Ec

vB

2

Is Maxwell Eq.s (Light)of invariance?Magnetism

2'

'2

dt

ydmmg

maF

2

2

dt

ydmmg

maF

불변성(invariance)

Edward Morley

(1838-1923)

Albert Michelson

(1852-1931)

The aether wind?

Michelson-Morley Experiment: Details

If light requires a medium, then its velocity depends on the velocity of

the medium. Velocity vectors add.

Parallel

velocities

Anti-parallel

velocities

vlight

vlight

vaether vaether

vtotal

vtotal

v v+v ligtotal ht aether v v-v ligtotal ht aether

Perpendicular

velocity to mirror

Perpendicular

velocity after mirror

Michelson-Morley Experiment: Details 2

In the other arm of the interferometer, the total velocity must be

perpendicular, so light must propagate at an angle.

vlight

vaether

vtotal

2 2v vv ligh atotal rt ethe

vlight

vaether

vtotal

Michelson-Morley Experiment: Details 3

Perpendicular

propagation

vaether

Parallel and

anti-parallel

propagation

2 2 2 2

2 2

2 2

v v

( v) ( v)

v v

2

v

2 1

[1 v / ]

L Lt

c c

L c L c

c c

Lc

c

L

c c

2 2

2 2

2

v

2 1

1 v /

Lt

c

L

c c

The delays for the two arms depend

differently on the velocity of the aether!

Let c be the speed of light, and v be the velocity of the aether.

Michelson-Morley Exp’t: More Details

2 2

2 1

[1 v / ]

Lt

c c

2 2

2 1

1 v /

Lt

c c

The delay reverses, and any fringe

shift seen in this second experiment

will be opposite that of the first.

Because we don’t know the direction of the aether velocity,

Michelson and Morley did the measurement twice, the second time

after rotating the apparatus by 90.vaether

Actually, they rotated the apparatus

continuously by 180º looking for a

sinusoidal variation in the shift with this amplitude.

Michelson-Morley Experiment Analysis…

Upon rotating the apparatus by 90, the optical path lengths are

interchanged producing the opposite change in time. Thus the

time difference between path differences is given by:

Copying:

2 2 2 2

2 1 12 2

1 v / 1 v /

Lt t

c c c

2

2 2 2 2

2

2 2 v2 1 v / 1 v / 2 2

2

L Lc c

c c c

Assuming v << c:

2 2

2 1

[1 v / ]

Lt

c c

2 2

2 1

1 v /

Lt

c c

2

3

v2 2t t L

c

Michelson-Morley Experimental Prediction

•The Earth’s orbital speed is: v = 3 × 104 m/s

•

•and the interferometer size is: L = 1.2 m

•So the time difference becomes: 8 × 10−17 s

•which, for visible light, is a phase shift of: 0.2 rad = 0.03 periods

•Although the time difference was a very small number, it was well within the experimental range of measurement for visible light in the Michelson interferometer, especially with a folded path.

2

3

v2 2t t L

c

Recall that the phase shift is

w times this relative delay:

2

3

v2 L

cw

2

2

v4

L

c

or:

Michelson’s and Morley’s set up

They folded the path to increase the total path of each arm.

Michelson-Morley

Experiment: Results

Michelson and Morley's results

from A. A. Michelson, Studies in

Optics

Interference fringes showed no

change as the interferometer

was rotated.

The Michelson interferometer

should’ve revealed a fringe shift as

it was rotated with respect to the

aether velocity. MM expected 0.4

periods of shift and could resolve 0.005

periods. They saw none!

Their apparatus

• The laws of physics are the same (invariant) in all inertial frames

• The speed of light is the same (invariant) in all inertial frames.

Two postulates of the Special Theory of Relativity

Absolute space & absolute time Relativistic space-time

Galilean Transform

2 2

v

1 v /

x tx

c

2

2 2

v /

1 v /

t x ct

c

Lorentz Transform

Vvv

v V

C !

Galilean Relativity

Inertial frame

Inertial frame

Vcc

c V ?

Special Relativity

Inertial frame

Inertial frame

Speed, u’

0.25c

Speed,u

0.50c 0.75c

v = 0.75c

1.0c

0.9c

0.8c

1.1c Galilean velocity

addition

Relativistic velocity

addition

0

V

u

t

v( v )

[ (v/ ) ] 1+ v/

xx 2 2

x

udx dx dtu

dt dt c dx u c

ut

sounds vv

cvs

sounds vv

Galilean Transform

2 2

v

1 v /

x tx

c

Lorentz Transform

My waste is 30 inchesI think so.

I don’t think so.

My waste is 30 inches

Spatial length contraction

Lorentz Transform

Both lights turn on at the same time.

The front light turns on earlier

Simultaneity Problem2

2 2

v /

1 v /

t x ct

c

Albert Einstein (1879-1955)

Hermann MinkowskiHenri PoincareHendrik Lorentz

누가먼저특수상대론을만들었나?

누가일반상대론을먼저만들었는가?

David HilbertAlbert Einstein

2 2

v

1 v /

x tx

c

2

2 2

v /

1 v /

t x ct

c

y y

z z

Lorentz Transformation

If v << c, i.e., β ≈ 0 and ≈ 1, yielding the familiar Galilean transformation.

2 2

v

1 v /

x tx

c

2

2 2

v /

1 v /

t x ct

c

y y

z z

Length

contraction

Simultaneity

problems

Time

dilation

xct '' xct

C is an invariance

'

'

'

'

2

1

00

0100

0010

00

t

z

y

x

vc

v

t

z

y

x

Linear coordinate Transform

Rotational Transform in 4D

Rotational Transform in 2D

Something never change under Transform

“invariance”

Invariance in 2D

Invariance in 3D

Invariance in 4D

X, Y, Z

t

s2 = x2 + y2 + z2 +(ict)2

= (x’)2 + (y’)2 + (z’)2 + (ict’)2 = (s’)2

v

x

cti Lorentz invariance in 4D Space-time (Minkowski diagram)

X`

t`

v

Space + TimeMinkowski space

Relativistic space and time Inseparable space-time

ds

Rest framevF qE q B

총전하= 자유전자(-) + 구리이온(+) = 0

vF q B

Invariant in the inertial moving frame

vF qE q B

F qE

LL

w