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 19th century

•Cavendish (1771,73), Coulomb (1785-91):

force between two charges

(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

21~r

qqforce

Maxwell (1873) summarises these results in

four equations (here stated for vacuum)

t

BE

t

EjB

B

E

000

0

0

/

Coulomb’s law

no magnetic monopole

• Maxwell showed that these equations can

be reduced to wave equations for E and B

• The speed c of the wave is given by

ε0 permittivity;

μ0 permeability (of free space)

and is identified as the speed of light

• Solutions of wave equations:

;01

;01

2

2

2

2

2

2

2

2

t

B

cB

t

E

cE

;ˆ;ˆ )()( ctxikctxik eBBeEE

002

1

c

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 ×108 m/s

• Fizeau (1849), using spinning cogwheel:

c ~ 3.133×108 m/s

• Heinrich Hertz (1887) measure speed of light by

sending and receiving radio waves

• Today: c ~ 2.99792458×108 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,

1851-19011881, 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!

• But if E doesn’t change, also B doesn’t,

electromagnetic theory would collapse!

→ Einstein decides to reinvestigate

Galilean transformation

))((ˆ tVcxikeEE

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

• E=mc2 as consequence of the new Lorentz

transformation (replacing Galileian transformation)

(details in your

lectures on

special relativity:

PY1T10, PY2P20)

All these predictions have been

confirmed by experiments.

Examples:

• E=mc2; 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

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= minertial a and gravitational mass,

but experiments show they are the same

2

21

r

mmGF

Consider reference frames that are

accelerated

On earth watch hits

floor due to gravity.

Absence of gravity in

space. Watch hits floor

due to acceleration of

rocket.

Astronaut about to drop

watch in space-ship.

Impossible for astronaut to distinguish whether in

gravitational field or accelerating rocket.

(Yo

un

g a

nd

Fre

ed

ma

n, F

igu

re 3

7.2

4)

Einstein’s field equation for General Relativity is often written as:

Space time curvature tensor expressed as Gμν - related to the

stress-energy tensor Tμν , which is related to the distribution of

mass in spacetime.

4

8 GG T

c

Einstein needed to use more complicated tensor calculus to

express this mathematically as well as a new flexible coordinate

frame or geometry

• 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.

• 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

Bending of light

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

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.

As time goes by (Herman Hupfeld 1931, Casablanca 1942)

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

Desolation Row, Bob Dylan 1965