量子的故事
The Story of the Quantum
張志義 Cheung, Chi-Yee
2007.10.13 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
event
Well accepted by everybody!
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
1948: CMB T~
Expt. 2.7 K (1965)
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)
(2)
(3)
(4)
Double slit (1801)
Young’s Modulus
Vision of color
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) 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 - 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 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 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!