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Gravity
Lecture Focus Question
Terms in this set (226)
What forces are included in the standard model of particle physics?
ElectroMagnetic, Weak, Strong.
Name some of the particles in the standard model of particle physics. In the quantum field theories describing the standard model, what is the structure of these fundamental particles?
( ),/They are known as points.
What is the structure of the fundamental particles in string theory? How does string theory account for the differences between fundamental particle properties like the mass and charge of electrons and quarks?
The strings/By differences in vibration
In what sense does string theory simplify our view of fundamental particles?
There is one fundamental entity, which is the string.
What size is a string particle expected to be?
Planck's Size= 10^-33cm
What parameters in the standard model might string theory be able to explain?
Standard model has many unexplained parameters, such as the mass of fundamental particles. Particles in the standard model are points with no size.
When string theory was first discovered what was it used to explain?
It was used to try and explain the Strong Force. Turns out the strong force is described by quantum mechanics and became apart of the standard model.
In 1974 what did Schwarz and collaborators show the massless messenger particle of string theory could describe?
Showed that string theory can describe gravity. Massless particles that didn't seem to belong became graviton (the force particle for gravity).
What string theory success led to the 1st string theory revolution?
M. Greene and Schwarz showed that string theory is anomaly-free & Can unify all 4 forces.
What string theory success led to the 2nd string theory revolution?
M-Theory, which uses non-approximation techniques to show that there are 5 different string theories that were all related to each other
Lecture 23
...
Why does the string tension need to be so large?
Because the force of gravity is weak. String tension is inversely proportional to gravity. For gravity to be small, string tension must be large.
Name three consequences of a large string tension.
1. Makes string very small.PLanck's size= 10^-33cm
2.A lot of energy is needed to vibrate the string. High energy mass or energy scale of a string is large (Planck Mass of Planck Energy)
Mpl=10^19 GEV
Mproton=1GEV
3. Masses occur in integer multiples of the Planck Mass (Mpl)
Explain how a fundamental string can have mass.
Mass is proportional to energy & String energy is related to string vibration or frequency and amplitude
What is the natural mass scale for a string?
Mpl= 10^-19GEV
What needs to happen for a string to have a small or zero mass?
It turns out quantum mechanics gives rise to cancellations. It is easy to get 0 mass, but difficult to get small mass
Has string theory been able to predict the mass of a graviton? An electron?
String Theory predicts the massless graviton. Not an electron because they have small, unpredictable finite mass
Why are there an infinite number of massive expected string particles in integer multiples of the Planck mass?
Because of high tension. It can keep increasing as long as far as energy can increase.
What point is Brian Greene trying to make by introducing the art competition between Slim and Jim? Explain.
...
In particle physics experiments how are probes of small wavelength created?
They are put into accelerators
Using today's particle accelerators what length scale can be probed? How does this length compare with the Planck length? Will a manmade particle accelerator ever be able to probe the Planck length?
The World's best accelerator, The Large Hadron Collider (LHC) can only probe down to length=10^-21cm, whereas Plank's Length= 10^-33. No because It would take a colider the size of galaxy to create enrgy to see plank's scale. Strings can't probe Planck's scale. WHen we increase energy the string creates more passive particles, not smaller scales.
Why can a string not be used to probe sub-planck-length distances?
Because with strings as fundamental entity, we can't get to or below planck's scale, so it turns out that quantum foam is not as rough as we thought with particles as the fundamental entity.) Strings smooth the roughness of the quantum foam.
What is (are) the conflict(s) between general relativity and quantum mechanics?
General relativity requires smooth spacetime. QM suggests quantum foam
Brian Greene discusses two answers for how string theory resolves the conflict between general relativity and quantum mechanics. (Rough Answer & Why shouldn't we be satisfied with this)
We try to probe 10^-33 cm. For the small probe, we use large energy frequencies or small wavelengths. For string particles, to see 10^-33 cm, we need 10^19 GEV of energy. We need to increase the energy to excite the string, creating more massive particles, not smaller scale/length.
Conclusion: We can't probe the planck scale with strings or anything smaller. Therefore we don't worry about it. When the fundamental entity is a string, we can't get down below the planck scale. So the problem we thought we had was not a problem.
Brian Greene discusses two answers for how string theory resolves the conflict between general relativity and quantum mechanics.(Precise)
The quantum foam (with strings as the fundamental entity) is not as rough as we thought (with particles as the fundamental entity).
Strings smooth the roughness of the quantum foam.
What is the more precise answer for how string theory allows for a consistent theory of quantum gravity?
For point particles, the interaction point is a point.
For string particles, the interaction point is spread out.
The quantum foam is not as rough as we thought. Whereas string particles make a smoother quantum foam, the interaction point is not at one precise point.
The interaction point depends on your state of motion, due to the relativity of simultaneity.
or
1.QUantum foam (less rough)
2.Infinities in Quantum Gravity disappear.
Explain how two observers in relative motion can not agree on the interaction point of two strings?
The interaction point depends on your state of motion. This is due to the relativity of simultaneity.Because observers in different places don't see simultaneity.
Can two observers in relative motion agree on the interaction point for two point particles? Explain.
Observers in relative motion agree when 2 point particles interact with each other
What is the anti-particle of an electron called?
Positron (Identical in mass but has a positive charge)
In the past when physicists tried make a quantum field theory of non-point particles what problems did they encounter? Who were some of these physicists?
I Don't Know. Sorry.
25
...
What Does the super in Superstring refer to?
Supersymmetry
What are the known symmetries of space, time, and motion?
1. Spatial Symmetry- Does not depend on location (conservation of momentum)
2. Time Symmetry- Does not depend on when you do the experiment (Conservation of energy)
3. Motion Symmetry-
a.) The laws of physics are the velocity or are at rest, principle of relativity
b.) Can't tell the difference between acceleration and gravity, equivalence principle
What property of a particle determines if it is a boson or fermion? Give examples of both types of particles.
Fermion- particles with half integer spin
Boson- particles with integer spin
Electron, spin (½) (fermion) selectron, spin 0(boson)
Quark Spin ½ (fermion) Squark, Spin 0 (bosons)
ex. Higgs, spin 0
ex.photon, gluon, weake guage bosons, spin 1
How is the spin of a particle determined?
Spin is the particles(StringS) are spinning in a cirlce. To determine the spin you can use a magnetic field
Define supersymmetry
An idea physicists have come up with that for every particle in the standard model( both matter and force particles) there is a super partner with spin differing by one-half(½) unit of hbar of (hbar/2).
Name the superpartners of the particles in the standard model and their corresponding spin.
Electron spin ½, Fermion
Selectron spin 0, Boson
Quark, spin ½, Fermion
Squark, spin 0, Boson
Photon, spin 1, Fermion
Photino, spin ½, Fermion
Graviton, spin 2, Boson
Gravitino, spin ½, Fermion
Do we expect to be able to find superpartner particles experimentally? If so, when and where might they be discovered?
IDK
Name three reasons why we might expect supersymmetry to be a symmetry of nature?
1. "The math works"- Why wouldn't nature obey this last undiscovered symmetry available to her?
2. If all standard model and matter particles have superpartners the E&M, weak and strong magically unify at small distance or high energy.
3. Fine Tuning Problem: Without SUSY, physicists have to fine-tune their equations.
27
...
Name 3 reasons why we might expect supersymmetry to be a symmetry of nature?
IDK
Under what conditions do the strong, electromagnetic, and weak forces unify?
When all standard model force and matter particles have superpartners. And if they're at high energy or small distance.
Explain with a picture why the electromagnetic force gets stronger when probed at small distance or high energy?
IDK.Energy fluctuation "shield" the base charge of the electron at large distances, the electron charge strength is less.
At small distances, less shielding, stronger charge and stronger force.
What type of particles did the first string theory explain?
The string Theory Veneziano discovered only had bosonic vibrations or excitations.
Problems:
1. Can't describe Fermions( or matter particles
2. alas has Tachyons (particles moving faster than speed of light)
Why do string theorists no longer have to worry about the tachyon particle traveling faster than the speed of light?
Five new SUSY theories were discovered, none of which had tachyons.
THese theories also need 10 spacetime dimensions.
In what sense did supersymmetry find its beginning in string theory?
...
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?
1. I
2. IIA
3. IIB
4. HO
5. HE
. What did you like most about the video on compact dimensions?
...
Why does the EM force increase with strength at smaller distances at higher energy.
Energy fluctuation "shield" the base charge of the electron at large distances, the electron charge strength is less.
At small distances, less shielding, stronger charge and stronger force.
Lecture 1&2
...
1. What are the goals of string theory? (In class we discussed three related goals)
To resolve the conflict of quantum mechanics and general relativity.
To unify the 4 forces: weak, strong, electromagnetic and gravity.
To explain the Fundamental Theory of Physics.
2. What are the four known fundamental forces of nature? Give an example of each.
Gravitational- an apple falling towards the Earth
Electromagnetic- the touch of a hand, compass, a balloon on the hair, radio, visible light, TV, electromagnetic waves.
Weak- radioactive decay (neutrons, muons)
Strong- Holds quarks together to make neutrons and protons. Holds nucleus together. Nuclear decay results from strong force.
3. In string theory what ARE fundamental particles such as electrons and photons?
Strings vibrating in different patterns.
4. How does string theory force us to think differently about space?
It makes us see things in different dimensions.
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?
The conflict between general relativity (galaxies, universe, structures) and quantum mechanics (single scales, atoms, particles, molecules).
When you make a quantum theory of gravity, you get nonsense, which is infinity, which means that something is wrong.
6. Is string theory accepted?
Yes, by those who work on it.
No, because it has failed to make a testable prediction.
7. What is the reductionist viewpoint?
If you understand fundamental particles, you understand all forces and interactions that make up all matter; therefore we know everything.
Physics 111 Lecture 3 and 4 Focus
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1. According to James Clerk Maxwell, what is light?
Electromagnetic radiation as vibrating and magnetic fields.
2. What precedence is there in physics for unification of forces?
Maxwell unified with equations the electric and magnetic forces to create the electromagnetic force to describe light.
3. What two ideas (postulates) form the foundation for Einstein's special theory of relativity?
The speed of light is constant, regardless of motion or speed relative to light.
Laws of Physics are the same for all observers moving at constant velocity or at rest. NOT WHEN ACCELERATING. Also called the principle of relativity.
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?
Refer to notes for image. It's paradoxical because light always moves the speed of light, relative to anything.
5. What is meant by the principle of relativity?
Laws of physics are the same for all observers moving at constant velocity or at rest.
6. State three observations about space and time that can be made by observers moving relative to each other.
Time Dilation- Moving clocks run slow relative to an identical clock at rest.
Lorentz Contraction- Moving length shortens/contracts relative to an identical meter stick at rest.
Relativity of Simultaneity- A simultaneous event at rest is not simultaneous for a moving observer.
7. Into what particles does a muon decay? What force plays a role in muon decay?
A muon decays into an electron and two neutrinos through weak force.
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?
Muon at rest has a lifespan of 2 x 10^-6 seconds.
For us on Earth, the lifetime is 10x lifetime of the muon at rest. 2 x 10^-5.
From the muon's perspective, it is at rest. The Earth is rushing up towards the muon. The Earth muon distance moves fast and contracts to 600 meters.
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?
Through Lorentz Contraction, which says that a moving length shortens/contracts relative to an identical meter stick at rest.
10. Give an example demonstrating the relativity of simultaneity.
EX. Einstein's Train, train moves toward "B", the lightning goes off. Person sees lighting at "B" before "A". However an outsider's standpoint shows that the lighting hit both points at the same time.
Physics 111 Lecture 5 Focus
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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.
Einstein's train. Because the distance to "B" is less, the simultaneous event is not simultaneous for a moving observer.
2. What is a light clock?
A light clock measures a photon moving between two mirrors. One tick of the light clock is the photon moving once, back and forth between the two mirrors.
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?
What happens to a light clock also happens to a Rolex watch. When we put the light clock into motion, we can actually see light having to travel a longer path. Basically we see time dilation. It travels a longer path and takes a longer time. Because the distance changes. d=c∆t
4. How can we know that conclusions we reach about a light clock also apply to a Rolex watch?
Due to the principle of relativity, which at states that we can't tell what's moving and the experiment of the Rolex attached to the clock.
They both slow down, whatever happens to a light clock happens to a Rolex watch.
5. Using a light clock, clearly state the argument for why time slows for moving clocks relative to stationary observers.
Because it has a further distance to travel.
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.
We can easily see time slowing down because we can see that the distance changes.
The speed of light is constant. If the distance is bigger, the time takes longer.
7. Using the fact that time slows for moving clocks, explain how we can understand moving objects shortening relative to stationary observers.
Because the moving object still covers the same amount of distance, but to the stationary observer their clock is moving slower so they cover that same space in less time because their clock isn't ticking as fast?????????
Physics 111 Lecture 7 Focus
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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?
They will view each other's time as slowing down.
2. Explain how it is possible to understand the answer to question #1.
Time slows down when one moves relative to speed of light. The traveling twin accelerates, which makes time go by slower for him.
Acceleration: Time slows down
10 hours go by on the clock of the person at rest, while only 1 goes by on Br. Bob, who travels in space. When Dr. Bob says it's 1:00, its 10 pm.
Light doesn't travel instantaneously.
3. What is the twin paradox?
Two twins, one on Earth and one in space. Upon return, the traveling twin is younger than the twin on Earth.
4. Has something similar to the twin paradox been confirmed experimentally? Explain.
Yes, two jets with atomic clocks have proven this.
5. From whose perspective can one easily explain the twin paradox? Explain.
From Gracie's perspective on Earth.
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.
Einstein says, "All objects in the universe are traveling through spacetime at the speed of light."
Physics 111 Lecture 8 Focus
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2. Name two technological applications of Einstein's famous equation, E=mc2.
Diablo Canyon Nuclear Power Plant
Nuclear Weapons
3. In what sense did Newton unify the heavens and earth with his theory of gravity?
Mass creates the gravitational field and force.
This theory predicts almost all motions of the planets and what's needed to get to the moon, unifying the heavens with the Earth.
The moon and the apple both fall towards the Earth.
4. What is the conflict between Newton's theory of gravity and Einstein's theory of special relativity?
Newton's gravity acts instantaneously, which means it goes the speed of light.
Einstein's theory says that nothing goes faster than the speed of light.
5. In the video we saw, what example was used to depict the conflict in question 4?
If the sun disappears, it takes about 8 minutes for darkness to reach us.
6. How does Einstein's general theory of relativity resolve the conflict in question 4?
Einstein showed that mass warps space and time, which influences how matter moves.
Physics 111 Lecture 9 Focus
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1. Newton was embarrassed by what aspect of his theory of gravity?
He couldn't explain gravity and it wasn't as instantaneous as he thought
2. Explain in one concise sentence the essence of Einstein's general theory of relativity.
Matter warps spacetime, and warped spacetime influences how matter moves.
3. What was Einstein's happy thought and why did it make him happy?
"A freely falling person does not feel their own weight"
This is due to the fact that one can't tell the difference between acceleration and gravity.
4. What is the equivalence principle? Explain with the aid of a picture.
The equivalence between gravity and acceleration.
.
Acceleration warps space and time, so gravity must also warp space and time.
The picture shows equivalence, by showing you can't tell the difference between gravity and acceleration
5. Starting with the equivalence principle, explain the logical connections allowing Einstein to discovery the general theory of relativity.
"The Happy Thought", which tells us that we can't tell the difference between gravity and acceleration.
Shows acceleration warps spacetime, which shows that gravity also warps spacetime.
6. Using the tornado ride as an example, clearly explain how space is warped (or curved).
Using special relativity:
Slim, on the outside of the tornado measures a larger circumference due to his contracting ruler (Lorentz Contraction), whereas Jim measures radius with a non-contracted ruler. His motion and ruler is perpendicular to velocity. Jim measures the same radius as someone would off the ride.
This shows that space is warped because Euclidian geometry is neglected. Circumference is actually greater than 2r.
7. If the tornado ride were in deep space far from gravitating objects, in what sense would the ride mimic gravity experienced on earth?
At the center there is no gravity, further and further out on the ride shows no gravity.
8. As Slim stands still on the outside edge of the tornado ride moving at constant speed, why is he accelerating?
Because the velocity is constantly changing direction.
Physics 111 Lecture 10 Focus
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1. Starting with the equivalence principle, explain the logical connections allowing Einstein to discovery the general theory of relativity.
a) "Happy thought", the equivalence principle
We can't tell the difference between gravity and acceleration.
b) Shows acceleration warps spacetime, which also means that gravity warps spacetime.
2. Is the geometry you learned in high school obeyed on the tornado ride? Explain.
No, because it isn't Euclidean geometry. The circumference > 2r.
3. Using the tornado ride as an example, explain how acceleration leads to warping of time.
Time is also warped on the tornado ride. For someone off the ride, Slim's clock is running slow. Moving clocks run slow. Therefore an accelerating clock runs slow.
The clock at the center is at rest and would show the same time as a clock off the ride at rest.
Acceleration warps space and time therefore gravity must also warp space and time.
The warping of time is due to the fact that there is time dilation from special relativity.
4. Name three problems with figure 3.5?
It only shows space curvature and not time curvature.
Only shows space warping in 2-D.
Looks like an external object is pulling down the sun.
5. For weak gravitational fields like the earth, is spatial curvature or time curvature more important?
For weak gravitational fields like Earth, time curvature is easier to detect, thereby making it more important.
6. How does the flow of time on earth compare to an identical clock 6,000 miles above the surface? How do we know?
Time goes faster for the clock 6k miles in the air. The accelerated clock slows down, which means that time goes slower for the atomic clock on Earth.
Less gravity=Less Acceleration=Time runs faster.
Physics 111 Lecture 11 Focus
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1. Name two early confirmations of Einstein's general theory of relativity.
Precession of Mercury's elliptical orbit at a rate of ⅙ per century.
1919- Masters the bending of light by the sun's gravitational field.
2. Explain using the equivalence principle and a picture why light bends in a gravitational field.
...
3. What makes a black hole black?
The Schwarzschild Radius marks the boundary for where light can escape and where light can't escape.
The gravity of the black hole is so strong that light can't escape.
4. Where in the universe do physicists and astronomers have strong evidence to suggest the existence of black holes? What is the evidence?
Massive stars in the late stage of life (After they go supernova, explode)
Black holes in the center of galaxies.
5. What is Einstein's biggest blunder?
Einstein's equations naturally predict expanding universe.
He later introduced a "cosmological constant" to make universe constant/stat.
Found out later that it was true.
Physics 111 Lecture 13 and 14 Focus
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1. Einstein spent his life trying to unify which forces of nature?
To Unify Gravity and Electromagnetism.
2. Name some of the interesting phenomena found in the quantum cafe (video) or in H-bar (text).
a) Disappearing and reappearing in another place
b) Ice cubes rattling and shooting through glass.
c) Asked for OJ, got something else
d) Parallel universes
3. Name four primary characteristics of quantum mechanics.
1. Quanta (i.e. photons and gluons as force quanta, quarks and electrons as particle quanta)
2. Wave/Particle Duality- Everything at the microscopic level has wave and particle characteristics.
3. Probability- Can't predict a definite outcome. A quantum state is a superposition of many possible states in many universes.
4. Uncertainty- There are 2 uncertainty principles.
4. Given the crazy ideas coming from quantum mechanics why should we believe it?
1. Because we didn't believe other things in the past that we have found to be true.
2. There were almost 100 years that went by where no experiment has contradicted it.
5. What is blackbody radiation?
Any object with temperature radiates photons (particles) or electromagneticicity (wave).
Cooler objects radiate less. Warmer objects radiate more and is more white.
6. What happens when you try to explain blackbody radiation with classical physics?
If we use Maxwell's theory of light and calculate the energy from a warm object, you get infinity.
7. Name four characteristics of a wave?
Frequency- # of cycles per second (back and forth)
Amplitude- height of the wave
Period- Time to go peak to peak
Wavelength- Length of a wave
8. How are wavelength and frequency related for light waves?
They are inversely related.
Larger frequency is shorter wavelength.
Shorter frequency is longer wavelength.
9. What did Plack have to assume to properly predict blackbody radiation?
Light is quantized with energy coming in quanta.
Energy quanta is proportional to frequency.
Physics 111 Lecture 15 Focus
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1. In the quantum mechanical explanation of blackbody radiation why can't very high-energy photons contribute to the radiated energy?
High energy photons don't have enough
2. In the analogy between blackbody radiation and the warehouse landlord, what physics concepts correspond to people, coins, temperature, furnace setting payment, and money?
Infinite people- Oscillator (possible vibrations from atoms and electrons)
Furnace temp- Temperature
Payment- Energy radiated
Coins/Bills- Quanta of energy is proportional to frequency
Money- Energy
3. What is the photoelectric effect?
There is a minimum energy threshold for light to liberate electrons from the metal.
4. Who was the first person to properly explain the photoelectric effect?
Einstein
5. What do you have to assume to properly explain the photoelectric effect?
Money thrown to kids- incoming light
children-electrons
kids to get out, need 85 cents- the amount of energy for electrons to come off metal
parents throw down 100 pennies- quanta energy is too small to liberate the electron
kids fight- not enough to get down
throw down one dollar, kids get out with change to spare- electron has enough energy to liberate and wiz away with some energy.
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?
Each electron leaves the surface with the same energy---and hence the same speed, regardless of total intensity of impinging light.
7. Explain the result in question 6. using quantum physics.
97-108
Lecture 16
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1. What pattern do you observe on the detection screen when a high intensity light source illuminates a double slit apparatus?
You observe an interface pattern, which is a dotted line wherein some spots are brighter than others.
This is a result from waves combining together, constructive and destructive, thereby canceling each other out.
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?
...
3. How do you explain the results in questions 2. above according to Schrodinger?
Schrodinger: The particle has equal probability to go through each slot. (particle is in both places at once.)
4. What happens when you repeat the experiments in questions 1. and 2. using electrons instead of photons?
Electrons, like photons, display the double slit results.
5. How do you explain the results in questions 2. above according to Feynman?
Feynman: particles take all possible paths simultaneously (i.e. goes through both slits or know both slits are open giving an interference pattern.)
6. What is Louis de Broglie's contribution to physics?
Introduced the idea of matter waves. Thinking: e=mc^2 .
E 𝝰 frequency(f) 𝝰 1/⋋ 𝝰 m
h= Planck's Constant E=hf h^--=h/2ℿ( )<---r?
7. Why can we not see the wavelength of a baseball flying through the air?
Planck's constant if very small thus small wavelengths arise. The baseball wavelength are too small for us to see.
...
8. Why does Stephen Hawking say, Einstein was confused, not the quantum theory?
He says this because quantum theory was proved over and over again in experiments.
Lecture 16 Note: If you observe which slot the particle goes through the interference pattern disappears. (behavior-like a classical particle.) The active observing changes the outcome of the experiment. The observer influences the outcome of the experiment.(or reality)
...
Lecture 17
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1. Explain how you can understand the four big concepts in quantum mechanics using the double slit experiment?
...
2. What are the two Heisenberg uncertainty relations we discussed in class?
1. It involves position and momentum (or velocity)
2. Energy and Time
Position-Momentum Uncertainty Relation: You cannot know precise position and momentum simultaneously. The more precisely you know position, momentum becomes more uncertain and vice versa.
3. Why is the Heisenberg uncertainty relation not relevant for our everyday world?
Uncertainty in position and momentum numbers are always larger than h bar/2.
4. If I wanted to detect something with a size of 1cm what wavelength of light would I need to use? Explain.
1 cm or less. We see things with wavelength 400-700 nm (or 4 x 10^-7 m to 7 x 10^-7 m)
Larger wavelengths bend around the small object. Therefore you can't detect it with high precision.
Smaller wavelength allows one to detect with higher precision.
5. Why can't I measure the position of a particle to high precision with long wavelength light?
Objects can borrow energy from nothing to go through the barrier as long as you only use it for a short amount of time. This is derived from Heisenberg's Uncertainty Principle.
6. What happens to the velocity (or momentum) of a particle when you use short wavelength light to detect its position?
Higher energy photons with smaller wavelength
High energy photons change the momentum or velocity of the particle you want to detect.
This increases the momentum uncertainty.
7. Explain quantum tunneling.
To tunnel through an energy barrier that classically can't be penetrated, a particle borrows energy from nothingness for a short amount of time, consistent with the energy time uncertainty. Once through the barrier, energy is returned.
8. In the quantum cafe, why are the ice cubes rattling around in the glasses?
It's quantum weirdness at the microscopic level.
Lecture 18 & 19
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1. Explain in words the key features of a quantum field theory (Q.F.T.).
Quantum field theories incorporate the ideas from quantum mechanics, special relativity and force fields. The first QFT described the electromagnetic force and was called quantum electrodynamics.
chromodynamics
2. How does the force in quantum electrodynamics (Q.E.D.) work?
For QED, the force meditating (or messenger) particle is the photon.
3. Are infinities encountered in Q.E.D.? Are they controllable? Why?
They are controllable. The calculations produce infinite answers, but the infinities are controllable.
4. Give an example of the precision of Q.E.D.
One technique to handle infinities was determined, precise predictions for many types of particle interactions could be made.
For example, anomalous magnetic movement of the electron.
From QED Ae Theory= 0.001159652154(24)
From the Lab Ae experiment = 0.001159652188(43)
5. In what sense is quantum chromodynamics (Q.C.D.) like Q.E.D.?
...
6. What is quantum electroweak theory and why is it important?
It led to the unification of the weak force with the electromagnetic force.
7. What is the standard model of particle physics?
Strong, electromagnetic and weak. Not gravity.
8. What happens when calculations are made in a quantum field theory of gravity?
They don't work. They give infinities in answers.
9. What happens to spacetime at small space and time scales? How small is small?
The quantum foam shows particles being created out of nothing for a short amount of time.
Lecture 28
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1. Why does string theory need extra dimensions to work?
With any dimensions outside of 10, the probabilities just don't add up.
To create an acceptable range of probability 0-1.
2. How many space and time dimensions are in the original string theory?
There are 9 space and 1 time dimensions in the original string theory.
3. How many space and time dimensions are in M-theory?
11 dimensions
10 space, 1 time
4. Does string theory say it is impossible to have more than one time dimension?
No it's possible, but it is simpler to consider only 1.
5. Where are the extra dimensions we don't see?
We can't see Calabi Yau dimensions. There are six.
6. 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?
His idea was that you could unify E&M with gravity with one extra dimension. His theory wasn't accepted, but later was.
7. Why can't you move past somebody if you are a being in lineland?
Because everything is in 1 dimension.
8. If a very small compact dimension were to grow in lineland and become visible, what type of surface would you have?
A tube or a ribbon.
9. In string theory what controls the number dimensions which are large and extended instead of being small and compact?
We don't know
Lecture 29
...
1. What space(s) with compact dimensions and large extended dimension(s) can we properly visualize with a drawing?
A garden hose.
2. How many spatial dimensions are being represented in figures 8.4, 8.7, 8.8, 8.9, and 8.10?
8.4(circles)
2 large, 1 small
8.7(sphere)
2 large, 2 small
8.8
2 large, 2 small
8.9
6 small
8.10 (Calabi-Yau)
2 large, 6 small
3. 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 properties we see are due to vibrations from the strings.
The vibration of the electron predicts it's mass.
4. 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?
Original-9 space, 1 time.
Calabi-Yau shapes meet the stringent requirements of string theory.
5. 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.
The calabi-yau space has 3 holes which produces three families of particles. It is not unique, it can be distorted in many ways because it can have many different numbers of holes.
Lecture 30
...
1. Which of the force particles in nature depend on the shape of the compact dimensions and which don't?
All the force particles except the graviton.
2. What does Witten mean when he says that string theory predicts gravity?
Gravity is a robust feature of string theory. If we hadn't already discovered gravity, string theory could have predicted it.
3. Why can physicists not make precise calculations about the shape of compact dimensions?
Physicists have been using approximate calculations which cannot yield precise answers about compact dimensions.
4. If supersymmetry is discovered at the Large Hadron Collider, will string theory be validated? Explain.
Supersymmetry is a fundamental element of string theory. Therefore yes, it will validate superstring theory. But it won't prove superstring theory because there are other theories that have point particles in them.
5. If supersymmetry is not discovered at the Large Hadron Collider, will string theory be proven wrong? Explain.
No, we can amp up the energy at the LHC, meaning we still have the possibility of finding supersymmetry.
6. Name three possible scenarios for which string theory could be validated.
1.) Ed Witten says a string from early universe could get so large we can see it with a telescope.
2.) A fifth force is discovered.
3.) Discovering a particle with an electric charge of 1/7.
Lecture 31
...
1. What is the difference between Riemannian geometry and Quantum geometry? For our universe, at what length scales is each geometry important?
Riemann Geometry: Geometry of smoothly curving surfaces in Einstein's General theory of relativity.
This works for scales much larger than the Planck scale. It is also based on points.
Quantum Geometry: Describes the geometry of space near/at the Planck's scale. Based on strings.
2. In regards to a compact dimension, how is string motion different from a point-particle?
Strings and points can move in compact dimensions or large extended dimensions.
Unlike points, strings can wrap around compact spaces. This gives a new type of energy due to winding.
3. How does the string winding energy depend on the radius of the compact space?
Ewinding=NR
N= # of winds
R= radius of the compact space
4. How does the string uniform motion energy depend on the radius of the compact space?
Eu.v.= Nu.v./R
Nu.v.=Uniform Vibration number
R=radius of compact dimensions
5. What are the two types of vibrational energies associated with a string? Briefly explain what each energy corresponds to?
1. Ordinary vibration energy
Physical vibration of the string
2. Uniform (motion) vibration energy: due to motion
Also applies to point particles.
6. 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?
...
Lecture 33
...
1. What are two consequences of quantum geometry?
1. Smallest a dimension can be is the Planck size.
2. There are two ways to measure distance. Which are the two notions of distance, using the winding probe or the uniform vibration probe.
3. Duality
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?
You have to decide what probe to use.
If you use the natural choice, the low energy probe. R=1/10 use winding vibration energy probe to measure the larger size to be R=10
If you use the low energy probe, you'll always measure a size larger than Planck's size.
If you use the high energy probe, you'd only be able to measure the small radius, a size less than the Planck's size.
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?
If you interchange the two, you get the same total energy.
4. What do we mean by duality in string theory? Give an example.
You can't tell the difference between the two physics of the two different spaces.
Examples:
1. The mirror symmetry.
2. Type IIB
3. Strong-Weak Coupling
You can between the way the two spaces are compactified.
5. When R is large what are the heavy probes and light probes? Why?
Winding probe is massive and heavy whereas the uniform vibration probe is light.
It depends on whether R>1 or R<1.
Winding is proportional to R,
Uniform vibration is inversely proportional to 1/R.
6. When R is small what are the light probes and heavy probes? Why?
Winding is light and uniform vibration is heavy.
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 low mass, low energy probe must be used for large distances. This is the natural choice because it's the easy thing to do.
Lecture 34
...
1. Name a physicist who worked on orbifolding.
Greene.
2. What is orbifolding?
Taking a Calabi-Yau space and creating a new, distinct C-Y space.
3. What do we mean by an even or odd-dimensional hole?
Even: a hole in an even number figure (hole in paper)
Odd: holders going through odd dimensions (hole in table)
4. Does the number of particle families depend on the number of even-dimensional holes or odd-dimensional holes? Explain
The number of families only depends on the number of holes. If there are 3 holes in an even or odd dimensional space, they are dual to each other, therefore they yield the same physics.
5. What is mirror symmetry in string theory? Why is it important to mathematicians and string theorists? Give an example.
Calculations in dual space apply to Calabi Yau space. If both yield the same physics, if the math is hard in one calabi yau space, it is the same in its dual.
Lecture 35
...
1. Can space tear in Einstein's general theory of relativity? Explain.
.
No. GR says space can't tear.
String theory says space can tear
2. If you wanted to create a wormhole to travel between your house and Cal Poly what would you need to do to space?
You would need to tear space as the first step.
Einstein's equations allow for wormholes, but you'd have to be there already.
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?
If you do it in the dual space, the physics is identical. We can't directly compare it because the math is too hard.
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?
Nothing dramatic happens during the dual description.
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. Determining the correct Calabi-Yau space.
2. Difficult to calculate masses of particles in mirror symmetry.
6. What was Witten's insight into the space-tearing flop transition?
He yielded an insight into why the space trying transition is allowed by showing that the word sheet of a string can protect the tearing space.
7. What physical properties stay the same and which ones change in a space-tearing flop transition?
Only masses of particles are altered by space-tearing. Other properties like charge force, or number of families remain the same.
8. Can large spatial dimensions tear? Explain why we believe this to be true or not.
Yes. Because size doesn't matter. Space is space.
Physics 111 Lecture 36 Focus
...
1. What is the tool used by physicists to understand the approximate equations of string theory?
Perturbation theory
2. What is the physical significance of the string coupling constant?
It can be anything.
Weak coupling means that the string coupling constant is less than 1.
Strong coupling means that the string coupling is greater than 1.
It determines the strength of the interaction.
3. For what values of the string coupling constant does perturbation theory work? Explain why.
Weak coupling, when string coupling constant is less than 1.
Each term has more interactions. When the terms are added up, the total number is more precise.
4. When string theorists try to calculate the string coupling constant what do they find?
String coupling x 0 = 0
Which tells us that string coupling could be ANYTHING.
5. What point does Greene make by introducing the word syzygy?
Supersymmetry gets us to understand these BPS states, which have 3 defining characteristics.
It's the shortest word in the dictionary to give us 3 y's, which represents a charge 3
Shortest word represents minimal mask.
The supersymmetry represents the english dictionary.
This goes to show BPS states are highly constrained. That's what makes them special.
6. In what sense are B.P.S. states non-perturbative?
Beyond perturbation theory. In addition to being highly constrained, their properties don't depend on string coupling strength.
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?
Looking at both BPS states, they have the same BPS states. It indicates that the physics is the same so they are Strong-Weak dual.
Lecture 37
...
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-theory Witten discovered. What is (are) the shape(s) of the extra dimension that emerges?
Heterontic-E at strong coupling leads to M-theory by the string growing an extra dimension to become like a ribbon. A similar thing happens to type-2 theory. The string grows to become like an inner tube.
2. If the string coupling constant is small (less than 1), how many dimensions does string theory or M-theory have?
String theory has 10 dimensions.
The coupling causes 11 in M-Theory.
3. Explain the types of dualities depicted in figure 12.10 and give an example of each type.
Heterotic-O and Heterotic-E were shown to be dual using the R and 1/R duality when the winding numbers are uniform vibration numbers are interchanged. Likewise for Type IIA and Type IIB.
4. What is supergravity and how is it related to M-theory?
Supergravity is a point particle theory of supersymmetric gravity in 11 dimensions.
M-theory at low energy is the same and dual to 11D symmetry.
5. Why do some people say the 'M' in M-theory refers to membrane?
No one knows. Someone thinks it's a
'M' for magic, mystery, murky, matrix, membrane, mother
Upside down 'W' for Witten.
6. In light of M-theory developments in what sense are strings still special?
Strings are special in M-Theory because when the string coupling is weak. Strings are the lightest or slowest energy objects.
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