PHY 102 – Atoms to Galaxies

Our early human ancestors most

certainly looked at the night sky,

and wondered.

PHY 102 – Atoms to Galaxies

• Newton’s corpuscular theory of light had a few difficulties, such as explaining refraction.

Light: Particle or Wave?

• Newton discovered that white light is composed of the same system of colors that can be seen in the rainbow (refraction).

Diffraction: Thomas Young, 1803.

Light: Particle or Wave?

• From the diffraction experiment with light there is good evidence that light is a wave.

Chapters 13 & 14

Quantum Mechanics

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Quantum Physics

Unlike mechanics (Newton), or electrodynamics (Maxwell), or relativity (Einstein), quantum mechanics was not developed by one individual.

It was rather the result of the work of several scientists in conjunction with a few unexpected experimental measurements.

Quantum Physics

Even though it was born about a century ago, there is no general consensus as to what its fundamental principles are. It still is “work in progress.”

“If you are you are not confused by quantum physics then you haven’t really understood it.”

Niels Bohr

“I think I can safely say that nobody understands quantum mechanics.” Richard Feynman

Blackbody Radiation Blackbody (radiation):

Theoretical object that absorbs 100% of the radiation that hits it; perfect emitter too (carbon-graphite: 97%).

Ultraviolet catastrophe: the theoretical prediction of early 1900s physics was that an ideal blackbody would emit radiation with infinite power. This was in total contrast with experimental results.

Quantum Physics: December of 1900

Max Planck

• proposed that oscillating electrons emitted radiation according to Maxwell’s laws of E & M

• proposed that the energy must increase in discrete amounts (quantized) because the frequencies of the oscillating electrons could only take certain values (digital versus analog).

Quantum Physics

Planck’s approach produced a theory with results that matched experimental measurements.

Quantum Physics

Planck’s approach produced a theory with results that matched experimental measurements.

Max PlanckMax Planck, 1918 Physics Nobel Prize

”in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta”

Quantization of Light

Quantum Physics

Revisit the double slit experiment with light.

Quantization of Light Revisit the double slit experiment with light, this time using extremely dim light.

Quantum Physics What is coming through the slits? We expect it to be waves, but then how can we explain the particle-like impacts of light on the screen?

We may expect it to be disturbances in the electromagnetic field (light wave), but, as we understand it today, it is a “quantized” magnetic field.

For example, take yellow light with a frequency of 5 x 1014 Hz. The EM field allowed to carry this light is allowed to have energies

0 J zero

3.2 x 10-19 J 1 E

6.4 x 10-19 J 2 E

9.6 x 10-19 J 3 E etc.

Quantum PhysicsConsider a typical 100 watt light bulb. About 10% of this energy (10 watt = 10 joule/second) emerges as visible light.Assuming this light to be yellow, in 1 second

10 J / 3.2 x 10-19 J = 3 x 1019 photons

are emitted. These are 30 million trillion quanta of energy. So, the amount of energy in 1 photon is really, really, really, really small.

We do not notice quantization in our everyday lives.

Quantum Physics

When carrying radiation of frequency f , an EM field is allowed to have only the following particular values of total energy:

Etotal = 0, hf , 2hf , 3hf , etc.,

where h = 6.6 x 10-34 J s.

Quantum Physics

So, Planck’s equation E = nhf indicates that electromagnetic waves carry only well defined discrete amounts of energy.

When this particle-like waves hit the screen they produce a dot which corresponds to a specific amount of energy.

The quantized particle-like waves are called photons. They are energy quanta that act like particles.

Note that each individual photon “knows” about the interference pattern regardless of the other photons.

The precise impact point of each photon is unpredictable, but the emerging statistical pattern is predictable.

Like dice throws, individual outcomes are unpredictable but overall statistics are predictable. Unpredictability, or uncertainty, is characteristic of quantum mechanics.

Photoelectric Effect

The most dramatic prediction of Maxwell’s theory of electromagnetism (1865) was the existence of electromagnetic waves moving at the speed of light. Light itself was just such a wave.

Experimentalists then came up with experimental setups to test the theory.

Photoelectric EffectFirst reported in 1839 by Becquerel. Hertz observed it in 1887 but did not explain the phenomenon:

An electric current is produced when a metallic surface is exposed to electromagnetic radiation (visible light or x-rays, for example)

In fact, electrons are emitted from the metallic surface due to absorption of the electromagnetic radiation.

Quantum PhysicsPhotoelectric Effect

Quantum PhysicsPhotoelectric Effect

Quantum PhysicsPhotoelectric Effect

The photoelectric effect was successfully explained by Albert Einstein who assumed quantization of energy.

hf = + K.E.electron

hf = e.m. radiation energy

= work function K.E.electron = electron kinetic energy

Albert EinsteinAlbert Einstein, 1921 Physics Nobel Prize

"for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect"

Waviness of Matter

In 1923, Louis de Broglie proposed that matter should possess wave properties, as much as waves displayed particle characteristics.

Even though there was no experimental evidence, he considered

energy = m v v = p f = h f = h / p

Compute the wavelength associated with a 1 kg ball moving at a speed of 1 m/s:

= h / p = 6.6 x 10-34 J s / (1 kg 1 m/s)

= 6.6 x 10-34 m

Louis de BroglieLouis de Broglie, 1929 Nobel Prize

“for his discovery of the wave nature of electrons”

How do we know that matter has wave properties?

Use electrons, not light, in the double slit experiment. What do we get?

Compare with the output using light.

The Wave Theory of Matter

Every material particle has wave properties with a wavelength equal to h/mv where m is the particle’s mass and v is its speed.

• http://video.google.com/videoplay?docid=390849738419231822

The Wave Theory of Matter

Electrons are not tiny particles that follow a specific path from the electron source through the slits to the screen. Instead, electrons are quanta, increments of the energy of a spread-out field, just as photons are quanta.

The Wave Theory of MatterRange of visible light: ~ 4 to 7 x 10-7 mSize of the atom: ~ 10-10 m

Nature: Nonlocal and Uncertain

Nonlocality: This is one of the most exotic behaviors of microscopic objects such as electrons and photons. A microscopic object knows what happens to another instantaneously, regardless of how far apart they happen to be.

In the double-slit experiment with light and with matter, the entire EM field or matter field changed its character instantaneously when an impact appeared on the screen.

Nature: Nonlocal and UncertainUncertainty: It is impossible to know exactly both position and momentum of a particle. The more accuracy applied to the measurement of one of them, the less precision is obtained with the other:

x p ≈ h (Heisenberg uncertainty principle)

Werner HeisenbergWerner Heisenberg, 1932 Physics Nobel Prize

"for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen"

Niels Bohr, in 1913, proposed a partially quantized version of the planetary atom.

He postulated that the electron would follow specific trajectories around the nucleus of the atom, performing quantum jumps from one trajectory to the other depending on its amount energy.

Niels BohrNiels Bohr, 1922 Physics Nobel Prize

"for his services in the investigation of the structure of the atom and the radiation emanating from them”

In the 1920s, Bohr along with Max Born, Werner Eisenberg and others, developed a view of what quantum theory means.

Max Born proposed that the wave patterns observed in experiments on microscopic particles were probability patterns.

Max BornMax Born, 1954 Physics Nobel Prize

"for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction"

In 1926, Erwin Schroedinger developed an equation for studying the motion of matter waves.

Schroedinger’s equation is consistent with the energy quantum levels and the probability character of the wave function.

Schrödinger Equation

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ih∂Ψ

∂t= −

h2

2m∇ 2Ψ +VΨ

Erwin SchrödingerErwin Schrödinger, 1933 Physics Nobel Prize

"for the discovery of new productive forms of atomic theory”

Paul DiracPaul Dirac, 1933 Physics Nobel Prize

"for the discovery of new productive forms of atomic theory”

Chaos Theory

Late 1800s: The N-body Problem

Old and famous: find exact solutions to N point masses moving under their mutual (Newtonian) gravitational forces.

N = 2, straightforward solutions, known for a long time.

N = 3, chaos breaks loose, literally.

Oscar II, King of Sweden and Norway

1887 Prize for the solution of the three body problem (solar system stability).

Henri Poincaré won the competition

Mathematical error found in the manuscript.

In fixing the mistake Poincaré discovered sensitive dependence on initial conditions.

“If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately.”

“If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.”

The Königsberg Problem

Early 1960sLorenz in 1963 published a paper titled “Deterministic non-periodic flows” that went mostly unnoticed until the mid 1970s.

It contained a set of differential equations meant to represent the behavior of the atmosphere.

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dx

dt= σ (y − x)

dy

dt= x (r − z) − y

dz

dt= xy − bz

Edward Lorenz, 1963

Back in the 1960s Lorenz was one of a few scientists who had a computer to help with numerical calculations.

In the course of his computations Lorenz “discovered” sensitive dependence on initial condition.

“When our results concerning the instability of non-periodic flow are applied to the atmosphere, which is ostensibly non-periodic, they indicate that prediction of the sufficiently distant future is impossible by any method, unless the present conditions are known exactly. In view of the inevitable inaccuracy and incompleteness of weather observations, precise very-long range forecasting would seem to be non-existent.”

Imagine a butterfly flipping its wings in the middle of the Amazon forest. The small perturbation the wings produce in the atmosphere propagates, enlarges and a few weeks later evolves into a big storm in Japan.

This is one landmark of chaotic systems: small variations on initial conditions may lead the system into unpredictable behavior some time later.

The Butterfly Effect

The Butterfly Effect: From nearly the same starting point the trajectories evolves farther and farther apart.

The Butterfly Effect: From nearly the same starting point the trajectories evolves farther and farther apart.

This is the so called sensitivity dependence on initial conditions of chaotic systems.

http://www.exploratorium.edu/complexity/java/lorenz.html

The Lorenz equations intended as a model for the weather are similar to the waterwheel equations as well as laser equations.

D:\ISU Waterwheel.mov

Another example of sensitive dependence on initial conditions: Plasmas

Plasma movie

Poincaré surface of section

Logistic Map & Bifurcation

xn+1 = r xn (1 - xn)

Set r = 4.0: n xn

0 0.499000 1 0.999996 2 0.000016 3 0.000064 4 0.000256 5 0.001024 6 0.004090 7 0.016295 8 0.064117 9 0.24002410 0.72964911 0.78904512 0.665812

In the mid 1970s Mitchell Feigenbaum was working at Los Alamos Nat Lab when he attended a lecture given by Stephen Smale, about the period doubling behavior of quadratic functions.

A Universal Constant

Feigenbaum discovered a constant value between ratios of ranges of periodic windows, in the limit when n ∞

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δn =rn − rn−1

rn+1 − rn

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δ∞ =4.669202L

James Yorke & T.Y. Li (1975), paper entitled “Period Three Implies Chaos.”

Plasma movie

Fractals

We live in a 3-dimensional world need 3 numbers to specify the position of a point: longitude, latitude and altitude, or x y z in Cartesian coordinates.

Number of dimensions: Space 3 Plane 2

Line 1 Point 0

Cantor (ternary) set: Set of points lying on a single line segment with some remarkable properties (Georg Cantor, 1883)

What is the dimension of this set?

Example: Koch snowflake

What is the length of the line?

What is the size of the area inside the line?

Benoit Mandelbrot (late 1960’s) coined the word “fractal.”

Fractals are fragmented geometric shapes such that parts are a reduced-size copy of the whole (self-similarity).

Chapter 15

The Nucleus and Radioactivity

Size of atom: ~10-10 m

nucleus: ~10-14 m

subnuclear particles: ~10-19 m

How come that like electrically charged nuclear particles, such as protons (+) do not get away from each other? In other words, how come that the nucleus of the atom is stable?

Gravitational forces?

Nuclear Forces

There must exist a third force besides electric and gravitational forces. This force must be a strong attractive force between nuclear particles to prevent the nucleus from being blown apart by electrical repulsion.

Strong Forces

Experiments show that this strong nuclear force, or simply strong force, has a short range of action, only 10-15 m (about the distance between adjacent nuclear particles).

Fundamental Forces in Nature

So far to our knowledge, every force in nature can be reduced to the action of four fundamental forces:

• gravitational • electric • strong • weak

Radioactive DecayIn 1896, the French physicist Becquerel left some uranium compound in a drawer containing an unexposed photographic plate. To his surprise he notice later that the film had been exposed, even though it had been kept in the dark.

Becquerel did some chemical treatment to the uranium, but the effect persisted.

Notice that the atomic nucleus had not been discovered yet.

Radioactive Decay

Henri Becquerel, 1903 Physics Nobel Prize, “in recognition of the extraordinary services he has rendered by his discovery of spontaneous radioactivity”

Radioactive DecayIn 1898, the French physicists Marie and Pierre Curie detected radioactivity in pitchblende. The surprise was that the radiation was more intense than the radiation from pure uranium.

The Curies separated a new radioactive substance from 8 tons (~16000 pounds) of pitchblende to get about 0.01 g of the new substance. They named it radium.

Radioactive Decay

Marie and Pierre Curie, 1903 Physics Nobel Prize, “in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena”

Radioactive Decay

Experiments show that radioactive materials emit three types of radiation:

• alpha rays • beta rays • gamma rays