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Quantum theory evolved as a new branch of theoretical
physics during the first few decades of the 20th century
in an endeavour to understand the fundamental properties
of matter. It began with the study of the interactions
of matter and radiation. Certain radiation effects could
neither be explained by classical mechanics, nor by the
theory of electromagnetism. In particular, physicists
were puzzled by the nature of light. Peculiar lines in
the spectrum of sunlight had been discovered earlier by
Joseph von Fraunhofer (1787-1826). These spectral lines
were then systematically catalogued for various
substances, yet nobody could explain why the spectral
lines are there and why they would differ for each
substance. It took about one hundred years, until a
plausible explanation was supplied by quantum theory.
Quantum theory is about the nature of matter.
In contrast to Einstein's Relativity, which is about the
largest things in the universe, quantum theory deals
with the tiniest things we know, the particles that
atoms are made of, which we call "subatomic" particles.
In contrast to Relativity, quantum theory was not the
work of one individual, but the collaborative effort of
some of the most brilliant physicists of the 20th
century, among them Niels Bohr, Erwin Schrödinger,
Wolfgang Pauli, and Max Born. Two names clearly stand
out: Max Planck (1858-1947) and Werner Heisenberg
(1901-1976). Planck is recognised as the originator of
the quantum theory, while Heisenberg formulated one of
the most eminent laws of quantum theory, the Uncertainty
Principle, which is occasionally also referred to as the
principle of indeterminacy.
Planck's constant: Energy is not continuous.
Around 1900, Max Planck from the University of Kiel
concerned himself with observations of the radiation of
heated materials. He attempted to draw conclusions from
the radiation to the radiating atom. On basis of
empirical data, he developed a new formula which later
showed remarkable agreement with accurate measurements
of the spectrum of heat radiation. The result of this
formula was so that energy is always emitted or absorbed
in discrete units, which he called quanta. Planck
developed his quantum theory further and derived a
universal constant, which came to be known as Planck's
constant. The resulting law states that the energy of
each quantum is equal to the frequency of the radiation
multiplied by the universal constant: E=f*h, where h is
6.63 * 10E-34 Js. The discovery of quanta revolutionised
physics, because it contradicted conventional ideas
about the nature of radiation and energy.
The atom model of Bohr.
To understand the gist of the quantum view of matter, we
have to go back to the 19th century's predominant model
of matter. Scientists at the time believed -like the
Greek atomists- that matter is composed of indivisible,
solid atoms, until Rutherford proved otherwise.
The British physicist Ernest Rutherford (1871-1937)
demonstrated experimentally that the atom is not solid
as previously assumed, but that it has an internal
structure consisting of a small, dense nucleus about
which electrons circle in orbits.
Bohr's atom model Niels Bohr (1885-1962) refined
Rutherford's model by introducing different orbits in
which electrons spin around the nucleus. This model is
still used in chemistry. Elements are distinguished by
their "atomic number", which specifies the number of
protons in the nucleus of the atom. Electrons are held
in their orbits through the electrical attraction
between the positive nucleus and the negative electron.
Bohr argued that each electron has a certain fixed
amount of energy, which corresponds to its fixed orbit.
Therefore, when an electron absorbs energy, it jumps to
the next higher orbit rather than moving continuously
between orbits. The characteristic of electrons having
fixed energy quantities (quanta) is also known as the
quantum theory of the atom.
The above model bears a striking similarity with the
Newtonian model of our solar system. Electrons revolve
around the nucleus, just as planets revolve around the
Sun. It is therefore not surprising that physicists
tried to apply classical mechanics to the atomic
structure. The forces between nucleus and electrons were
equated with the gravitational forces between celestial
bodies. This idea worked quite well for the hydrogen
atom, the simplest of all elements, but it failed to
explain the behaviour of more complex atoms.
If matter is not infinitely divisible, why should energy
be?
The idea that energy could be emitted or absorbed only
in discrete energy quanta seemed odd, since it could not
be fitted into the traditional framework of physics. The
quantum behaviour of electrons in atoms contradicted not
only classical mechanics, but also Maxwell's
electromagnetic theory, which required it to radiate
away energy while orbiting in a quantum energy state.
Even Max Planck, who was a conservative man, initially
doubted his own discovery. The traditional view was that
energy flows in a continuum like a smooth, unbroken
stream of water. That there should be gaps between the
discrete entities of energy seemed wholly unreasonable.
In fact, Planck's idea only gained credence when
Einstein used it in 1905 to explain the photoelectric
effect. - After all, if matter is not infinitely
divisible, why should energy be?
In the course of time, physicists descended deeper into
the realm of the atom. Bohr's atom model was remarkably
successful in describing the spectrum of the hydrogen
atom by using Planck's formula to relate different
energy levels of electrons to different frequencies of
light radiation. Unfortunately, it did not work well for
more complex atoms, and so a more sophisticated theory
had to be developed. The problem seemed to be rooted in
the assumption that an electron rotates around the
nucleus like a massive object revolves around a centre
of gravity. De Broglie, Schrödinger, and Heisenberg
showed that classical mechanics had to be abandoned in
order to describe the subatomic world adequately. In an
inference not less dramatic than Planck's discovery of
quanta, they stated that particles don't really have a
trajectory or an orbit, much less do they behave like a
ball that is shot through a corridor or is whirled
around on the end of a cord.
The wave-particle duality.
Just as light is thought to have a dual nature,
sometimes showing the characteristic of a wave, and
sometimes that of a particle (photon), quantum theory
attributes a similar dual wave-particle nature to
subatomic particles. Electrons that orbit around the
nucleus interact with each other by showing interference
patterns, not unlike those of wave interference. If the
velocity of the electron is thought of as its
wavelength, the crests of neighbouring electron waves
amplify or cancel each other, thereby creating a pattern
that corresponds to Bohr's allowed orbits.
Probability cloud model Bohr's model of the atom was
superseded by the probability cloud model that describes
physical reality better. The orbital clouds are
mathematical descriptions of where the electrons in an
atom are most likely to be found, which means the model
shows the spatial distribution of electrons. The
(simplified) picture to the left shows electron
probability clouds in a water molecule.
Even cloud models are only approximations. The
computation of the actual distribution of electrons in
an atom is extremely laborious and the result is too
complicated to be illustrated in a single layer 3D
model.
About misbehaved electrons, or: the probability cloud
model.
The nature of electrons seems odd. Seemingly they exist
in different places at different points in time, but it
is impossible to say where the electron will be at a
given time. At time t1 it is at point A, then at time t2
it is at point B, yet without moving from A to B. It
seems to appear in different places without describing a
trajectory. Therefore, even if t1 and A can be
pinpointed, it is impossible to derive t2 and B from
this measurement. In other words: There seems to be no
causal relation between any two positions. The concept
of causality cannot be applied to what is observed. In
case of the electrons of an atom, the closest we can get
to describing the electron's position is by giving a
number for the probability of it being at a particular
place. Moreover, particles have other "disturbing"
properties: They have a tendency to decay into other
particles or into energy, and sometimes -under special
circumstances- they merge to form new particles. They do
so after indeterminate time spans. Although we can make
statistical assertions about a particle's lifetime, it
is impossible to predict the fate of an individual
particle.
What does quantum physics say about the universe?
Can we derive any new knowledge about the universe from
quantum physics? After all, the entire universe is
composed of an unimaginable large number of matter and
energy. It seems to be of great importance to understand
quantum theory properly in view of the large-scale
structure of the cosmos. For example, an interesting
question in this context is why the observable matter in
the universe is packed together in galaxies and is not
evenly distributed throughout space. Could it have to do
with the quantum characteristics of energy? Are quantum
effects responsible for matter forming discrete
entities, instead of spreading out evenly during the
birth of the universe? The answer to this question is
still being debated.
If cosmological conclusions seem laboured, we might be
able to derive philosophical insights from quantum
physics. At least Fritjof Capra thinks this is possible
when he describes the parallels between modern physics
and ancient Eastern philosophy in his book The Tao of
Physics. He holds that in a way, the essence of modern
physics is comparable to the teachings of the ancient
Eastern philosophies, such as the Chinese Tao Te Ching,
the Indian Upanishads, or the Buddhist Sutras. Eastern
philosophies agree in the point that ultimate reality is
indescribable and unapproachable, not only in terms of
common language, but also in the language of
mathematics. That is, science and mathematics must fail
at some stage in describing ultimate reality. We see
this exemplified in the Uncertainty Principle, which is
elucidated in the following section.
Molecules and atoms cannot be split into independent
units. All parts interact at all levels.
The oriental scriptures agree in the point that all
observable and describable realities are manifestations
of the same underlying "divine" principle. Although many
phenomena of the observable world are seemingly
unrelated, they all go back to the same source. Things
are intertwined and interdependent to an unfathomable
degree, just as the particles in an atom are. Although
the electrons in an atom can be thought of as individual
particles, they are not really individual particles,
because of the complicated wave relations that exist
between them. Hence, the electron cloud model describes
the atomic structure more adequately. The sum of
electrons in an atom cannot be separated from its
nucleus, which has a compound structure itself and can
neither be regarded a separate entity. Thus, in the
multiplicity of things there is unity. Matter is many
things and one thing at the same time.
The Eastern scriptures say that no statement about the
world is ultimately valid ("The Tao that can be told is
not the eternal Tao." Tao Te Ching, Verse 1), since not
even the most elaborate language is capable of rendering
a perfect model of the universe. Science is often
compared to a tree that branches out into many
directions. The disposition of physics is that it
follows the tree upward to its branches and leaves,
while meta-physics follows it down to the root. Whether
the branches of knowledge stretch out indefinitely is
still a matter of debate. However, it appears that most
scientific discoveries do not only answer questions, but
also raise new ones.
The German philosopher, FriedrichHegel formulated an
idea at the beginning of the 19th century that describes
this process. He proposed the dialectic triad of thesis,
antithesis, and synthesis, in which an idea (thesis)
always contains incompleteness and thus yields a
conflicting idea (antithesis). A third point of view
(synthesis) arises, which overcomes the conflict by
reconciling the truth contained in both, thesis and
antithesis, at a higher level of understanding. The
synthesis then becomes a new thesis, generates another
antithesis, and the process starts over. In the next
section, we shall see how 20th century physics embodies
Hegel's dialectical principle. We will also take a close
look at the philosophical implications of Heisenberg's
Uncertainty Principle.
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