Download Experimental basis for special relativity

Experimental basis for
special relativity
• Experiments related to the ether
hypothesis
• Experiments on the speed of light from
moving sources
• Experiments on time-dilation effects
• Experiments to measure the kinetic energy
of relativistic electrons
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The luminiferous ether
• Mechanical waves, water, sound, strings,
etc. require a medium
• The speed of propagation of mechanical
waves depends on the motion of the
medium
• It was logical to accept that there must be a
medium for the propagation of light, so that
em waves are oscillations in the ether
• Newton, Huygens, Maxwell, Rayleigh all
believed that the ether existed
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Consequences of the ether
• If there was a medium for light wave
propagation, then the speed of light must be
measured relative to that medium
• Thus the ether could provide an absolute
reference frame for all measurements
• The ether must have some strange properties
– it must be solid-like to support high-frequency
transverse waves
– yet it had to be of very low density so that it did not
disturb the motion of planets and other astronomical
bodies too much
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The aberration of starlight
(James Bradley 1727)
• Change in the apparent position of a
star due to changes in the velocity of
the earth in its orbit
• Fresnel attempted to explain this
from a theory of the velocity of light
in a moving medium
• According to Fresnel, the ether was
dragged along with the earth and this
gave rise to the aberration effect
• However, Einstein gave the correct
explanation in terms of relativistic
velocity addition. A light ray will have
a different angle in different
relativistic frames of reference
4
Fizeau’s measurements of the speed of
light in a moving fluid (1851)
• He measured c and got 315,000,000 m/s
• He used interference effects to attempt to
measure the speed of light in moving water
• He expected to measure c + v, but the
magnitude of the result was << expected
5
Michelson-Morley experiment (1887)
• Attempt to detect the
relative motion of matter
through the ether
•
http://galileo.phys.virginia.edu/cla
sses/109N/lectures/michelson.ht
ml
• Used interference of light
due to path length
differences (fringe shift
when apparatus was
rotated.
• Found no measurable
effect
•  NO ETHER
Optical table was a 1½ ton
granite slab floating in a pool
of mercury, to minimize the
effects of vibrations, and to
allow it to be rotated easily.
6
Einstein’s postulates
of special relativity
I. The laws of physics (mechanics and
electrodynamics) are valid in all
inertial frames of reference. There is
no absolute frame of reference.
II. Light is always propagated in
empty space with a definite velocity
c with respect to any frame of
reference, regardless of the state of
motion of the emitting body.
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Faraday’s law of
electromagnetic induction
Einstein was motivated by the fact that the induced
voltage in the coil did not depend on whether the magnet
was moved toward the coil or if the coil was moved
toward the magnet.
8
Test of the second postulate of the
special theory of relativity in the GeV region
(Alvager et al., Phys. Lett. 12, 360, 1984)
 Used the CERN Proton Synchrotron to
accelerate protons to 19.2 GeV/c which
then slammed into a Be target producing 0
mesons at 6 GeV   = 0.99975.
 The 0’s decay into 2 photons. A time-offlight method was used to measure the
photon speed
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Experimental setup
target
0 beam
Bending magnets
to eliminate
charged particles
A’
B’
B
A
collimator
d = 31.450  0.0015 m
(A, A’) and (B, B’) are
gamma detectors
0   experiment
• This amounts to measuring c produced on
a source (the 0 s) moving at 0.99975 c
• Results c’ = c + kv
• k = (3  13) x 105
11
Muon decay and time dilation
• Muons are produced by decays of ’s in
cosmic ray collisions with nuclei in the
upper atmosphere.
• The half-life of muons at rest is 0 = 1.52 s
• The muons move at 0.98c, so in one 0 ,
they would travel < 500 m, and would not
be detected on earth.
• Muons are detected on earth
12
Muon decay and time dilation,
continued
• We observe muons on earth because of
the relativistic time dilation effect.
• The proper lifetime of the muon is

0
1 v c
2
 7.6  s
• With this lifetime, the muons would travel
roughly 2.25 km, so some would be
detected on earth.
13
Measurements of the speed and kinetic
energy of relativistic electrons
• Classically K = ½ m v2, where m = constant
• There is no limit on v, so that if a force
continually acts on an object, it will eventually
reach a speed in excess of c, in contradiction to
Einstein’s second postulate.
• Two types of experiments:
– using relativistic electrons emitted by a radioactive
source (Am. J. Phys. 77, 757, 2009)
– Using a Van de Graff device to accelerate electrons
to high speeds and measuring
(Am. J. Phys. 32, 551, 1964).
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Experiment – use radioactive
source that emits electrons
S1
S2
source
collimator
L
S1 and S2 are very thin scintillation detectors that produce a light
Pulse when electrons hit them. The light pulses measure the time interval
For the electrons to travel the know distance L, this v is measured. The
Kinetic energy of the electrons emitted by the radioactive nuclei is known.
15
Experiment using a Van De Graff
electron accelerator
The kinetic energy of the electrons is measured by the heat produced when
they slam into the aluminum disk at the end (calorimetry). The calorimeter
is calibrated by heating it using a resistor embedded in the disk. A thermocouple is used to measure the increase in temperature.
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Results: Classical physics fails!
Radioactive sources: 133Ba (25 - 80 keV) and 207Bi (240 -1047 keV)
17
Results using a linear accelerator
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Results using the van de Graff
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