173 terms

1. What are the goals of string theory? (In class we discussed three related goals)

(a) Resolving conflict between Einsteins Gravity (General Relativity) and Quantum Mechanics.

(b) Unified Field Theory (Unification of all 4 forces of nature)

c) Theory of Everything (T.O.E)

(b) Unified Field Theory (Unification of all 4 forces of nature)

c) Theory of Everything (T.O.E)

2. What are the four known fundamental forces of nature? Give an example of each.

1) Gravity: Keeps the earth going around the sun

2) Electromagnetic: Signal sent from one cell phone to another, electromagnetic radiation or light.

3) Strong: Holds quarks together to make up a proton or neutron.

4) Weak: Decay of some particles, e.g. neutron, MUON

2) Electromagnetic: Signal sent from one cell phone to another, electromagnetic radiation or light.

3) Strong: Holds quarks together to make up a proton or neutron.

4) Weak: Decay of some particles, e.g. neutron, MUON

3. In string theory what ARE fundamental particles such as electrons and photons?

Strings

4. How does string theory force us to think differently about space?

In the original, there are NINE space and ONE time dimension.

In the M-theory, there are TEN space and ONE time dimension.

In the M-theory, there are TEN space and ONE time dimension.

5. What is the biggest conflict in modern day physics that string theory hopes to resolve? What problems in physics require resolution of this conflict in order to be more fully understood?

-Resolving conflict between general relativity and quantum mechanics

-This will allow us to understand black holes and early Earth. (universe)

-This will allow us to understand black holes and early Earth. (universe)

6. Is string theory accepted?

-Many would like to, but we NEED experimental verification.

-To date there is no experimental proof only tantalizing hints.

-To date there is no experimental proof only tantalizing hints.

7. What is the reductionist viewpoint?

If you know all the forces and interactions with a theory of everything (T.O.E) you know love (i.e. emotions, thoughts etc.) are explained by equations.

1. According to James Clerk Maxwell, what is light?

-Electromagnetic Radiation

-Oscillating and magnetic field

oscillating electromagnetic fields

-Oscillating and magnetic field

oscillating electromagnetic fields

2. What precedence is there in physics for unification of forces?

-Unified electric and magnetic forces

3. What two ideas (postulates) form the foundation for Einstein's special theory of relativity?

(1) Constancy of speed of light: light moves at a constant speed of light.

(2) Principle of Relativity

- Cant tell the difference between constant velocity and motion and being at rest. The laws of physics don't depend on constant velocity motion.

(2) Principle of Relativity

- Cant tell the difference between constant velocity and motion and being at rest. The laws of physics don't depend on constant velocity motion.

4. Explain with a picture and a few words why the speed of light being a constant for all observers regardless of their state of constant velocity motion seems paradoxical?

Postulate 1 is paradoxical but we believe it because it is continuously verified by experiment.

(See pic)

(See pic)

5. What is meant by the principle of relativity?

Cant tell the difference between constant velocity motion and being at rest.

The laws of physics don't depend on constant velocity motion.

The laws of physics don't depend on constant velocity motion.

6. State three observations about space and time that can be made by observers moving relative to each other.

(1) Moving back slows down relative to a person (observer) at rest [TIME DILATION]

(2) Moving lengths shorten relative to a person (observer) at rest [LORENTZ CONTRACTION]

(3) [THE RELATIVITY OF SIMULTANEITY]

-Events which are simultaneous for one observer are not simultaneous for an observer moving relative to the first.

(2) Moving lengths shorten relative to a person (observer) at rest [LORENTZ CONTRACTION]

(3) [THE RELATIVITY OF SIMULTANEITY]

-Events which are simultaneous for one observer are not simultaneous for an observer moving relative to the first.

7. Into what particles does a muon decay? What force plays a role in muon decay?

-Decay to at least an electron and two neutrinos.

-Particles that have a net charge spin of zero.

-Decay via the weak interaction.

-Particles that have a net charge spin of zero.

-Decay via the weak interaction.

8. As viewed from earth how does the lifetime of an approaching muon compare to a muon at rest? How does this change in a muon's lifetime affect how far the muon travels as viewed from earth?

-Approaching one is moving fast relative to the observer at rest, so the lifetime shortens.

-The one at rest-distance to earth contracts! (Moving lengths/Lorentz contraction)

-Distance = 600 m

-The one at rest-distance to earth contracts! (Moving lengths/Lorentz contraction)

-Distance = 600 m

9. From the point of view of the muon at rest, how do we explain the fact that the earth reaches the muon before it decays?

-Moving lengths

-Lorentz contraction

-Lorentz contraction

10. Give an example demonstrating the relativity of simultaneity.

(See train pic)

Person on train sees "B" than "A" because he is moving toward "B" and light has less distance to travel!

Person on train sees "B" than "A" because he is moving toward "B" and light has less distance to travel!

1. In class we discussed three ways of understanding the relative nature of simultaneity. Choose the one way you like best and explain what is meant by relativity of simultaneity.

-Concept of simultaneity-- Whether two events occur at the same time-- is not absolute, but depends on observers reference frame. (see train pic)

2. What is a light clock?

-Two small mirrors mounted on a bracket facing one another, with a single photon of light bouncing back and forth between them.

3. Why do we use a light clock instead of a Rolex watch when we discuss how time slows for moving clocks relative to stationary observers?

Its mechanical simplicity pares away extraneous details, providing us with the clearest insight into how motion affects the passage of time.

4. How can we know that conclusions we reach about a light clock also apply to a Rolex watch?

Through application of the principle of relativity.

5. Using a light clock, clearly state the argument for why time slows for moving clocks relative to stationary observers.

We can conclude that in comparison to a stationary clock, the rate of thinking of the sliding clock becomes slower and slower as it moves faster and faster.

Moving clocks must travel farther to achieve 1 tick, and will tick less frequently.

Moving clocks must travel farther to achieve 1 tick, and will tick less frequently.

6. Using a light clock, explain why we can only easily see time slowing for moving clocks relative to stationary observers when the clock moves close to the speed of light.

Photon of the moving clock has further to travel.

7. Using the fact that time slows for moving clocks, explain how we can understand moving objects shortening relative to stationary observers.

Jim's clock is running slower than Slims

Length is proportional to time, and if time is shorter for person at rest then length is shorter

Length is proportional to time, and if time is shorter for person at rest then length is shorter

1. How will two people (such as Gracie and George in the text) moving away from each view time passing on the other person's clock?

From their perspective they are motionless and that is the "Stationary" muon that are moving in the opposite direction.

George will undergo acceleration.

George will undergo acceleration.

3. What is the twin paradox?

-Identical Twins

- (Synchronized clocks), one stays on earth, the other travels fast to another planet, stops, comes back fast and is younger than the twin on earth.

- (Synchronized clocks), one stays on earth, the other travels fast to another planet, stops, comes back fast and is younger than the twin on earth.

4. Has something similar to the twin paradox been confirmed experimentally? Explain.

Yes, physicists sent an atomic clock 6,000 into space and had one on earth. The one that went into space sped up compared to the one on earth.

5. From whose perspective can one easily explain the twin paradox? Explain.

From perspective on earth b/c traveler's clock appears to slow down

6. With the aid of a picture explain what Einstein means by our motion through spacetime is at the speed of light. Locate points of no motion through space and time, and maximal motion through space and time on the diagram.

-Speed through time on the Y axis. Speed through space on X.

-arched line connecting the two.

-Point on Y is max motion through time and no motion through space.

-Point on X is motion through space and no motion through time

-arched line connecting the two.

-Point on Y is max motion through time and no motion through space.

-Point on X is motion through space and no motion through time

2. Name two technological applications of Einstein's famous equation, E=mc2.

1) Nuclear weapons

2) Nuclear power

3) Particle accelerators

2) Nuclear power

3) Particle accelerators

3. In what sense did Newton unify the heavens and earth with his theory of gravity?

Declared the force of gravity to be the invisible hand at work in each realm.

Describes

-motion of planets about the sun

-moon about the earth

-and putting a man on the moon

Describes

-motion of planets about the sun

-moon about the earth

-and putting a man on the moon

4. What is the conflict between Newton's theory of gravity and Einstein's theory of special relativity?

Special relativity says no information can be transmitted faster than the speed of light.

Not even instantaneous transmissions.

Newton's law of gravity acts instantaneously

Not even instantaneous transmissions.

Newton's law of gravity acts instantaneously

5. In the video we saw, what example was used to depict the conflict in question 4?

A quantum world of strings that is unpredictable.

The sun exploding

The sun exploding

6. How does Einstein's general theory of relativity resolve the conflict in question 4?

United gravity and acceleration motion

1) Gravity is warped spacetime

2) Gravity does not act simultaneously

1) Gravity is warped spacetime

2) Gravity does not act simultaneously

1. Newton was embarrassed by what aspect of his theory of gravity?

That the mechanical philosophy was false.

He believed that gravity was caused by an agent and not by or force acting at a distance.

He believed that gravity was caused by an agent and not by or force acting at a distance.

2. Explain in one concise sentence the essence of Einstein's general theory of relativity.

Special Relativity is the absolute barrier set of light.

Moving through spacetime at the speed of light

Moving through spacetime at the speed of light

3. What was Einstein's happy thought and why did it make him happy?

-"A falling person doesn't feel their own weight"

- Today we call it equivalence principle

→ Which says you cant tel the difference between acceleration and gravity.

- Gravity is curved spacetime

- Today we call it equivalence principle

→ Which says you cant tel the difference between acceleration and gravity.

- Gravity is curved spacetime

4. What is the equivalence principle? Explain with the aid of a picture.

4. What is the equivalence principle? Explain with the aid of a picture.

5. Starting with the equivalence principle, explain the logical connections allowing Einstein to discovery the general theory of relativity.

-Gravity does not act instantaneously

-Cant tell the difference between acceleration and gravity

-Acceleration is tangible where as gravity is mysterious.

-Cant tell the difference between acceleration and gravity

-Acceleration is tangible where as gravity is mysterious.

6. Using the tornado ride as an example, clearly explain how space is warped (or curved).

-acceleration is related to curved space time

-Although your speed is constant it is changing direction and thus is accelerating.

(See pic)

-Although your speed is constant it is changing direction and thus is accelerating.

(See pic)

8. As Slim stands still on the outside edge of the tornado ride moving at constant speed, why is he accelerating?

Because he is changing direction → thus accelerating

Time slows down on the edge more than the middles b/c of special relativity

Time slows down on the edge more than the middles b/c of special relativity

2. Is the geometry you learned in high school obeyed on the tornado ride? Explain.

High School Geometry → C=2rEuclidion (flat surfaces)

Tornado Ride Geometry → C> 2rReunominon (curved)

When, C<2r, on surface of sphere → POSITIVE CURVATURE

Tornado Ride Geometry → C> 2rReunominon (curved)

When, C<2r, on surface of sphere → POSITIVE CURVATURE

3. Using the tornado ride as an example, explain how acceleration leads to warping of time.

- middle no speed/acceleration

- biggest on the outside

- special relativity shows C>2r

- biggest on the outside

- special relativity shows C>2r

4. Name three problems with figure 3.5?

1) Only 2-D

2) Doesnt show time warping (only space warping)

3) No external object of force bending space, the mass itself curves space. (the mass of the object curves the space without gravity)

2) Doesnt show time warping (only space warping)

3) No external object of force bending space, the mass itself curves space. (the mass of the object curves the space without gravity)

6. How does the flow of time on earth compare to an identical clock 6,000 miles above the surface? How do we know?

-Clock went up 6,000 mi (less gravity), gravity went faster (1976).

→ Precession of perihelion of mercury

→ Total solar eclipse to view the bending of light by the sun from distant star

The one experiencing acceleration (earth) slows down

→ Precession of perihelion of mercury

→ Total solar eclipse to view the bending of light by the sun from distant star

The one experiencing acceleration (earth) slows down

1. Name two early confirmations of Einstein's general theory of relativity.

1) Precession of perihelion of mercury

2) Total solar eclipse to view the bending of light by the sun from distant star

2) Total solar eclipse to view the bending of light by the sun from distant star

2. Explain using the equivalence principle and a picture why light bends in a gravitational field.

(see pic)

Sun cause surrounding space/time to warp influencing path taken by the sunlight

Sun cause surrounding space/time to warp influencing path taken by the sunlight

3. What makes a black hole black?

Infinite Density

-Event horizon

Immense amount of gravity

-Event horizon

Immense amount of gravity

4. Where in the universe do physicists and astronomers have strong evidence to suggest the existence of black holes? What is the evidence?

-Super massive black holes in the center of galaxies.

-Evidence → Binary star systems with one star missing but the other one we know is there by observations (wiggling) its mass is big enough to be a black hole and X-rays are emanating from nothingness.

-Evidence → Binary star systems with one star missing but the other one we know is there by observations (wiggling) its mass is big enough to be a black hole and X-rays are emanating from nothingness.

5. What is Einstein's "biggest blunder"?

Cosmological constant- to try and say universe not expanding

GR cant coincide with Quantum Mechanics

GR cant coincide with Quantum Mechanics

1. Einstein spent his life trying to unify which forces of nature?

Quantum Mechanics, and General Relativity

2. Name some of the interesting phenomena found in the quantum café (video) or in H-bar (text).

Rattling ice cubes leaving the glass, cigar going through his head, walking through walls.

3. Name four primary characteristics of quantum mechanics.

1) Quanta → Black body radiation and Photo electric effect

2) Particle wave duality

3) Probabilistic

4) Uncertainty

2) Particle wave duality

3) Probabilistic

4) Uncertainty

4. Given the crazy ideas coming from quantum mechanics why should we believe it?

Yep, the idea behind the quantum world is that it is unpredictable. Even though, this does not work with GR, if we believe in string theory, that all the elementary particles are strings, we can better understand it.

5. What is blackbody radiation?

Electromagnetic Radiation emitted by anything with nature

6. What happens when you try to explain blackbody radiation with classical physics?

Equations for light describe a wave

7. Name four characteristics of a wave?

1) wave length ()

2) Amplitude (A)

3) Frequency (F)

4)Period (T)

2) Amplitude (A)

3) Frequency (F)

4)Period (T)

8. How are wavelength and frequency related for light waves?

The higher the wave length, the lower the frequency

9. What did Plack have to assume to properly predict blackbody radiation?

"Energy" proportional to frequency

1. In the quantum mechanical explanation of blackbody radiation why can't very high-energy photons contribute to the radiated energy?

Not enough thermal energy to excite the high energy quanta

2. In the analogy between blackbody radiation and the warehouse landlord, what physics concepts correspond to people, coins, temperature, furnace setting payment, and money?

People-oscillators

Coins-quanta

Payment- total energy of all

Temp-temp

Money-energy

Coins-quanta

Payment- total energy of all

Temp-temp

Money-energy

4. Who was the first person to properly explain the photoelectric effect?

Albert Einstein

5. What do you have to assume to properly explain the photoelectric effect?

Electrons are ejected from a metallic surface when light is shown upon it.

Energy comes in quanta (packets) called photons

Energy comes in quanta (packets) called photons

6. If low intensity light is shining on a metal and no electrons are emitted, using classical physics what do we expect to happen as the intensity is increased?

-All wavelengths and corresponding frequences have the same amplitude at any given time temperature. Since there are infinite frequencues, it results in INFINITE energy!

-Equate intensity w/energy, would think high intensity light would pop off more electrons

-Equate intensity w/energy, would think high intensity light would pop off more electrons

1. What pattern do you observe on the detection screen when a high intensity light source illuminates a double slit apparatus?

-Don't see two peaks (expected if light is a particle)

-Instead you see a interference patter characteristics of light as a wave.

(See pic)

-Instead you see a interference patter characteristics of light as a wave.

(See pic)

2. What pattern do you observe on the detection screen when one photon at a time illuminates a double slit apparatus over a long period of time?

-We see an interference when we send one photon at a time.

3. How do you explain the results in questions 2. above according to Schrodinger?

The particle/wave has a probability distribution (wave) associated with it.

4. What happens when you repeat the experiments in questions 1. and 2. using electrons instead of photons?

Go through both along every path at the same time

5. How do you explain the results in questions 2. above according to Feynman?

The particles/wave takes all paths with differing probabilities to yield same result.

6. What is Louis de Broglie's contribution to physics?

So electrons behave like waves and particles.

Electrons have mass and he was the first to hypothesize "matter waves".

Electrons have mass and he was the first to hypothesize "matter waves".

7. Why can we not see the wavelength of a baseball flying through the air?

Mass of baseball is huge compared to mass of electron

8. Why does Stephen Hawking say, "Einstein was confused, not the quantum theory"?

Einstein does not like the probabilistic nature of quantum mechanics.

"God does not play dice"

"God does not play dice"

1. Explain how you can understand the four big concepts in quantum mechanics using the double slit experiment?

1. Quanta-being projected through slits; photon or electron

2. Particle/Wave Duality-- manifests in one single spot on screen

3. Probability- we don't know position of electron

there is probability it will hit somewhere on the screen

QM doesn't know which slit it will go through

4. Uncertainty- if you know which slit particle goes through

you have reduced uncertainty in position

increased velocity

2. Particle/Wave Duality-- manifests in one single spot on screen

3. Probability- we don't know position of electron

there is probability it will hit somewhere on the screen

QM doesn't know which slit it will go through

4. Uncertainty- if you know which slit particle goes through

you have reduced uncertainty in position

increased velocity

2. What are the two Heisenberg uncertainty relations we discussed in class?

1. (uncertainty in position)(uncertainty in velocity or momentum) h/2

X V

THUS, X V

2. (uncertainty in Energy)(uncertainty in time) h/2

E t

THUS, t E

X V

THUS, X V

2. (uncertainty in Energy)(uncertainty in time) h/2

E t

THUS, t E

3. Why is the Heisenberg uncertainty relation not relevant for our everyday world?

Can't borrow and break a barrier

Only happening at the micro level

Only happening at the micro level

4. If I wanted to detect something with a size of 1cm what wavelength of light would I need to use? Explain.

Smaller wavelength the finer the details you can observe.

Need wavelength smaller than 1cm

Need wavelength smaller than 1cm

5. Why can't I measure the position of a particle to high precision with long wavelength light?

The more you know about a particles position, the less you know about its momentum. Can't know postion and velocity at the same time.

6. What happens to the velocity (or momentum) of a particle when you use short wavelength light to detect its position?

Increases

7. Explain quantum tunneling.

-We can barrow enerygy ("from nothing") as long as we return it within time, t

8. In the quantum café, why are the ice cubes rattling around in the glasses?

-Because the energy barrier is too large

Small space; > velocity

Doesn't like being constrained

Quantum claustrophobia

Small space; > velocity

Doesn't like being constrained

Quantum claustrophobia

1. Explain in words the key features of a quantum field theory (Q.F.T.).

Involves QM SR and force field.

Explains the interactions between electrons and photons

Explains the interactions between electrons and photons

2. How does the force in quantum electrodynamics (Q.E.D.) work?

- Q.E.D. force electrons to repel due to E&M force

3. Are infinities encountered in Q.E.D.? Are they controllable? Why?

- -There are infinities when performing calculations but Feynman shows they are controllable because there are only 3 of them.

4. Give an example of the precision of Q.E.D.

-Q.E.D. provides the correspondence between theory and experiment of any theory.

Correspondent is better than one part in a billion

Correspondent is better than one part in a billion

5. In what sense is quantum chromodynamics (Q.C.D.) like Q.E.D.?

Both are quantum field theories for force fields (strong/ em force)

6. What is quantum electroweak theory and why is it important?

Q.F.T for the weak force ONLY doesnt work, but when combined with Q.E.D. it does (i.e. unification of weak and EM), called the electroweak theory.

-It is important because it Unifies EM and the weak

-It is important because it Unifies EM and the weak

7. What is the standard model of particle physics?

The 3 forces (string, weak, & EM--NO gravity) and the fundamental particles with interaction are described by Q.F.T.

Fundamental objects are points

Fundamental objects are points

8. What happens when calculations are made in a quantum field theory of gravity?

There is no Q.F.T. of gravity that does not produce UNCONTROLLABLE infinities.

-There are infinity infinities!

-There are infinity infinities!

9. What happens to spacetime at small space and time scales? How small is small?

Quantum foam- particles jumping in and out of existence

planck length

planck length

1. What are two consequences of quantum geometry?

Two consequences:

a)The smallest a dimension can be is a planck length (10 to the -33 cm).- Black holes.

b) Dualities- Shows the relations between the 5 string theories and M-theory.

b) two notions of measuring distance-different probes

a)The smallest a dimension can be is a planck length (10 to the -33 cm).- Black holes.

b) Dualities- Shows the relations between the 5 string theories and M-theory.

b) two notions of measuring distance-different probes

2. When comparing an R=10 universe with an R=1/10 universe, what difficulties arise when a direct measurement of the radius is made?

The physics behind both are the same. However....

3. For a universe of size R to be dual to a universe of size 1/R, what must happen to the winding mode number and uniform vibration number?

you switch the numbers...(i am pretty sure)

4. What do we mean by duality in string theory? Give an example.

Equal to or the same. An example would be the two universes: R = 10 and R = 1/10 having the same physics (energies and particle properties)

5. When R is large what are the heavy probes and light probes? Why?

Winding energy is heavy and uniform vibration energy is light

6. When R is small what are the light probes and heavy probes? Why?

I would assume the opposite...

light probes=winding and heavy=vibration

light probes=winding and heavy=vibration

7. To conclude that the minimum size for a dimension is greater than 1 (the Planck size), what type of probe must be used? Why is this the natural choice of probe?

The easiest probe to use is the light probe for measuring distance. (it is the standard idea for measuring distance)

1. Name a physicist who worked on orbifolding.

Dixon, Harvey, Vafa, Witten, Greene

2. What is orbifolding?

Orbifolding is a procedure in which a new Calabi-Yau shape is produced by gluing together various points on an initial Calabi-Yau shape.

3. What do we mean by an even or odd-dimensional hole?

An even or odd dimensional hole gives rise to the geometric shape of the Calabi-Yau space.

An odd-dimensional hole is a hole in an odd dimensional space 1,3.5.

An even-dimensional hole is a hole in an even dimensional space 2,4,6.

An odd-dimensional hole is a hole in an odd dimensional space 1,3.5.

An even-dimensional hole is a hole in an even dimensional space 2,4,6.

4. Does the number of particle families depend on the number of even-dimensional holes or odd-dimensional holes? Explain.

It doesn't matter if its even or odd dimensional. It doesn't depend on the number of dimensions

Depends on # of holes

Depends on # of holes

5. What is mirror symmetry in string theory? Why is it important to mathematicians and string theorists? Give an example.

When working out a very difficult math calculation that is impossible, you can think to mirror symmetry and remember that this CY space (you're doing your equation on) has a mirror partner. So you can manipulate your calculation in terms of its mirror, and the physics for the rest of your equation should be the same (p. 260).

Another example calculating the number of spheres in a CY shape

Another example calculating the number of spheres in a CY shape

1. Can space tear in Einstein's general theory of relativity? Explain.

Einsteins G.R. allow holes to exist but G.R. says you cant tear space to create wormhole.

2. If you wanted to create a wormhole to travel between your house and Cal Poly what would you need to do to space?

Tear space

3. Make a cartoon sketch showing the before, during and after of a space-tearing flop transition. Why can string theorists not compare physics with the "before" picture directly with the "after" picture?

It would imply space can tear and nothing totally crazy happens.

It was just too complicated at end or the "after".

It was just too complicated at end or the "after".

4. Make a cartoon sketch showing the before, during and after of a space-tearing flop transition using the mirror Calabi-Yau. Does anything dramatic happen to the mirror Calabi-Yau space during the tear?

No, its an indication that space can tear

Note: No tearing in the dual space

Note: No tearing in the dual space

5. Name two major difficulties Greene and collaborators encountered when comparing the "after" space-tearing flop transition Calabi-Yau manifold with it's mirror.

1)Find proper mirror space Ic with IIc

2) Mass calculations in Ic space needed computer code

In his office hours he said he messed up in class and it is actually:

Mass calculations in 2c space needed computer code

2) Mass calculations in Ic space needed computer code

In his office hours he said he messed up in class and it is actually:

Mass calculations in 2c space needed computer code

6. What was Witten's insight into the space-tearing flop transition?

The string world sheet protects space tears from disastrous consequences

7. What physical properties stay the same and which ones change in a space-tearing flop transition?

Particles, charges, and families stay the same. Masses change.

8. Can large spatial dimensions tear? Explain why we believe this to be true or not.

Yes, since space is space, and small spatial dimensions can tear, than so can large ones!

1. What is the tool used by physicists to understand the approximate equations of string theory?

Pertebation Theory

2. What is the physical significance of the string coupling constant?

The strength of string interactions. (small coupling is weak interactions and large is strong)

3. For what values of the string coupling constant does perturbation theory work? Explain why.

Perturbation theory only works when the string coupling is small. (less than 1)

4. When string theorists try to calculate the string coupling constant what do they find?

(coupling strength)(0)=0 i.e. you don't know what it is.

5. What point does Greene make by introducing the word syzygy?

The analogy aims to help explain the BPS state, and how it is highly constrained. It has three units of electric charge (like the word has 3 y's), has the minimum mass for chosen electric charge, (smallest word with most ys), it is supersymmetric, (like the word is limited to the English dictionary).

6. In what sense are B.P.S. states non-perturbative?

They are BEYOND perturbation states (states meaning excitations or masses of the string)

BPS states are the lightest supersymmetric state with a given charge

BPS states are the lightest supersymmetric state with a given charge

7. How are B.P.S. states used to show the strong coupling limit of one string theory is dual to the weak coupling limit of another?

Example of Type I @ strong coupling is equivalent or dual to Heterotic O at weak coupling.

They have the same physics.

They have the same physics.

1. Witten discovered two paths to M-theory from the previously known five distinct string theories. Explain how an extra dimension emerges for the two paths to M-thoery Witten discovered. What is (are) the shape(s) of the extra dimension that emerges?

1) heterotic E. shaped like a ribbon

2) Type II A. shaped like a Taurus

Depends on the strength of the coupling which is made

2) Type II A. shaped like a Taurus

Depends on the strength of the coupling which is made

2. If the string coupling constant is small (less than 1), how many dimensions does string theory or M-theory have?

10 Dimensions

3. Explain the types of dualities depicted in figure 12.10 and give an example of each type.

By including the dualities involving the geometrtic form of spacetime, all five string theories and M-theory are joined in a web of dualities. ** p.312-314

4. What is supergravity and how is it related to M-theory?

Supergravity is a point particle quantum theory with supersymmetry in 11-D.

5. Why do some people say the "M" in M-theory refers to membrane?

Because a common feature of m-theory is membranes.

6. In light of M-theory developments in what sense are strings still special?

string itself creates space.

2. What is a p-brane? (This should have been on the previous lecture focus question).

A brane is any of the extended objects that arise in String Theory. A 1-brane is a string, a 2-brane is a membrane, 3-brane has three extra dimensions. But a p-brane, has "p" spatial dimensions. (p 316-317)

4. What is entropy?

A measure of disorder of a physical system; the number of rearrangements of the ingredients of a system that leave its overall appearance intact.

5. If black holes have entropy, they also have temperature and Hawking showed they....

hole's horizon

Antimatter

Matter with the same gravitational properties as regular matter, but with an opposite electric charge and opposite nuclear force charges.

Antiparticle

A particle of antimatter.

Big bang

The widely accepted theory concerning the origin of the universe. The big bang theory posits that the universe evolved approximately 10 to 15 billion years ago from the explosion of an incredibly dense, hot substance that was contained at one point. The universe has been expanding since the first fraction of a second after the big bang occurred.

Big crunch

The term referring to what some physicists believe will happen when the expanding universe stops and implodes. When the big crunch occurs, according to the theory, all space and matter will collapse together.

Black hole

A region of space formed when a giant star collapses and all of its mass compresses to a single point, forming a gravitational field so overpowering that it traps anything that comes close to it, including light.

Boson

A pattern of string vibration with an amount of spin measurable in whole numbers. A boson is most often a messenger particle.

Bosonic string theory

The first version of string theory. Bosonic string theory, which dealt with string's vibrational patterns, emerged in the 1970s. This version was later revised and replaced by supersymmetrical string theory.

Calabi-Yau shape/space

A theoretical configuration that many physicists believe might contain the additional dimension string theory requires. Many thousands of such possible configurations exist, but string theory has yet to verify the correct one.

Electromagnetism/electromagnetic force

One of the four fundamental forces, along with gravity, the strong force, and the weak force. Electromagnetism determines all types of electromagnetic radiation, including light, X-rays, and radio waves.

Electroweak theory

A relativistic quantum field theory that describes the weak force and the electromagnetic force within a single framework.

Elegance

To Greene, string theory defines elegance because it is extremely simple, but it may explain every event in the universe.

Elementary particle

The indivisible or "uncuttable" unit found in all matter and forces. Elementary particles are now categorized by quarks and leptons, and their antimatter counterparts.

Equivalence principle

The basic tenet of general relativity. The equivalence principle states that accelerated motion is indistinguishable from gravity. It generalizes the theory of relativity by showing that all observers, regardless of their state of motion, can say that they are at rest, provided they take the presence of a gravitational field into account.

Flop transitions

Also called topography-changing transitions. Flop transitions are the act of Calabi-Yau space ripping and repairing itself.

Force carrier particle

A particle that transmits one of the four fundamental forces. The strong force is associated with gluon; electromagnetism with the photon; the weak force with W and Z; and graviton (which hasn't yet been discovered) with gravity.

Fundamental force

There are four fundamental forces : electromagnetism, strong force, weak force, and gravity.

General theory of relativity

Albert Einstein's formulation that gravity results from the warping of spacetime. Through this curvature, space and time communicate the gravitational force.

Graviton

Physicists believe that graviton—which has not yet been proven to exist—is the particle carrier of the gravitational force.

Gravity

The weakest and most mysterious of the four fundamental forces. Gravity acts over an infinite range, and gravitation describes the force of attraction between objects containing either mass or energy.

M-theory

The theory under which all five previous versions of string theory fall. The most recent synthesis of string theory ideas, M-theory predicts eleven spacetime dimensions and describes "membranes" as a fundamental element in nature.

Mirror symmetry

A precept of string theory that demonstrates how two different Calabi-Yau shapes have identical physics.

Newton's laws of motion

Laws of motion based on an absolute and unchanging notion of space and time. Newton's laws of motion were later replaced by Einstein's theory of special relativity.

Particle accelerator

A machine that speeds up the movement of particles and then either shoots them out at a fixed target or makes them collide. Particle accelerators allow physicists to study the movement of particles in extreme conditions.

Perturbation theory

A formal framework for making approximate calculations. Perturbation theory is a linchpin of string theory in its current form. The approximate solution will be refined later as more details fall into place.

Photon

The smallest bundle of light. Photons are the messenger particles of the electromagnetic force.

Photoelectric effect

The action of electrons shooting from a metallic surface when light is shone onto that surface.

Planck energy

The energy required to probe Planck-length-scale distances.

Planck length

Planck length—approximately 10-33 centimeters—is the scale at which quantum fluctuations occur. Planck length is also the size of a typical string.

Planck mass

Planck mass is roughly equal to the mass of a grain of dust, or ten billion billion times the mass of a proton.

Planck's constant

Planck's constant is also known (and written) as the "h-bar." It is a fundamental component of quantum mechanics.

Planck tension

About 10 (to the 39th power) tons. Planck tension is equal to the tension of a typical string.

Quanta

According to the laws of quantum mechanics, the smallest physical unit that something can be broken into. Photons are the quanta of the electromagnetic field.

Quantum field theory

Also known as relativistic quantum field theory. Quantum field theory describes particles in terms of fields, as well as how particles can be created or annihilated, and how they scatter.

Quantum foam

Also known as spacetime foam. Quantum foam is the violent turbulence of spatial fabric at an ultramicroscopic scale. Its existence is one of the chief reasons that quantum mechanics is incompatible with general relativity.

Quantum mechanics

The framework of laws that describe matter on atomic and subatomic scales. The uncertainty principle is a pillar of quantum mechanics.

Quarks

A family of elementary particles (matter or antimatter) that make up protons and neutrons. There are many types of quarks: up, charm, top, down, strange, and bottom. Quarks are acted upon by the strong force. Murray Gell-Mann named quarks after he read James Joyce's Finnegans Wake.

Special theory of relativity

Einstein's description of particle motion, which hinges on the constancy of the speed of light. The theory of relativity states that even if an observer is moving, the speed of light never changes. Distance, time, and mass, however, all depend on the observer's relative motion.

Spin

The theory that all particles have an intrinsic amount of spin in either whole- or half-integer denominations.

Standard model

A quantum model that explains three of the fundamental forces—electromagnetism, the strong force, and the weak force—but does not take gravity into consideration.

String

Miniscule one-dimensional vibrating strands of energy. String theories posit that these filaments are the basis of all elementary particles. The length of a string is 10-33 cm; strings have no width.

Strong force

So called because it is the strongest of the four fundamental forces. It holds quarks together and keeps protons and neutrons in the nuclei of atoms.

Superstring theory

A theory that describes resonant strings as the most elementary units in nature.

Supersymmetry

A principle of symmetry relating the properties of particles with a whole-number quantity of spin (bosons) to those with half a whole number of spin (fermions). Supersymmetry posits that all elementary matter particles have corresponding superpartner force carrier particles. No one has yet observed these theoretical superpartners, which are thought to be even larger than their counterparts.

Tachyon

A particle that has a negative mass when squared. The existence of a tachyon usually indicates a problem with a theory.

Topology

The study of geometric figures' properties that exhibit ongoing transformations and are unchanged by stretching or bending.

Uncertainty principle

Heisenberg's uncertainty principle is the crux of quantum mechanics. It proclaims that you can never know both the position and the velocity of a particle simultaneously. To isolate one, you must somehow blur the other.

Unified field theory

A theory describing all four fundamental forces and all of matter within a single framework.

Weak force

One of the four fundamental forces. Weak force operates over a short range.