Physics 334Modern Physics

Credits: Material for this PowerPoint was adopted from Rick Trebino’s lectures from Georgia Tech which were based on the textbook “Modern Physics” by Thornton and Rex. Many of the images have been used also from “Modern Physics” by Tipler and Llewellyn, others from a variety of sources (PowerPoint clip art, Wikipedia encyclopedia etc), and contributions are noted wherever possible in the PowerPoint file. The PDF handouts are intended for my Modern Physics class, as a study aid only.

Class OverviewThe Birth of Modern Physics

1.1 Classical Physics of the 1890s1.2 The Kinetic Theory of Gases1.3 Waves and Particles1.4 Conservation Laws and Fundamental

Forces1.5 The Atomic Theory of Matter1.6 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

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t

BE

t

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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

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

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-rayUVvisi

ble

wavelength (nm)

microwave

radio

10-1

100

101

102

103

104

105106

gamma-ray

The electromagnetic spectrum is vast.

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

Michelson & Morley

Waves typically occur in a medium. So in 1887, Michelson and Morley attempted to measure the earth's velocity with respect to what was then called the aether and found it always to be zero. Yes, this was disturbing. But no one knew what to do about it.

Edward Morley (1838-1923)

Albert Michelson (1852-1931)

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.

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