M O ATA Z E M A M

S U N Y C O R T L A N D

OUTLINE

Classical v Quantum Fundamental Physics

The Standard Model

Gravity

The problems of fundamental physics

Superstring Theory as a solution

Supergravity Theory as a Classical version

A bit about the work I do

Can you help?

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CLASSICAL PHYSICS

Forces are represented by Vector Fields (Faraday) of attraction or

repulsion

The fields live and propagate in space and time

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CLASSICAL PHYSICS

Consider two similarly charged particles in motion

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QUANTUM FIELDS

Forces between objects are represented by particle exchange

Particles exchange other particles that didn’t exist before, quantum

weirdness!!

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QUANTUM FIELDS

“Quantum” momentum

conservation

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THE STANDARD MODEL

Is a collection of “particle exchange field theories” a.k.a quantum field

theories

Includes:

The electromagnetic field

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JFd

dF~~0

THE STANDARD MODEL

Is a collection of “particle exchange field theories” a.k.a quantum field

theories

Includes:

The strong nuclear force

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THE STANDARD MODEL

Is a collection of “particle exchange field theories” a.k.a quantum field

theories

Includes:

The weak nuclear force

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THE STANDARD MODEL

The matter particles

The force or field particles

(the ones that get exchanged)

All the forces of nature,

except one!

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GRAVITY

Gravity is still a classical theory, no definite quantum version

There are attempts, string theory is one of them

The main problem is experimental verification

Gravity is very weak, its quantum version would be very hard to detect

So what is the classical form of gravity?

Recall that the other three fields live and propagate in space and time

Gravity is space and time

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GRAVITY

Space and time work together, a single spacetime “fabric”

Energy and mass bend and warp spacetime

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TgG

GRAVITY

Space and time work together, a single spacetime “fabric”

Energy and mass bend and warp spacetime

Bent and warped time control the flow of energy and mass

Objects follow the shortest possible distance in warped space, like a bar

of soap in a sink

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TgG

GRAVITY

The ordinary fields in space and time are easily quantized to the

exchange particle model

Gravity is space and time (spacetime) how do you quantize that?

Futile attempts for many decades

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TgG

OTHER PROBLEMS

Quantizing gravity is not the only problem

Why do the particles have the masses they do?

Why are certain forces much stronger than others?

Divergences appearing in certain calculations, a sign of further structure

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0

dq

And the solution to all these problems is ….

Drumroll please ….

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SUPERSTRING THEORY

Is a model that unifies all of the four forces of

nature

Including Gravity

Explains a lot of problems in the old quantum

model

Consistent and elegant (doesn’t mean easy)

All particles, matter and force, are simply one

entity: the SUPERSTRING

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SUPERSTRING THEORY

So how does that work?

All particles are made of tiny tiny tiny

strings that oscillate differently

Oscillations = particles

Ps: We do not ask what is the string itself

is made of. That’s blasphemy!

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The string scale is roughly ~ 10-35m. This is called the

Planck Scale. Attached Homework: Calculate that number

SUPERSTRING THEORY

Remember this:

In string theory it is not really an

exchange, just a deformation of the

same superstring showing different

particles!

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“SUPER” IS FOR SUPERSYMMETRY (SUSY)

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Bosonic (force) side Fermionic (matter)

side

Photon Photino

Gluon Gluino

W Wino

Z Zino

Selectron Electron

Squark Quark

Graviton Gravitino

STRING THEORY IS A TOE

A THEORY OF EVERYTHING

AN OLD DREAM …

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MEDICINE

BIOLOGY

CHEMISTRY

PHYSICS

TOE

… etc.

THE MAIN ACHIEVEMENTS

All fields, including gravity, arise naturally (it’s a TOE)

Mathematical subtleties explained (The infinities are gone)

Unifies all fields and matter particles in one type of “string” that just

vibrates differently (total unification)

Explains the hierarchy problem, the masses of particles etc

All nice and fine, right?

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THE PROBLEMS OF SUPERSTRING THEORY

What is the string made of? Shhh!

Predicts unobserved particles (a lot more than the supersymmetric ones

we already discussed)

No experimental or observational verification as of yet

And the big one …

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SUPERSTRING THEORY

The theory predicts higher dimensions, all the way to ten extra spatial

dimensions

We live in three dimensions x, y, z (+ 1 of time “t”)

ST requires 10 (+ time) !!!!

(And you thought you were having trouble with 3d physics in class!!)

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THE EXTRA DIMENSIONS

Are either very small, wrapped around tiny six or seven dimensional

shapes, so every point in space is not just a point

Or they are unobserved because we are constrained to live in 3D and

the strings are not allowed to propagate into the higher dimensional

space (known as “the Bulk”)

Or a combination of both

In recent years, these models are explored

using “SUGRA”

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SUPERGRAVITY (SUGRA)

SUPERSTRING THEORY’S CLASSICAL FORM

If we look at the superstrings from a slightly larger scale, we don’t see the

strings any more, but before we zoom out all the way to ordinary physics,

we see something else:

Supergravity

A supersymmetric version of Einstein’s general theory of relativity

So we get curved spacetime with a boost

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SUGRA

The strings are represented by classical fields, not quite the same ones

we are used to, they are also higher dimensional

Those stringy fields propagate in curved spacetime

Supersymmetric versions exist in each SUGRA theory (yes there is

more than one)

Easier to work with, and in a sense more exact

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SUGRA

In both superstring theory and supergravity theory solutions known as

p-Branes (pun intended) emerge

Short for memBranes

They are multi-dimensional fundamental objects, so

0-brane: a point (particle)

1-brane: a string

2-brane: a membrane

3-brane: a volume-like object

>4-brane: no names

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BRANE THEORY (SOMETIMES: M-THEORY)

It is no longer just strings, we’ve got BRAAAANES

What are they?

Elementary objects like strings, charged

May have applications

Our universe could be just a 3-brane

floating into the bulk

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BRANE WORLDS

If our universe is a brane this explains

why we don’t see the higher dimensions

Our strings (matter and fields) are constrained

to live on one brane

Only the gravitonic string can propagate into the

bulk

There is some recent evidence of other brane-

worlds “touching” ours (maybe)

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BRANES IN SUGRA

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In SUGRA, branes can be thought

Of as charged objects, and the fields

Are stringy, not particles

WHAT AM I DOING?

Focus on the gravitational part using SUGRA (lots of general

relativity – lots of “branes” and stringy fields)

Eleven, five and four dimensions

Examples to follow

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HOW DOES ONE BECOME A STRING

THEORIST?

Study every physics and math course there is (at least it will feel like

you did)

Do research with someone until you learn to do it on your own

Must own a “perpetual coffee machine”

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HOW CAN YOU DO RESEARCH IN ST?

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Read popular books on physics (over the summer?) Teaches you the big picture without mathematics

Study: Special relativity (MUST)

General relativity (gravity) (MUST)

Topics in classical and/or quantum Field theory (MAYBE)

Differential geometry and some topology (MAYBE)

Practice with previously known results

Start your own problem

You may also learn : Computer programming with C/C++, Mathematica. Writing papers with LaTeX … etc

The end result will depend on how much time you are willing to give. No guarantee you will get to see your name on a paper.

CHARLES CANESTARO (CLASS OF 2013)

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JESSE CHANDLER (CLASS OF 2014)

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ANTHONY D’ACCOLTI (CLASS OF 2016)

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Ongoing project (almost done)

Studying elliptically symmetric solutions in four dimensional

spacetime

Static non-vacuum and time dependent vacuum solutions

May have applications in higher dimensions with stringy fields

QUESTIONS?

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