PHYSICS FINAL - Lecture Focus Questions (1-36)

What was Einsteins happy thought and why did it make him happy?

"if a man is free falling he cannot feel his own weight" - made einstein happy because he realized he could use acceleration (tangible, known) to understand gravity (abstract, mysterious)

What point does Greene make by introducing the word syzygy?

- 3 y's represent the charge - shortest word, minimal mass

If the original string theory is correct (disregard M-theory for the moment), how many spatial compact dimensions are there? What shapes meet the stringent requirements of string theory?

- 9 spacial 1 time dimension - calabi-yau meets the requirements

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

- coupling constant small = 10-D (string theory) - coupling constant large = 11-D (m-theory)

How will two people (such as Gracie and George) moving away from each other view time passing on the other persons clock?

- each will view the others clock as ticking slower relative to their own

In string theory what are fundamental particles such as electrons and protons?

- electrons and protons are vibrating strings - they vibrate at different frequencies (different musical instruments)

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

- figuring out correct calabi-yau space - calculating masses of particles in mirror symmetry

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

- flow of time on earth is slower bc of gravities warping of spacetime - we know this bc of experiment done w atomic clocks and planes

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

- fold it in half - tear it - create wormhole between two tears

What does Witten mean when he says that string theory predicts gravity?

- gravity is a post-theory of string theory - it would have been discovered through string theory regardless had we known about it already

What is the physical significance of the string coupling constant?

- how tightly quantum jitters are related, how tightly are the loops coupled together

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?

- light probe (low mass, low energy) - a light probe measures a large, expanding universe (R>1), heavy probe measures tiny, contracting universe

Give an example demonstrating the relativity of simultaneity.

- light turning on in moving train - simultaneous events in motion may seems nonsimultaneous relative to someone observing at rest

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

- matter warps spacetime, warped spacetime warps the way matter (mass/energy) moves

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

- muon at rest sees muon in motion as traveling at a slower speed relative to itself (muon on earth)

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

- muon at rest sees muon in motion as traveling at a slower speed relative to itself (muon on earth) - muons lifetime is extended by 10(2 x 10^-6)(10)) if the muon is traveling at the speed of light - life goes from 600m to 6000m

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

- no - equations of GR are firmly rooted in riemannian geometry which doesn't allow for tears

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

- no - in hs we used c = 2piR, but this only is relevant to flat space, not the curved space of the tornado ride (curved space c >2piR)

If supersymmetry is not discovered at the Large Hadron Collider, will string theory be proven wrong? Explain.

- no - superpartners could just be at higher energies

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

- non-perturbative because they don't rely on the approximate calculations of perturbation (you can calculate them with certainty) - doesn't rely on coupling unit #

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

- number of particle families depends on the number of holes regardless of even/odd space factor (they're the same) - odd dimensional holes in old shape = even dimensional wholes in new shape and vice versa

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

- one twin (he) leaves and the other twin (she) stays on earth. when he returns he has aged less than she has - we an easily explain this from her perspective since she stayed on earth - his acceleration slowed his time in relation to hers so he is therefore younger when he returns

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

- only works with small (less than 1) constants - less than 1 string coupling constant means virtual pairs of strings are UNLIKELY to erupt into existence - more interactions (loops) = more precise answer becomes

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

- physically equivalent yet geometrically different calabi-yau spaces (one complicated, one simple) - important because some incredibly complicated calabi-yau calculations can be solved much easier when using their simple mirror space with the same result

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?

- picture of a car moving 100mph with person moving 50mph, 50mph difference - car moving C - 2/3C = C - no matter your state of constant velocity motion light will always move away from you at C

What is the difference between Riemannian geometry and Quantum geometry? For our universe, at what length scales is each geometry important?

- riemannian geometry (points) applies to the macro world - quantum geometry (strings) applies to planck scales

Name three possible scenarios for which string theory could be validated.

- seeing a string through a telescope - 5th force is discovered - electron w charge of 1/7

What are two consequences of quantum geometry?

- smallest a dimension can be is planck size - 2 ways to measure distance (winding & uniform vibration energy)

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

- strings encircle the tear in order to protect rest of universe for catastrophic effects

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?

- strong coupling physics of one theory are described by weak coupling physics of another theory (strong-weak duality) - strong coupling limit solved using BPS state predict the weak coupling limit of another - you can solve a BPS state without perturbation with a large coupling unit and it is dual to a small coupling unit solved using perturbation

What type of particles did the first string theory explain?

- strong force (bosons) venezaino

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?

- the conflict/incompatibility between general relativity and quantum mechanics - if string theory is true, the incompatibility between the rules of the macroscopic and microscopic universe would be resolved

When Kaluza first postulated extra spatial dimensions in 1919 what was his motivation? How were his ideas received by Einstein? Why was his theory not accepted?

- to unify gravity and electromagnetism - good at first, then skeptical - wrong electron charge-to-mass ratio

If supersymmetry is discovered at the Large Hadron Collider, will string theory be validated? Explain.

- validated, not proven - other theories (supersymmetry) besides string that could be true

What is orbifolding?

- when you glue different points on a calabi-yau shape together to ensure a new shape is produced

With the aid of a graph (label each axis) 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.

- x-axis = space, y-axis = time - all the way up = no motion through space

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

- yes - size doesn't matter

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

1. constancy of the speed of light 2. principle of relativity

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

1. equivalence principle - gravity is indistinguishable from acceleration 2. acceleration equals warped spacetime 3. gravity is also warped spacetime

Name three problems with figure 3.5.

1. fig. 3.5 is in 2-d when it should be in 3-d (or 4-d) 2. does not take warping of time into account

Four fundamental forces of nature? (example of each)

1. gravity - newton and apple falling from tree 2. electromagnetism - magnet sticking to fridge 3. strong force - holds quarks together 4. weak force - uranium decay

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

1. length of moving ruler shorter than one at rest (Lorentz contraction) 2. moving clock ticks slower (time dilation) 3. relativity of simultaneity

Name three reasons why we might expect supersymmetry to be a symmetry of nature?

1. nature has used all of the other symmetries, why not this one? 2. fine tuning problem solved 3. at high energy or large distances 3 std model forces unite if SUSY is true

Name two technological applications of Einsteins famous equation E = MC^2

1. nuclear weapons - atomic bomb 2. nuclear power - power plants

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

1. precession of perihelion of mercury - 1915 2. suns bending of light - 1919

What are the goals of string theory? (3 goals)

1. resolve conflict between quantum mechanics and general relativity 2. discover theory of everything 3. unify the 4 fundamental forces

How many space and time dimensions are in M-thoery?

10 space 1 time

How many spatial dimensions are being represented in figures 8.4, 8.7, 8.8, 8.9, and 8.10?

2 spacial

How many space and time dimensions are in the original string theory?

9 space 1 time

Name a physicist who worked on orbifolding.

Brian Greene

Consider a string in a Universe with a compact circular dimension ten times the Planck length (i.e. R=10 in Planck length units). If the winding number is 3 and the uniform vibration number is 2, what is the total energy (in Planck units) from these excitations?

Etot = Ew + Euv Ew = NwR Euv = Nuv/R

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?

Heterotic-E: as string coupling constant is increased new dimension appears & string itself gets stretched into a cylindrical membrane shape (fig. 12.7) Type-IIA: as string coupling constant is increased, strings expand from 1-D loops to 2-D loops that look like the surface of donuts (fig. 12.8)

What precedence is there for unification in physics?

James Clerk Maxwell uniting electricity and magnetism

What are the names of the five different consistent superstring theories? In light of the second superstring revolution is five potential theories of everything a problem?

Type I Type IIA Type IIB Heterotic E Heterotic O - not a problem but a sixth is added in order to allow for the 11th dimension

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

a low string coupling constant using perturbative tools for Type I string theory is dual to Heterotic O with a high coupling constant that uses BPS states

What is the reductionist viewpoint?

absolutely everything (physics to daydreams) can be explained by the theory of everything

What did you like most about the video on compact dimensions?

afro-man

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

apple fell from tree - gravity is the invisible force that exerts force on everything - same force acts on earth as the heavens

Under what conditions do the strong, electromagnetic, and weak forces unify?

at high energy or small distances

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

because of the "membrane" that appears when the 11th dimension is present

Why do string theorists no longer have to worry about the tachyon particle traveling faster than the speed of light?

bosons and fermions cancel it out

What must string theorists assume about the compact space to create three families of particles as found in the standard model? Is this a unique answer? Explain.

calabi-yau shapes have three holes which describe 3 particle families - not unique, can be distorted

Where in the universe do physicists and astronomists have strong evidence to suggest the existence of black holes? Where is the evidence?

center of galaxies star pattern light things

What is Einstein's biggest blunder?

changing his equation to = 0 when it didn't

If the tornado ride were in deep space far from gravitation objects, in what sense would the ride mimic the gravity experienced on earth?

couldn't tell if ride was pulling you or gravity was

Where are the extra dimensions we don't see?

curled up, compact, hidden in small spaces

Which of the force particles in nature depend on the shape of the compact dimensions and which don't?

do - standard model particles (photon, gluon, weak gauge boson) don't - graviton

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

easier to visualize

Name the superpartners of the particles in the standard model and their corresponding spin.

electron 1/2 fermion - selectron 0 boson quark 1/2 fermion - squark 0 boson gluon 1 boson = gluino 1/2 fermion graviton 2 boson = gravitino 3/2 fermion higgs 0 boson = higgsino 1/2 fermion

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

electron, electron neutrino, muon neutrino via weak force

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

even = hole in 2-d shape (paper) odd = hole in 1-d shape (broken line segment) still applies to the rest of the even & odd #'s

Explain with a picture why the electromagnetic force gets stronger when probed at small distance or high energy?

farther apart forces get weaker - at a large distance energy fluctuations shield the charge of the electron - charge strength is less - small distance less shielding

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?

figure 11.5 - nothing dramatic happens

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?

figures 11.3 & 11.4 - can't compare because physics are identical, but complexity of mathematics is too hard

Define supersymmetry.

for every boson there is an antiparticle, a fermion and vice versa.

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

forces us to recognize there are 11 dimensions, not all of which we can see and observe

What space(s) with compact dimension(s) and large extended dimension(s) can we properly visualize with a drawing?

garden hose drawing

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

gravity warps the path light travels

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

he knew everything except how it actually worked

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

he's constantly changing direction

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

idk

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

indistinguishability between accelerated motion and gravity

Is string theory accepted?

kind of

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

light probe (always large distance) = winding energy (proportional to r) heavy probe (always small distance) = uniform vibration energy (inverse to r)

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

light probe = uniform vibration energy (large r, small uv) heavy probe = winding energy (large r, large winding)

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

more distance has to be covered by moving photon

What is meant by the principle of relativity?

motion only has meaning when compared to other objects or individuals - you cannot determine your state of motion without comparing it to something

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

must decide which probe to use - light energy probe measures large distances (larger than planck length) - heavy energy probe measures small distances (less than planck length)

Does string theory say it is impossible to have more than one time dimension?

no, just hard for most to grasp

What makes a black hole black?

not even light can escape due to strength of gravity

According to James Clark Maxwell, what is light?

nothing but a type of EM wave interacting w chemicals in the retina giving you the perception of light

What is the conflict between Newton's theory of gravity and Einsteins theory of special relativity?

nothing is instantaneous or can travel faster than the speed of light

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

only the strings are light enough to make contact with physics as we know it (the particles of table 1.1) and the four forces through which they interact

What are the two types of vibrational energies associated with a string? Briefly explain what each energy corresponds to?

ordinary - physical vibration of a string (fig. 6.2) uniform - quantum mechanical sliding/oscillating associated with energy due to point particles

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

perturbation theory

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

principle of relativity

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

slim and his ruler contraction (lorentz)

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

slim measures larger circumference on outside than someone would if the ride was stopped

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

stay same - number of families, types of particles within each family change - masses & energies of particles

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

string coupling constant x 0 = 0 - dissapointing bc this means it can be any number, giving us no information about the value

In regards to a compact dimension, how is string motion different from a point-particle?

strings can wrap around entire dimension, points can only move back and forth

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

supergravity = supersymmetric quantum field theories that try to incorporate general relativity (10-D) - pertains to M-theory in that when you increase coupling constant of Type IIA string the physics (BPS states) has a low-energy approximation that IS 11-D supergravity

In what sense did supersymmetry find its beginning in string theory?

superstring theory predicts supersymmetry

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?

switch uniform vibration and winding energies

Being as precise as possible, according to string theory what determines properties of particles we see in our large extended dimensions? You may use the electron mass as an example.

the vibrations of strings determine electrons charge, mass, and force

Why can physicists not make precise calculations about the shape of compact dimensions?

they're hidden

For weak gravitational fields like earth, is spatial curvature or time curvature more important?

time because it's easier to detect

Why does string theory need extra dimensions to work?

to satisfy acceptable probability range (0-1)

What is a light clock?

two mirrors w bouncing photon

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

un train example

How does the string uniform motion energy depend on the radius of the compact space?

uniform energy is inverse to radius Euv = Nuv/R

How is the spin of a particle determined?

use a magnetic field to determine the spin of strings surrounding particles

In string theory what controls the number dimensions which are large and extended instead of being small and compact?

we don't know

Explain how it is possible to understand the answer to question # 1.

which one is # 1

How does the string winding energy depend on the radius of the compact space?

winding energy is proportionate to radius Ew = NwR

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

yes, jet planes with atomic clocks

Do we expect to be able to find superpartner particles experimentally? If so, when and where might they be discovered?

yes, within the year at the LHC