Physics 1202: Lecture 19Today’s Agenda

• Announcements:– Lectures posted on:

www.phys.uconn.edu/~rcote/

– HW assignments, etc.

• Homework #6:Homework #6:– Due next FridayDue next Friday

f( )x

x

f( x

x

z

y

The EM Spectrum• EM waves take on any wavelength

- from angstroms to miles (and beyond).

Constant speed of light• By the end of the 19th century:

– All known waves seemed to require a medium to propagate.

– Physicists thought EM waves required a medium as well: luminiferous ether.

– It was believed that EM waves would propagate with different velocities with respect to the ether, depending on their relative velocities with respect to the Earth’s orbital velocity.

Constant speed of light• In late 1800, speed of light measured to within 1%

• “usual” waves propagate in a medium – Sound in air/liquid/solid

– Surf in water

• What about light (electromagnetic wave) ?– must require a medium: luminiferous ether or simply “ether”

• To try to detect it: Michelson-Morley experiment

– 1881 and 1887

– Interferometer:

c+v ?

c

v

Sun

Constant speed of light• Michelson-Morley

experiment:– 2 paths of same length

– 1 perp. To direction of “ether”

– 1 // to direction of “ether”

• If v of light varies– Interference pattern

• None detected with any orientation

• c is constant

• No evidence of ether !

Einstein’s relativity (1905)• Einstein incorporated this result in his 2 postulates

2- Constant speed of light:

The speed of light c is the same in all inertial

reference frames, regardless of the relative velocity

of the source and receiver of the light.

1- Principle of Relativity:

The laws of Physics are the

same on all inertial reference

frame.

These “simple” postulates have big implications …

Not intuitive• Our everyday life

– Speed add up

• The speed of light is an invariant quantity, and is the same as measured by all observers!

Relativity of Space and Time• “Simultaneous” measurements of events

– Physical “Happening” occurring at a specific position and time

• Distinct events simultaneous in one inertial frame need not be simultaneous in another inertial frame.– Measures of time and position are

not absolute: they depend on one’s inertial reference frame.

Implications of constant c• In Sharon’s inertial frame

– Light travels a distance 2d0 at speed c during a time t0

mirror

detector

d0

source

• In Sam’s inertial frame– Light travels a distance 2d

at speed c during a time t

source

mirror

d

vt

d0

vt/2

detector

d

Time dilation• In Sharon’s inertial frame

– Light travels a distance 2d0 at speed c during a time t0

• In Sam’s inertial frame– Light travels a distance 2d

at speed c during a time t

d0

vt /2

d

Relativistic factor

Relativistic Factor • No material particle can reach c ≥ 1 for 0 ≤ v < c

• If v>c

imaginary

Proper time• Time between two events is shortest in a reference

frame where the events occur at the same place: proper time.

Lecture 19, ACT 1• An astronaut moves away from Earth at close

to the speed of light. How would an observer on Earth measure the astronaut’s pulse rate?

a) it would be faster

b) it would be slower

c) it wouldn’t change

d) no pulse - the astronaut died a long time ago

Length contraction• Compare distances on rocket (d) and on Earth d0

• On Earth– Distance = d0

– Traveled in time t at speed v

• On ship– Distance = d

– Traveled in time tS at speed v

• But time dilation– Shorter in ship

than Earth

length contraction

a) no door hit the spaceship because for her the doors weren’t closed simultaneously

b) no door hit the spacecraft because length contraction makes the spaceship only 60 m long

Lecture 19, ACT 2A spacecraft has a length of 100 m when parked on Earth. It is now moving toward a tunnel with a speed of 0.8c ( =1.66). The lady living near the tunnel can control doors that open and shut at each end of the tunnel, which is 65 m long. The doors are open as the spaceship approaches, but in the very moment that she sees the back of the spaceship in the tunnel, she closes both doors and then immediately opens them again.

According to the lady living near the tunnel:

c) no door hits the spaceship because length contraction has made the tunnel 109 m long

d) a door hits the spaceship

a) no door hit the spaceship because

for her the doors weren’t closed

simultaneously

b) no door hit the spacecraft

because length con- traction

shortens the spaceship to 60 m

long

Lecture 19, ACT 2bSame situation but

According to the captain in the spaceship:c) no door hits the spaceship

because length contraction has

made the tunnel 109 m long

d) a door hits the spaceship

Relativistic velocity• Relativistic velocity addition:

v: relative velocity between

2 inertial frames

• This is a velocity equation– it involves a speed and a

direction.

• Velocities – positive when the object moves in

the + direction – negative when the object moves in

the – direction

• Compare to classical case: uA = uB + v

Relativistic Doppler Effect• Doppler effect for light

• Application: redshift of astrophysical objects

• Note: for v<<c, – get back “normal” doppler effect (e.g. for sound)

Relativistic momentum• Momentum increases with v

• In the limit of non-relativistic speeds ( v << c, ≈ 1 ):

which agrees with the classic formula!

Relativistic Kinetic Energy• It scales with

• For small v, it has to agree with classic expression

Relativistic Energy• Kinetic energy

Rest EnergyTotal Energy• Total relativistic energy

• Rest energy

• Energy-momentum relation:

Energy-Momentum relation• Square the total energy

• where

• since