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The Story of the Quantum

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Title: The Story of the Quantum


1
The Story of the Quantum
  • ?????

??? Cheung, Chi-Yee 2007.10.13 Academia Sinica
2
  • In the past century, the progress in physics
    is tremendous
  • Elementary particles, atoms, nuclei, solid
    states, , cosmology

Physics ? Technologies ? Our lives? World
3
  • Pillars of modern physics
  • (1) Relativity
  • (2) Quantum theory


4
Theory of Relativity (1905, 1915)
Structure of space-time Motion at high speeds
Well accepted by everybody!
C constant V lt C
event
3-d space time 4-d space-time
5
  • Quantum Theory (1901-1930)

Physics of the microscopic world
Predictions are all correct, but Underlying
physics is controversial!
Wavefunction
g.s. 0.1 nanometer
6
Quantum mechanics Real black magic calculus
  • --- Albert Einstein
  • (1879-1955, German, Swiss, US)
  • Nobel Prize 1921
  • (for photoelectric effect)

1999
7
"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)

8
I think I can safely say that no one understands
quantum mechanics
  • --- Richard
    Feynman

  • (1918-1988, American)

  • Nobel Prize 1965 (for QED)


9
  • WHY did great physicists have trouble
  • with Quantum Theory?
  • NOT difficulties in mathematics
  • (2) Didnt know how to interpret the results

10
  • The Quantum Revolution
  • Began 1901 Max Planck
  • (German, 1858-1947)
  • Nobel Prize 1918
  • Ended 1930 Paul Dirac
  • (English,1902-1984)
  • Nobel Prize 1933

11
George Gamow (1904-1968, Ukrainian, US)
1901-1930
1948 CMB T Expt. 2.7 K (1965)
Alpha-Bethe-Gamow
1965
12
  • 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.

13
  • Leonhard Euler
  • (1707-1783, Swiss)
  • Joseph-Louis Lagrange
  • (1736-1813, Italian French)
  • Pierre-Simon Laplace
  • (1749-1827, French)
  • William Hamilton
  • (1805-1865, Irish)

14
  • 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 Newtons equation to
    predict the future and retrodict the past of the
    whole universe with certainty.

15
(No Transcript)
16
  • Statistical mechanics
  • Ludwig Boltzmann (1844-1906, Austrian)
  • --- Boltzmann equation (1872)
  • --- (1877)
  • Willard Gibbs (1839-1903, American)
  • --- Gibbs ensembles (1876)

17
  • James Maxwell (1831-1879)
  • Treatise on Electricity and Magnetism (1873)
  • Maxwells equations (1864)
  • --- Unification of Electricity
  • and Magnetism
  • --- Maxwell eq. ? wave equation
  • wave velocityspeed of light
  • ? Light is electromagnetic wave

18
  • 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

19
  • Nature of Light Particle or wave?
  • Newton Particle
  • (1643-1727, English)
  • Christiaan Huygens Wave
  • (1629-1695, Dutch)

20
  • Thomas Young (1773-1829, English)
  • The last person who knows everything
  • Double slit (1801)
  • Youngs Modulus
  • Vision of color
  • Translation of Rosetta stone (1819)
  • http//en.wikipedia.org/wiki/Thomas_Young_28scien
    tist29

21
  • Waves interfer

(1) Flickr naughton321
(2) Flickr Mr. 7
22
  • Double-slit experiment

x
23
So light is wave! But
24
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
25
Birth of the quantum Max Planck (1858-1947,
German)
Nobel Prize 1918
(1901, Berlin)
So, light is also particles!
26
  • (2) Photoelectric effect
  • (first observed 1839 by Becquerel )

Critical frequency Below no emission, no matter
how intense Above emission, even weak
27
  • Albert Einstein (1879-1955, German, Swiss, US)
  • 1905 (annus mirabilis, year of wonders)
  • Brownian motion
  • Photoelectric effect
  • Special relativity

Note In 1905, he was a third-class examiner in
the Patent Office in Berne, i.e., an amateur
physicist!
28
  • Explanation of photoelectric effect

W Work function Minimum energy needed to
kick out an electron Therefore, if E lt W, no
electron at all if E gt W, some
electrons, no matter how dim is
the light
Again, light is particles, not wave!
29
  • 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!
30
  • 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)
31
  • Atomic models
  • Electron
  • J. J. Thomson, 1897

plum pudding
Nucleus E. Rutherford, 1911
Problem circulating electron radiates! How does
one stablize the atom?
32
  • The Bohr atom (1913)

--- Niels Bohr (1885-1962, Danish) Nobel
Prize 1922 (for atomic structure)
Semi-classical model of H atom rules, not
theory!
33
  • 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
    Bohrs genius and his personality.

34
  • 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!
35
  • 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!

36
  • 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!
37
  • 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!

38
  • 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.)

39
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!
40
  • 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!
41
  • 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?

42
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)
43
  • 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
44
  • 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)
45
  • W. Pauli Heisenberg over Schrodinger
  • Matrix mechanics precedes wave mechanics.
  • Matrix mechanics is more original, for wave
    mechanics relies on the idea of de Broglie.
  • Einstein Schrodinger over Heisenberg
  • I have the impression that the concepts
    created by him (Schrodinger) will extend further
    than those of Heisenberg.

46
Heisenberg
Schrodinger
Given the choice, which would you choose?
47
  • 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)

48
Quantum mechanics so successful that it can
explain all quantum phenomena!
However, QM itself needs an interpretation
itself! Why?
What is ???
  • Superposition Principle

49
  • What is this thing called wavefunction?

Copenhagen Interpretation (1927)
Heisenberg
Bohr
Max Born
50
  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.
51
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.
52
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)
53
  • 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!

54
  • 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.
55
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!
56
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.

57
  • 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)
58
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!

59
  • Einsteins last attack on QM
  • Einstein, Podolsky and Rosen (1935)
  • Can quantum-mechanical description of physical
    reality be considered complete?

60
Two-body superposition 1 red, 2 blue
Entangled state
EPRif, 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!
61
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 WholeW. Heisenberg
62
  • Schrodingers Cat (1935, after EPR)

What if cat ? person? Descartes cogito,
ergo sum
63
  • Delay choice experiments
  • (John Wheeler)

64
  • 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,
65
  • What is reality or real object?
  • Is an electron in a state of

real?
But this is philosophy!
66
  • Hidden Variables?

Reasonable hidden variable theories are shown
to be not possible!
67
  • John Bell (1964)

If 1 and 2 are separated by large distance,
then measurement done on 1 should not affect that
done on 2.
  • 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!
68
Many-worlds interpretation (Multiverse) Hugh
Everett (1957)
Each line represents a history of particle or
even person
69
  • 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.
70
  • Actually, after 1930s, 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 gt10,000 more
terms (2006/11/3)
71
  • Applications of a particles quantum nature
  • Uncertainty and wavefunction collapse
  • Quantum cryptography (1970, 1980s)
  • Wavefunction superposition
  • Quantum computing (1990s)

Classical bit
Quantum bit
72
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!
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