Spring 2013 | Daniel Finley |
Tuesday and Thursday, 3:30 - 5:00 PM , in Room 5, PandA Bldg. |
young Einstein, as a clerk | Albert Einstein, in 1939 | Einstein with blackboard |
Einstein (1879 - 1955) |
This course is intended for the general knowledge of
students of physics, in
all areas.
This should include
advanced undergraduates and also graduate students.
We
will go into more depth than is common in other classes,
where special relativity is only a small part of the course material,
concerning both underlying, fundamental principles and
detailed knowledge of useful and interesting approaches,
with applications to quantum
physics and (a bit of) differential geometry and general relativity.
extension of physical vectors from 3- to 4-dimensional vectors: displacement, velocity, momentum, force, acceleration | ||||||||||||||||||||||||||
some interesting 1+1- and 2+1-dimensional "paradoxes", and some unexpected visual effects associated with very fast motions | ||||||||||||||||||||||||||
some other 3-dimensional quantities require extension
to 4-dimensional tensors:
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| angular momentum, electric and magnetic fields, energy density, stress and strain
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| differential forms (often called covariant vectors) and metric tensors form very
useful foundations for further study;
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| | the Grassmann algebra of 1-forms leads to 4-dimensional extensions
of cross products, curls, and potentials, and has
applications to magnetic monopoles
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| area, volume, and hypervolume, each as differential forms, which are used under
integral signs are also very important
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| rotations and Lorentz boosts between reference frames: | the full structure of the Lorentz and Poincaré (Lie) groups, and their Lie algebras, and their representations, | |
with application to the Thomas precession of dipole moments
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| motions of observers moving under constant acceleration, as measured by
themselves
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| 2-dimensional spinors, applications to the Dirac equation
and other things
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The following are some general comments about the structure of the course.
Albert Einstein and Rabindranath Tagore, both Nobel Prize winners |
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