7. Motivation for Einstein's Theories of Relativity (1905, 1915)

7. Motivation for Einstein’s
Theories of Relativity (1905, 1915)
1879-1955
Photo: http://en.wikipedia.org/wiki/Albert_Einstein

7.1 Unification of Electricity
and Magnetism
Brief history of findings
•Greek philosophers: electric shocks, magnetic minerals
•thought of as unrelated phenomena until 19 th century
•Cavendish (1771,73), Coulomb (1785-91):
q1q2
force between two charges force ~ r
(similar to Newton’s gravitational law)
•Oersted (1819): electric current produces magnetic field
•Ampère: forces between two parallel currents, magnetic in nature
•Faraday: magnetism produces electricity (induction); concept of
fields
2

Maxwell (1873) summarises these results in
four equations (here stated for vacuum)
Coulomb’s law
no magnetic monopole
E
B
B
E
/
0
0
j
0
B
t
0
0
E
t

• Maxwell showed that these equations can
be reduced to wave equations for E and B
2
1
E
2
c
2
E
2
t
0;
• The speed c of the wave is given by
1
c
2
ε 0 permittivity;
μ 0 permeability (of free space)
and is identified as the speed of light
• Solutions of wave equations:
E
0
0
2
1
B
2
c
2
B
2
t
ˆ ik( xct
)
; ˆ ik(
xct
)
Ee B Be ;
0;

Measurements of the speed of light
• First attempts by Galilei (lanterns at mountain tops!)
• Ole Roemer (1676): orbital period of Jupiter moon Io
fluctuates with distance between Jupiter and earth
(22 minutes)
speed of light c ~ 2.14 ×10 8 m/s
• Fizeau (1849), using spinning cogwheel:
c ~ 3.133×10 8 m/s
• Heinrich Hertz (1887) measure speed of light by
sending and receiving radio waves
• Today: c ~ 2.99792458×10 8 m/s = 299792.458 km/s

The question of the ether
• Sound waves and water waves require a
medium, what about light
• Aristotle: “nature abhors a vacuum”
• Descartes: light as an instantaneous
disturbance in the ether (plenum)
• Maxwell: “We can scarcely avoid the
conclusion that light consists in the
transverse undulations of the same
medium which is the cause of electric and
magnetic phenomena.”

But ether could not be found
experimentally and was not
required theoretically.
• Michelson and Morley (1887): attempt to
detect the passage of earth through the
ether by measuring speed of light waves in
different directions; no effect!
• FitzGerald (1889), Lorentz (1892) object
moving through ether would be contracted!

Michelson-Morley experiment
observed interference fringes dependent upon optical path length
if the earth travelled
through an ether,
there should be a
time difference for the
two different paths;
thus a dependence
in interference
fringes on
orientation
No such detection–
a null result.
Young and Freedman, Figure 35.20

George Francis FitzGerald,
1851-1901
1881, TCD Erasmus Smith's Professor of Natural and Experimental Philosophy
1883, election to fellowship of the Royal Society (FRS)
Flying a Lilienthal glider from the Pav!

“The Ether and the Earth's Atmosphere.”
(Fitzgerald’s letter to Science Volume 13, Issue 328, pp. 390, 1889)
I HAVE read with much interest Messrs. Michelson and Morley's wonderfully
delicate experiment attempting to decide the important question as to how far
the ether is carried along by the earth. Their result seems opposed to other
experiments showing that the ether in the air can be carried along only to an
inappreciable extent. I would suggest that almost the only hypothesis that
can reconcile this opposition is that the length of material bodies
changes, according as they are moving through the ether or across it, by
an amount depending on the square of the ratio of their velocity to that of
light. We know that electric forces are affected by the motion of the electrified
bodies relative to the ether, and it seems a not improbable supposition that the
molecular forces are affected by the motion, and that the size of a body alters
consequently. ...
Dublin, May 2
fitzgerald_science_13_390_89.pdf

7.2 Motivation of Einstein’s
theory of special relativity
• Galilean transformation
(Young and Freedman, Figure 37.02)

• Galilei transformation in principle valid for
all velocities V of moving frame of
reference, but what happens to Maxwell’s
equations at V=c Time dependence
drops out!
E
ˆ
ik
Ee
( x(
cV
) t)
• But if E doesn’t change, also B doesn’t,
electromagnetic theory would collapse!
→ Einstein decides to reinvestigate
Galilean transformation

1905: Two Postulates
1. all physical laws valid in one frame of
reference are equally valid in any other
frame of reference moving uniformly
relative to the first (inertial frame)
2. speed of light in vacuum is the same in all
inertial frames, regardless of motion of
light source
Thus there is no frame at which c=0, no
frozen electromagnetic wave.

Startling Consequences
• Space and time are relative
Change in space and time must make up
for motion of light source in frame where
source is moving
• Relativity of simultaneity
• Time dilation
• Length contraction
(details in your
lectures on
special relativity:
PY1T10, PY2P20)
• E=mc 2 as consequence of the new Lorentz
transformation (replacing Galileian transformation)

All these predictions have been
confirmed by experiments.
Examples:
• E=mc 2 ; Cockroft and Walton
• decay of high speed cosmic ray produced
muons 10 times slower than if they were at rest
to observer

7.3 Motivation for Einstein’s
general theory of relativity
• Newton’s Law of Gravity
F G
m m
1
r
2
2
G: gravitational constant
• Instantaneous force: action at a distance
• But how is this force transmitted
• Also: strictly speaking two definitions of
mass; inertial mass (Newton’s second
law, F= m inertial a and gravitational mass,
but experiments show they are the same

Consider reference frames that are
accelerated
(Young and Freedman, Figure 37.24)
Astronaut about to drop
watch in space-ship.
Absence of gravity in
space. Watch hits floor
due to acceleration of
rocket.
On earth watch hits
floor due to gravity.
Impossible for astronaut to distinguish whether in
gravitational field or accelerating rocket.

Einstein needed to use more complicated tensor calculus to
express this mathematically as well as a new flexible coordinate
frame or geometry
Einstein’s field equation for General Relativity is often written as:
G
8
G
T
4
c
Space time curvature tensor expressed as G μν - related to the
stress-energy tensor T μν , which is related to the distribution of
mass in spacetime.

• Space is distorted by gravitational fields (stars, black
holes),
• Or: space is no longer absolute, but defined by matter
(Young and Freedman, Figure 37.25)

Again:
Predictions of theory of
general relativity have
been experimentally
confirmed.

Bending of light
• Beam of light emitted perpendicular to direction of
acceleration does not travel in straight line, but also
“falls” – Newton’s gravitation also predicts this, but
Einstein’s theory differs in the magnitude of effect –
predicts it to be double.
• Measurable effect in agreement with Einstein’s theory
- e.g Eddington’s measurement of 1919 – repeated
measurements with a definitive measurement in 1960
using radio waves

Explanation of anomalous precession of the
perihelion of mercury
• Perihelion: point in orbit nearest to the sun (furthest
point: aphelion)
• Precession: orbit not fully closed
• Only partly explained by classical physics (influence
of other planets)
Gravitational redshift – photons lose energy in
escaping a gravitational potential well

As time goes by (Herman Hupfeld 1931, Casablanca 1942)
This day and age we're living in
Gives cause for apprehension
With speed and new invention
And things like fourth dimension.
Yet we get a trifle weary
With Mr. Einstein's theory.
So we must get down to earth at times
Relax relieve the tension
And no matter what the progress
Or what may yet be proved
The simple facts of life are such
They cannot be removed.
You must remember this
A kiss is just a kiss, a sigh is just a sigh.
The fundamental things apply
As time goes by.

Desolation Row, Bob Dylan 1965
Einstein, disguised as Robin Hood
With his memories in a trunk
Passed this way an hour ago
With his friend, a jealous monk
He looked so immaculately frightful
As he bummed a cigarette
Then he went off sniffing drainpipes
And reciting the alphabet
Now you would not think to look at him
But he was famous long ago
For playing the electric violin
On Desolation Row