Robert McNeesBrown University

(Alum, National Science Bowl `91*)

Department of EnergyNational Science Bowl 2007

* Yes, that was the first one. Some of you were born that year.

OutlineOutline1. The System of the World2. 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

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3.`For every action there is an equal and opposite reaction.’

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And, of course, he inventedthe Calculus, did pioneeringwork in Optics, etc…

Newtonian Gravity

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Electricity and Magnetism

William Gilbert and the Scientific Method

“In the discovery of secret things, and in the investigationof hidden causes, stronger reasons are obtained from sureexperiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators.” - De Magnete (1600)

•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!

Hans Oersted Electric Current produces a magnetic effect!

Electricity and Magnetism

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 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.

The Early 20The Early 20thth Century: Century:Quantum Mechanics andQuantum Mechanics and

Special RelativitySpecial Relativity

Blackbody Radiation

A blackbody radiates based on itsTemperature, 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!The Ultraviolet Catastrophe!

Max Planck

Fits the data beautifully! It depends on a new constant, called `Planck’s Constant’

h = 6.6 x 10-34 Joule-seconds

Perhaps energy must be radiated in indivisible units…

This assumption leads to the correct result for a blackbody:

Einstein and the Photoelectric EffectShining 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!

Current

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 treatsit like a wave.

Werner Heisenberg developed a quantummechanical model of the electron that treatsit like a particle.

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.

“we cannot know, as a matter of principle,the present in all of its details.”

The more precisely you try to say where it is, the lessprecisely you can measure its momentum, and vice-versa. As he put it:

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 founda-tions 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 allThree together, you get contradictions.

Lorentz TransformationsEinstein said that Galileo’s 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’).

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Einstein:

Not consistent with Maxwell’s equations.

Consistent with Maxwell’s equations.

Space and time are no longer separate concepts:

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!

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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 ContractionAn observer who sees an object moving with a velocity v perceives thatobject’s length as being contracted. It is a small but real effect

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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.

“Matter tells space how to curve, and curved space tells matter how to move.”

General Relativity

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

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!

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

Einstein: The structure of spacetimeis influenced by matter and energy

Curved Spaces Curved Time?

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.

Consequences and Tests of General Relativity

Mercury

Sun

Earth

•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.

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 – propagateat the speed of light. Not instantaneous.

Gravitational Bending of Light

Path that light follows (a geodesic) bends due tothe sun’s 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.

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.

TheThe Standard Modelof Particle Physics

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.

Fields exist everywhere. Sometimes these fields are constant.Excitations – bumps and wiggles in the fields – are what wethink of as particles.

What is a field?

Propagation

A particles is an excitation of a field. The way it moves – or propagates – follows the rules of Special Relativity.

The excitation can propagate into this region: the `future’is t > 0.

The excitation could havewound up where it is nowby starting off somewherein here: the `past’ is t < 0.

This is where the excitationis right now: t = 0.

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InteractionsParticles 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.

Virtual ParticlesWe are interested in Quantum field theory. The Uncertaintyprinciple tells us that a particle and its anti-particle can popinto existence. They can’t 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!

The Building BlocksQFT 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

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 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.

Tests and Predictions of the Standard Model

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.

The Standard Model makes numerous predictions. Here are a few of them:

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 don’t we see any antimatter outside of the lab?Seems weird, right? We don’t know why natureshould 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 andFaint Supernovae andGlowing Black HolesGlowing Black Holes

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.

The Expanding Universe

Hubble Expansion

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A long time ago, galaxiesB and C were far, far awayfrom galaxy A (that’s us).

Now, their distances from A-as measured on the surfaceof the globe- have increased.

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.

What if we follow the expansion back in time? Things must have been very hot and dense.

The Big Bang

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 desireI hold with those who favor fire.But if it had to perish twice,I think I know enough of hateTo say that for destruction iceIs also greatAnd would suffice.

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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!

And then, 70 years later…And then, 70 years later…

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.

Faint supernova?

They found somethingtotally unexpected. Thesupernova were too dim.

The Accelerating Universe

Dark EnergyThe 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 don’t know what that is either.)

Not so fast, Dr. Einstein!

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That term Einstein wanted to drop from his equations – theCosmological Constant – seems to be the best candidate forDark Energy!

My Bad!

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 ourtheories can’t answer. A naïve application of QFT – the ruleswe use for the Standard Model – makes a prediction. It just happens to be super-wrong.

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Not bad! Only off by about 120 orders of magnitude. That’s a factorof 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

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 willprobably need a framework that combines the principles ofGeneral Relativity and Quantum Mechanics. We call it

Speaking of Quantum Gravity…Speaking of Quantum Gravity…

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.

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.

How Do We Detect Them?

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 physicistStephen Hawking realized thatBlack Holes actually radiate.

Sure, the stuff that falls into themIs 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.

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 Which are you more proud of: your groundbreaking work on singularity groundbreaking work on singularity theorems, or your appearance on theorems, or your appearance on the Simpsons?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 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.

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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It’s 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 can’t blame them. They knew they saw something. Saying “Arr! Check out yon sea-serpent!” sounds a lot better than “Idon’t 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.

String TheoryString Theory

I’ve 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 don’tmake 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.

The Origins of String TheoryOriginally proposed as a model of the strong nuclear force. Lost out to QCD (Quantum Chromodynamics).

String Tension = ConstantForce = 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 correspondto all the particles and forces we observe.

Strings ‘interact’ by joining and splitting. Anyother interaction is inconsistent with quantummechanics.

String theory requires – depending on who you ask – 10 or 11spacetime dimensions. That’s 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.

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.

“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)