- Conceptual:
-
Attached passages from Brian Greene, The Elegant Universe (Norton and Company, New York, 1999), pp 60 -- 65. - Technical:
-
Taylor & Wheeler 5.8 -- 5.10 (time dilation and Lorentz contraction) Berry section 4.3 (differential geometry, nonEuclidean surfaces)
The writing assignment deals particularly with paragraphs 2 through 7 of Greene's passage.
- Summary
- For each of paragraphs 2 through 8, write a sentence or two
summarizing the material presented in the paragraph. For example, a
summary of paragraph 1 might be ``Here Greene recalls that constant
velocity motion of a reference frame is undetectable: any experiment
within the reference frame obeys the same internally consistent
physical laws, with no observable consequence of a boost velocity. He
then introduces the equivalence principle, here stated as the
indistinguishability of forces due to gravity and those due to
accelerated reference frames, leading to the indistinguishability of
gravity and accelerated motion.''
- Analysis
- You need use full sentences only when specifically requested.
- Relative to unaccelerated space, show the instantaneous Lorentz boost
of a rider on the Tornado at radius
. Take your xy-axes to point in
the instantaneous tangential and radial directions.
- Using your Lorentz boost matrix from 1, what circumference and radius
do Slim and Jim measure for a Tornado of radius . In sentence(s), why
is this result consistent with Greene's paragraphs 4 and 5?
- What value for the curvature
, then, do Slim and Jim measure at Tornado radius ? Is this curvature positive or negative?
- Has this curvature been measured in a single locally inertial frame (LIF) or is it a tidal effect? State why, making contact with in-class definitions of locally inertial frames and tidal effects. (full sentences)
- Relative to unaccelerated space, show the instantaneous Lorentz boost
of a rider on the Tornado at radius
- Rewrite
- (Full sentences) Present the Tornado ride and curvature measurement of
Greene's paragraphs 2 -- 7 quantitatively, incorporating and
explaining your results from Analysis questions 1 -- 3 above. Assume
your reader is an undergraduate physics major, with background similar
to your own on entering this course. Thus you will need to minimally
explain, in general, 1) Lorentz boosts and how they affect spacetime
measurements; and 2) circles and curvature defined on curved surfaces,
before you use these ideas in your specific analysis of the
Tornado problem. Your writing should be fully self-contained, a passage of
comparable length to the original passage (that is, you need detail
only at the level of Analysis questions 1 -- 3, plus whatever
exposition you need to clearly introduce and explain them.)