The Faber Book of Science
Page 35
In March’s black boat
Einstein and April
have come at the time in fashion
up out of the sea
through the rippling daffodils
in the foreyard of
the dead Statue of Liberty
whose stonearms
are powerless against them
the Venusremembering wavelets
breaking into laughter…
Study of relativity theory prompted Williams to metrical experiment – a ‘variable’ poetic foot and a poetic line that was only ‘relatively stable’. Taking up these ideas other American poets furthered developments in free verse – Louis Zukofsky (who translated a biography of Einstein), and the ‘Black Mountain’ poets, Charles Olson (who demanded ‘What is measure when the universe flips?’), Robert Creeley and Robert Duncan. Poetic equivalents to relativity theory were at best vague, however, for lines of verse do not move relative to the observer at speeds approaching that of light, and if they did their lengths would become variable without any help from the poet.
Similar difficulties hindered the adoption of relativity theory in novels. Major novelists such as James Joyce and William Faulkner were aware of the new ideas and made efforts to incorporate them. But language inevitably reflects human perceptions of space and time, and cannot represent space-time. Virginia Woolf’s The Waves (1931) merges spatial and temporal images and modishly adopts Einstein’s contractable train. ‘The train slows and lengthens, as we approach London,’ one character remarks. But since the speaker is here on the train he would not be aware of any lengthening, even supposing Einstein’s effects applied perceptibly to railway trains. The Waves, with its six characters all talking like Virginia Woolf, has really nothing to do with relativity.
Einstein was often misunderstood as saying that everything was relative, including truth, or that all observations were subjective. Some writers imagined they were being Einsteinian if they presented events from a number of different viewpoints. Lawrence Durrell made prominent claims, on these grounds, for his Alexandria Quartet (1957–60) – ‘Three sides of space and one of time constitute the soup-mix of a continuum. The four novels follow this pattern.’ In fact switches of viewpoint had been common practice since the epistolary novels of the eighteenth century, and Durrell’s understanding of mathematics was so limited that he could not even master the game of chess.
Far from condoning subjectivity, Einstein believed in mathematical certainty, arguing that measurements within any reference-frame are definite and unalterable, and that measurements within other reference-frames can be accurately predicted. He told the Saturday Evening Post on 26 October 1929:
Everything is determined, the beginning as well as the end, by forces over which we have no control. It is determined for the insect as well as the star. Human beings, vegetables, or cosmic dust, we all dance to a mysterious tune, intoned in the distance by an invisible piper.
Einstein’s most famous equation (E = mc2) did not belong to the original theory of relativity, but was the subject of a supplementary paper in 1905. As he later explained to readers of Science Illustrated, the huge amounts of energy the formula attributes to any given mass are not apparent in ordinary life since they are locked up in atoms of the mass, and can be released only by atomic fission:
It is customary to express the equivalence of mass and energy (though somewhat inexactly) by the formula E = mc2, in which c represents the velocity of light, about 186,000 miles per second. E is the energy that is contained in a stationary body; m is its mass. The energy that belongs to the mass m is equal to this mass, multiplied by the square of the enormous speed of light – which is to say, a vast amount of energy for every unit of mass.
But if every gram of material contains this tremendous energy, why did it go so long unnoticed? The answer is simple enough: so long as none of the energy is given off externally, it cannot be observed. It is as though a man who is fabulously rich should never spend or give away a cent; no one could tell how rich he was…. We know of only one sphere in which such amounts of energy per mass unit are released: namely, radioactive disintegration….
Now, we cannot actually weigh the atoms individually. However, there are indirect methods for measuring their weights exactly…. Thus it has become possible to test and confirm the equivalence formula. Also, the law permits us to calculate in advance, from precisely determined atom weights, just how much energy will be released with any atom disintegration we have in mind. The law says nothing, of course, as to whether – or how – the disintegration reaction can be brought about.
Einstein’s equation states that mass is convertible into energy, and vice versa. Mass becomes, as it were, simply very, very concentrated energy. The formula extends the law of the conservation of energy (that energy can neither be created nor destroyed) into a law of the conservation of energy and mass (energy and mass can be neither created nor destroyed, though one form of energy or matter can be converted into another form of matter or energy).
Einstein had not anticipated, in his 1905 paper, that his formula could have any practical use. When the atomic age dawned, however, he found himself portrayed as a sinister prophet. The cover of Time magazine for 1 July 1946 carried a portrait of Einstein, with the mushroom-cloud of an atomic explosion in the background, and the caption ‘Cosmoclast’. As Alan Friedman and Carol Donley put it in their book Einstein as Myth and Muse (1983), the benign scientist had become a modern Prometheus.
Sources: Albert Einstein, Relativity: The Special and General Theory, A Popular Exposition, trans. Robert W. Lawson, London, Methuen, 1920. Bertrand Russell, The ABC of Relativity, London, Kegan Paul, Trench, Trubner, 1925. A. S. Eddington, Space, Time and Gravitation: an Outline of the General Theory of Relativity, Cambridge University Press, 1920. Lyndon Bolton’s essay from Scientific American, 5 February 1921, pp. 106–7. Einstein on E = mc2 from Science Illustrated (April 1946), copyright McGraw Hill Publishing Co Inc: Philosophical Library Inc. William Carlos Williams, The Complete Collected Poems 1906–38, Norfolk, Conn., New Directions, 1938.
Uncertainty and Other Worlds
The development of the quantum theory of matter at the beginning of the twentieth century drastically altered conventional scientific wisdom. The conviction that the world was understandable had been science’s most important gift to civilization. It had redeemed mankind from centuries of superstition. The new physics destroyed this cherished certainty. It found that the subatomic world was random and ultimately unintelligible. Electrons and other subatomic particles do not move along predictable paths, and they behave, incomprehensibly, like waves as well as like particles. It seems that, though they are the basic components of our material world, and of us, they are not ‘things’ at all, in the sense of having an independent identity, but remain in a suspended state until someone observes or measures them, whereupon they ‘collapse’ into one of many possible versions of reality. Thus the observer effectively creates the universe, or his version of it, by his observations. As the Danish physicist Niels Bohr (1885–1962) – one of the founders, with Max Planck (1858–1947), of quantum theory – puts it, there are:
fundamental limitations, met with in atomic physics, of the objective existence of phenomena independent of their means of observation.
The ‘uncertainty principle’, formulated in 1927 by the German Werner Heisenberg (1901–76), established this indeterminacy as an inherent feature of subatomic matter. Heisenberg declared that:
For the first time in history man, on this planet, is discovering that he is alone with himself … The conventional division of the world into subject and object, into inner and outer world, into body and soul, is no longer applicable.
Even before Heisenberg propounded his principle, alert and imaginative writers had seized on the idea that the new physics put reality back inside the human head, and made the material world unreal, just as mystics and religious thinkers had always insisted it was. The apprentice-mystic Mr Calamy,
in Aldous Huxley’s novel Those Barren Leaves (1925), explains that:
The human mind … has invented space, time and matter, picking them out of reality in a quite arbitrary fashion… Everything that seems real is in fact entirely illusory – maya, in fact, the cosmic illusion.
Calamy (and Huxley) found this release from scientific ‘fact’ exhilarating. But others were dismayed. In March 1929 P. W. Bridgman, Professor of Mathematics and Philosophy at Harvard, told readers of Harper’s Magazine that, though it was ‘enormously upsetting’, they must accept that:
Nature is intrinsically and in its elements neither understandable nor subject to law … The physical properties of the electron are not absolutely inherent in it, but involve also the choice of the observer… This means nothing more nor less than that the law of cause and effect must be given up … The world is not a world of reason, understandable by the intellect of man … It is probable that new methods of education will have to be painfully developed and applied to very young children in order to inculcate the instinctive and successful use of habits of thought so contrary to those which have been naturally acquired.
All human languages would have to be remodelled too, Bridgman predicted, since our present verbal habits are based on assumptions about cause and effect that have been proved to be no longer valid.
According to the conventional ‘Copenhagen’ interpretation of quantum theory only our world ‘really’ exists. The potential alternative worlds not brought into being at any moment of observation remain only potential. However, the ‘many-universe’ interpretation of quantum theory argues that the other possible worlds we do not select when we make an observation do really exist. Paul Davies, Professor of Mathematical Physics at the University of Adelaide, envisages the results of this in his book Other Worlds: Space, Superspace and the Quantum Universe:
Taking the widest possible view of superspace, it seems that every situation that can be reached along some convoluted path of development will occur in at least one of these other worlds. Every atom is offered billions of trajectories by the quantum randomization, and in the many-worlds theory it accepts them all, so every conceivable atomic arrangement will come about somewhere. There will be worlds that have no Earth, no sun, even no Milky Way. Others may differ so much from ours that no stars or galaxies of any kind exist. Some universes will be all darkness and chaos, with black holes roaming about swallowing up haphazardly strewn material, while others will be seared with radiation.
Universes will exist that look superficially like ours but have different stars and planets. Even those with essentially the same astronomical arrangement will have very different life forms: in many, there will be no life on Earth, but in others life will have progressed more rapidly and there will be Utopian societies. Still others will have suffered total destruction from war, while in some the whole Milky Way will be colonized by aliens, Earth included.
Heinsenberg’s uncertainty principle states that the position and momentum of a particle cannot be specified simultaneously: the greater the precision with which one property is specified, the less will be the precision of the other measurement. Not all scientists, regard this as a fatal blow to understanding the world, however, as P. W. Atkins explains:
Although most people appear to consider that the uncertainty principle abolishes any chance we once might have thought we had to comprehend the world, it is more optimistic (and perhaps more correct) to consider that the uncertainty principle is an indication that our classically inspired template for understanding the world is over-elaborate. Classical physics, the physics of the farmyard of everyday experience, forged a template that led us to expect that we should be able to describe the world using the language of speed and location simultaneously. Quantum mechanics takes its axe to this naive, superficial view. It reminds us of what should be obvious: that farmyard-inspired theories may be too gross and unsophisticated, too covered in the dung of their own origin. It provides a template that in effect requires us to choose one language or another. It tells us to speak in terms either of location or of speed, and never to mix the two. It tells us to speak German for complete sentences or to speak English for complete sentences. It warns us not to start a sentence in German and then end it in English. Quantum mechanics tells us that the mathematization of Nature should be done using formulas drawn from the language of position or from the language of speed. It instructs us to separate the muddled classical template into two sheets and to use either one sheet or the other. Quantum mechanics clarifies our vision of the world and in so doing exposes more sharply its mathematical structure. That is just one example. In the end, if there is an end, we shall possess a mathematical theory of the universe that matches it in every test: the fit of reality to the template will be exact and we shall have a theory of everything.
Sources: P. W. Bridgman, ‘The New Vision of Science’, Harper’s Magazine, March, 1929, pp. 443–51. Paul Davies, Other Worlds: Space, Superspace and the Quantum Universe, London, Penguin Books, 1990; first published by J. M. Dent and Sons, 1980. Peter Atkins, Creation Revisited: The Origin of Space, Time and the Universe, London, Penguin Books, 1994.
Quantum Mechanics: Mines and Machine-Guns
The German physicist Max Born (1882–1970) collaborated with his pupil Werner Heisenberg (see p. 277) in developing the mathematical formulation of quantum theory. Born fled the Nazis in 1933 and came to Britain, becoming Professor of Natural Philosophy at Edinburgh in 1936. This extract is from his inaugural lecture, where he tries to explain the problems underlying quantum theory to a non-specialist audience – using as illustration the weapons of the coming conflict, mines and machine-guns.
Let us start with the old problem of the constitution of light. At the beginning of the scientific epoch two rival theories were proposed: the corpuscular theory by Newton, the wave theory by Huygens. About a hundred years elapsed before experiments were found deciding in favour of one of them, the wave theory, by the discovery of interference. When two trains of waves are superposed, and a crest of one wave coincides with a valley of the other, they annihilate one another; this effect creates the well-known patterns which you can observe on any pond on which swimming ducks or gulls excite water-waves. Exactly the same kind of pattern can be observed when two beams of light cross one another, the only difference being that you need a magnifying-lens to see them; the inference is that a beam of light is a train of waves of short wave-length. This conclusion has been supported by innumerable experiments.
But about a hundred years later, during my student days, another set of observations began to indicate with equal cogency that light consists of corpuscles. This type of evidence can best be explained by analogy with two types of instruments of war, mines and guns. When a mine explodes you will be killed if you are near it, by the energy transferred to you as a wave of compressed air. But if you are some hundred yards away you are absolutely safe; the explosion-wave has lost its dangerous energy by continuously spreading out over a large area. Now imagine that the same amount of explosive is used as the propellant in a machine-gun which is rapidly fired, turning round in all directions. If you are near it you will almost certainly be shot, unless you hastily run away. When you have reached a distance of some hundred yards you will feel much safer, but certainly not quite safe. The probability of being hit has dropped enormously, but if you are hit the effect is just as fatal as before.
Here you have the difference between energy spread out from a centre in the form of a continuous wave-motion, and a discontinuous rain of particles. Planck discovered, in 1900, the first indication of this discontinuity of light in the laws governing the heat radiated from hot bodies. In his celebrated paper of 1905, Einstein pointed out that experiments on the energetic effect of light, the so-called photoelectric effect, could be interpreted in the way indicated as showing unambiguously the corpuscular constitution of light. These corpuscles are called quanta of light or photons.
This dual aspect of the luminous phenomeno
n has been confirmed by many observations of various types. The most important step was made by Bohr, who showed that the enormous amount of observations on spectra collected by the experimentalists could be interpreted and understood with the help of the conception of light quanta. For this purpose he had also to apply the idea of discontinuous behaviour to the motion of material particles, the atoms, which are the source of light.
I cannot follow out here the historical development of the quantum idea which led step by step to the recognition that we have here to do with a much more general conception. Light is not the only ‘radiation’ we know; I may remind you of the cathode rays which appear when electric currents pass through evacuated bulbs, or the rays emitted by radium and other radioactive substances. These rays are certainly not light. They are beams of fast-moving electrons, i.e. atoms of electricity, or ordinary atoms of matter like helium. In the latter case this has been proved directly by Rutherford, who caught the beam (a so-called α-ray of radium) in an evacuated glass vessel and showed that it was finally filled with helium gas. Today one can actually photograph the tracks of these particles of radiating matter in their passage through other substances.
In this case the corpuscular evidence was primary. But in 1924 de Broglie, from theoretical reasoning, suggested the idea that these radiations should show interference and behave like waves under proper conditions. This idea was actually confirmed by experiments a short time later. Not only electrons, but real atoms of ordinary matter like hydrogen or helium have all the properties of waves if brought into the form of rays by giving them a rapid motion.