The Story of the Quantum

量子的故事

2006.11.11 Academia Sinica

In the past century, the progress in physics is tremendous:

Elementary particles, atoms, nuclei, solid states, …, cosmology

Physics Technologies Our lives World

Pillars of modern physics:

(1) Relativity

(2) Quantum theory

…

Theory of Relativity (1905, 1915):

Structure of space-timeMotion at high speeds

Well accepted by everybody!

3-d space + time = 4-d space-time

Quantum Theory (1901-1930)

Physics of the microscopic world

g.s. ~ 0.1 nanometer ~

Predictions are all correct, but …Underlying physics is controversial!

“Wavefunction”

--- Albert Einstein (1879-1955, German, Swiss, US)

Nobel Prize: 1921

(for photoelectric effect)

“Quantum mechanics: Real black magic calculus”

1999

--- Niels Bohr (1885-1962, Danish)

Nobel Prize: 1922

(for atomic model)

"And anyone who thinks they can talk about quantum theory without feeling dizzy hasn't yet understood the first thing about it."

--- Richard Feynman (1918-1988, American)

Nobel Prize: 1965 (for QED)

“I think I can safely say that no one understands quantum mechanics”

The Quantum Revolution:

Began 1901: Max Planck (1858-1947)

Nobel Prize: 1918

Ended 1930: Paul Dirac (1902-1984)

Nobel Prize: 1933

George Gamow (1904-1968, Ukrainian, US)

1948: CMB T~

Alpha-Bethe-Gamow

1965

Physics at the end of 19th century

Issac Newton (1643-1727)

1687: Principia (Philosophiae Naturalis Principia

Mathematica)

Alexander Pope: “Nature and nature's laws lay hid in night;

God said "Let Newton be" and all was light.”

Leonhard Euler (1707-1783, Swiss)

Joseph-Louis Lagrange(1736-1813, Italian French)

Pierre-Simon Laplace(1749-1827, French)

William Hamilton(1805-1865, Irish)

A mechanical, deterministic world view:

Laplace (~1800): A being equipped with unlimited computational p

ower, and given complete knowledge of the positions and momenta of all particles at one instance of time, could use Newton’s equation to predict the future and retrodict the past of the whole universe with certainty.

Statistical mechanics:

Ludwig Boltzmann (1844-1906, Austrian)

--- Boltzmann equation (1872)

--- (1877)

Willard Gibbs (1839-1903, American)

--- Gibbs ensembles (1876)

James Maxwell (1831-1879)“Treatise on Electricity and Magnetism” (1873)

Maxwell’s equations (1864):--- Unification of Electricity

and Magnetism

--- Maxwell eq. wave equation

wave velocity=speed of light

Light is electromagnetic wave

Thus, at 1900, it seems that the classical theories of Newton and Maxwell are able to explain everything on earth and in the sky.

Well, almost …

Cracks in classical physics: (1) Nature of light (2) Blackbody radiation (3) Spectrum of hydrogen

Nature of Light: Particle or wave?

Newton: Particle(1643-1727, English)

Christiaan Huygens: Wave(1629-1695, Dutch)

Thomas Young (1773-1829, English)

“The last person who knows everything”(1) Double slit (1801)

(2) Young’s Modulus

(3) Vision of color

(4) Heart and arteries

(5) Translation of Rosetta stone (1918)

Waves interfer:

(1) Flickr: naughton321 (2) Flickr: Mr. 7

Double-slit experiment

x

Black-body radiation

A blackbody is a theoretical object which absorbs radiation of all wavelengths. (Reflects nothing, therefore black)

(Jean-RayleighUltraviolet catastrophe)

Black-bodyTemp = T

Birth of the quantum

Max Planck (1858-1947, German)

(1901, Berlin)

Nobel Prize: 1918

So, light is particles!

(2) Photoelectric effect (first observed 1839 by Becquerel )

Critical frequencyBelow: no emission, no matter how intenseAbove: emission, even weak

Albert Einstein (1879-1955, German, Swiss, US)

1905 (annus mirabilis, year of wonders)

(1) Brownian motion(2) Photoelectric effect(3) Special relativity

Note: In 1905, he was a third-class examiner in the Patent Office in Berne, i.e., an amateur physicist!

Explanation of photoelectric effect

W = Work function

= Minimum energy needed to kick out an electron

Therefore, if E < W, no electron at all

if E > W, some electrons, no matter how

dim is the light

Again, light is particles, not wave!

Spectrum of Hydrogen

Johann Balmer (1825-1898, Swiss)

Bamler Series (1885):

No one cared much about this result in 1885, because no one knew what atoms are!

Note:

Electron (1897): J. J. Thomson

(1856-1940, English)

Nobel prize: 1906

Nucleus (1911): Ernest Rutherford (1871-1937, NZ, English) Nobel prize: 1908 (Chemistry, radioactivity of atoms)

Atomic model

Electron:

J. J. Thomson, 1897

Nucleus:

E. Rutherford, 1911

plum pudding

Problem: circulating electron radiates!How does one stablize the atom?

The Bohr atom (1913)

--- Niels Bohr (1885-1962, Danish)

Nobel Prize: 1922

(for atomic structure)

Semi-classical model of H atom: rules, not theory

1914, Bohr became famous after the success of his atomic model, and the Royal Danish Academy of Science gave him financial support to set up an Physics Institute.

The fund was actually donated by Carlsberg Brewery (beer)!

The Institute quickly became the center of quantum science in the 1920s and 1930s, due to Bohr’s genius and his personality.

Birth of Quantum Theory (1925)

Werner Heisenberg (1901-1976, German)Nobel Prize: 1932

Matrix Mechanics:

Matrices:

p and x are represented as matrices of infinite dimension

Commutation relation/Quantization condition

Wave Mechanics (precursor)

1924: Louis de Broglie (1892-1987, French) Nobel Prize: 1929

Ph.D. thesis: Electron as wave

If undulating light has particle nature, may be

particles like electrons have wave properties too!

Wave Mechanics (1926) (a few months after Heisenberg)

Erwin Schrodinger (1887-1961, Austrian)Nobel Prize: 1933

Schrodinger Equation: The state of a particle is represented by a “wavefunction” which satisfies

Where H(p,x)

Note: • 1925: Heisenberg was recuperating in a North S

ea island after an severe attack of hay fever. (summer, 1925)

• 1926: Schrodinger was recuperating in Arosa (a 1700m alpine resort) due to suspected tuberculosis, in the company of a girlfriend.

(Christmas, 1925- early 1926) (The identity of the lady of Arosa was never known.)

Max Born (1882-1970, German) Nobel Prize: 1954

Paul Dirac (1902-1984, English) Nobel Prize: 1933

Theories of Heisenberg and Schrodinger are in fact equivalent!

Relativistic quantum mechanics

(Schrodinger equation + special relativity)

Paul Dirac (1928)

Dirac equation

--- for electron, not photon

--- gives the correct magnetic moment

But…It had negative energy solutions!

Dirac:

All the negative levels have already been occupied by other electrons!

Pauli principle then excludes other electrons from these levels.

(1) One-body becomes many-body…

(2) Is the negative electron sea observable?

Dirac: hole = proton (In the old days, physicists are much more conservative at proposing new particles.)

In 1932 Carl Anderson found positron(1905-1991; Nobel prize: 1936)

Dirac said yes!

Later we found that “Dirac sea” is actually not necessary!

So, sometimes one could get the right answer for the wrong reason!

(That is, if you are clever enough!)

Story: Dirac and fish

Nobel Prizes:

1932: W. Heisenberg

"for the creation of QM…"

1933: E. Schrodinger and P. Dirac

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

Prizes conferred in the same year 1933 (no prize given in 1931 and 1932)

W. Pauli: Heisenberg over Schrodinger(1) Matrix mechanics precedes wave mechanics.

(2) Matrix mechanics is more original, for wave mechanics relies on the idea of de Broglie.

A. Einstein: Schrodinger over Heisenberg “I have the impression that the concepts created by

him (Schrodinger) will extend further than those of Heisenberg.”

Heisenberg:

Schrodinger:

As we shall see, the physical principle presented by QM is so revolutionary that it totally changed our understanding of nature forever!

Deterministic vs Probabilistic (classical) (quantum)

(1) Heisenberg Uncertainty Principle

(2) Superposition Principle

However, QM itself needs an interpretation itself! Why?

Quantum mechanics so successful that it can explain all quantum phenomena!

What is this thing called wavefunction?

Copenhagen Interpretation (1927):

Heisenberg BohrMax Born

(1) = Probability density

(2) Measurement (or disturbance) causes wavefunction collapse.

Remember: Newtonian mechanics is deterministic!Probability occurs in Newtonian mechanics Too, but in a different context, e.g. dice

Probability =

Double-slit experiment:

Feynman:

“…a phenomenon which is absolutely impossible to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery.”

Double-slit experiment with electron:

An electron is interfering with itself, not with other electrons!

Electrons: C. Jonsson (Tubingen, Germany, 1961)Single electron: P. G. Merli et al. (Bologna, Italy, 1974)Single electron: A. Tonomura et al. (Hitachi, Japan, 1989)

Like dice

Tonomura et al. (1989)

Wave or Particle?

Copenhagen (Bohr, Heisenberg, Born):

--- depends on how you observe it, before observation, it is just a quantum state represented by .

Not acceptable to many people!

Source of the trouble: Quantum particles do not have deterministic

trajectories like classical ones. (Counterintuitive!)

So physical process cannot be understood in intuitive terms.

In the double-slit experiment, the photon/electron must go through both slits in order to form interference pattern.

If one tries to find out which way it goes, then no interference pattern will be seen, because…

Disturbance due to measurement causes

“wavefunction collapse”

But how does it happen?No answer from the Copenhagen School

Superposition: If there are two routes by which you can go home, then you could actually go home via both routes!

Measurement: However if someone tries to find out which way you take, then they will find you on one and only one of the routes.

In everyday language:

Einstein is very upset by the CopenhagenInterpretation:

(1) God does not play dice!(2) Is the moon there when no one is looking at it?

Einstein & Bohr, debating QM (1920s)

Hot and long debates with Bohr et al.

(1) One of the founders of the quantum concept

(2) A first, thought there must be something wrong with the quantum theory.

(3) After much debate with Bohr, he finally was convinced that QM gives correct results, but it could not be the final theory. It is incomplete!

Einstein:

Einstein’s last attack on QM:

Einstein, Podolsky and Rosen (1935):

“Can quantum-mechanical description of physical reality be considered complete?

EPR:“if, without in any way disturbing a system, we can predict with certainty the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.”

EPR Paradox: Issue unsolved!

Two-body superposition 1: red, 2: blue

“Entangled state”

Schrodinger’s Cat (1935, after EPR)

Schrodinger was also not satisfied with the probabilistic interpretation…

What if: cat person?Descartes: ``cogito, ergo sum”

Delay choice experiments

(John Wheeler)

Bohr: “No phenomenon is a phenomenon until it is

an observed phenomenon” (…rephrased by John Wheeler)

Einstein: “You believe in a dice-playing God and I in

perfect laws in the world of things existing as real objects, …”

Bishop Berkeley (1700s): “to be is to be perceived”

Bohr: Before observation, one cannot attribute classical qualities to the particle.

What is reality or real object?

Is an electron in a state of

reality?

But this is philosophy!

Hidden Variables?

Reasonable hidden variable theories are shown to be not possible!

John Bell (1964):

If 1 and 2 are separated by large distance, then measurement done on 1 should not affect that done on 2.

A. Aspect (1982):

Experiments show that that is not the case!

There is influence! In fact, it seems to be faster than the speed of light!

Many-worlds interpretation (Multiverse)

Hugh Everett (1957)

Each line represents a history of particle or even person

R. Feynman:

“We cannot make the mystery go away by ‘explaining’ how it works. We will just tell you how it work.”

In other words, it is a black box.

“I think I can safely say that no one understands quantum mechanics”

Actually, since 1930’s, most physicists just accepted the quantum theory as a useful tool, and do not worry too much about the interpretation problem, etc.

And by doing so, tremendous progresses have been made in many areas of physics:

elementary particles, atom, nucleus, solid-state, …, cosmology

~1,000 terms, improvement needs >10,000 more terms (2006/11/3)

Applications of a particle’s quantum nature:

(1) Uncertainty and wavefunction collapse Quantum cryptography (1970, 1980’s)

(2) Wavefunction superposition

Quantum computing (1990’s)

Classical bit

Quantum bit

Conclusion

The mystery of the quantum remains

with us today as much as in 1920s.

No breakthrough is in sight, but …

Maybe none is needed.Maybe, that is the way it is!

And maybe, you will find one!