Galilean velocity transformation
u
x
... -3
-2
-1
0
1
2
... -3
-2
-1
v
3 ...
x’
0
1
2
3 ...
If an object has velocity u in frame S (note:
velocities have a direction!), and if frame S’ is moving
with velocity v along the positive x-axes of frame S,
then the position of the object in S’ is: x' (t )  x(t )  vt
Announcements
• Reading for Monday (due noon): TZD 1.71.9
• Homework #1 is due at noon, Wednesday
this week (in ‘2130’ box in G2B90).
The velocity u’ of the object in frame S’ is therefore:
A) u + v
B) v - u
C) u - v
D) u
E) -v
Today
• Maxwell vs. Galileo
Strange things about the speed of light
• Is there a luminiferos ether?
Let’s find out!
• Interferometers
Light: the ultimate yardstick.
Last class we found a problem!!
Mr. Maxwell told us, the speed of light ‘c’ is:
c
1
 0 0
 3.00  108 m / s
Mr. Galileo told us that c’ = c – v
If the laws of physics are the same in all
inertial frames then ε0 and µ0 (and c) have
to be the same in all inertial frames.
So let’s make up the “luminiferous ether” to fix
Galileo’s velocity transformation law (u’ = u - v)!
(We will have to check if there is a luminiferous ether!..)
Peculiar light-waves
• A sound wave propagates through air, with a
velocity relative to the air (~330 m / sec)
• A water wave propagates through water, with a
velocity relative to the water (1..100 m / sec)
• “The wave” propagates through a crowd in a
stadium, with a velocity relative to the audience.
• An electromagnetic wave propagates through...
Ideas behind Einstein’s relativity
Is there an ether ?
(There where various other
motivations for special
relativity, but for simplicity we
will focus here on the quest
for detecting the ether.)
Answer (19th century physics): The “luminiferous ether.”
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Quiz on reading
The ether
v
(closed book, no talking)
The Michelson-Morley Experiment tests if the speed
of light in all inertial frames…
c
A – …is not the same in air and in vacuum
Suppose the earth moves through the ether fixed in space with
speed v. A light wave traveling at speed c with respect to the
ether is heading in the opposite direction. According to Galilean
relativity, what is the magnitude of the speed of the light wave
as viewed from the earth? (Assume the earth is not
accelerating).
a) |c|
b) |c|+|v|
c) |c|-|v| d) |v|-|c| e) something else
B – …is not the same in accelerating frames
C – …is not the same in all directions
D – …does not depend on the wavelength or color
E – …does not change when reflected by mirror.
Frame of reference
Michelson and Morley…
Observer on the sun:
‘Ether’
v
…performed a famous*)
experiment that effectively
measured the speed of
light in different directions
with respect to the “ether
wind.”
Ether ‘viewed’ in the laboratory on the earth:
-v
*)
-v
some say, the most successful failure…
Measuring only differences in c
Ether in the laboratory frame
v
L
v
u'-v
-v
-v
u’+v
L
How can we measure the speed v of the ether?
If the ether would be a river, we could measure the speed
of the water using a boat that travels at a known speed u’.
(u’ is the relative velocity between the boat and the water.)
If the boat travels the distance L within the time t, then we
know v: L=(u’-v)t, therefore v = u’ – L/t
But: Very difficult with light! u’ = c  t ~ 10ns and v ~ 0.0001*c.
 We would have to measure t with an absolute precision of
~0.0000000000001s and we have to know c very precisely!
B
A u’-v
L
Compare the round-trip times tA and tB for paths A and B.
This has the great benefit, that we do not have to
measure the absolute times tA and tB (which are only a
few ns) and we are less sensitive to uncertainties in the
speed of light. Instead we can measure the difference
(more or less)
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Michelson and Morley
Intermezzo: Interferometers
Mirrors
L
-v
Detector
1881 Michelson invented a device now known as the
‘Michelson Interferometer.’ 1907 he received the Nobel
prize for it!
-v
L
We will see it in action in the famous Michelson-Morley
experiment, which will lead us to the special relativity
theory.  So the interferometer had a huge impact!!
“Interferometer”
Semi-transparent
mirror
Such interferometers are nowadays widely used for
various precision measurements. State-of-the-art
visible-light interferometers achieve resolutions of
~100pm! (X-ray interferometers are ~1pm).
Light source
(100pm = 1Å = diameter of a Hydrogen atom.)
The detector measures differences in the position of the maxima or minima
of the light-waves of each of the two beams. (Yes, light is a wave!)
Electromagnetic waves
The Michelson interferometer
E-field (for a single color):
E(x,t) = E0 sin[ (2πx/λ ) ̶ ωt +]
Mirrors
Light source
Light source
E
λ
λ = 2πc/ω, ω = 2πf = 2π/T
E0
x

Wavelength λ of visible light
is: λ ~ 400 nm → 750 nm.
E
Semi-transparent
mirror
x
B
Detector
Free physics simulations!
http://phet.colorado.edu
EM-Waves in an interferometer
Mirrors
L
Light source
L
Radio Waves.jar
Wave interference.jar
Semi-transparent
mirror
3
Constructive interference
Unequal arm lengths
Esum(x,t) = ½ ·E0 sin(ωt+2πx/λ +) + ½ ·E0 sin(ωt+2πx/λ +) = ?
=
L
E0 sin(ωt+2πx/λ +) = Elight source(x,t)
Light source
L+ΔL/2
+
=
ΔL/
2
?
ΔL
Screen:
Destructive interference
Moving mirror: What do you see?
Esum(x,t) = ½ ·E0 sin(ωt+2πx/λ +) + ½ ·E0 sin(ωt+2π(x+Δx)/λ +)
= ½ ·E0 sin(ωt+2πx/λ +) - ½ ·E0 sin(ωt+2πx/λ +) = 0
Light source
if Δx = λ / 2:
sin(x+π) = - sin(x)
ΔL
+
=
?
Screen:
Tilted mirror: What
do you see?
Fringes!
Screen
Intensity
λ/
2
ΔL
Interference in daily life:
Light source
Screen
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Do you want a bigger ‘interferometer’?
There you go…
Gravitational wave detectors
Blue iridescence in animals?
Summary for Interferometers
The blue color and iridescence originate from constructive
interference of blue light and destructive interference of all other
colors.
Michelson interferometers allow us to measure tiny
displacements. Displacements of less than 100 nm are
made visible to the eye!
Interferometers find many applications in precision
metrology such as for displacement, distance and
mechanical stress measurements, as well as flatness
measurements.
Interferometers have played an important role in
physics:
Michelson-Morley experiment  special relativity
Testing general relativity: Gravitational wave detection
Global survey of groundwater (GRACE satellites)
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