Please pardon our mess.
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This page is almost always under construction. Please pardon our mess. |
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The idea of computing with a device that makes use of the nature of quantum mechanical wave functions has been around since Richard Feynman (and others) first considered the subject in the early 1980's. Since the discovery in 1994 (P. Shor) that certain problems in factorization can be solved exponentially faster on a QM computer than on a conventional computer, interest in finding an experimentally realizable QM computer has risen dramatically. Check out the Centre for Quantum Computation for a selection of online tutorials on the subject, as well as Samuel Braunstein's online tutorial. See also John Preskill's Advanced Math Methods course at Cal Tech and the UMass course on quantum computing (a.k.a. Electrical and Computer Engineering 723). See also the P284 bibliography section on quantum computation. |
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Here's a link to a discussion of apparently superluminal galaxy motion. Relevant for the honor's discussion of apparent superluminal motion in black hole jets. The image at left of jets emitted by the black hole GRS1915 is curtesy of the astronomy picture of the day. |
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Link to the Nobel press release for the 1997 Nobel prize awarded to Steven Chu, Claude Cohen-Tannoudji and William D. Phillips for development of methods to cool and trap atoms with laser light. This plus the link to background material for physicists provides a very nice overview of the technology of laser cooling. The image at the left shows sodium atoms (the bright spot in the center) trapped in a confining region called "optical molasses", produced at the intersection of three orthogonal pairs of opposing laser beams. |
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Looking for a brain-bender? After you've decided you more or less understand the special relativity twin paradox, perhaps you would like to spend a few moments trying to figure out the following variation. Frank and Mary are now in circular (free-fall) orbits around the earth, going in opposite directions. After half an orbit they meet again. Which one is older at this point? This ingenious problem is discussed at some length by two UMass physicists in the following article. You may also wish to check out the relativity FAQ discussion on twin paradoxes. Thanks to Peter B. for putting me on the road to this problem. |
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This one is more for fun than for education. If you have an mpeg viewer installed, you may enjoy this link to a list of relativistic flight simulators. For a more scientific description of "the visual appearance of rapidly moving objects", see Weisskopf's article of that name in the bibliography. |
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Gravitational lenses were first proposed by Albert E. as the lens-like
action of a massive body on light rays that pass by. However, when he
first considered this process in 1936, he supposed that the odds of ever
seeing gravitational lensing were remote. The Hubble Space Telescope
image at the left shows multiple images of background galaxies stretched
into thin arcs by an intervening galaxy cluser acting as a gravitational
lens. Curtesy of
astronomy picture of the day.
Here's a link that discusses gravitational lenses
in some detail.  A better (color) image of gravitational
lensing at left. Also a nice
example
of an Einstein cross from microlensing.
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Link to the The Laser Interferometer Gravitational-Wave Observatory home page. |
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Link to the home page for the gravity probe B experiment. See also the DISCOVER article by Gary Taubes on reserve, which gives an update on the Stanford gyroscope experiment that hopes to detect the effect of frame dragging near the Earth. |
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Should you feel the need, here is a link to a brief tutorial on Gaussian wave packets; and another link to a review of complex exponentials. |
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Prince Louis de Broglie proposed a theory that there is always associated with a particle of mass m a periodic internal phenomenon of frequency nu. He later expanded on this idea in the first chapter of his thesis entitled "Recherches sur la thÈorie des Quanta". This link from Davis Associates, Inc. gives a nice description of de Broglie's ideas, with a translation of his first publication in Comptes Rendus. |
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Looking for more practice on Schroedinger equation problems? Here is a link to the discussion of the finite square well potential. |
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Micro electronic structures now confine electrons to such tiny dimensions that quantization of electron energies becomes significant. The confinement can take place in one dimension (quantum wells), two dimensions (quantum wires) or three dimensions (quantum dots). In the latter case, quantum dots can be engineered to create a desired pattern of energy levels in what are essentially artificial atoms. Among the many applications are "atoms" which can produce laser light of specifically desired frequencies. Here is a link to a Scientific American article from October 1997 on small scale electronic structures and here is a link to a 1996 report from Optical Engineering on self-assembled quantum dots that lase. |
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The commonly accepted notion of teleportation involves scanning an object to ascertain its complete detailed construction, then transporting the information to another location in order to reconstruct the original object. From what we know of Quantum Mechanics, this would appear to be impossible. Heisenberg teaches us that we cannot scan a wave function without altering it. We should never be able to determine an object's wave function as it was before we tried to measure it. However, it turns out it is possible to transfer the wave function of one particle to another remote particle, without ever knowing that wave function. The wave function of the first particle is of course destroyed in the process, making this process "teleportation" rather than "duplication". Here is a link to a Scientific American article describing the first experiment to demonstrate quantum teleportation. |
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One would think that no information about an object can be obtained without some form of interaction with the object. It turns out that in the quantum world there is one notable exception to this rule. In a specially constructed experiment it is possible to gain some limited information about an object (e.g. the fact that an object is present) by using the features of quantum interference in what is called an interaction-free measurement. Here is a link to a tutorial on this class of experiments. |
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The construction and viewing of holograms provide some very interesting applications of the quantum mechanical behavior of wave functions. The fact that a hologram can be viewed with incoherent light but can be produced only with coherent light is understood from the nature of distinguishable and indistinguishable paths. This is a topic we will pursue in honors class. The logo at the left is a link to holo.com, a centralized site for holography enthusiasts. |
| Instructor: | Prof. Guy Blaylock |
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| Office: | Lederle Grad Research Tower Rm 928 | |
| Phone: | (413) 545-0993 | |
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blaylock@phast.umass.edu | |
| Office hours: | open |
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A first course in modern physics covering special relativity, general relativity and quantum mechanics. Designed for physics and related majors with prior
background in classical physics.
The first two weeks are spent on Einstein's special theory of relativity, a theory describing motion at high speeds (near the speed of light). We explore the rather bizarre relativistic phenomena of length contraction (objects get smaller) and time dilation (clocks go slower). Favorite topics include the very famous twin paradox, Bessy the relativistic cow. and laser cooling (a.k.a. "optical molasses"). The third and fourth weeks concentrate on aspects of general relativity, Einstein's theory to explain accelarated reference frames and the warping of spacetime by energy. We cover the concepts of curved space, bending of light, time delay in a gravitational well, gravitational redshift, the geodetic effect and frame dragging. Many famous experimental tests of general relativity, past and future, are reviewed. These include the perihelion shift of mercury, the 1919 test of light bending during a total eclipse, the evidence for black holes, the Harvard University stairwell test of redshift by Pound and Rebka, |
the Stanford gyroscope experiment Gravity Probe B,
the search for gravitational waves (LIGO experiment), and the 1983 discovery
of the binary pulsar by two UMass researchers (awarded the Nobel prize in
1993).
The remainder of the semester is devoted to an introduction to quantum mechanics, a theory to describe the behavior of microscopic systems. We discuss the particle like behavior of light, the wavelike behavior of particles, and Heisenberg's famous statement about the inherent limits of physical knowledge (the uncertainty principle). We develop some of the basic mathematical tools of importance to every good quantum mechanic. Popular digressions include quantum computing, quantum cryptography, quantum erasure experiments, quantum entanglement and the Einstein-Podolsky-Rosen paradox, interaction-free measurement, Bose-Einstein condensates and quantum teleportation. Course is three credits. Weekly homework sets. Two midterm exams and one comprehensive final. Physics 283 is a prerequisite. Optional 1 credit honors section meets an additional 1 hour per week with additional weekly problems and reading assignments. |
Make sure you know the exam rules.
The Grading Policy
and
a running record of homework and exam scores
are available here.
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Link to the web version of the Usenet Relativity FAQ (Frequently Asked Questions). Good coverage of many topics in special and general relativity. |
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Link to a FAQ list specializing in questions about black holes. |
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Link1 and Link2 to two archives of questions and answers about relativity. From the ask the space scientist series. |
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Link to a tutorial on special and general relativity that concentrates on the use of spacetime diagrams. |
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Link
to "Falling into a Black Hole", a site providing a lot of background
on general relativity and black hole physics. Some of the material
is fairly advanced but much of it can be appreciated by students taking
an introductory undergraduate course in GR. The site includes many
wonderful (and more or less scientifically accurate) animations of
life near a black hole. For a very clear and complete description of
the effects you should expect if you fall into a black hole, see the
prologue of Kip Thorne's book.
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The following is a link to the visual quantum mechanics java demo page for quantum tunneling. The image at the left is a kanji representation of "atom" done in iron atoms on copper, both constructed and "photographed" using a scanning tunneling microscope. Curtesy of the IBM scanning tunneling microscope image collection. |
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Link to a popular FAQ sitefor questions in Quantum Mechanics, maintained by Paul Budnick, and another more mathematically oriented QM FAQ site written by Jim Carolan. The cat pictured at left is actually NOT Schroedinger's cat. It is a picture of my cat (Colette) who was known to exhibit a number of quantum mechanical characteristics relating to Heisenberg's uncertainty principle. |
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Several alternatives to the Copenhagen interpretation of QM have been proposed over the years. Here is one link to a FAQ for the "many worlds" interpretation of Quantum Mechanics, initiated by Hugh Everrett. Another popular approach to the interpretation of QM was developed by David Bohm (portrait at left), which is described in the Sci. Am. article by D. Albert in the bibliography. |
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The words "quantum teleportation" are used to describe the process of destroying a wave function (by measuring it) in a particular location and recreating it in every detail in another location. In the last few years experimenters have discovered how to perform this amazing feat on a simple single photon system. Check out this link to IBM research on quantum teleportation. See also the P284 bibliography section on quantum teleportation. |
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For those of you who like to get your hands dirty, here's an online blueprint for how to perform your own quantum tunneling experiment on your kitchen table. |
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A number of quantum experiments are now performed on entangled states, QM teleportation, Bell experiments, interaction-free measurement and QM dense coding. One of the most active groups in this field is the photon group at the Innsbruck laboratory under the direction of Anton Zeilinger. The image at the left shows the light from a type II downconversion crystal (a source that produces an entangled pair of photons), which was used to demonstrate a violation of Bell's inequality. |
Last updated May 11, 99