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 the Michelson-Morley experiment. H.5.4Discuss the result of the Michelson-Morley experiment and its implication. H.5.5Outline an experiment that indicates that the speed of light in vacuum is independent of its source. Option H: Relativity H5 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. Option H: Relativity H5 Evidence to support special relativity FYI  The implication is that time dilation allows the muons to survive for more than 600 m.

Solve some problems involving the muon decay experiment. Option H: Relativity H5 Evidence to support special relativity time dilation ∆t =  ∆t 0 where  = v 2 /c 2  2.2  is the proper time because it is measured in the frame of the muon.  = 1 /( ) 1/2 = 1/ /2 =  ∆t =  ∆t 0 = 5.025(2.2  ) = 1.1  s.

Solve some problems involving the muon decay experiment. Option H: Relativity H5 Evidence to support special relativity time dilation ∆t =  ∆t 0 where  = v 2 /c 2  For Earth observer use ∆t = 1.1  s.  Then d = v ∆t = 0.98(3.00  10 8 )(1.1  ) = 3234 m.

Solve some problems involving the muon decay experiment. Option H: Relativity H5 Evidence to support special relativity time dilation ∆t =  ∆t 0 where  = v 2 /c 2  For muon observer use ∆t 0 = 2.2  s.  Then d = v ∆t = 0.98(3.00  10 8 )(2.2  ) = 647 m.

Solve some problems involving the muon decay experiment. Option H: Relativity H5 Evidence to support special relativity time dilation ∆t =  ∆t 0 where  = v 2 /c 2  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: Relativity H5 Evidence to support special relativity Outline 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. FYI  The mercury allowed easy rotation and absorbed vibrations from road traffic outside the lab. Vat of liquid mercury Floating table of heavy marble Source Beam splitter Detector Mirrors Michelson

Option H: Relativity H5 Evidence to support special relativity Outline 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 Source Beam splitter Detector Mirrors v orb 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 v orbital ).  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. Option H: Relativity H5 Evidence to support special relativity

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.” Option H: Relativity H5 Evidence to support special relativity

Outline the Michelson-Morley experiment. Option H: Relativity H5 Evidence to support special relativity  To measure the speed of Earth through the ether.  To find the absolute reference frame.

Outline the Michelson-Morley experiment. Option H: Relativity H5 Evidence to support special relativity

Outline the Michelson-Morley experiment. Option H: Relativity H5 Evidence to support special relativity  To vary the relative speeds of each ray so that interference could be detected.

Outline the Michelson-Morley experiment. Option H: Relativity H5 Evidence to support special relativity  To measure the exact shift in time/wavelength/speed of each beam.

Outline the Michelson-Morley experiment. Option H: Relativity H5 Evidence to support special relativity  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. Option H: Relativity H5 Evidence to support special relativity FYI  The 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.