H.5.1Discuss muon decay as experimental evidence to support special relativity. H.5.2Solve some problems involving the muon decay experiment. H.5.3Outline

H.5.1 Discuss muon decay as experimental evidence to support special relativity.

H.5.2 Solve some problems involving the muon decay experiment.

H.5.3 Outline the Michelson-Morley experiment.

H.5.4 Discuss the result of the Michelson-Morley experiment and its implication.

H.5.5 Outline an experiment that indicates that the speed of light in vacuum is independent of its source.

Option H: RelativityH5 Evidence to support special relativity

Discuss muon decay as experimental evidence to support special relativity.

●Muons are created about 3 km above the ground by the collision of cosmic rays (protons) with Earth’s atmospheric gases.

●In the laboratory, a muon will decay in about 2 s into an electron and 2 neutrinos.

●In 2 s light can only travel about 600 m.●Muons from the atmosphere (much farther than 600 m) reach the ground.

●They travel at about 99% the speed of light.


FYIThe implication is that time dilation allows the muons to survive for more than 600 m.

Solve some problems involving the muon decay experiment.


time dilation∆t = ∆t0 where = 1

1 - v2/c2

2.210-6 is the proper time because it is measured in the frame of the muon.

= 1 /(1 - 0.982)1/2 = 1/0.03961/2 = 5.025.

∆t = ∆t0 = 5.025(2.210-6) = 1.110-5 s.




1 - v2/c2

For Earth observer use ∆t = 1.110-5 s.

Then d = v ∆t = 0.98(3.00108)(1.110-5) = 3234 m.




1 - v2/c2

For muon observer use ∆t0 = 2.210-6 s.

Then d = v ∆t = 0.98(3.00108)(2.210-6) = 647 m.




1 - v2/c2

Time dilation is the relativistic effect that causes time to elapse more slowly in a fast-moving IRF.

As the previous example showed, if time dilation did NOT occur, a muon created at 3 km would not live long enough to be detected.

But muons ARE detected, providing evidence.

Option H: RelativityH5 Evidence to support special relativityOutline the Michelson-Morley experiment.

A driving force behind special relativity was the Michelson-Morley experiment.

A large vat was filled with liquid mercury on which was floated a slab of stone.

On the slab was an interferometer which could be freely rotated with the slab.

The interferometer used a beam- splitter which insured that the two beams were coherent.

FYIThe mercury allowed easy rotation and absorbed vibrations from road traffic outside the lab.

Vat of liquid mercury

Floating table of heavy marble

SourceBeam splitter

Detector

Mirrors

Michelson

Option H: RelativityH5 Evidence to support special relativityOutline the Michelson-Morley experiment.

The basic idea behind the device was that as the floating table was rotated, the beam parallel to the earth's orbital velocity would squish.

The beam perpendicular to the earth's orbital velocity would act as the control - it would not be squished.

In the region where the beams rejoined, interference would be detected.

Destructive interference would result in seeing dark in the eyepiece of the detector while rotating.

Constructive interference would result in seeing bright in the eyepiece of the detector.

Vat of liquid mercury

SourceBeam splitter

Detector

Mirrors

vorb

Squished beam

Control beam

Region of interference

Discuss the result of the Michelson-Morley experiment and its implication.

The null results showed that there was no interference. Thus the light waves did not squish in the direction of motion.

Thus the speed of light is the same, whether in a stationary reference frame (the control one) or a moving reference frame (one moving at vorbital).

This result baffled scientists who thought that being a wave, light must travel through a medium.

They gave this particular medium the name ether and assumed that the ether permeated all of space, and even matter itself.

The MM experiment was really a method to determine how Earth was moving through the ether, and thus of establishing an absolute frame of reference, that of the ether.


Discuss the result of the Michelson-Morley experiment and its implication.

The null results of the Michelson-Morley experiment thus showed that

(1)there is no ether, and therefore no absolute reference frame.

(2)the speed of light is the same, whether in a stationary reference frame or a moving reference frame.

The latter point was used to establish that time, and distance, were not absolute. (See Topic H3.)

It led Einstein to formulate his second postulate of special relativity; namely “The speed of light is the same in all inertial reference frames.”


Outline the Michelson-Morley experiment.


To measure the speed of Earth through the ether. To find the absolute reference frame.





To vary the relative speeds of each ray so that interference could be detected.



To measure the exact shift in time/wavelength/speed of each beam.



No change was measured indicating that the speed of light was the same, regardless of the speed of source or observer. No ether.There was no absolute reference frame.

Outline an experiment that indicates that the speed of light in vacuum is independent of its source.


FYIThe point here is that even though the source of the photons (the pion) was moving very fast, each photon still traveled at exactly c.

EXAMPLE: Pions are unstable particles that decay into two gamma-ray (-ray) photons, which are very high-energy photons.

●Neutral pions (0), a type of particle made from a quark and an antiquark, were made to travel at nearly the speed of light in a particle accelerator such as CERN.

●The speed of each of the decay photons was measured precisely, and was found to be exactly c in accordance with the second postulate.

Documents

H.5.1Discuss muon decay as experimental evidence to support special relativity. H.5.2Solve some problems involving the muon decay experiment. H.5.3Outline