A Brief Guide to the Great Equations (30 page)
Any bending, Dyson continued, would have the effect of ‘throwing the star away from the Sun’; that is, making it look farther away. He briefly reviewed the events of the expedition, mentioning the defect discovered in the larger instrument. A good scientist, Dyson knew that all data are not created equal – some instruments perform better than others, in a way that one can evaluate independently of the result. Emphasizing the smaller instrument’s measurements, Dyson concluded: ‘A very definite result has been obtained that light is deflected in accordance with Einstein’s law of gravitation.’ Crommelin followed, offering a brief explanation of the defect in the larger instrument.
Eddington, a little outclassed by Dyson and by the quality of Crommelin’s results, recounted his expedition and its frustrations with the weather. He painted his results as positively as possible, finding good in bad, pointing out that the cloud cover and uniform temperature at Principe had a beneficial side effect in reducing the mirror distortion that had adversely affected the larger Sobral mirror. Gamely admitting that he was ‘making the most of a small amount of material’, Eddington noted that his result of 1.6’ value for displacement at the limb ‘supports the figures obtained at Sobral.’ Disposing of the refracting matter explanation, Eddington concluded that the results support Einstein’s law – the statement that light bends – though not necessarily Einstein’s theory, the ideas about curvature of space behind it.
Thomson then took the floor again. He called the reports a ‘momentous communication.’ He said, ‘This is the most important result obtained in connection with the theory of gravitation since Newton’s day, and’ – alluding to the portrait of this early member
hanging nearby – ‘it is fitting that it should be announced at a meeting of the Society so closely connected with him.’
Some discussion lamented the mathematical complexity of the theory, which seemed out of the reach of most physicists. ‘I cannot believe’, one said, ‘that a profound physical truth cannot be clothed in simpler language… Cannot Prof. Eddington translate his admirable treatise from the tensor notation into some such form?’ A skeptic, citing the continuing absence of evidence of a spectroscopic shift, argued that the deflection result – ‘an
isolated
fact’ – did not necessarily confirm Einstein’s theory. ‘We owe it to that great man’, he said, dramatically pointing to Newton’s portrait – ‘to proceed very carefully in modifying or retouching his Law of Gravitation.’ But the arguments against Einstein’s theory would all but die out within 2 years.
The experimental differences between his theory and those of Newton were tiny – small shifts in the positions of a few stars and spectral lines, and of a minuscule wobble in Mercury’s orbit. But the differences could hardly be more profound, for they implied a fundamental difference in the way the universe was structured.
In Newton’s theory, gravitation involves an attractive force – a tug – that each mass exerts on all others at a distance. That force operates instantly and everywhere, and is inversely proportional to the square of the distance between the masses. Masses experiencing that force respond by accelerating toward its source. Different masses are accelerated at the same rate, because the force pulls them in proportion to their mass: a small mass experiences a small pull, a greater mass a greater pull. In Einstein’s theory, by contrast, gravitation involves in effect a curvature of space. That curvature is structured by the masses around it. When matter and energy move through space they follow the paths that are open to them.
It was one of the great rearrangements of fundamental concepts in the history of science. As Eddington wrote:
The Newtonian framework, as was natural after 250 years, had been found too crude to accommodate the new observational
knowledge which was being acquired. In default of a better framework, it was still used, but definitions were strained to purposes for which they were never intended. We were in the position of a librarian whose books were still being arranged according to a subject scheme drawn up a hundred years ago, trying to find the right place for books on Hollywood, the Air Force, and detective novels.
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By 1921, the only prominent figure who continued to be disappointed in the theory was Einstein himself. To his exacting eyes, which wanted symmetry throughout the theory, the left-hand side was solid, for it was expressed in the geometry of space-time, while the right-hand side was not. He once compared it to a poorly planned building, one half of which was ‘fine marble’, the other ‘low-grade wood.’
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Dissatisfied, he would spend much of the rest of his life in a futile effort to fix that building. Though he would work for over three decades on that repair, he would never succeed.
SCIENCE CRITICS
The equations of the gravitational field which relate the curve of space to the distribution of matter are already becoming common knowledge.
Cosmicomics
Hence the pathetic paradox that Einstein’s discoveries, the greatest triumph of reasoning mind on record, are accepted by most people on faith.
Time
, July 1, 1946
The process by which the public comes to understand new scientific developments often appears in the form of what might be called the Moses and Aaron model. Like Moses, the scientist seems to have one foot in the sphere of the divine, bringing into the human world some discovery from beyond. The meaning of this primordial activity is then communicated by some Aaron, who translates for the public via images and popular language.
The Moses and Aaron model is essentially a two-step process. We see it reenacted all the time – in the nightly TV news, for instance, when a spokesman or talking head tries to explain some novel development before the allotted 60 seconds run out. Some Aarons are more effective and entertaining than others.
Einstein’s general theory of relativity poses a particular burden on would-be Aarons. A one- or two-step translation process is difficult to achieve. The theory involves complex mathematics, and unfamiliar ways of thought, that take physicists years to master. Learning the theory is like acclimatization into a culture, with no shortcuts. Sometimes – as
The New York Times
famously did after the November 6, 1919, announcement – journalists simply throw up their hands and say that a discovery cannot be explained to nonscientists. And physicist Hermann Bondi once said that members of the public would not understand relativity until they had relativistic toys to play with.
But talking about science to outsiders is like talking about a city to noninhabitants; what you say depends on the interests of your audience. If they intend to become inhabitants, you give them one kind of talk, focusing on regulations, institutions, laws, and so forth, that may take them awhile to master. If your listeners are just tourists with no intention to become inhabitants, on the other hand, you can focus on the public attractions, not go into too much detail, and safely condense a lot.
Many interesting attempts have been made to make general relativity accessible to a tourist audience. One way is by selecting and elaborating clever illustrations that show its implications in an accessible way: for instance, the twin paradox, wherein one twin who travels in space at near the speed of light ages differently from the other twin who remains on Earth; or the astronaut who cannot tell whether he or she is accelerating or in a gravitational field. Another way is through biographies: witness the phenomenal popularity of Walter Isaacson’s recent book
Einstein: His Life and Universe
, or of Abraham Pais’s earlier, more difficult but American Book Award–winning
‘Subtle is the Lord’: The Science and the Life of Albert Einstein
. Still another way to convey the meaning of general relativity to
outsiders is by dramatic images, such as that of weights on a rubber sheet. A weight on a rubber sheet bends the sheet, by an amount that depends on the heaviness of the object, in a way that affects the path of marbles rolling past – in an analogous manner that an object distorts space, by an amount that depends on its mass, in a way that affects the paths of objects, including light, that pass through it. And some authors use all three methods at once, as Brian Greene in his wonderful books
The Fabric of the Cosmos
and
The Elegant Universe.
Other clever strategies to convey complicated science to outsiders include Edwin A. Abbott’s
Flatland: A Romance of Many Dimensions
, a famous novel involving an extended conversation between a square and a sphere that illustrates the problem of conceiving multiple dimensions. And Michael Frayn’s brilliant play
Copenhagen
dramatizes an encounter between Niels Bohr and Werner Heisenberg that ends up illustrating many points about quantum physics.
What most needs bolstering in the contemporary discourse about science, however, is what might be called science critics. At least two individuals – the political scientist Langdon Winner and the philosopher Don Ihde – have called for such critics. In the arts, Winner points out, critics are instinctively understood as playing ‘a valuable, well established role, serving as a bridge between artists and audiences.’ A critic of literature, for instance, ‘examines a text, analyzing its features, evaluating its qualities, seeking a deeper appreciation that might be useful to other readers of the same text.’ Unfortunately, Winner lamented, the same kind of function is not performed in the sciences. One obstacle is that scientists tend to regard as suspect anyone who plays the role of critic, as if science critics are by definition objecting to science or insisting on its limitations.
Don Ihde, meanwhile, actively calls for science critics and even outlines what he thinks they should be like. ‘The science critic would have to be a well informed – indeed [a] much better
than simply well informed – amateur, in [the sense of] a ‘lover’ of the subject matter, and yet not the total insider.’ The reason why the science critic must not be a total insider – just as an arts critic would not be a practicing artist or literary author – is because, as Ihde puts it, ‘we are probably worst at our own self-criticism.’
Science critics, according to Winner and Ihde, would have an essential function. They would be there to assess the impact of science and technology on our political world (Winner) and on the human experience (Ihde). So, for example, Winner writes about the ‘politics’ of technological artifacts, while Ihde writes about the transformation of experience by instruments. The kind of criticism advocated and practiced by Winner and Ihde, in short, judges the presence of science and technology in society, and has clear moral and political dimensions.
But there is another, complementary model for science criticism, one that involves another kind of interpretation, outlining the impact of scientific discoveries on our understanding of ourselves, the world, and our place in it. This model would require not a one-step translation process, but the kind of multiple roles that art criticism performs. It would involve a kind of ‘science criticism’ just as elaborate and extensive as art criticism, whose presence is required for a thriving art culture. The necessary steps would include a complex field of several different niches of writings – books, articles, and columns, but also novels and plays, comments and reviews of these novels and plays, and so forth. This would allow the knowledge generated by science to have a cultural, and not merely an instrumental, presence, taking advantage of the processes by which culture enacts itself.
This model might be called
impedance matching
. In acoustics and electrical engineering, impedance matching involves taking a signal – produced inside a speaker, say – and putting it in a new environment with a different ‘load’ – the surrounding
environment – in a way that allows the signal to be heard. This is not a one- or two-step process, but requires a smooth and continuous matching or stepping down of the load. Scientific discourse, that is, bears one load – a heavy one – and public language a much different one. To connect the two effectively cannot be a matter of basic education plus popularization, but many different overlapping steps. Each of these steps requires more than rhetorical expertise, but connecting the signal with public issues and hopes.
Why should we bother? Our system seems to work relatively well as it is. Why make an effort to do more than paraphrase, to trace out the moral and spiritual impact of scientific work such as general relativity on the world? Part of the answer is to avoid being infantilizing and patronizing to the public. To the extent that Einstein’s general theory of relativity represents humanity’s best efforts at understanding the basic structure of the world, it is desirable for citizens – and not just professional scientists – to have the ability to acquire some
sense
of Einstein’s general theory of relativity, some feel for what it means to our understanding of the universe, and a duty to make this possible. To put it more strongly, making this possible belongs to the human quest to acquire an understanding of ourselves and our place in the world. What is at stake is our own humanity.
‘The Basic Equation of Quantum Theory’:
SCHRÖDINGER’S EQUATION
