The quantum age begins
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It is hard to realise that the electron was discovered less than 100 years ago in 1897. That
it was not expected is illustrated by a remark made by J J Thomson, the discoverer of the
electron. He said
I was told long afterwards by a distinguished physicist who had been present
at my lecture that he thought I had been pulling their leg.
The neutron was not discovered until 1932 so it is against this background that we trace
the beginnings of quantum theory back to 1859.
In 1859 Gustav Kirchhoff proved a theorem about blackbody radiation. A blackbody is an
object that absorbs all the energy that falls upon it and, because it reflects no light, it
would appear black to an observer. A blackbody is also a perfect emitter and Kirchhoff
proved that the energy emitted E depends only on the temperature T and the frequency v of
the emitted energy, i.e.
E = J(T,v).
He challenged physicists to find the function J.
In 1879 Josef Stefan proposed, on experimental grounds, that the total energy emitted by a
hot body was proportional to the fourth power of the temperature. In the generality stated
by Stefan this is false. The same conclusion was reached in 1884 by Ludwig Boltzmann for
blackbody radiation, this time from theoretical considerations using thermodynamics and
Maxwell's electromagnetic theory. The result, now known as the Stefan-Boltzmann law,
does not fully answer Kirchhoff challenge since it does not answer the question for specific
wavelengths.
In 1896 Wilhelm Wien proposed a solution to the Kirchhoff challenge. However although his
solution matches experimental observations closely for small values of the wavelength, it
was shown to break down in the far infrared by Rubens and Kurlbaum.
Kirchhoff, who had been at Heidelberg, moved to Berlin. Boltzmann was offered his chair in
Heidelberg but turned it down. The chair was then offered to Hertz who also declined the
offer, so it was offered again, this time to Planck and he accepted.
Rubens visited Planck in October 1900 and explained his results to him. Within a few hours
of Rubens leaving Planck's house Planck had guessed the correct formula for Kirchhoff's J
function. This guess fitted experimental evidence at all wavelengths very well but Planck
was not satisfied with this and tried to give a theoretical derivation of the formula. To do
this he made the unprecedented step of assuming that the total energy is made up of
indistinguishable energy elements - quanta of energy. He wrote
Experience will prove whether this hypothesis is realised in nature
Planck himself gave credit to Boltzmann for his statistical method but Planck's approach
was fundamentally different. However theory had now deviated from experiment and was
based on a hypothesis with no experimental basis. Planck won the 1918 Nobel Prize for
Physics went to Planck for this work.
In 1901 Ricci and Levi-Civita published Absolute differential calculus. It had been
Christoffel's discovery of 'covariant differentiation' in 1869 which let Ricci extend the
theory of tensor analysis to Riemannian space of n dimensions. The Ricci and Levi-Civita
definitions were thought to give the most general formulation of a tensor. This work was
not done with quantum theory in mind but, as so often happens, the mathematics necessary
to embody a physical theory had appeared at precisely the right moment.
In 1905 Einstein examined the photoelectric effect. The photoelectric effect is the release
of electrons from certain metals or semiconductors by the action of light. The
electromagnetic theory of light gives results at odds with experimental evidence. Einstein
proposed a quantum theory of light to solve the difficulty and then he realised that Planck's
theory made implicit use of the light quantum hypothesis. By 1906 Einstein had correctly
guessed that energy changes occur in a quantum material oscillator in changes in jumps
which are multiples of hv where h is Planck's constant and v is the frequency. Einstein
received the 1921 Nobel Prize for Physics, in 1922, for this work on the photoelectric
effect.
In 1913 Niels Bohr wrote a revolutionary paper on the hydrogen atom. He discovered the
major laws of the spectral lines. This work earned Niels Bohr the 1922 Nobel Prize for
Physics. Arthur Compton derived relativistic kinematics for the scattering of a photon (a
light quantum) off an electron at rest in 1923.
However there were concepts in the new quantum theory which gave major worries to many
leading physicists. Einstein, in particular, worried about the element of 'chance' which had
entered physics. In fact Rutherford had introduced spontaneous effect when discussing
radio-active decay in 1900. In 1924 Einstein wrote:-
There are therefore now two theories of light, both indispensable, and - as one
must admit today despite twenty years of tremendous effort on the part of
theoretical physicists - without any logical connection .
In the same year, 1924, Niels Bohr, Kramers and Slater made important theoretical
proposals regarding the interaction of light and matter which rejected the photon. Although
the proposals were the wrong way forward they stimulated important experimental work.
Niels Bohr addressed certain paradoxes in his work.
(i) How can energy be conserved when some energy changes are continuous and some are
discontinuous, i.e. change by quantum amounts.
(ii) How does the electron know when to emit radiation.
Einstein had been puzzled by paradox (ii) and Pauli quickly told Niels Bohr that he did not
believe his theory. Further experimental work soon ended any resistance to belief in the
electron. Other ways had to be found to resolve the paradoxes.
Up to this stage quantum theory was set up in Euclidean space and used Cartesian tensors of
linear and angular momentum. However quantum theory was about to enter a new era.
The year 1924 saw the publication of another fundamental paper. It was written by
Satyendra Nath Bose and rejected by a referee for publication. Bose then sent the
manuscript to Einstein who immediately saw the importance of Bose's work and arranged
for its publication. Bose proposed different states for the photon. He also proposed that
there is no conservation of the number of photons. Instead of statistical independence of
particles, Bose put particles into cells and talked about statistical independence of cells.
Time has shown that Bose was right on all these points.
Work was going on at almost the same time as Bose's which was also of fundamental
importance. The doctoral thesis of Louis de Broglie was presented which extended the
particle-wave duality for light to all particles, in particular to electrons. Schrdinger in
1926 published a paper giving his equation for the hydrogen atom and heralded the birth of
wave mechanics. Schrdinger introduced operators associated with each dynamical variable.
The year 1926 saw the complete solution of the derivation of Planck's law after 26 years. It
was solved by Dirac. Also in 1926 Born abandoned the causality of traditional physics.
Speaking of collisions Born wrote
One does not get an answer to the question, What is the state after collision?
but only to the question, How probable is a given effect of the collision? From
the standpoint of our quantum mechanics, there is no quantity which causally
fixes the effect of a collision in an individual event.
Heisenberg wrote his first paper on quantum mechanics in 1925 and 2 years later stated his
uncertainty principle. It states that the process of measuring the position x of a particle