JPU200Y - Final Exam
May, 2000
Answers, Marking
Scheme and Results
SHORT ANSWER (60 points total)
Who marks what?
Question 1 will almost certainly take the longest to mark. Also,
Arno assisted in invigilating the test so gets the lightest marking
load. |
Suresh |
1,2,3,4,5 |
Ele |
6,7,8,9,10,11 |
Arno |
12, 13, 14, 15 |
David |
Long Answer |
Each question is worth 4 points.
Questions 1 and 2 refer to the following figure and
explanation. |
|
Although not drawn to scale, we assume that relative to the
Earth, the Planet of the Apes and Alpha Centauri are the same distance of 4.35
light years away but in opposite directions. Assume that the Planet of the Apes
and Alpha Centauri are both at rest relative to the Earth. Assume that the
theories of relativity are correct.
Sue and Lou are twins, born at the same time and therefore are the
same age. Sue blasts off for Alpha Centauri at one-half the speed of light
relative to us on Earth. When she arrives at Alpha Centauri she lands on one of
its planets for a rest. Lou stays on Earth for ten years. He then radios Sue
that he is going to go to the Planet of the Apes, and invites Sue to join him.
He blasts off for the Planet of the Apes at half the speed of light relative to
us on Earth; when he arrives at the Planet of the Apes he lands. When Sue
receives Lou's invitation she blasts off for the Planet of the Apes at half the
speed of light relative to us on Earth; when she arrives at the Planet of the
Apes she lands, and has a nice reunion with her brother Lou. |
- Draw a spacetime diagram relative to us on the Earth including Sue's
worldline for her trip to Alpha Centauri, resting on a planet of Alpha
Centauri, and then travelling to and landing on the Planet of the Apes. Include
the worldline of Lou waiting on Earth and then travelling to and landing on the
Planet of the Apes. Include the worldline of Lou's radio message to Sue
inviting her to join him. Be sure to clearly label the axes and
worldlines.
Sue and Lou's worldlines not clearly for speeds < c: -1
point
Signal from Lou to Sue not clearly at the speed of light: -1
point
- When they rejoin on the Planet of the Apes, which twin is younger?
Describe how you arrived at this answer.
Sue is the younger twin.
Correct answer: 2 marks only
Any
correct explanation: +2 marks. One hopefully popular answer will be "Because
Sue's worldline is longer than Lou's."
- A common form of the Second Law of Thermodynamics is: Heat never
spontaneously flows from a colder body to a hotter body. However, this
common form is not quite correct. What is wrong with it?
The word "never" should be replaced by "almost never", "usually"
or similar.
Answering that the term "closed system" is misssing: 2 marks
only since it is implied by the word "spontaneously."
- For a black hole, the curvature of spacetime at the event horizon is
so intense that not even light from inside the horizon can escape to outside
the horizon. And yet Hawking and Bekenstein predict that black holes do radiate
away their energy. What mechanism, believed to occur everywhere in the world
all the time including just outside the event horizon, explains how a black
hole can radiate energy?
Virtual pair production
"Pair production" only: 3 marks
only
"Virtual electron-positron production" only: 3 marks only
- The Feigenbaum number is irrational and has an approximate value of
4.6692016090.... What does the number describe? Three sentences maximum please.
It was originally discovered as the ratio of increases in the
free parameter of the logistic map for successive bifurcations just before the
onset of chaos.
Identifying that it has to do with chaos: 1
mark.
Identifying that is has to do with bifurcation: 1 mark.
Identifying
that the bifurcations are infinite: 1 mark.
-
All gases share the behavior that if a fixed quantity of the
gas at constant volume has its pressure and temperature varied, the data will
lie roughly on a straight line as shown. Further, if the line is extrapolated
back to zero pressure, the intercept of the line with the temperature axis
occurs at the same temperature value for all gases; the value of this
temperature is about -273.16 Celsius. What is this value of the temperature
called? |
|
Absolute zero
"Absolute temperature"only : 2
marks
-
Multiple Choice: Balmer's formula for the wavelengths of the
lines of the Hydrogen spectrum is shown to the right. Balmer came up with this
formula by:
- A: Applying the Schrödinger equation to the
Hydrogen atom.
- B: Working out the mathematics of vibrating organ
pipes and applying that mathematics to the spectrum.
- C: An exercise in pure numerology.
- D: Realising that electromagnetic theory requires
this equation.
The correct answer will be awarded four marks. Incorrect
answers will have one mark subtracted. Blank answers will be ignored. |
|
Answer is C: An exercise in pure numerology
- The planetary model of the atom has the electrons in orbit around the
nucleus just as the planets are in orbit around the sun. However, according to
classical physics this model is impossible. Why?
Because in this model the electrons are accelerating and
therefore radiate away energy, causing them to spiral into the
nucleus.
"Radiate away energy" only: 2 marks only
Failure to mention
acceleration or radiation: 3 marks only
Spiraling into nucleus without any
mechanism: 1 mark only
-
One arrangement of the Mach-Zehnder interferometer is shown to
the right. What percentage of the photons that leave the light source end up in
Detector 2? |
|
25%
Accept "1/4" for full marks also.
- We have stated that no signal, information, or influence travelling
faster than the speed of light and that connects two regions of spacetime, say
A and B, can be causal. By this we mean that we cannot
have some event at A cause an effect at B via such a superluminal connection.
Why is this so?
Because for any such superluminal signal two different inertial
observers will disagree on which direction the signal is travelling, so the
"cause" and "effect" cannot be distinguished.
A mention of locality was
worth 1 mark.
-
Electrons from an electron gun are passed though 10 successive
spin filters, where each filter is oriented at 90o relative to the
previous filter. What fraction of the electrons from the electron gun emerge
from the tenth filter? |
(1/2)10
"(1/2)9" : 3 marks only
"50%
of those that passed the ninth filter": 1 mark only
- Stapp has characterised one particular discovery as the most
important one in the entire history of science. David Harrison stated that he
agrees with Stapp. To what discovery is Stapp referring?
Bell's Theorem
"Bell's Inequality": 4 marks
- In our everyday life we believe that the following common sense
assumptions are true:
» There exists a reality separate from its
observation.
» No signal can travel faster than the speed of
light.
» Logic is a valid way to reason.
However, recent
experimental tests have given us further information on these assumptions. What
information have the experiments given us?
That one or more of the assumptions is wrong.
"One of the
assumptions is wrong": 2 marks only
"All of the assumptions are wrong": 1
mark only
- We have learned that a field, such as an electromagnetic field, has a
complementary particle aspect, which is the photon in this example. The force
that holds the atomic nucleus together is called the strong field. What is the
name of the complementary particle aspect of the strong field?
Meson or Pi Meson
- The standard view of Elementary Particle Physics is that stuff is
made of atoms, atoms are made of electrons and nuclei, nuclei are made of
protons and neutrons, and protons and neutrons are made of quarks. In this view
what are quarks made of?
Nothing
LONG ANSWER (40 Points Total)
Choose two of the topics below and write about them in the
supplied examination book. Be sure to clearly indicate which topic is being
discussed. Each topic will be marked out of 20 points.
Answers will not be marked on the basis of length. In fact, excessive
verbosity tends to make markers irritable. Illegibility has a similar negative
effect on markers.
Note: the notes following the questions below are only partially a
marking scheme. They are also some key points I looked for when marking the
questions.
- The direction of time's arrow distinguishes the past from the future.
What are some possible causes that could determine the direction of time's
arrow? Conclude by discussing any possible relationships between these
causes.
Thermodynamics, Expanding Universe and Consciousness. Naming and
describing: up to 9 marks.
Thermodynamics and Expanding Universe may be
connected via an analysis similarly to the Hawking-Bekenstein black hole
thermodynamics,
A speculation by David Harrison may connect Consciousness to
these.
- All chaotic systems share some universal properties. Name and
describe as many of these properties as you can. Conclude by discussing how the
word chaos used in describing these systems compares to our everyday use
of the same word.
Sensitive Dependence on Initial Conditions; trajectory
never repeats; transition preceded by infinite bifurcations; bifurcations
characterised by the Feigenbaum number; non-integer fractal dimensionality: up
to 10 marks.
Discussing Lyapunov plots, return maps, etc. a bonus of up to 2
marks.
- Heisenberg wrote about Schrödinger's formulation of Quantum
Mechanics: "The more I ponder the physical part of Schrðdinger's theory,
the more disgusting it appears to me." Schrödinger wrote about
Heisenberg's formulation of Quantum Mechanics: "If one has to stick to this
damned quantum jumping, then I regret ever having been involved in this thing."
Compare and contrast these two formulations of Quantum Mechanics. Conclude by
discussing how these two giants could have held such strong views when they
both knew that the two formulations are formally
identical.
Schrödinger: continuous wave function; Heisenberg:
discontinuous matrix purely in terms of observables: up to 12 marks
- Popular interpretations of Quantum Mechanics include the simple
probabilistic one of Born, the so-called Many-Worlds interpretation, and the
Copenhagen Interpretation. Briefly describe these three interpretations.
Conclude by discussing how, despite the well-known existence of these
interpretations, Nobel laureate Richard Feynman (and David Harrison) can claim
to not understand Quantum Mechanics.
Born: a wave function related to but
not equal to the probablility; represents partly a fact and partly our
knowledge of the fact: up to 4 marks.
Many Worlds: the "collapse" of the
wave function is actually a splitting of the universe; the collapse is really
an illusion; the totality is all these worlds: up to 4 marks.
Copenhagen:
from Complementarity; there is no quantum world, the observer and the observed
can not be separated: up to 4 marks.
- In exploring the idea of non-local hidden variables, David Bohm and
his school proposed that there are two ordering principles in the universe: the
everyday explicate one and a more unusual implicate one.
Describe, compare, and contrast these two orders and how they interact with
each other.
Explicate: space, time, parts make up the whole, causal,
things, describable: up to 6 marks.
Impliciate: holographic, whole makes up
the parts, acausal and non-local, interference between things and no-thing: up
to 6 marks.
The process is one of enfolding and unfolding between the
orders.
Some Results of the Exam
Short Answer
Mean: 62.4%. Standard Deviation: 20.5%. Quartiles: 50%, 63%, 80%.
Long Answer
The figure to the right shows boxplots of the results of the five
long answer questions.
Briefly, the "waist" of the box is the median, the "shoulders" and
"hips" are the first and third quartiles, and the "whiskers" extend to the
highest and lowest marks.
For all the long answer questions, the Mean was 49.35, the
Standard Deviation was 24.2%, and the Quartiles were 35%, 50%, 65% |
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Total Mark
The total "raw" exam marks had a Mean of 56.8%, Standard Deviation 19.8%
and Quartiles 46%, 57%, 72%. The marks were then re-scaled to U of T Marks with
the following breakpoints:
Raw Mark |
U of T Mark |
0 |
0 |
20 |
50 |
40 |
60 |
60 |
70 |
80 |
80 |
100 |
100 |
The total U of T exam marks had a Mean of 68.2%, Standard Deviation
12.2% and Quartiles 63%, 68%, 76%. The results by letter grade were:
Letter Grade |
Number |
Percent |
A |
11 |
14% |
B |
25 |
31% |
C |
30 |
38% |
D |
9 |
11% |
F |
4 |
5% |