Harry Varvoglis
University of Tübingen &
University of Thessaloniki
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Quantum Mechanics begins with the idea of Max
Planck (1858-1947) that the “ultra-violet
catastrophe“may be avoided if we accept the noncontinuous emission of E/M radiation in “packets”
(the “quanta”).
The term quantum is probably of medical origin
(quantum satis, QS, the needed amount), and was used
originally by Mayer and Helmholtz, both doctors, to
describe quantities of heat.
Planck used the word to describe quantities of matter
and electricity.
The term quantum of light was introduced by Einstein
in 1905, in his famous paper interpreting the
photoelectric phenomenon.
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The current is
related not
only to the
flux of light
and to the
potential
difference, but
also to its
color!
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Rutherford
scattering
experiment showed
that atoms have a
tiny nucleus, while
electrons lie at large
distances.
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In contrast to the
“English muffin”
model of J.J.
Thomson.
Electrons cannot
“stay still”; they
have to move!
Rutherford
proposed the “solar
system” model.
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Born in New Zealand.
Received the 1908 Nobel Prize in chemistry,
because
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“he discovered the concept of radioactive half-life, proved
that radioactivity involved the transmutation of one
chemical element to another, and also differentiated and
named alpha and beta radiation, proving that the former
are essentially helium ions.”
But he is known as the “father” of Nuclear Physics.
In 1911 his students Hans Geiger and Ernest
Marsden performed the “gold foil experiment”.
The analysis of the results showed that the positive
charge of the atom is concentrated in a nucleus,
contrary to the J.J. Thomson model (muffin).
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Rutherford had a great impact on the scientific
affairs of his time and the selection of Nobel
laureates.
He nominated the following candidates for the
Nobel prize in Physics (NLP = Nobel Laureate in
Physics)
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1912: John H. Poynting
1918: Charles G. Barkla (1917 NLP)
1919/22: Niels Bohr (1922 NLP)
1924/26/27: Charles T. R. Wilson (1927 NLP)
1929: Owen W. Richardson (1929 NLP)
1930: Chandrasekhara V. Raman (1930 NLP)
1935: James Chadwick (1935 NLP)
1937: John D. Cockroft and Ernest T. S. Walton (both 1951
NLP)
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Interesting details:
Henry Moseley would probably have won the Nobel
in Physics of 1917, but he was killed in Gallipoli.
Then Rutherford nominated Barkla, citing as one of his
“advantages” that he did not believe in photons! Although
Barkla had just 1 nomination, while his competitors,
Einstein and Planck, had 6 each one, the prize went to
Barkla.
The later history did not justify at all the selection of
the committee. In his final years Barkla kept his seat as
professor in the University of Edinburgh, under the
condition that he would not supervise PhD students!
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Bohr proposed (1913) the quantization principle and introduced
the 1st quantum number (principal number, the “radius” of the
electron’s orbit).
His theory explained the “coarse” hydrogen spectrum, but not the
fine structure.
A few months later Sommerfeld introduced the 2nd quantum
number (azimuthal number), allowing elliptical orbits and
interpreting the fine structure.
After the observation of the Zeeman effect, a third quantum
number was introduced (magnetic number).
Finally Sommerfeld introduced the 4th quantum number (spin), in
order to explain the superfine structure.
In 1917 Einstein proposed his “quantization rules”, based on the
concept of conjugate variables of Hamiltonian Mechanics and, in
particular, action-angle variables.
Old quantum theory, in its full scale version, could explain the
spectrum of hydrogen-like atoms.
Then came Heisenberg’s uncertainty principle and changed all that.
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Obtained his PhD under Rutherford.
Introduced the first quantization rules of the
Old Quantum Mechanics.
Founded in the University of Copenhagen the
best, probably, research group in Quantum
Physics.
His interpretation of Schrödinger’s equation
and its solution are generally accepted today
and are known as “the Copenhagen
interpretation”.
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Introduced the 2nd and 4th quantum numbers.
Acted as supervisor for 4 Nobel laureates
(Heisenberg, Pauli, Debye, Bethe).
Hired as post-docs 3 more Nobel laureates
(Pauling, Rabi, von Laue).
Was nominated 81 times (!) for a Nobel prize.
Yet he never was honored with that prize.
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In 1925 Heisenberg borrowed the idea of non-commuting
multiplication from abstract Mathematics and Hamiltonian
Theory (Poisson brackets – Lie algebra).
Max Born, the referee of the paper, recognized that the best
mathematical object, that has this property, is a matrix. In
this way he founded Matrix Mechanics.
Born wrote a paper with his former student, Pascual Jordan,
which was published just 2 months after Heisenberg’s
paper.
Later the three of them published a common paper.
Heisenberg published in 1927 his famous results on the
“uncertainty principle”.
After that OQM was dead, since the concept of a trajectory
was meaningless.
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Unconventional life.
Published his paper on Schrödinger’s equation in
January 1926.
Later that year (May 1926) he showed the
equivalence of his approach to that of
Heisenberg’s.
Proposed the famous “Schrödinger’s cat”
gedanken experiment.
Extreme example: “Is the Moon There When
Nobody Looks? (David Mermin, Physics Today,
1985).
Heisenberg , Schrödinger and the police officer .
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Schrödinger's formalism, based on the wave equation,
is the most popular. Heisenberg's formalism, based on
the notion of quantum jumps, was innovative but more
difficult to handle.
The difference on the formalism reflects their different
views on the interpretation of Quantum Mechanics.
Schrödinger was more a realist and he was sharing
Einstein’s view that randomness is not desirable in the
description of sub-atomic physics.
Heisenberg was more a supporter of the Copenhagen
Interpretation of Quantum Mechanics, which interprets
the sub-atomic randomness as an innate characteristic
of the sub-atomic world and the very heart of
Quantum Physics Theory.
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The Schrödinger picture implies an active
unitary transformation. The state vector is
transformed, but all operators are constant in time
unless they contain time explicitly. The basis
vectors are not changing.
The Heisenberg picture implies the equivalent
passive unitary transformation. The state vector
is constant. However the basis vectors are
changing, and therefore the operators are
changing.
So now you know what I'm going to talk about. The next
question is, will you understand what I'm going to tell you?...
No, you're not going to be able to understand it.
It is my task to convince you not to turn away because you don't
understand it. You see, my physics students don't
understand it either. That is because I don't understand it.
Nobody does....
It's a problem that physicists have learned to deal with: they've
learned to realize that whether they like a theory or they
don't like a theory is not the essential question. Rather, it is
whether or not the theory gives predictions that agree with
experiment.
It is not a question of whether a theory is philosophically
delightful, or easy to understand, or perfectly reasonable
from the point of view of common sense....
QED: The Strange Theory of Light and Matter (1985)
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Copenhagen interpretation
Example: lights is particles AND waves?
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We cannot measure IN THE SAME EXPERIMENT both
particle and wave properties!
In the same way, we cannot measure position AND
velocity (momentum), since the measurement of
position affects momentum!
Not compatible with Aristotelian logic!
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NO! It is EITHER particles OR waves!
The problem is ours’, not Nature’s!
Similar philosophical problems appear in Relativity
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Even worse in Quantum Gravity (e.g. see Susskind about the
picture of the event horizon for a far away and a free falling
observer).
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5th Solvay Conference (1927): simultaneous measurement of
position (slit) and momentum (recoil on the wall) of an
electron in the “double-slit” gedanken experiment.
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6th Solvay Conference (1930): simultaneous measurement of
time and energy (Einstein’s box gedanken experiment).
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Bohr: How do you “weight” the box?
1935: EPR experiment
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Bohr: How do you measure the wall’s momentum?
Bohr’ answer was “fuzzy” (according to Bell), but see slide on
Einstein in relativity!
Hidden-variables theories
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Proved wrong by experiments confirming Bell’s inequality