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Announcements 1st midterm: grades are online project: I’m in the process of reading …. A few words on the test ... Well done !!!!!! Average score: 19.5/25  B-/C+ Lecture 14 Special relativity I: Speed limit 186000 mi/s and common sense makes no sense A few definitions ...

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announcements
Announcements
  • 1st midterm: grades are online
  • project: I’m in the process of reading ….

Astronomy 201 Cosmology - Lecture 14

a few words on the test
A few words on the test ...
  • Well done !!!!!!
  • Average score: 19.5/25  B-/C+

Astronomy 201 Cosmology - Lecture 14

lecture 14 special relativity i speed limit 186000 mi s and common sense makes no sense

Lecture 14Special relativity I: Speed limit 186000 mi/s and common sense makes no sense

Astronomy 201 Cosmology - Lecture 14

a few definitions
A few definitions ...
  • Inertial Observer: An inertial observer is an observer whose rest frame is inertial
  • Invariance: A quantity is said to be invariant if all inertial observers would obtain the same result from a measurement of this quantity
  • Relativity: A quantity is said to be relative if different inertial observers obtain different results from their measurement.

Astronomy 201 Cosmology - Lecture 14

examples
Examples
  • invariant: time, mass, acceleration, force
  • relative: velocity, position

 Galilean relativity

but: Maxwell’s equations (electromagnetism)

are not Galilean invariant !!!

Astronomy 201 Cosmology - Lecture 14

the michelson morley experiment
The Michelson-Morley experiment

Astronomy 201 Cosmology - Lecture 14

result of the michelson morley experiment the big surprise
Result of the Michelson-Morley experiment: the big surprise
  • Expectation:
    • only in the reference frame of the ether, the speed of light should bec = 299 792 458 m/sec
    • in other reference frames, the velocity should be different (e.g. by 30 km/sec, the speed with which the Earth orbit the Sun)
  • Observation:
    • the velocity of light was the same to less than 5 km/sec  there is no ether !!!

Astronomy 201 Cosmology - Lecture 14

fitzgerald s proposal
FitzGerald’s proposal
  • Objects that move through ether at velocity v are physically contracted in length according to strange proposal ?!

Astronomy 201 Cosmology - Lecture 14

einstein s new relativity
Einstein’s new relativity
  • Galileo:
    • The laws of mechanics are the same in all inertial frames of reference
    • time and space are the same in all inertial frames of reference
  • Einstein:
    • The laws of physics are the same in all inertial frames of reference
    • the speed of light in the vacuum is the same in all inertial frames of reference

Astronomy 201 Cosmology - Lecture 14

constancy of speed of light
Constancy of speed of light

Astronomy 201 Cosmology - Lecture 14

consequence i breakdown of simultaneity
Consequence I: Breakdown of simultaneity
  • Consider observer inside a space ship moving at a speed comparable to the speed of light:
  • Consider observer inside a space ship moving at a speed comparable to the speed of light: for an observer inside the ship, light hits the outer walls at the same time

Astronomy 201 Cosmology - Lecture 14

consequence i breakdown of simultaneity12
Consequence I: Breakdown of simultaneity
  • For an outside observer (relative speed to the ship v):
  • For an outside observer (relative speed to the ship v): for an observer outside the ship, light hits the outer walls at the different times

 simultaneity is relative

Astronomy 201 Cosmology - Lecture 14

consequence ii time dilation
Observer comoving with the space ship

Outside observer

Mirror

Mirror

H

H

d

vtR

Consequence II: time dilation

 moving clock must go slower !!

Astronomy 201 Cosmology - Lecture 14

consequence ii time dilation14
Time measured by passenger in the ship:tp=2H/c

Distance traveled by light in rest frame:d2 = H2 + (0.5vtR)2

relation between tpand tR:

Consequence II: time dilation

Mirror

H

d

vtR

Astronomy 201 Cosmology - Lecture 14

how can we test this
How can we test this ?
  • Proposal A:take two atomic clocks, put one in an airplane and have the airplane fly once around the Earth. Compare the clock with the other one that stayed at rest. Result: the traveling clock is indeed somewhat behind.

Astronomy 201 Cosmology - Lecture 14

how can we test this16
How can we test this ?
  • Proposal B:There exist an elementary particle, the muon, which is created when cosmic rays hit the upper levels of the atmosphere. Their lifetime is so short, that they should decay before they reach the surface of the Earth. Nevertheless they are detected. Solution: muons move at speeds close to the speed of light, “life” proceeds much slower.

Astronomy 201 Cosmology - Lecture 14

what don t we see it in daily life
What don’t we see it in daily life ?
  • Effect is too small since v is usually much smaller than the speed of light
  • Example:Fly daily and for one year with the Concorde from JFK to Paris and back. Speed: 700 m/sec Travel time: 6 hours time difference: 1/50 000 sec

Astronomy 201 Cosmology - Lecture 14

consequence iii length contraction
Consequence III: length contraction
  • Consider distance between two space stations, measured using travel time of a space ship moving at speed v
    • Observer in one of the stations: space ship moves with velocity v, travel time istR  distance: d=vtR
    • Observer in the ship: space ship moves with velocity v, travel time istP  distance:

Astronomy 201 Cosmology - Lecture 14