Science

Questions of Science: Wave mechanics and stable atoms…

GRAVITATIONAL PUSH AND PULL

In an atom, why doesn’t the negatively charged electron collapse into the positively charged nucleus?

Is this in any way similar to the reason why large systems like stars and planets do not collapse into each other under the pull of gravity?

WHEN Ernest Rutherford, the New Zealand-born founder of nuclear physics, first discovered the atomic nucleus he did suggest that electrons did not fall toward the nucleus of the atom. This was because, he said, that the attractive forces of the nucleus were being balanced by the orbital velocity of the electron, in much the same way as a planet orbits a star.

However, the Danish physicist Niels Bohr modified this theory after Albert Einstein and Max Planck found that energy could only exist in certain discrete amounts, or quanta. This meant that electrons could be seen to have both wave and particle properties, and required that the circumference of the orbit of an electron could not be zero. This means, of course, it could never reach the nucleus.

Science has since adopted the model by the Austrian and Nobel Prize-winning theoretical physicist Erwin Schrödinger. Instead of orbiting the nucleus like planets, his model has electrons occupying ‘clouds’ where it is statistically probable that they will exist, although it has to be appreciated we may never determine an electron’s position and velocity at the same time.

Niels Bohr’s insight in 1913 is worth further explanation. The atom was known to have a small heavy nucleus, and the much lighter electrons were thought to orbit it like planets around the sun. As long as a planet does not lose energy, it can continue its orbit indefinitely.

According to the laws of electromagnetism, charged particles moving in a circle ought to radiate energy as waves. Bohr calculated that a hydrogen atom should collapse with a flash of light in a matter of femtoseconds. Because this does not happen, he proposed what has become known as the ‘old’ quantum mechanics. It asserted that the electron’s angular momentum had to be a multiple of Planck’s constant.

The rule meant that electrons could only occupy particular orbits, and there was a minimum size of orbit. Using this, Bohr was able to predict the entire spectrum of excited states of hydrogen, which, of right, was quite an astounding achievement.

But Bohr’s theory was difficult to apply to more complex atoms and was superseded by Erwin Schrödinger’s wave mechanics in 1927. This became the start of modern quantum theory.

Schrödinger’s formulation shows that an electron has a wave character, and a stable atom can be thought of as a box confining the wave. An electron has a wavelength equal to Planck’s constant divided by its momentum, so the faster an electron moves, the shorter its wavelength. To confine the electron near the nucleus the electron must move very quickly.

Conversely, a fast-moving electron can escape the pull of the nucleus. So you can think, too, of the size of an atom as resulting from a compromise between the electrons having enough kinetic energy for their waves to fit in the box, but so much that they can escape.

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Arts, Education, Philosophy, Society

Philosophy: An introduction…

Philosophy & Ethics

While the earliest philosophers sought to understand the earlier universe, it was not long before philosophy turned its attention to humans themselves, and the way we lead our lives. The idea of virtue was central to life in classical society, but difficult to define; concepts of good and evil, happiness, courage and morality became the subjects of debate in the branch of philosophy known as ethics, or moral philosophy.

In trying to ascertain the nature of a virtuous life, philosophers raised the question of what the goal of life should be – what is its ‘purpose’? How should we lead our lives, and to what end? The concept of the ‘good life’, eudemonia, figured largely in Greek philosophy, and embodies not only a virtuous life, but also a happy one. Several different schools of thought emerged as to how this ‘good life’ could be achieved, including the cynics, who believed in harmony with nature, the Epicureans, who believed pleasure to be the greatest good, and the stoics, who believed in acceptance of things beyond our control.

Where ethics and moral philosophy seek to define virtue and what constitutes the ‘good life’, the closely related branch of political philosophy examines the nature of concepts such as justice, and what sought of society can best allow its citizens to lead ‘good’ lives. The problems of how society should be organised and governed were of paramount importance not only to classical Greece, but also in the development of nation-states in China at much the same time, and elsewhere as new civilisations emerged.

As a branch of philosophy, political philosophy deals with ideas of justice, liberty and rights, and the relationship between a state and its citizens. It also examines various forms of government, such as monarchy, aristocracy, oligarchy, tyranny and democracy, and how each affects the rights and freedoms of the individual, as well as examining the relationship in how they exert their authority through the rule of law.

Aesthetics

As the classical Greek philosophers sought to define concepts such as virtue and justice, giving rise to the branches of moral and political philosophy, they also asked the question: ‘What is beauty?’ This is the fundamental question of aesthetics. As a branch of philosophy, aesthetics tries to establish what, if any, objective criteria there are for judging whether something is beautiful, but, in a wider sense also examines all aspects of art – including the very basic question ‘What is art?’

At various times in history, the emphasis of aesthetics has moved from what constitutes art to the religious or socio-political significance of works of art, a general theory of our appreciation of art and how we perceive it, and the process of artistic creativity itself. Philosophical and ethical problems are also raised when considering such matters as the authenticity of a work of art or the sincerity of its creator.

Eastern and Western philosophies

Although the tradition that began in ancient Greece still tends to dominant philosophical discussion in the Western world, philosophy is by no means restricted to that single tradition. Thinkers such as Laozi and Confucius in China also founded their own traditions of philosophy from different starting points, as, arguably, did Buddha in India. For them, and subsequent Eastern philosophers, questions of metaphysics were considered to be adequately explained by religion – hence the Eastern traditions are much more focused on concepts of virtue and the way in which we should lead our lives. In China especially, this moral philosophy was adopted by the ruling dynasties and took on a political dimension.

Eastern and Western philosophies developed very separately until the 19th century, when European philosophers, notably Schopenhauer, began to take an interest in Indian religious and philosophical thought. Elements of Eastern philosophy have subsequently been incorporated into some branches of Western philosophy.

Philosophy vs. religion

Religion and philosophy offered two distinctly different approaches to answering our questions about the world about us – religion through belief, faith and divine revelation, and philosophy through reason and argument – but they often cover much the same ground and are sometimes interrelated. Eastern philosophy developed side by side with religion, and Islam saw no incompatibility between its theology and the philosophy it inherited from the classical world, but the relationship between Western philosophy and Christianity was very often uneasy. Church authorities in the medieval period saw philosophy as a challenge to their dogma, and Christian philosophers risked being branded as heretics for attempting to incorporate Greek philosophical ideas into Christian doctrine. But more than that, philosophy also brought into question issues of belief as opposed to knowledge, faith as opposed to reason – questioning, for example, whether there was any evidence for miracles or even whether the existence of God could be proved.

Philosophy vs. science

Throughout much of the history of philosophy, there was no such thing as science in its modern form: in fact, it was from philosophical enquiry that modern science has evolved. The questions that metaphysics set out to answer about the structure and substance of the universe prompted theories that later became the foundations of ‘natural philosophy’, the precursor of what we now call physics. The process of rational argument, meanwhile, underpins the ‘scientific method’.

Since the 18th century, many of the original questions of metaphysics have been answered by observation, experiment and measurement, and philosophy appeared to be redundant in these areas. Philosophers have since changed their focus to examine science itself. Some, like Hume, challenged the validity of inductive reasoning in science, while others sought to clarify the meaning of terms used by science, opening up a ‘philosophy of science’ that considers areas such as scientific ethics and the way science makes progress.

 

ONE of the features of philosophy that distinguishes it from other ways at looking at the world is that its students are encouraged not to accept the conclusions of their teachers, but to discuss, argue and even disagree. This is exactly what happened in the very first school of philosophy, the Milesian school founded by Thales: his student Anaximander asked if the Earth was supported by water then what supported that? He suggested that the Earth was a drum-shaped cylinder hanging in space, with one of the flat surfaces forming the world we live on. Anaximander, also had a pupil, Anaximenes, who said that the world was self-evidently flat and floated on air. Using the same sort of arguments as Thales, he concluded that the single element from which everything is made is air. Although the conclusions of the Milesian philosophers seem to us hopelessly wrong in the light of later scientific discoveries, the process of reasoning used to reach them – especially argument and counter-argument – still forms the basis for philosophical investigation.

The argument Anaximander used to challenge his teacher’s theory of the Earth floating on water involved an idea that crops up in several strands of philosophy. If the world is supported by a body of water, then what supports the water? And then, what supports that? And so on, ad infinitum. The same pattern can be seen in arguments involving cause and effect: if something causes something else, then what causes that? This apparently unending chain is called infinite regress. Some philosophers saw the existence of infinite regress as proof that the universe is eternal, but many were uncomfortable with the idea and proposed that there must be an original or first cause for everything (an idea that chimes with the modern theory of the Big Bang). For some, the first cause or ‘prime mover’ was an abstract idea akin to pure thought or reason, but, for medieval Christian philosophers especially, it was God: indeed, the idea of a first cause was at the heart of Thomas Aquinas’s cosmological argument for the existence of God.

Heraclitus: everything is in flux

In contrast to the school of philosophy founded by Thales at Miletus, just along the Ionian coast in the city of Ephesus lived a solitary thinker, Heraclitus, who had very different philosophical views. Rather than suggesting a single element from which everything was derived, he suggested an underlying principle – that of change. Heraclitus saw everything as consisting of opposing properties or tendencies, which come to together to make up the substance of the world. The analogy he gave was that the path up a mountain is the same as the path down.

In this theory, known as the ‘unity of opposites’, the tension and contradiction of opposing forces is what creates reality, but is inherently unstable. Therefore, everything is constantly changing: everything is in a state of flux. Just as the water in a river is constantly flowing onwards, but the river itself remains the same, that which we consider to be permanent, unchanging reality consists not of objects, but processes.

– This concludes An introduction to Philosophy. Further entries in this area will be offered in the future.

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Britain, History, Military, Second World War, Society, United States

Dresden and the Allied bombings of World War II…

70 YEARS ON

Today, the blossoming of Dresden in the east of Germany stands in stark contrast to how the city looked from the ruins of the Allied bombings towards the end of World War II.

British and American bombers dropped 3,900 tonnes of explosives on the Saxony city during four raids on 13th-15th February 1945, killing an estimated 25,000 people and reducing the city to rubble.

The bombing, ordered by Royal Air Force marshal Sir Arthur ‘Bomber’ Harris, was widely criticised because of the indiscriminate and ‘blanket bombing’ which hit civilian areas as well as military targets – killing thousands of innocents.

Over two days and nights in February 1945, 722 heavy bombers of the British Royal Air Force (RAF) and 527 of the United States Army Air Forces (USAAF), turned the city into a sea of flames and rubble.

The resulting firestorm is said to have reached temperatures of over 1,500C (2,700F), destroying over 1,600 acres of the city centre.

The victims – mostly women and children – died in savage firestorms whipped up by the intense heat of 2,400 tons of high explosive and 1,500 tons of incendiary bombs.

It was initially claimed that up to 250,000 civilians lost their lives in the Dresden bombings but an official report released after the war showed the casualty figure was in fact closer to between 22,500 and 25,000.

A police report written shortly after the bombings showed that the city centre firestorm had destroyed almost 12,000 houses, including 640 shops, 18 cinemas, 39 schools, 26 public houses and the city zoo.

The destruction of Dresden has been subjected to much fierce debate in the 70 years since the war. No one has ever been charged over the bombings, but several historians both in Germany and former Allied nations hold the opinion that the bombing was a war crime.

British Prime Minister Winston Churchill, ultimately responsible for the attack, distanced himself from the bombing of Dresden shortly afterwards.

An RAF memo issued to airmen on the night of the attack said:

… ‘Dresden, the seventh largest city in Germany and not much smaller than Manchester is also the largest unbombed built-up area the enemy has got. In the midst of winter with refugees pouring westward and troops to be rested, roofs are at a premium, not only to give shelter to workers, refugees, and troops alike, but to house the administrative services displaced from other areas.

… At one time, and well known for its china, Dresden has developed into an industrial city of first-class importance…. The intentions of the attack are to hit the enemy where he will feel it most, behind an already partially collapsed front… and incidentally to show the Russians when they arrive what Bomber Command can do.’

Bomber Command, which suffered the highest casualty rate of any British unit, losing 55,573 of its 125,000 men, eventually gained a memorial in 2012, but sections of society in Britain were outraged and disgusted with public recognition being given to such attacks. It is the view of many that such a memorial should never have been authorised by the British Government because of the attacks on civilians and on non-strategic targets.

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