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The Story of the Quantum

- ?????

??? 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

Well accepted by everybody!

C constant V lt C

event

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?
- NOT difficulties in mathematics
- (2) Didnt 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)

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

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.

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- 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)
- Maxwells equations (1864)
- --- Unification of Electricity
- and Magnetism
- --- Maxwell eq. ? wave equation
- wave velocityspeed 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
- Double slit (1801)
- Youngs Modulus
- Vision of color
- Translation of Rosetta stone (1819)
- http//en.wikipedia.org/wiki/Thomas_Young_28scien

tist29

- 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)
- 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!

- 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!

- 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

Bohrs 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
- 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.

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)

Heisenberg

Bohr

Max Born

- 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!

- Einsteins 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

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!

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

- Schrodingers 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.

- 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 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)

- Applications of a particles quantum nature
- Uncertainty and wavefunction collapse
- Quantum cryptography (1970, 1980s)
- Wavefunction superposition
- Quantum computing (1990s)

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!