CHAPTER 1 The Birth of Modern Physics

1.1 Classical Physics of the 1890s

1.2 The Kinetic Theory of Gases

1.3 Waves and Particles

1.4 Conservation Laws and Fundamental

Forces

1.5 The Atomic Theory of Matter

1.6 Outstanding Problems of 1895 and

New Horizons

The more important fundamental laws and facts of physical science have all been

discovered, and these are now so firmly established that the possibility of their

ever being supplanted in consequence of new discoveries is exceedingly

remote… Our future discoveries must be looked for in the sixth place of decimals.

- Albert A. Michelson, 1894

There is nothing new to be discovered in physics now. All that remains is more

and more precise measurement. - Lord Kelvin, 1900

James Clerk Maxwell

1.1: Classical Physics of the 1890s

Mechanics →

← Thermodynamics

Electromagnetism →

Mechanics began with Galileo (1564-1642)

The first great experimentalist: he established experimental

foundations.

He described the Principle of Inertia.

Newton’s third law (Law of action and

reaction): The force exerted by body 1 on body

2 is equal in magnitude and opposite in direction

to the force that body 2 exerts on body 1:

Mechanics achieved maturity

with Isaac Newton

Isaac

Newton

(1642-

1727)

Three laws describing the relationship

between mass and acceleration.

Newton’s first law (Law of inertia):

An object with a constant velocity will

continue in motion unless acted upon

by some net external force.

Newton’s second law: Introduces force

(F) as responsible for the change in

linear momentum (p = mv):

0 0

EB

t

BE

t

0B

0/E q

Electromagnetism culminated

with Maxwell’s Equations

Gauss’s law:

(electric field)

Gauss’s law:

(magnetic field)

Faraday’s law:

Ampère’s law:

James Clerk Maxwell

(1831-1879)

in the presence of

only stationary

charges.

The Laws of Thermodynamics

First law: The change in the internal

energy ΔU of a system is equal to the

heat Q added to a system plus the

work W done by the system:

ΔU = Q + W

Second law: It’s impossible to convert

heat completely into work without some

other change taking place.

The “zeroth” law: Two systems in thermal equilibrium with a third

system are in thermal equilibrium with each other.

Third law: It’s impossible to achieve absolute zero temperature.

Added later:

Lord Kelvin

Primary results of 19th-century

Thermodynamics

Established the atomic theory

of matter

Introduced thermal equilibrium

Established heat as energy

Introduced the concept of internal energy

Created temperature as a measure of internal energy

Realized limitations: some energy processes cannot take place

1.2: The Kinetic Theory of Gases

The ideal gas equation for n

moles of a “simple” gas:

PV = nRT

where R is the ideal gas

constant, 8.31 J/mol · K

Primary Results of the Kinetic Theory

Internal energy U is directly related to the average molecular kinetic

energy.

Average molecular kinetic energy, K, is directly related to absolute

temperature.

Internal energy equally is distributed among the number of degrees of

freedom (f ) of the system:

where NA = Avogadro’s Number

f = 3 for simple

translations in 3D space

3/ 2

2 2(v) 4 v exp( v / 2 )2

mf N m kT

kT

More Results of the Kinetic Theory

Maxwell derived a relation

for the molecular speed

distribution f(v):

thus relating energy to

temperature for an ideal

gas.

Boltzmann determined the

root-mean-square molecular

speed:

speed

2 3v vrms

kT

m

Other successes for Kinetic Theory

It predicted:

Diffusion

Mean free path

Collision frequencies

The speed of sound

1.3: Particles and Waves

Two ways in which energy is transported:

Point mass interaction:

transfers of momentum

and kinetic energy:

particles.

Extended regions wherein

energy is transferred by

vibrations and rotations:

waves.

The Nature of Light

Newton promoted the corpuscular

(particle) theory

Particles of light travel in straight

lines or rays

Explained sharp shadows

Explained reflection and refraction

"I procured me a triangular glass prism to

try therewith the celebrated phenomena of

colours." (Newton, 1665)

Newton in action

The Nature of Light

Huygens promoted the wave theory.

He explained polarization,

reflection, refraction, and double

refraction.

Double refraction

Christiaan Huygens

(1629-1695)

He realized that light propagates as

a wave from the point of origin.

He realized that light slowed down

on entering dense media.

Diffraction confirmed light to be a wave.

Diffraction patterns

One slit

Two slits

While scientists of Newton’s time

thought shadows were sharp, Young’s

two-slit experiment could only be

explained by light behaving as a wave.

Fresnel developed an accurate theory

of diffraction in the early 19th century.

Augustin Fresnel

Light waves were found to be solutions to

Maxwell’s Equations.

All electromagnetic waves

travel in a vacuum with a

speed c given by:

10-1

100

101

102

103

104

infrared X-ray UV vis

ible

wavelength (nm)

microwave

radio

10-1

100

101

102

103

104

105 106

gamma-ray

The electromagnetic spectrum is vast.

where μ0 and ε0 are the permeability and permittivity of free space

Triumph of Classical Physics:

The Conservation Laws

Conservation of energy: The sum of energy

(in all its forms) is conserved (does not

change) in all interactions.

Conservation of linear momentum: In the

absence of external forces, linear

momentum is conserved in all interactions.

Conservation of angular momentum: In the

absence of external torque, angular

momentum is conserved in all interactions.

Conservation of charge: Electric charge is

conserved in all interactions.

These laws remain

the key to interpreting

even particle physics

experiments today.

1.5: The Atomic

Theory of Matter

Initiated by Democritus and Leucippus

(~450 B.C.), who were the first to

use the Greek atomos, meaning

“indivisible.”

Proust (1754 – 1826) proposed the Law of definite proportions

(combining of chemicals always occurred with the same

proportions by weight).

Dalton advanced the atomic theory to explain the law of definite

proportions.

Avogadro proposed that all gases at the same temperature, pressure,

and volume contain the same number of molecules (atoms):

6.02

1023 atoms.

Cannizzaro (1826 – 1910) made the distinction between atoms and

molecules advancing the ideas of Avogadro.

Opposition to atomic theory

Ernst Mach was an extreme “logical

positivist,” and he opposed the theory on

the basis of logical positivism, i.e., atoms

being “unseen” place into question their

reality.

Wilhelm Ostwald (1853 – 1932) supported

Mach, but did so based on unexplained

experimental results of radioactivity,

discrete spectral lines, and the formation of

molecular structures. (These are good

points, but not against atomic theory, as it

turned out.)

Boltzmann committed suicide in 1905, and it’s

said that he did so because so many

people rejected his theory.

Ernst Mach

(1838-1916)

Unresolved questions for atomic theory at the

end of the 19th century

The constituents of

atoms became a

significant question.

The structure of matter

remained unknown.

The atomic theory wasn’t

actually universally

accepted.

The atomic-theory controversy raised fundamental questions.

Scanning Tunneling Microscope image of

76 individually placed iron atoms on a

copper surface. This image (taken almost

100 years later) nicely proves the atomic

theory!

1.6: Problems in 19th-century physics

In a speech to the Royal Institution in 1900, Lord Kelvin

himself described two “dark clouds on the horizon” of physics:

The question of the

existence of an electro-

magnetic medium—

referred to as “ether” or

“aether.”

The failure of classical

physics to explain

blackbody radiation.

More problems: discrete spectral lines

Wavelength

Emission

spectra

from

gases of

hot

atoms.

For reasons then unknown, atomic gases emitted only certain narrow

frequencies, unique to each atomic species.

Absorption

spectra

from a cold

atomic gas

in front of a

hot source.

More problems for 19th-century physics

There were observed differences in the electric and magnetic fields

between stationary and moving reference systems.

When applying a simple Galilean transformation, Maxwell’s

Equations changed form.

The kinetic theory failed to predict

specific heats for real (non-ideal)

gases.

How did atoms form solids?

Bismuth crystal, an interesting solid

Additional discoveries in 1895-7 contributed to

the complications.

X-rays (Roentgen)

Radioactivity (Becquerel)

Electron (Thomson)

Zeeman effect

Roentgen’s x-ray

image of his wife’s hand

(with her wedding ring)

Overwhelming evidence for

the existence of atoms didn’t

arrive until the 20th century.

Max Planck advanced the atom concept

to explain blackbody radiation

by use of submicroscopic quanta.

Boltzmann required the existence of atoms

for his advances in statistical mechanics.

Einstein used molecules to explain Brownian motion (microscopic

“random” motion of suspended grains of pollen in water) and

determined the approximate value of their size and mass.

Jean Perrin (1870 – 1942) later experimentally verified Einstein’s

predictions.

Max Karl Ernst Ludwig Planck

(1858-1947)

The Beginnings of Modern Physics

These new discoveries and the

many resulting complications

required a massive revision of

fundamental physical

assumptions.

The introduction (~1900) of the

modern theories of special

relativity and quantum

mechanics became the starting

point of this most fascinating

revision. General relativity

(~1915) continued it. Log (size)

Speed

0

c

19th-century

physics

Genera

l re

lativity

Quantu

m m

echanic

s

Special

relativity