of space and
time itself.
Well what about the future?
Until very recently we assumed that one of two things would
happen to the expansion of the universe:
1. Gravity stops the expansion. The Universe collapses in a
fiery Big Crunch.
2. 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.
Some say the world will end in fire,
Some say in ice.
From what I've tasted of desire
I hold with those who favor fire.
But if it had to perish twice,
I think I know enough of hate
To say that for destruction ice
Is also great
And would suffice.
The Cosmological Constant
XX
R  12 g  R   g  
Einstein had added an extra term to his equations, called the cosmological constant. He needed this term to describe a universe that was
static. But since the universe is expanding, he could get rid of it!
And then, 70 years later…
Faint supernova?
In the late `90s two
groups of astronomers
were observing distant
supernovae.
The type Ia SN are
thought to be good
standard candles. We
know how bright they
should be, so we can
figure out how far
away they are.
They found something
totally unexpected. The
supernova were too dim.
The Accelerating Universe
Dark Energy
The data is telling us that 70% of the stuff in the universe is a
mysterious force that we call Dark Energy. It does the opposite
of what gravity is supposed to do: it makes space want to expand instead of contract.
(And another 20% is Dark Matter… we don’t know what that is either.)
Not so fast, Dr. Einstein!
That term Einstein wanted to drop from his equations – the
Cosmological Constant – seems to be the best candidate for
Dark Energy!
My Bad!
R  12 g  R   g  
So, what’s on the next slide? Do we predict the
cosmological constant with amazing accuracy?
The Cosmological Constant is an example of a question our
theories can’t answer. A naïve application of QFT – the rules
we use for the Standard Model – makes a prediction. It just
happens to be super-wrong.
kg
 observed  6 10
3
m
95 kg
 predicted  10
3
m
 27
Not bad! Only off by about 120 orders of magnitude. That’s a factor
of 1000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000
000000000000000000000000000.
What went wrong?
We asked our theory a question it didn’t know how to answer,
so it gave us a nonsense result. To get the right answer we will
probably need a framework that combines the principles of
General Relativity and Quantum Mechanics. We call it
Speaking of Quantum Gravity…
Black Holes
Predicted in context of Newtonian gravity by John Mitchell in
1784, then by Laplace in 1796. Based on escape velocity.
Modern view based on Relativity: gravity – the curvature of
space – becomes so strong that nothing can escape a region.
The boundary of this region is the Event Horizon.
How Do We Detect Them?
We observe the things around them. Gas spiraling in is heated
to millions of degrees, emitting x-rays and other forms of radiation, as well as energetic jets of particles.
We detect them by seeing things around them – gas and stuff
spirals in and radiates.
Nothing Can Escape
We think of this as a defining characteristic of Black Holes. But…
Glowing Black Holes?
In the 1970s the British physicist
Stephen Hawking realized that
Black 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 quantum
mechanics, and his predictions
show up no matter what route
you take to describing the physics
of Black Holes.
In 2003 I had a chance to have dinner with Stephen
Hawking. I wasn’t 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?
Where did all the info go?
There is a problem with Black Holes – one we still don’t know
how to resolve. What happens to the stuff that falls in?
We assume that Quantum Mechanics is something really fundamental. But the idea that something can disappear into the
Black 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 central
assumptions of Quantum Mechanics seems to break down.
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.
F~
1
(R  d )2
F~
F~
1
(r  d ) 2
1
R2
F~
1
r2
Eventually they would reach a region where gravity is so violently
strong that everything we know about physics breaks down. What
happens here? No one is sure.
It’s kind of like the old maps drawn by sailors. Sailors have
pretty vivid imaginations. They might see a pod of whales
from a distance, and not recognize it for what it was. So they
would 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 can’t blame them. They knew they saw something. Saying
“Arr! Check out yon sea-serpent!” sounds a lot better than “I
don’t know what happens in a Black Hole.”
Knowing which questions you can or cannot answer is just as
important as the answers themselves. Right now, what we know
about General Relativity and Quantum Mechanics is not
capable of probing too far into a Black Hole. Maybe a theory of
Quantum Gravity could tell us more. Anything else is a story
told by a sailor.
String Theory
I’ve given you two examples of problems at the intersection
of Gravity and Quantum Mechanics. Physicists have been
working for many years to try and devise a quantum model
of gravity.
There are a few different approaches out there. They are all
models – frameworks that may lead to a theory, but don’t
make many concrete predictions yet.
The model I work on is called String Theory. It is based on the
idea that, in addition to the point particles used in QFT, we
should also consider extended, one dimensional objects.
The Origins of String Theory
Originally proposed as a model of the strong nuclear force.
Lost out to QCD (Quantum Chromodynamics).
String Tension = Constant
Force = Tension x Separation
Restoring Force grows with distance.
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 correspond
to all the particles and forces we observe.
Strings ‘interact’ by joining and splitting. Any
other interaction is inconsistent with quantum
mechanics.
String theory requires – depending on who you ask – 10 or 11
spacetime dimensions. That’s a high price to pay, but we get
a model of quantum gravity for our trouble. Think of an extra
sphere ‘attached’ to every point in space.
The extra dimensions tend to curl up in shapes called CalabiYau manifolds. They are 6 dimensional shapes with special
properties. The details of the shape have an impact on
features of the theory – like the number of generations of
particles we see in the Standard Model.
“The simplicity of nature is not to be measured by that
of our conceptions. Infinitely varied in its effects, nature
is simple only in its causes, and its economy consists in
producing a great number of phenomena, often very
complicated, by means of a small number of general
laws.”
- Pierre Simon LaPlace
Exposition du Systeme du Monde
(On the System of the World)