Download CHAPTER 1: The Birth Of Modern Physics

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
James Clerk Maxwell
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
1.1: Classical Physics of the 1890s
Mechanics →
Electromagnetism →
← Thermodynamics
Mechanics began with Galileo (1564-1642)
The first great experimentalist: he established experimental
foundations.
He described the Principle of Inertia.
Mechanics achieved maturity
with Isaac Newton
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.
Isaac
Newton
(16421727)
Newton’s second law: Introduces force
(F) as responsible for the change in
linear momentum (p = mv):
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:
Electromagnetism culminated
with Maxwell’s Equations
Gauss’s law:
(electric field)
Gauss’s law:
(magnetic field)
  E  q / 0
B  0
Faraday’s law:
B
 E  
t
Ampère’s law:
E
 B  0 0
t
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.
Lord Kelvin
Added later:
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.
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:
f = 3 for simple
translations in 3D space
where NA = Avogadro’s Number
More Results of the Kinetic Theory
speed
Maxwell derived a relation
for the molecular speed
distribution f(v):
Boltzmann determined the
root-mean-square molecular
speed:
v rms 
v
2
3kT

m
thus relating energy to
temperature for an ideal
gas.
3/ 2
 m 
f (v)  4 N 

 2 kT 
v2 exp(mv2 / 2kT )
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
Newton in action
"I procured me a triangular glass prism to
try therewith the celebrated phenomena of
colours." (Newton, 1665)
The Nature of Light
Huygens promoted the wave theory.
He realized that light propagates as
a wave from the point of origin.
He realized that light slowed down
on entering dense media.
Christiaan Huygens
(1629-1695)
He explained polarization,
reflection, refraction, and double
refraction.
Double refraction
Diffraction confirmed light to be a wave.
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.
Diffraction patterns
One slit
Augustin Fresnel
Two slits
Light waves were found to be solutions to
Maxwell’s Equations.
microwave
2
1
106
10
10
radio
visible
The electromagnetic spectrum is vast.
infrared
0
105
10
-1
4
10
10
3
10
wavelength (nm)
UV
2
10
X-ray
1
10
0
10
-1
10
gamma-ray
All electromagnetic waves
travel in a vacuum with a
speed c given by:
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 atomic-theory controversy raised fundamental questions.
The constituents of
atoms became a
significant question.
The structure of matter
remained unknown.
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!
The atomic theory wasn’t
actually universally
accepted.
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 electromagnetic medium—
referred to as “ether” or
“aether.”
The failure of classical
physics to explain
blackbody radiation.
More problems: discrete spectral lines
For reasons then unknown, atomic gases emitted only certain narrow
frequencies, unique to each atomic species.
Emission
Absorption
spectra
spectra
from a cold
from
gases of
atomic
gas
hot
in
front of a
atoms.
hot
source.
Wavelength
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.
Max Karl Ernst Ludwig Planck
(1858-1947)
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.
The Beginnings of Modern Physics
Special
relativity
19th-century
physics
0
Log (size)
General relativity
Quantum mechanics
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.
c
Speed
These new discoveries and the
many resulting complications
required a massive revision of
fundamental physical
assumptions.