Experimental basis for special relativity

1
Experimental basis forspecial 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

2
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

3
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

4
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

5
Fizeaus 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 ltlt expected

6
Michelson-Morley experiment (1887)

• Attempt to detect the relative motion of matter
  through the ether
• http//galileo.phys.virginia.edu/classes/109N/lect
  ures/michelson.html
• 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.
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Einsteins 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.

8
Faradays 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.
9
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 ?0s decay into 2 photons. A time-of-flight
method was used to measure the photon speed
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Experimental setup
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?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

12
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 lt 500 m, and would not be detected
  on earth.
• Muons are detected on earth

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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
• With this lifetime, the muons would travel
  roughly 2.25 km, so some would be detected on
  earth.

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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
  Einsteins 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 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.
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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 thermo- couple
is used to measure the increase in temperature.
17
Results Classical physics fails!
Radioactive sources 133Ba (25 - 80 keV) and
207Bi (240 -1047 keV)
18
Results using a linear accelerator
19
Results using the van de Graff