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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

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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

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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

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Michelson-Morley experiment (1887)

• Attempt to detect the relative motion of matter through the ether

• http://galileo.phys.virginia.edu/classes/109N/lectures/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 tongranite slab floating in a poolof mercury, to minimize the effects of vibrations, and to allow it to be rotated easily.

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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.

Faraday’s law of electromagnetic induction

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Einstein was motivated by the fact that the inducedvoltage in the coil did not depend on whether the magnetwas moved toward the coil or if the coil was movedtoward the magnet.

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Test of the second postulate of thespecial 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-of-flight method was used to measure the photon speed

Experimental setup

target

Bending magnetsto eliminatecharged particles

beam

collimatorA

A’

BB’

d = 31.450 0.0015 m(A, A’) and (B, B’) aregamma detectors

d

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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 105

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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

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• 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.

Muon decay and time dilation, continued

0

27.6

1s

v c

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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 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

source

collimator

S1 S2

L

S1 and S2 are very thin scintillation detectors that produce a lightPulse 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 whenthey slam into the aluminum disk at the end (calorimetry). The calorimeteris calibrated by heating it using a resistor embedded in the disk. A thermo-couple 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)

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Results using a linear accelerator

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Results using the van de Graff