Download Physics 120 Homework Set #1 (due Sunday

Physics 120 Reading Assignment #6
Due: Sunday 10 PM, March 5
Please insert your name where indicated in the upper right-hand corner of this page.
Expected length of answers is one paragraph for each question. Please explain your
answers so that they could be understood by another student. Please expand this word-file
and insert your answers in-place below.
Please feel free to discuss questions and concepts with other students from the class. This
is encouraged. However, when you sit down to answer the questions in the reading
assignment, you should submit your own answers.
Your completed homework assignments must be uploaded in assignments for this class
on Canvas by the specified due date and time in order to receive credit.
1) a) Explain how knowing “which way” information affects the outcome of the
Double Slit Experiment.
b) Explain briefly how a quantum eraser can “change” something that actually
“happened” in the past. (Use the Double Slit Experiment to explain your answer.)
a) The “which-way” information causes the interference pattern on the screen to
disappear and be replaced by two bright spots corresponding to the two slits. This
effect can be interpreted as a consequence of the Principle of Complementarity
whereby the wave aspect of a quantum object (wave interference) cannot be
observed at the same time that we measure a particle property (position).
b) In a quantum eraser experiment the “which-way” information is deleted. The
erasure must happen in well-controlled circumstances to work as a quantum eraser.
In particular, it has to restore the correlation between photons that went through
different slits, which is lost the moment that the “which-way” information is
collected. However, the erasure itself does not have to happen before the photons hit
the screen. The reading “Duality in Matter and Light” states that quantum erasure
is of extremely difficult realization and proposes a thought experiment. Quantum
erasure has been recently achieved in a number of experiments which usually
involve quantum entanglement (will be presented in the next class).
2) a) What is the primary difference between the Higgs Field and the
Electromagnetic Field?
b) If the Higgs Field had the same field strength as the Electromagnetic Field, what
would be the consequences for the W and Z bosons and the strength of the Weak
Interaction?
a) The Higgs field has a constant non-zero strength in vacuum, i.e. in the absence of
any source. On the contrary the strength of the Electromagnetic Field is zero in
vacuum and it needs a source (e.g. a charged particle) to assume a non-zero value.
b) If the Higgs field were zero in vacuum, the W and Z bosons would still acquire
some mass thanks to the confinement property of the strong interaction; however,
their masses would be much smaller compared to those that they have in our
universe. As a consequence, the Weak Interaction would have a longer range and
beta decays would happen at a much faster rate.
3) a) What is the effect of supersymmetry on the forces in the GUT era?
b) How does it affect their strengths?
At low interaction energy the strong, weak and electromagnetic forces have very
different strengths. In the Standard Model, when extrapolated to very high
interaction energy the strengths of the force get much closer but they do not
converge exactly at the same point together. Supersymmetry allows for a perfect
matching of the strengths of the strong, weak and electromagnetic force at very high
energy, or when the Universe was very hot in the GUT era. This makes it more
plausible that the forces were unified in the early universe.
4) What is the hierarchy problem? Give three of the various ways that have been
proposed to resolve it and explain how each would “do the job.”
The hierarchy problem arises when considering the quantum corrections to the
Higgs mass due to other particles. These corrections have generally the effect of
increasing the Higgs mass, however we observe a very light Higgs boson, leading to
the hierarchy problem.
i) One possible solution is to assume a precise cancellation between different
quantum corrections. This solution is not preferred by most physicists because
stated like this, it does not provide any deeper principle or symmetry that explains
why this precise cancellation happens.
ii) Supersymmetry can resolve the hierarchy problem in a more elegant way by
introducing a new symmetry in particle physics: each particle has a superpartner
with the exact same mass. Supersymmetry is spontaneously broken, leading to
different masses between partner particles. If these mass differences are not too
large, they could explain the cancellation of the quantum corrections to the Higgs
mass.
iii) Technicolor assumes that the Higgs is not an elementary particle, so the
hierarchy problem does not exist anymore since the mass of the Higgs would not be
a fundamental constant anymore.
iv) Extra dimensions can also solve the hierarchy problem. If we assume that extra
dimensions exist, the strengths of the forces (and the masses of the particles) may
partially be “hidden” in the extra dimensions.
5) What’s different about laser light compared to a regular flashlight? How do
lasers get such an intense beam of light? Explain how it is possible to have different
colors of laser light?
Laser light is monochromatic (single wavelength), coherent (emitted photons are in
phase with each other) and directional (tight, strong and concentrated beam). These
properties do not generally apply to a flash light that usually emits diffuse light in a
broad wavelength spectrum, with photons that are not in phase with each other.
The color of the laser light depends on the medium (i.e. the atoms) used to generate
the light. A sample of atoms or molecules of the same kind is “pumped” to a high
degree of population inversion where most atoms are in an excited state. Light is
produced via stimulated emission by excited atoms going to the ground state (or a
less excited state). The energy difference between the excited state and the lower
state determines the wavelength of the emitted photon. Therefore, by using different
atoms with different energy levels one can obtain photons with different
wavelengths, i.e. different colors.
6) a) What role does the laser play in the storage of data on CD, DVD, Blu-Ray
disks?
b) Which of these devices would you select over the other two to store the highest
density of information and why?
a) Lasers are used to etch the plastic of the disc with micrometer-sized pits. Lasers
are used also to scan the discs to read the information.
b) The Blu-Ray discs can store the highest density of information. This is achieved
by using lasers with shorter wavelengths which give smaller diffraction laser spots.
7) a) Which topics did you find particularly complicated and had difficulty
understanding? What specific questions do you have about this (these) topic(s)?
b) Which topics did you find particularly interesting and would like to discuss
further in class? Any specifics or questions that you wish to add on each topic?
Any answer to this question gets credit.