Lecture3

Lecture3 - Lecture
3:
Integrals,
Iner1a
...

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Unformatted text preview: Lecture
3:
Integrals,
Iner1a
 Ph
1a

 October
6,
2010
 Demonstra1on
 •  •  •  •  Video
capture
of
falling
ball
 Analysis
of
trajectory,
frame
by
frame
 Posi1on
vs
1me
is
a
parabola,
as
expected
 Fit
to
measured
data
yields
value
for
g
 Gallileo’s
Law
(1638)
 •  Earth’s
gravity
causes
all
bodies
fall
with
the
same
constant
 accelera1on
(in
a
vaccuum)
 •  An
interes1ng
experimental
fact
(e.g.
feather
&
penny
demo)
 •  Thought
experiment:
flying
in
a
spaceship
 –  
g
=
9.8
m/s2
 •  Einstein
1907:
we
assume
the
complete
physical
equivalence
of
a
 gravita6onal
field
and
a
corresponding
accelera6on
of
the
reference
 system
 –  Galileo’s
law
is
a
fundamental
assump6on
of
Einstein’s
general
 rela1vity
 –  Why
does
nature
work
like
this
?
 –  Engine
off:
objects
float
inside
cabin,
are
“weightless”
 –  Engine
on:
all
objects
inside
cabin
appear
to
accelerate
at
the
same
 rate
toward
“rear”
of
cabin.
 –  So:
accelera1on
of
the
frame
of
reference
(the
cabin)
appears
to
have
 the
same
effect
as
gravity

 Experimental
status
 PRL 100, 041101 (2008) PHYSICAL REVIEW LETTERS week ending 1 FEBRUARY 2008 Test of the Equivalence Principle Using a Rotating Torsion Balance S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger Center for Experimental Nuclear Physics and Astrophysics, University of Washington, Seattle, Washington, 98195, USA (Received 4 October 2007; revised manuscript received 3 December 2007; published 28 January 2008) We used a continuously rotating torsion balance instrument to measure the acceleration difference of beryllium and titanium test bodies towards sources at a variety of distances. Our result aN;Be-Ti ˆ …0:6  3:1†  10ÿ15 m=s2 improves limits on equivalence-principle violations with ranges from 1 m to 1 ¨¨ by an order of magnitude. The Eotvos parameter is Earth;Be-Ti ˆ …0:3  1:8†  10ÿ13 . By analyzing our data for accelerations towards the center of the Milky Way we find equal attractions of Be and Ti towards galactic dark matter, yielding DM;Be-Ti ˆ …ÿ4  7†  10ÿ5 . Space-fixed differential accelerations in any direction are limited to less than 8:8  10ÿ15 m=s2 with 95% confidence. DOI: 10.1103/PhysRevLett.100.041101 PACS numbers: Galileo’s
law
confirmed
to
~
2
parts
in
1013
!
04.80.Cc (for
1tanium
vs
beryllium
towards
Earth)
 of the apparatus and Figure 1 shows a schematic drawing The equivalence of gravitational mass and inertial mass Earth
vs
Moon
towards
Sun:
Tom
Murphy’s
APOLLO
LLR
experiment
 library.caltech.edu
‐>
Quick
Links
‐>
Web
of
Knowledge
 is assumed as one of the most fundamental principles in nature. Practically every theoretical attempt to connect general relativity to the standard model allows for a violation of the equivalence principle [1]. Equivalence-principle tests are therefore important tests of unification scale physics far beyond the reach of traditional particle physics experiments. The puzzling discoveries of dark matter and dark energy provide strong motivation to extend tests of the equivalence principle to the highest precision possible. Over the past two decades we have conducted laboratory tests of the equivalence principle [2 – 5]. This Letter reports our latest and most precise measurement using a new, Eric
Adelberger:
Caltech
BS
1960,
PhD
1967

 the 70.3 g pendulum. The pendulum body is a thin aluminum shell with fourfold azimuthal symmetry and up down reflection symmetry. It carries four beryllium and four titanium test masses in a horizontal dipole configuration. These two materials were chosen primarily to maximize the difference in baryon number (B= is 0.998 68 for Be and 1.001 077 for Ti), and secondly for experimental reasons, such as densities, magnetic properties, and machinability. The Ti test bodies are hollow to match the external shape and mass of the 4.84 g Be test bodies to within 50 g. The test-body shape allows us to reproducibly interchange the test bodies, to minimize alignment errors, ...
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This note was uploaded on 02/22/2011 for the course PH 1a taught by Professor Goodstein during the Fall '07 term at Caltech.

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