量子的故事

The Story of the Quantum

張志義

2007.10.13

Cheung, Chi-Yee 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-time Motion at high speeds Well accepted by everybody!

event C = constant V < C 3-d space + time = 4-d space-time

Quantum Theory

(1901-1930) Physics of the microscopic world Predictions are all correct, but … Underlying physics is controversial!

“ Wavefunction ” g.s. ~ 0.1

nanometer

~

“ Quantum mechanics: Real black magic calculus ”

---

Albert Einstein (1879-1955, German, Swiss, US) Nobel Prize: 1921 (for photoelectric effect) 1999

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

-- Niels Bohr (1885-1962, Danish) Nobel Prize: 1922 (for atomic model)

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

Richard Feynman (1918-1988, American) Nobel Prize: 1965 (for QED)

WHY did great physicists have trouble with Quantum Theory?

(1) NOT difficulties in mathematics (2) Didn’t know how to interpret the results

The Quantum Revolution:

Began 1901:

Max Planck

(German, 1858-1947) Nobel Prize: 1918 Ended 1930:

Paul Dirac

(English,1902-1984) Nobel Prize: 1933

George Gamow

(1904-1968, Ukrainian, US) 1901-1930 1965 1948: CMB

T

~ Expt. 2.7 K (1965) Alpha-Bethe-Gamow

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 power, 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) Translation of Rosetta stone (1819) http://en.wikipedia.org/wiki/Thomas_Young_%28scientist%29

Waves interfer: (1) Flickr:

naughton321

(2) Flickr:

Mr. 7

Double-slit experiment x

So light is wave! But …

Black-body radiation

A blackbody is a theoretical object which absorbs radiation of all wavelengths.

(Reflects nothing, therefore black) (Jean-Rayleigh Ultraviolet catastrophe) Black-body Temp =

T

Birth of the quantum

Max Planck (1858-1947, German ) Nobel Prize: 1918 (1901, Berlin)

So, light is also particles!

(2) Photoelectric effect

(first observed 1839 by Becquerel )

Critical frequency

Below: no emission, no matter how intense Above: emission, even weak

Albert Einstein

( 1879-1955 , German, Swiss, US ) 1905 (

annus mirabilis

, year of wonders)

(1) Brownian motion

(2) (3)

Photoelectric effect 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)

(Chemistry -

Nobel prize: 1908 chemistry of radioactive substances

)

Atomic models

Electron: J. J. Thomson, 1897

plum pudding

Nucleus: E. Rutherford, 1911

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

Then he was able to explain the spectrum of hydrogen!

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)

It was also able to explain the spectrum of hydrogen!

The state of a particle is represented by a wavefunction called It contains everything you can know about the particle However, from the existence of “i”, we know that cannot be a real wave (like water waves). It is only a tool for predicting experimental results!

•

Note:

1925:

Heisenberg was recuperating in a North Sea island after an severe attack of hay fever.

(summer, 1925) •

1926:

Schrodinger was recuperating in Arosa (a Swiss 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

in fact equivalent!

are

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 said yes!

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)

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:

Given the choice, which would you choose?

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)

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

However, QM itself needs an interpretation itself!

Why?

What is ???

Superposition Principle

What is this thing called wavefunction?

Copenhagen Interpretation (1927): Max Born Heisenberg Bohr

(1) = Probability density

Remember: Newtonian mechanics is deterministic!

Probability occurs in Newtonian mechanics Too, but in a different context, e.g. dice

Probability = (2)

Measurement

(or disturbance) causes

wavefunction collapse.

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: Tonomura et al. (1989) Like dice 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)

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 Or anybody!

In everyday language:

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.

Einstein is very upset by the Copenhagen Interpretation:

God does not play dice!

Hot and long debates with Bohr et al.

Einstein & Bohr, debating QM (1920s)

Einstein:

(1) One of the founders of the quantum concept (2) A first, thought there must be something wrong with the quantum theory.

(3) After many debates with Bohr, he finally was convinced that QM gives correct results, but it could not be the final theory.

It is incomplete!

Einstein’s last attack on QM:

Einstein, Podolsky and Rosen (1935):

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

Two-body superposition 1: red, 2: blue

“ Entangled state ”

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!

Schrodinger

was also not satisfied with the probabilistic interpretation …

He told Bohr in Copenhagen in 1926

“If we are still going to have to put up with these damned quantum jumps, I am sorry that I ever had anything to do with quantum theory.”

“ The Part and the Whole ” W. Heisenberg

Schrodinger’s Cat

(1935, after EPR)

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)

Bishop Berkeley

(1700s): “ to be is to be perceived ”

Bohr:

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

Einstein:

“You believe in a dice-playing God and I in perfect laws in the world of things existing as real objects, …”

What is reality or real object?

Is an electron in a state of real?

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

In other words, it is still a

black box .

Actually, after 1930’s, most physicists just accepted the quantum theory as an useful tool, and did not worry too much about the interpretation problem.

If you cannot remove a stone in front of you, just go around it!

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, one of you will find the real answer!