FINAL  PRACTICE PROBLEMS / STUDY GUIDE for 201

(1)
A previously unknown manuscript by Einstein is discovered, in which by assuming only 
that the Higgs boson exists, he concludes that the universe must be supersymmetric.
John Bell's grandson reads this work, and stimulated by it, proves that if the Higgs boson
exists, quantum mechanics makes incorrect predictions.
Which of the following is/are valid conclusion(s) for us to draw?
a. The Higgs boson doesn't exist.
b. The universe is not supersymmetric.
c.  If neither Einstein nor John Bell III has made an error, then the Higgs boson doesn't exist.
d.  If neither Einstein nor John Bell III has made an error, then the universe is not supersymmetric.
e. If neither Einstein nor John Bell III has made an error, and if quantum mechanics is correct, then the Higgs boson doesn't exist.
f.  If neither Einstein nor John Bell III has made an error, and if quantum mechanics is correct, then the universe is not supersymmetric.

(1') 
The month after the events described in (1), CERN announces experimental evidence that
the universe is not supersymmetric.  Meanwhile, careful analysis of Einstein's and Bell III's proofs
shows without a doubt that they have not made any errors in their logic or calculations.
Which of the following (if any) is/are valid conclusion(s) for us to draw?
a.  The Higgs boson exists
b.  The Higgs boson does not exist
c.  Quantum mechanics makes incorrect predictions
d.  Quantum mechanics does not make incorrect predictions

(2)
I show you four odd playing cards marked with letters & numbers, and I tell you that every card with a "3" 
on one side has an "E" on the other.  I lay the four cards on the table, and you see an "E", a "D", a "3", and
a "5".  To be sure that I'm not lying to you, which of these cards must you turn over?

(3) 
What are the principal assumption and the principal conclusion of the EPR paper?

(4)
What are the principal assumptions & conclusions of Bell's Theorem?
What does this lead us to conclude about quantum mechanics?

(5)
What is the complementarity principle?

(6)
What about the Uncertainty Principle?

(7)
What controls the curvature of spacetime?

(8) 
What is the difference between Special Relativity and General Relativity?

(9)
What is the principle of equivalence?

(10)
Which of the following are relative and which are not, in the Special Theory of Relativity?
a. the velocity of an object
b. the length of a ruler
c. the duration of some process in time
d. which of two flashes of light reaches the CN Tower
e. which of two flashes of light occurs first
f.  which of two twins is older right now, if they are far apart
g. which of two twins is older right now, if they are at the same place

(11)
Which things would Galileo have called relative?
a. the position of an object
b. the velocity of an object
c. the acceleration of an object
d. the speed of a clock
e. the length of a ruler
f.  the mass of an object

(12)
Explain in a few sentences why quantum mechanics allows more communications security than classical mechanics.

(13)
Does the Bohm - de Broglie theory invoke hidden variables?

(14) 
Write a paragraph discussing whether Schrödinger's cat is any stranger than saying "I haven't been home in a while, 
so I don't really know if my cat is alive or dead?"

(15)
What do magnetic forces depend on which make them inconsistent with Galilean relativity?
a. charge
b. mass
c. velocity
d. acceleration
e. which way is North

(16)
You are riding in the center of a train.  In your reference frame, two lightning strikes occur simultaneously at the
front and the back of the train.  Which do you see first?

(17)
You are riding in the center of a train.  In the Earth's reference frame, two lightning strikes occur simultaneously
at the front and the back of the train.  Which do you see first?  Which do you believe happened first (i.e., in your
reference frame)?

(18)
You are riding at the back of the train.  In the Earth's reference frame, two lightning strikes occur simultaneously
at the front and the back of the train.  Which do you see first?  Which do you believe happened first?

(19)
Alice is riding on a train, and Bob is standing still on the ground as the train passes.
If two lightning strikes hit the Earth at the same time in Alice's frame but at different times in Bob's, which
observer is right?

(20) What is entropy?  (Explain in a few sentences)

(21) What was Eddington's observation and its significance?

(22) Why did Hulse & Taylor win a Nobel Prize for their observations of a binary pulsar system?

(23) In the famous twin paradox, which twin is older while they're moving? 

(24) Which twin is older when they get back?

(25) How does one "prove" a scientific theory?

(26) In the photoelectric effect, if shining light A on the metal produces lower-energy electrons than shining light B
does, and it also produces fewer electrons than light B, which of the following can we conclude?
a.  light A is redder than light B
b.  light A is bluer than light B
c.  light A is more intense than light B
d.  light A is less intense than light B
e. light A has more photons (hitting the metal in a given time) than light B
f.  light B has more photons (hitting the metal in a given time) than light A

(27) Explain the difference between Planck's and Einstein's quantum hypotheses

(28) What was de Broglie's hypothesis?

(29) Write a few sentences describing our evidence that light is a wave, followed by a few describing
our evidence that light is a particle.

(30) I send C60 molecules into a double-slit, carrying out an interference experiment.  I set up a camera 
so that it takes a picture of which slit each molecule goes through.  Will the interference pattern be observed if
a. I forget to turn the camera on
b. I forget to look at the picture on the camera
c. I delete the picture on the camera
d. I send millions of molecules through the slit at the same time, so that the camera sees lots of them coming
out of each slit but can't tell which one went which way.

(31) Why did Dirac fail to discover antimatter?

(32) Explain in a few sentences what is meant by the "Dirac sea".

(33) Explain what features chaotic systems have as far as determinism or predictability go.

(34) Give an example of a chaotic system.

(35) What is one problem a quantum computer is believed to be capable of solving more efficiently than a classical one?

(36) Explain in a sentence or two why a quantum computer might ever be expected to be more powerful than a classical one.

(37)  Wow does the assumption that electrons are waves rather than particles (so somehow "continuous" rather than "discrete") gibe with the feature that gives quantum mechanics its name, that the "allowable orbits" of the electron are discrete rather than continuous?

(38) What is meant by "collapse of the wave function"?

(39)  What is the answer to the paradox about the two ships accelerating uniformly (from the Earth's perspective),
connected by a taut rope?

(40) Draw the x (space) and t (time) axes according to a moving observer in Galilean ("everyday") relativity…

(41) Write an essay about the consequences of Einstein's insistence that time is what a clock measures and distance is what a ruler measures…

(42) We sometimes hear it said that QM seems to have randomness (not be deteministic).
Which of the following things does quantum mechanics predict with certainty and which does it predict only probabilistically,
assuming we know the quantum state (e.g., wave function) at this instant in time?
a.  The position of an electron at this instant
b.  The momentum of an electron at this instant
c.  The position of an electron five minutes from now
d.  The momentum of an electron five minutes from now
e.  The quantum state five minutes from now
f.   Whether or not a photon will be transmitted through a horizontal polarizer
g.  Whether or not if the photon makes it through one horizontal polarizer, it will make it through a second, subsequent
horizontal polarizer.

(43) What is a up quark?
a.  A somewhat heavier "version" of the electron
b.  A somewhat heavier "version" of the proton
c.  One of the components of a proton
d.  One of the components of an electron
e.  The antiparticle of a down quark

(44)  What are the mass and charge of a positron (anti-electron), relative to that of an electron?
a.  Same mass, bigger charge
b.  Bigger mass, same charge
c.  Opposite charge, same mass
d.  Same charge, opposite mass
e.  Same mass and same charge

(45) Who is the Québecois scientist who might well share in a Nobel Prize one day for his/her role in laying some of the foundations of Quantum Information in the 1980s?
a.  Charlie Bennett
b.  Gilles Brassard
c.  Chien-Shiung Wu
d.  Aephraim Steinberg
e.  Alain Aspect
f.   John Stewart Bell

[And of course you should review the questions from the midterm and the practice problems I suggested at the time,
along with all of the homework questions and any reading you may not have done sufficiently thoroughly earlier in the term.]

Good luck with your studying and all your exams!