A Brief Guide to the Great Equations (26 page)
Three weeks later, on August 6, 1945, the first atomic bomb incinerated the Japanese city of Hiroshima. The next day, headlines all over the world revealed the existence of a new and particularly horrible type of bomb that, as
The New York Times
put it, ‘was the first time that Prof. Albert Einstein’s theory of relativity has been put to practical use outside the laboratory.’
30
On August 9, 3 days after the bombing of Hiroshima, another atomic bomb destroyed the city of Nagasaki.
The equation
E
=
mc
2
had not played any direct role in the events leading up to the Manhattan Project, except as a key ingredient of the nuclear physics theory by which fission was understood. The atomic bomb, involving as it did the conversion of matter into energy via fission, was only an example of the equation
E
=
mc
2
– and a rare one in the comings and goings of life on earth – not an outgrowth of it. But the equation almost immediately became associated with it, partly thanks to
Atomic Energy for Military Purposes
, a report written by Princeton physicist Henry D. Smyth, an official of the Manhattan Project.
The Smyth report, as it was called, was released to the public on August 11, 2 days after the bombing of Nagasaki. ‘A weapon has been developed that is potentially destructive beyond the wildest nightmares of the imagination’, Smyth wrote. It was created ‘not
by the devilish inspiration of some warped genius but by the arduous labour of thousands of normal men and women working for the safety of their country.’ The report’s intended audience was ‘engineers and scientific men’ who might be able to ‘explain the potentialities of atomic bombs to their fellow citizens.’ But the book was a crossover hit, becoming a huge popular success and selling over a hundred thousand copies in its first 5 months.
31
Right at the beginning, the Smyth report used
E
=
mc
2
as a cornerstone for explaining the weapon. An early implication of relativity theory, it said, was the equivalence between mass and energy.
To most practical physicists and engineers this appeared a mathematical fiction of no practical importance. Even Einstein would hardly have foreseen the present applications, but as early as 1905 he did clearly state that mass and energy were equivalent and suggested that proof of this equivalence might be found by the study of radioactive substances. He concluded that the amount of energy,
E
, equivalent to a mass,
m
, was given by the equation
=
mc
2
where
c
is the velocity of light.
The Smyth report was the mediating document through which nonscientists learned about the Manhattan Project. It more than any other single document made
E
=
mc
2
an emblem of atomic energy and weaponry.
Ethnographers say that when two cultures interact, they do not meet all of a piece but through ‘congeners’ through which certain members of one culture look at, try to understand, and respond to the other. Congeners can include artifacts, rituals, practices, and art; fear, fascination,
and exoticism usually play a role. A congener is like a little lens that allows the members of the one culture to approach the other culture in a focused way, to get an introductory grip. A congener is thus more than a symbol or logo of the other culture, but guides and disciplines curiosity and fascination into a first interaction with it.
The equation
E
=
mc
2
served as a congener in this sense, between a public anxious for information about atomic energy and the scientific developments that made it possible. In the process, it grew into even more – a symbol of physics, of science, even of knowledge – to the point where it acquired a mythic status.
The French intellectual Roland Barthes once wrote an essay on Einstein in which he noted that, while photographs of Einstein often show him next to a blackboard covered with impenetrable symbols and equations, cartoons of him often portray him, chalk in hand, next to a clean blackboard on which he has just written down this particular formula as if it just came to him out of the blue. Barthes observed of the symbolic character of this equation that it restores the image of ‘knowledge reduced to a formula…science entirely contained in a few letters.’ It has become a Gnostic image: ‘the unity of nature, the ideal possibility of a fundamental reduction of the world, the unfastening power of the word, the age-old struggle between a secret and an utterance, the idea that total knowledge can only be discovered all at once, like a lock which suddenly opens after a thousand unsuccessful attempts.’ Barthes’s essay helps explain the transformation of this equation from a scientific tool into a congener.
Einstein himself began to use the equation in its now-famous, simplified form. In April 1946, the first issue of a new popular magazine,
Science Illustrated
, appeared with an article written by Einstein entitled ‘
E
=
mc
2
.’
‘It is customary’, he wrote, ‘to express the equivalence of mass and energy (though somewhat inexactly) by the formula
E
=
mc
2
.’
32
Then, on July 1, 1946, less than a year after the explosions over Hiroshima and Nagasaki, and just shy of 41 years after it first appeared in its initial form,
E
=
mc
2
made the cover of
Time
magazine.
The issue coincided with an atomic test in the South Pacific. The
Time
cover juxtaposed a portrait of the now white-haired, 66-year-old Einstein, whom it called a ‘shy, almost saintly, childlike little man’, next to a fiery mushroom cloud rising above the hulks of warships. Red flames at the base gave way to orange and purple on the column, topped by a gray mushroom cap. On it was inscribed a now-in-famous equation:
E
=
mc
2
. Now it was a celebrity.
InterludeCRAZY IDEAS
In order to understand this we need some crazy idea. Has anyone a crazy idea?
The scientist and science writer Jeremy Bernstein writes that he occasionally fantasizes the following:
It is the year 1905 and I am a professor of physics at the University of Bern. The phone rings and a person I have never heard of identifies himself as a patent examiner in the Swiss National Patent Office. He says that he has heard I give lectures on electromagnetic theory and that he has developed some ideas which might interest me. ‘What sort of ideas?’ I ask a bit superciliously. He begins discussing some crazy sounding notions about space and time. Rulers contract when they are set in motion; a clock on the equator goes at a slower rate than the identical clock when it is placed at the North Pole; the mass of an electron increases with its velocity; whether or not two events are simultaneous depends on the frame of reference of the observer; and so on. How would I have reacted?
1
Bernstein’s thought experiment highlights an occupational side-effect of writing about science: letters from strangers bearing
crazy ideas. Once upon a time these letters arrived in brown envelopes in crabbed handwritten script; today they are emailed with links to flashy Web pages. The usual subjects are astrophysics, cosmology, unification theories, and the overthrow of Western science. Einstein is often invoked, either as emblematic of mainstream science (as the author’s archenemy) or of the misunderstood loner outside it (as the author’s precursor). One or more of the following are generally mentioned: gravity, electromagnetism, and planetary orbits; the most primitive and readily recognizable versions mention also psychic phenomena, astrological signs, herbal remedies, the stock market, baseball scores, and rock lyrics. Many crackpot letters explode into
italics
,
boldface
, and CAPITAL LETTERS in a way reminiscent of far-right newsletters and software licensing agreements. Some authors warn of a government or scientific conspiracy to suppress their ideas; others are generously allowing you into the Fold.
2
Few who receive crazy-idea letters reply. It’s assumed to be counterproductive and perhaps even dangerous, reinforcing the authors’ sense of being misunderstood and inviting more urgent appeals. The recipients quickly peruse the letters, then toss them into a ‘crackpot letter’ drawer. Hardly anyone I know throws them out.
Why not?
One of my colleagues compares his ‘crackpot letter’ drawer to the neighbourhood art show; if you’re thorough and patient enough you might find
something
of value, but the search would take so long you never do it. Others offer psychological explanations: We admire and even envy the authors of crackpot letters for their energy and zeal. We feel a closet affinity – don’t we all feel in possession of misunderstood truth? Still darker, we’re thrilled to read them – it’s like watching a mental train wreck. Yet other colleagues keep them because, they tell me, ‘You never know…’
Crazy-idea letters have interesting philosophical, psychological,
and social dimensions. It’s much harder than it seems to characterize crazy-idea letters and their appeal. Great scientists, too, have gone weird: recall the obsessions of Einstein with unified field theories and Pauling with vitamin C. And aren’t scientists fond of and even dependent on ‘crazy ideas’? Haven’t we all heard the famous story about how Wolfgang Pauli charged Niels Bohr with holding a crazy theory, and how Bohr replied that the trouble was his theory was ‘not crazy enough’ and called for a ‘crazier idea’?
Finally, several cautionary tales suggest we should not be too confident of our ability to recognize crazy-idea letters.
Cautionary tale 1 is the story of 25-year old Srinivasa Ramanujan, an Indian who in 1913 sent correspondence to several British mathematicians. Like several others, G. H. Hardy tossed it aside initially as the work of a crackpot, then read it, realized its genius, and soon invited Ramanujan to England, where he became recognized as one of the leading mathematicians of all time. Our own prejudices, rather than content, can determine whom we deem a nut.
But cautionary tale 2 is the story of Nicholas Christofilos, a Greek electrical engineer at an elevator installation company whose hobby was particle accelerators. In 1949, he sent a manuscript proposing a novel scheme to physicists at Berkeley, who wrote back pointing out flaws. Christofilos incorporated corrections, applied for U.S. patents, and sent the revised scheme back to the Berkeley physicists, who this time simply ignored it. In 1952, reading that U.S. physicists had ‘discovered’ a new accelerating method identical in principle to his own, he contacted a legal firm and got his priority recognized. I once asked a physicist who had seen Christofilos’s original papers why they had been ignored. ‘The first violated Maxwell’s equations’, he said, shrugging without elaborating, his body language indicating that this was equivalent to mentioning psychic phenomena, and that he therefore needed to make
no apology for ignoring the rest. Bad physics does not necessarily make a crackpot.
Jeremy Bernstein insists that, had he seen a copy of his correspondent’s recently published paper, ‘The Electrodynamics of Moving Bodies’, he would have been able to tell that this was not a crank paper, and cites two clues. The first clue is ‘connectivity’, or the fact that the theory gave the same answers as Newtonian mechanics when the speeds of bodies are low compared with that of light. Crank theories ‘usually start and end in midair’ without genuinely connecting with the existing body of scientific knowledge. The second clue is the presence of testable predictions.
I would add two more clues. The first involves the way the authors handle equations. Crazy-idea letters almost always include either no equations or a small number treated like fetish objects. Equations in such letters, indeed, generally illustrate Barthes’ observation about the Gnostic fantasy of knowledge reduced to a formula. The equations appear unaccompanied, as if they were independent nuggets of truth. They are treated as aphorisms, encapsulizing entire philosophies in miniature. The role of the equation in the paper is like that of a musical instrument that someone carries around without ever playing. In genuine scientific papers, by contrast, equations hardly ever occur unaccompanied, but are embedded in a sequence as co-participants in an extensive logical argument, fragments of an extensive intellectual edifice to which they owe their very existence, only a small part of which is reproduced on the page. The equations, that is, are not treated as standing completely on their own.
But I think that the most important clue to a crackpot is the lack of an engaged attitude coupled with playfulness – the sort of attitude that Einstein displayed in his fear he mentioned to Habicht that God was leading him around by the nose, but in his willingness to go along.
As evidence I submit the following story. It took place in September 1946 in New York City at one of the first postwar annual meetings of the American Physical Society. At one session, the presentation by the young Dutch theorist Abraham Pais, who was struggling to explain the strange behaviour of a puzzling, recently discovered new particle, was interrupted by Felix Ehrenhaft, an elderly Viennese physicist. Ever since 1910, Ehrenhaft had been claiming to have evidence for the existence of ‘subelectrons’, charges whose values were smaller than the electron’s, and his efforts to advance his claims had long ago exhausted the patience of the physics community. Now approaching seventy, Ehrenhaft was still seeking an audience, and approached the podium demanding to be heard.
A young physicist named Herbert Goldstein – who told me the story – was sitting next to his mentor and former colleague from the MIT Radiation Laboratory, Arnold Siegert. ‘Pais’s theory is far crazier than Ehrenhaft’s’, Goldstein asked Siegert. ‘Why do we call Pais a physicist and Ehrenhaft a nut?’
Siegert thought a moment. ‘Because’, he said firmly, ‘Ehrenhaft
believes
his theory.’
The strength of Ehrenhaft’s conviction, Siegert meant, had interfered with the normally playful attitude that scientists require, an ability to risk and respond in carrying forward their dissatisfactions. (Conviction, Nietzsche said, is a greater enemy of truth than lies.) What makes a crackpot is not simply our prejudices, nor necessarily the claim, but our recognition of the disruptive effects of the author’s conviction. For conviction tends to wipe out not only the dissatisfaction but also the playfulness, the combination of which produces such a powerful driving force in science.