The largest neutron-star mass yet recorded has broad implications

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Neutron stars are presumed to contain the densest matter in the cosmos. These remnants of core-collapse supernovae pack more than the Sun’s mass (M _⊙) into a sphere less than 30 km across. There is considerable uncertainty about the character of matter squeezed to such ultrahigh densities, which cannot be reproduced in the laboratory.

As the name implies, much of a neutron star’s interior is probably just neutrons packed together at a density of about 10¹⁵ g/cm³—a few times that of a typical nucleus. The protons and electrons of the progenitor material have mostly merged into neutrons by inverse beta decay.

Theorists speculate, however, that at the highest densities near the cores of the most massive neutron stars there may be phase boundaries that enclose more exotic states: free-quark matter rich in strange quarks, Bose–Einstein condensates of K mesons, or simply nuclear matter in which a significant fraction of the neutrons have become hyperons (baryons harboring strange quarks).

But now much of that speculation has abruptly been laid to rest by a single astrophysical weighing. Using the National Radio Astronomy Observatory’s 100-meter-diameter telescope in Green Bank, West Virginia, NRAO’s Paul Demorest and coworkers have measured the highest neutron-star mass ever determined in a precision weighing.¹ The neutron star in the binary-pulsar system J1614−2230, they report, has a mass of 1.97 ± 0.04 M _⊙. The previous record was 1.67 ± 0.01 M _⊙.

Ruling out exotic cores

Now we know for the first time that neutron stars can be twice as massive as the Sun. So what? “Actually, it’s quite amazing how much that simple fact tells you,” says NRAO team member Scott Ransom. To begin with, it rules out most of the proposed equations of state (EOSs) that predict exotic phases for sufficiently compressed nuclear matter.

Every putative EOS is characterized by some maximum neutron-star mass M _max beyond which collapse to a black hole would be inevitable. It turns out that the predicted M _max is generally smaller for EOSs that allow transitions to exotic phases than for those that don’t. In effect, the extra degrees of freedom introduced by the possibility of such transitions make the star less resistant to contraction.

Both nuclear and quark matter are fermionic systems of spin-1⁄2 particles for which the Pauli exclusion principle dictates that increasing compression requires increasing particle momenta. Conjectures of exotic fermionic phases with abundant hyperons or strange quarks are speculative attempts to lower ground-state energies by mitigating the exclusion principle’s energy cost. So is the introduction of bosonic meson condensates.

For various classes of proposed EOSs, figure 1 shows the range of predicted M _max and, below those upper limits, the dependence of a neutron star’s radius on its mass. For almost all EOSs that yield exotic hadronic matter (hyperons, kaonic Bose condensates, and the like) the mass–radius tracks terminate well below the newly measured J1614 mass, and they are therefore ruled out by that measurement.

Fig 1.

Figure 1. Predicted dependence of a neutron star’s radius on its mass is shown for various classes of proposed equations of state (EOSs) that yield different phases of matter at maximum compression: neutron matter (blue), exotic hadronic matter (pink), and strange-quark matter (green). Each swath’s upper edge indicates the range of maximum masses allowed by that EOS class. The horizontal red bands show individual precision mass measurements, and the wider yellow band shows a range of measurements from double-neutron-star binaries. The highest band, marking the neutron-star mass measured in the binary pulsar J1614−2230, rules out any EOS whose maximum allowed mass falls short of it. The gray corner regions were already ruled out by other observational or theoretical constraints. (Adapted from ref. 1.)

View first occurrence of Fig. 1 in article.

Some EOSs that yield strange-quark matter are barely consistent with the new record mass, but only if the quarks, far from being “free,” interact almost as strongly as they do in hadrons. Such detailed implications of the record neutron-star mass are discussed in a follow-up paper by Feryal Özel (University of Arizona) and two other theorists, in collaboration with the NRAO observers.²

Precision weighing

A spinning neutron star usually generates a radio beam along its magnetic-field axis. If that axis is misaligned with the star’s spin axis, the radio beam sweeps out a lighthouse pattern, and a fortunately situated observer sees the neutron star made manifest as a radio pulsar whose pulse frequency is the star’s spin rate.

The binary pulsar J1614 was discovered in 2003, at a distance of about 3000 light-years. Its rapid spin yields a very stable pulse period of 3.15 milliseconds. The neutron star and its lighter, white-dwarf companion orbit the system’s center of mass with a period of about nine days. The orbit is evident in the pulsar’s nine-day Doppler-shift period. But that’s not enough for a mass determination of the neutron star or its companion.

For binary-pulsar pairs of neutron stars in tight, highly eccentric orbits, one can often exploit the general-relativistic precession or decay of those orbits to measure both masses with high precision. The many neutron-star masses thus measured in recent decades cluster in the range 1.25–1.4 M _⊙ (see the yellow band in figure 1). But that narrow range probably reflects a bias introduced by requiring double-neutron-star binaries.

Therefore radio astronomers, in their search for heavier neutron stars, have been looking at heterostellar binaries like J1614, with orbits too large and circular for good measurement of decay or precession. Instead, they aim to exploit another observational consequence of general relativity, which went unnoticed until 1964.

In that year, Irwin Shapiro pointed out—and soon demonstrated with radar beams bounced off planets—a general-relativistic increase in the travel time of light passing by a massive object. The Shapiro effect is above and beyond that due simply to increased path length from gravitational bending. In the case of a felicitously oriented binary-pulsar system, radio pulses from the neutron star would be delayed for a few microseconds whenever in the orbital cycle they pass close to a sufficiently compact companion on their way to the observer (see the cartoon orbits in figure 2). White dwarfs, though not nearly as compact as neutron stars, are 10⁵ times denser than the Sun.

Fig 2.

Figure 2. Over the 9-day orbital cycle of the binary pulsar J1614−2230, measurements of the general-relativistic Shapiro delay of radio pulses (yellow in the cartoons) from the neutron star (red dot) as they traverse the gravitational field of its companion (blue dot) yield precision determinations of both masses. The delay relative to arrival times one would expect in the absence of the Shapiro effect is plotted against orbital cycle phase, whose zero is taken to be the moment when the companion is closest to the line of sight. (From Earth, the orbital plane is seen almost perfectly edge-on.) The curve shows the best theoretical fit to the data. (Adapted from ref. 1.)

View first occurrence of Fig. 2 in article.

A good measurement of how the Shapiro delay varies over an orbital cycle would yield the masses of both the pulsar and its companion. But a random pulsar with a white-dwarf companion in our corner of the Milky Way would exhibit only a very weak Shapiro signal. The amplitude of the periodic signal is proportional to the companion’s mass, and the sharpness of its peak depends sensitively on the inclination of the orbital plane to the line of sight. The effect is strongest when the orbital plane is seen edge-on.

”Low-resolution timing measurements of J1614 over the years suggested it might yield a fairly decent Shapiro signal,” recalls Demorest. “But what we found in our recent high-resolution nine-day observation [shown in figure 2] was spectacular beyond all expectation.”

J1614 turned out to be the most nearly edge-on binary pulsar yet seen. The data revealed an angle of 89.17 ± 0.02° between the orbital plane’s normal and the line of sight. The strength and clarity of the observed signal also benefit from two other fortunate circumstances, one natural, the other instrumental: The companion’s mass, 0.500 ± 0.006 M _⊙, is three times that of a typical white dwarf in a binary-pulsar system. And the observation owes much to GUPPI, the innovative Green Bank Ultimate Pulsar Processing Instrument installed on the radio telescope shortly before the nine-day observation last March.

Performing ultrahigh-speed computer processing of each pulse as it arrives, GUPPI provides a fourfold improvement in the telescope’s timing resolution. It also corrects for signal smearing due to dispersion by interstellar electrons.

As a function of orbital phase in the nine-day circuits of the pulsar and its companion, figure 2 plots the measured delay of the pulse arrivals relative to what one would expect in the absence of the Shapiro effect. The zero of the orbital phase is taken to be the moment when the white dwarf is closest to our line of sight to the pulsar.

Demorest and company took a large fraction of their data near that moment of “orbital conjunction,” where one expects the strongest and most rapidly varying Shapiro delay. The cusped curve shows the best theoretical fit to the single-orbit GUPPI measurements plus auxiliary longer-term Doppler data. That fit yields the impressively precise determinations of the two masses and our viewing angle of their orbital plane.

Merging neutron stars

Beyond ruling out most proposed scenarios for exotic matter in neutron stars, the new record mass has other important implications.² Among them is a possible answer to the long-standing puzzle of what causes the short-duration minority subclass of gamma-ray bursts (see PHYSICS TODAY, November 2005, page 17 ). There’s much evidence that short GRBs signal the cataclysmic merger of two neutron stars into a black hole. But short GRBs typically last a second or two, which is much too long for the naive dynamical time scale of such mergers.

But now that we know that neutron stars can be heavier than 1.8 M _⊙, Özel and company argue, two scenarios for prolonging the GRB become possible: The merged system might be momentarily supported by centrifugal forces that take about a second to dissipate and allow the final collapse. Alternatively, the formation of the black hole might not be delayed, but in the process a massive accretion disk could form and be devoured in something like a second.

Neutron-star mergers are also expected to be a principal source of gravitational-wave signals recorded by ground-based detectors in the near future. A later generation, capable of recording such signals at frequencies beyond a kilohertz, should reveal much about the inner characteristics of the merging neutron stars. But how much can one learn from the lower-frequency components to which LIGO and the next generation of detectors are limited?

In that regard, the existence of 2-M _⊙ neutron stars is encouraging. If neutron stars had the highly condensed cores expected for exotic matter, little information about their interiors would be encoded at frequencies below 600 Hz by tidal deformation during a merger. But having largely ruled out such condensed cores, the collaboration concludes that the detection of gravitational waves, even at low frequencies, “will allow accurate measurements of the equation of state of neutron-star matter in the near future.”²

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Science controversies past and present

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Science—especially the science behind climate change—is under fire. The climate issue has sparked a vigorous, and at times surreal, public debate that seems to pit experts against one another on even the most basic facts, such as whether human greenhouse gas emissions dominate natural ones, whether added carbon dioxide alters the planetary emission of thermal radiation to space, and whether global temperatures are rising.¹ At its heart, global warming is a physics problem, albeit a messy one that cannot proceed far without bringing in meteorology, oceanography, and geology. (See the article by Raymond Pierrehumbert in PHYSICS TODAY, January 2011, page 33 .) The climate debate has spread far beyond the confines of any of those scientific circles and into the media and public sphere, where politicization and vitriol are legion.

Although nearly all experts accept that the greenhouse gases emitted by humans have caused significant warming to the planet and will likely cause much more, only about half the US public agrees, even after years of heavy media coverage. How did we get into such a mess? What are the implications for science, for how it should be communicated, and for how debates should be interpreted? Some insights may be gained by noting that global warming is not the first “inconvenient truth” in physics. Consider this description of another, bygone debate:

The decision [whether to accept the new theory] was not exclusively, or even primarily, a matter for astronomers, and as the debate spread from astronomical circles it became tumultuous in the extreme. To most of those who were not concerned with the detailed study of celestial motions, Copernicus’s innovation seemed absurd and impious. Even when understood, the vaunted harmonies seemed no evidence at all. The resulting clamor was widespread, vocal, and bitter.²

Thus does science historian Thomas Kuhn describe the difficulties experienced by astronomers in convincing the public of the heliocentric theory of the solar system, which ultimately ushered in the scientific revolution. The “clamor” prevailed around the time of Galileo Galilei, more than a half century after Nicolaus Copernicus, on his deathbed, published the heliocentric model in 1543. Copernicus’s calculations surpassed all others in their ability to describe the observed courses of the planets, and they were based on a far simpler conception. Yet most people would not accept heliocentricity until two centuries after his death.

Why did it take so long? To modern minds, the Ptolemaic model of the solar system, with its nested cycles and epicycles, seems rather silly. Surely, the need for a new tweak to the model each time more accurate observations came along should have been a tip-off that something fundamental was wrong. The heliocentric model’s elegance and simplicity, on the other hand, are now appreciated as the hallmarks of credibility for a scientific theory.

Paradigm shifts

It did take scientists a while, although not two centuries, to see the heliocentric model’s merit. Astronomers quietly adopted Copernicus’s calculations soon after they were published, but without at first accepting the heliocentric premise on which they were based. As young, open-minded astronomers replaced their elders, a paradigm shift toward the modern view began. By the time of Johannes Kepler’s recognition of simple elliptical orbits in 1609 (see the article by Owen Gingerich in PHYSICS TODAY, September 2011, page 50 ) and Galileo’s observations the following year, many top astronomers had converted to the Copernican view.

The revelations from Galileo’s telescope (lunar craters, migrating sunspots, planetary moons, and more), though spectacular, didn’t directly validate the heliocentric model. Instead, their most important effect was to challenge the preconceived notions that prevented the model’s acceptance: that the heavens were perfect, that all celestial objects orbited Earth, that Scripture fully described the universe (exemplified by Dante Alighieri’s conception of a geocentric divine arrangement, shown in figure 1).² Once those errors were revealed, the mind reopened to new possibilities. Modern educators have recently realized that a similar process is important in teaching physics in the classroom: Identifying and revealing incorrect intuitions—based on, say, friction-dominated systems—is sometimes necessary before students will truly assimilate an understanding of more general validity, such as Newton’s laws of motion. (See the article by Edward Redish and Richard Steinberg in PHYSICS TODAY, January 1999, page 24 .)

Fig 1.

Figure 1. The Copernican paradigm shattered prevailing conceptions of how God had organized the world (left, adapted from C. Singer, ed., Studies in the History and Method of Science, Clarendon Press, Oxford, UK, 1917). Popular commentators such as Jean Bodin (top right) ridiculed the idea. John Donne (bottom right) expressed deep despair over the new theory in his 1611 poem An Anatomy of the World.

View first occurrence of Fig. 1 in article.

More astute critics such as Tycho Brahe had a legitimate objection to the Copernican theory: If Earth is moving, one should see evidence of parallax in the shifting of the stars over the course of a terrestrial orbit, and Tycho could find none. But stars in Galileo’s telescope remained point-like even under strong magnification, which suggested that they were very distant indeed, and that the parallax would therefore be unobservably small; Galileo’s observations thereby removed Tycho’s objection. (Parallax was eventually observed in 1838.)

Despite the power of the new theory and its observational successes, many people, even in the scientific community, could not relinquish the idea that the universe was built around them. Their belief was so strong that some scientists simply refused to look through Galileo’s telescope, and others invented ridiculous explanations for what it showed.² Compromise models became popular; Tycho himself proposed that the planets orbit the Sun but maintained that the Sun and its entourage all orbit Earth. Over time such crutches fell by the wayside; Copernicus’s view was generally accepted among scientists by the late 17th century and among the public by the late 18th century.²

The progression of the global warming idea so far has been quite similar to that of Copernicanism. The idea that changes in atmospheric greenhouse gas concentrations can and do cause significant climate changes (a notion for which I will use the shorthand term “greenhouse warming”) was proposed qualitatively in 1864 by renowned physicist John Tyndall, when he discovered carbon dioxide’s opacity to IR radiation. In 1896 Nobel laureate Svante Arrhenius quantitatively predicted the warming to be caused in the future by coal burning; the prediction was tested and promoted by steam engineer Guy Callendar in the late 1930s. At first few could accept that humans were capable of inﬂuencing the climate of an entire planet, but over time, and with more calculations, scientists found the possibility increasingly difficult to dismiss.

As with Copernicanism, astute observers found legitimate objections. The 15-micron absorption of atmospheric CO₂ was already largely saturated, which some argued would prevent additional CO₂ from having any effect. The ocean, with its large carbon-storing capacity, seemed poised to soak up most of the human emissions. By the 1970s, however, those objections had deﬂated in the face of contrary evidence,³ and a growing number of papers on climate were noting the likelihood of future warming.⁴

Many who are unwilling to accept the full brunt of greenhouse warming have embraced a more comforting compromise reminiscent of the Tychonic system: that CO₂ has some role in climate but its importance is being exaggerated. But accepting a nonzero warming effect puts one on a slippery slope: Once acknowledged, the effect must be quantified, and every legitimate method for doing so yields a significant magnitude. As the evidence sinks in, we can expect a continued, if slow, drift to full acceptance. It took both Copernicanism and greenhouse warming roughly a century to go from initial proposal to broad acceptance by the relevant scientific communities. It remains to be seen how long it will take greenhouse warming to achieve a clear public consensus; one hopes it will not take another century.

Backlash and politicization

Inconvenient scientific claims also show parallels in their political progression. In the decades before Galileo began his fervent promotion of Copernicanism, the Catholic Church took an admirably philosophical view of the idea. As late as 1615, Cardinal Robert Bellarmine acknowledged that “we should . . . rather admit that we did not understand [Scripture] than declare an opinion to be false which is proved to be true.” But the very next year he officially declared Copernicanism to be false, stating that there was no evidence to support it, despite Galileo’s observations and Kepler’s calculations.² Institutional imperatives had forced a full rejection of Copernicanism, which had become threatening precisely because of the mounting evidence.

Even Albert Einstein was not immune to political backlash. His theory of general relativity, excerpted on the notebook page in figure 2, undermined our most fundamental notions of absolute space and time, a revolution that Max Planck avowed “can only be compared with that brought about by the introduction of the Copernican world system.”⁵ Though the theory predicted the anomalous perihelion shift of Mercury’s orbit, it was still regarded as provisional in the years following its publication in 1916.

Fig 2.

Figure 2. The theory of relativity’s mathematical difficulty and its repudiation of bedrock concepts of space and time threatened many physicists of the day. Philipp Lenard (right), previously a strong supporter of Albert Einstein, became a harsh critic and fought the theory until his death. Others such as Ernest Rutherford (left) did not deny its validity but feared the direction in which it would take physics.¹⁶ (Center image adapted from the Albert Einstein Archives, #5-219.10, © The Hebrew University of Jerusalem.)

AIP Emilio Segrè Visual Archives

View first occurrence of Fig. 2 in article.

When observation, by Arthur Eddington and others, of a rare solar eclipse in 1919 confirmed the bending of light, it was widely hailed and turned Einstein into a celebrity. Elated, he was finally satisfied that his theory was verified. But the following year he wrote to his mathematician collaborator Marcel Grossmann:

This world is a strange madhouse. Currently, every coachman and every waiter is debating whether relativity theory is correct. Belief in this matter depends on political party affiliation.⁶

Instead of quelling the debate, the confirmation of the theory and acclaim for its author had sparked an organized opposition dedicated to discrediting both theory and author. Part of the backlash came from a minority of scientists who apparently either felt sidelined or could not understand the theory. The driving force was probably professional jealousy,⁶but scientific opposition was greatly amplified by the anti-Semitism of the interwar period and was exploited by political and culture warriors. The same forces, together with status quo economic interests, have amplified the views of climate contrarians.⁷

The historical backlashes shed some light on a paradox of the current climate debate: As evidence continues to accumulate confirming longstanding warming predictions and showing how sensitive climate has been throughout Earth’s history, why does climate skepticism seem to be growing rather than shrinking? All three provocative ideas—heliocentricity, relativity, and greenhouse warming—have been, in Kuhn’s words, “destructive of an entire fabric of thought,” and have shattered notions that make us feel safe.² That kind of change can turn people away from reason and toward emotion, especially when the ideas are pressed on them with great force.⁸

The agitations of modern greenhouse proponents appear to have provoked an antiscience backlash similar to the one against Galileo. In the space of only two years, almost as fast as Bellarmine changed his position on Copernicanism, leading moderates have been squeezed out of the main conservative political parties in both the US and Australia and replaced by hard-line rejecters of climate science. In Australia, climate policy was the leading issue behind the backlash; in the US it was one of many contributing factors. Because the Catholic Church of Galileo’s day had generally been a supporter of science and open inquiry, the condemnation of Copernicanism as it grew scientifically solid shocked many devout Catholics.² Likewise, modern conservative political parties have until recently been friends of science, including climate and environmental studies. In the 1970s Republicans and Democrats in Congress were equally concerned about climate change, and as recently as 2004 leading Republicans were—at least in public—enthusiastic in their support of science. Their recent rejections of climate science have probably shocked many supporters. In both cases the backlash seems to have come when leaders were pushed to act on the basis of new evidence. (Figure 3 further illustrates the connection between economic incentives and rejection of climate science.)

Fig 3.

Figure 3. Greenhouse warming and its perceived policy implications challenge widely held libertarian ideals and provoke economic fears, as evidenced by the negative correlation between acceptance of anthropogenic climate change and coal production, especially among the wealthiest nations.¹⁷ Large dots show nations where more than 80% of survey respondents had heard “a lot” or “some” about global warming; small dots show nations where 70–80% had. The vertical axis is the percentage of respondents who agree that humans affect climate, not necessarily who accept the greenhouse theory.

View first occurrence of Fig. 3 in article.

The ugly nature of the current climate debate, with its increasingly frequent characterization of scientists as opportunists, totalitarians, or downright criminals, is also, unfortunately, not new. Copernicus (posthumously) and his prominent followers through Isaac Newton were all accused of being heretics or atheists. Einstein was derided by his political opponents through the 1920s and 1930s as a Communist—despite his dim view of the Soviet Union—or simply as a fraud. When a group of American women tried to prevent him from entering the US because of his supposed Communism, he quipped, “Never before have I experienced from the fair sex such energetic rejection of all advances, or if I have, then certainly never from so many at once.”⁹ At one point Einstein stopped giving public lectures out of fear for his personal safety, also now a worry for some greenhouse warming proponents.

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The curious aftermath of Neptune’s discovery

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The sensational news of Neptune’s observation reached the US about a month after the initial sighting at the Berlin Observatory just after midnight on 23 September 1846. The discovery was seen as a remarkable accomplishment of celestial mechanics. Not only was Neptune just the second major planet detected in recorded history, but the planet had been mathematically predicted before it was observed. The ensuing dispute over the priority of that monumental discovery captured both scientific attention and popular interest in Europe and the US. A handful of ambitious US scientists, by dint of personality and nationality, viewed the Neptune affair as a welcome opportunity to advance the visibility of US science and assert national scientific competence on an international stage. Prominent among them was Harvard mathematician Benjamin Peirce (pronounced “purse”), who questioned the mathematical particulars of Neptune’s discovery and thus ignited controversy on both sides of the Atlantic.

Ambitions in the US

In the late 1830s and early 1840s, a core of elite scientists in the US worked to develop specialized publication outlets, improve advanced scientific training, and find funding to support research. They aspired to establish and define US science in response to perceived European scientific superiority. It seemed unlikely that the newly emerging scientific community in the US could eclipse European research in any well-established area. Continental researchers enjoyed the advantages of well-developed scientific infrastructure and quick access to new results, but US scientists would seek creative solutions.

In their short-lived research journal The Cambridge Miscellany of Mathematics, Physics, and Astronomy, Peirce and Harvard physicist Joseph Lovering planned to communicate European mathematics to their readers in hopes of engaging them in research. Peirce and Lovering aimed to focus US mathematical attention on light, astronomy, mechanics, and probability. They especially highlighted the field of astronomy as an area in which mathematical sciences might excel—if support could be found. In advocating for science, the journal circulated impassioned appeals to national honor. The few astronomical observers that the US now has, Peirce wrote,

must leave the field or become martyrs to their perseverance, if their midnight toil is not to supply them their daily bread. The observer, who withdraws from all society, in order to devote his nights to watching the stars, is enervated by his loss of sleep, and unfitted for the labors of the day. He cannot live two lives; and if he works while others sleep, he must sleep while others work. While he sustains science, we must sustain him.¹

The planet Neptune was discovered in 1846 by German astronomer Johann Galle and his assistant Heinrich Louis d’Arrest. This image was captured by the Voyager 2 spacecraft in the summer of 1982. (Courtesy of NASA.)

Peirce specifically requested that Harvard president Josiah Quincy fund William Cranch Bond, the first director of the Harvard Observatory, at “the same salary with one of the professors, so that he may devote the remainder of his life to the cause of American astronomy with undivided zeal.”² Peirce emphasized the importance of Bond’s work and stressed how “his observatory must compete with those of [George Biddell] Airy and [Friedrich] Bessel and [Otto] Struve. We are proud of his skill and genius,” Peirce concluded, “let us give them fair play.”

A new planet

Harvard University mathematician Benjamin Peirce championed US science and challenged the validity of the European claim of Neptune’s discovery. This portrait was painted by Daniel Huntington in 1857.

Neptune had been sighted before its 1846 discovery, but it had never been recognized as a major planet. In 1843 University of Cambridge graduate John Couch Adams began to pursue the idea that the well-documented orbital deviations of Uranus resulted from an unknown body, probably a planet. Astronomer Royal Airy ignored Adams’s computations. Telescope time from Cambridge Observatory director James Challis also eluded Adams, who needed observational data to confirm his prediction.

In the summer of 1845, French scientist Urbain Jean Joseph LeVerrier also started to study the irregularities of the orbit of Uranus. LeVerrier’s predicted location for the perturbing body, “a planet as yet unknown,” appeared in the Times of London in July 1846. Earlier that month LeVerrier had written about his predictions to Airy, who recalled Adams’s previous work and pressed Challis to conduct a search at the Cambridge Observatory. Airy asked Adams to prepare a star catalog to facilitate British observations, which began in late July. Although Challis did sight Neptune, his search technique did not allow him to realize he had in fact located the new planet.

Meanwhile, after a lukewarm reception from French observational astronomers, LeVerrier sent his request to Johann Galle at the Berlin Observatory. Galle agreed to look for the unknown planet, guided by LeVerrier’s prediction. Galle’s student assistant Heinrich Louis d’Arrest chose their complete copy of the detailed Berlin Academy star map for the project. According to d’Arrest, after less than an hour of observing, Galle reported “there is a star of the 8th magnitude in such and such a position, whereupon I immediately exclaimed: that star is not on the map!”³ The observation occurred 15 minutes after midnight on 23 September 1846. Although 19th-century contemporaries awarded the optical discovery to Galle, scholars now generally agree that Galle and d’Arrest jointly discovered the planet at the telescope in Berlin.

Galle verified the initial observation the following night. The next morning he sent word to LeVerrier saying, “The planet whose position you have indicated really exists.”⁴ By 1 October, the news reached London, where it appeared in the Times. Controversy ensued. Some at the University of Cambridge lamented their near victory, swapped accusations of blame, and fought to salvage a share of the fame. Others in the UK argued that Adams did not deserve any credit. In France, too, some scientists quibbled about particulars of the discovery and regretted that the first sighting had not happened in France. As claims of priority and charges of plagiarism ricocheted across the channel, both the Paris Academy of Sciences and the Royal Society of London waved flags of national pride.

Eventually, tempers cooled and enough facts came to light for the fellows of the Royal Society of London to award the Copley Medal to LeVerrier in 1846. At the time they deemed Adams’s involvement too tentative, although he did receive the Copley Medal in 1848. The Royal Astronomical Society, on the other hand, eventually gave up after extensive deliberation and decided not to award its Gold Medal to anyone in 1847. The following year the Royal Astronomical Society voted to suspend the bylaws relative to medals and instead awarded 13 testimonials to individuals—including Adams and LeVerrier—whose astronomical services would have been “under ordinary discussion for the medal of 1848.”⁵

Traditionally, historians have credited both LeVerrier and Adams with independent mathematical predictions for the location of the planet Neptune. In 1999, however, the “Neptune File” of correspondence related to the planet’s discovery appeared in Chile after having been missing from the Royal Observatory, Greenwich, for decades. That same year St. John’s College library in Cambridge completed a computer index of the John Couch Adams archives. Together, those two events fueled scholarship that reevaluated the traditional story; the revised narrative attempted to claim sole priority for LeVerrier, asserting that the recovered documents demonstrated how Adams’s credit resulted from intentional post-discovery spin formulated by some British administrators of science.

Enter US scientists

In this letter to Harvard University president Josiah Quincy, Benjamin Peirce argues for the importance of adequately funding Harvard Observatory director William Cranch Bond and his son, George. The letter begins, “The tender, which has just been made to Mr Bond of the superintendance of the National Observatory at Washington, and the opportunity of securing to his son, George, an excellent situation in the same observatory, have most forcibly pressed upon me the somewhat mortifying fact that Mr Bond and his son are laboring at our observatory without any other compensation than the mere rent of his house.”² (Courtesy of the Harvard University Archives.)

Once word of Neptune’s discovery reached America via steamship, the sensational news became a hot topic for newspaper articles and letters to the editor. Not only were matters of planetary theory, predictive accuracy, and, ultimately, national pride paramount in those accounts, but newspapers also included mathematical details on which US astronomers staked a claim. Daily papers in Boston and Washington, DC, would, in fact, serve as primary outlets for American results.

How had LeVerrier and Adams arrived at their predictions? Locating an unknown perturbing body was a difficult business at best and involved a determination of its orbital elements from the discrepancies in the orbit of Uranus. In their approach to the problem, Adams and LeVerrier used the Titius–Bode law—an empirical rule that adequately approximates the semimajor axes for planets Mercury through Uranus—to determine the orbital radius of the perturbing body. Both Adams and LeVerrier relied on Laplace’s theory of perturbations as it appeared in Philippe le Doulcet de Pontécoulant’s text Théorie analytique du système du monde (The System of the World). Adams used perturbation theory and tinkered with various values for orbital elements of a possible eighth planet to decrease the differences between the calculated and observed orbits of Uranus. The assumption of the Titius–Bode law distance for the hypothesized eighth planet produced a highly eccentric orbit. The computation of Adams and LeVerrier involved a Fourier expansion with 79 separate cosine arguments and 144 terms. Suffice it to say, the two scientists had chosen a challenging problem.

When LeVerrier’s first published predictions for the location of the as yet undiscovered planet reached Washington, DC, in August 1846, US Naval Observatory scientist Sears Cook Walker suggested to his superintendent Matthew Fontaine Maury an immediate investigation. Although Maury listened to Walker’s idea, more pressing duties took priority. But when word of Galle and d’Arrest’s discovery reached Washington two months later, Maury remembered the suggestion and appointed Walker to investigate the new planet. They hoped to earn credit for some related discovery.

Walker initially examined old catalogs of star sightings, searching for something seen and recorded in approximately Neptune’s location. He discovered that about 50 years earlier, on 10 May 1795, French astronomer Joseph Jérôme Lalande had observed something of the eighth magnitude within the limits of the Neptunian region Walker had calculated. Walker then refined his orbital calculations under the assumption that Lalande had seen Neptune. His new computation suggested a nearly circular orbit for the planet. Walker published that result in the Washington Daily Union newspaper on 9 February 1847, along with an announcement identifying Lalande’s earlier sighting as Neptune.

The following week Maury reprinted Walker’s findings in the Boston Courier. A copy of that newspaper arrived in London, where a state agent sent it on to LeVerrier in Paris. LeVerrier received Walker’s conclusions the same day he got word from German astronomers who had also discovered the Lalande sighting. LeVerrier then asked Victor Mauvais at the Paris Observatory to consult Lalande’s original manuscripts for more unpublished observations. LeVerrier reported those new developments to the Paris Academy, which published Walker’s results in its March 1847 proceedings.

“A happy accident”

The Berlin Observatory was the site of Neptune’s discovery. This etching of the observatory was created by Ernest Grünewald in 1835. (Used with permission of the Bildarchiv Preussischer Kulturbesitz, Berlin/Art Resource, New York.)

In the same month that the Paris Academy published Walker’s results, Peirce communicated them to Boston’s American Academy of Arts and Sciences. He explained that he had undertaken a careful reexamination of the data, inasmuch as the details of Walker’s orbits deviated so widely from the predictions of Adams and LeVerrier. Peirce verified Walker’s results and also asked Harvard Observatory director William Bond and his son George to investigate Neptune’s distance and motion from observations conducted only at the Harvard Observatory. Walker’s twice-confirmed results convinced Peirce that the actual orbit of Neptune differed from that predicted by LeVerrier and Adams. Before Boston’s academy, Peirce asserted that “Neptune is not the planet to which geometrical analysis had directed the telescope; that its orbit is not contained within the limits of space which have been explored by geometers searching for the source of the disturbances of Uranus; and that its discovery by Galle must be regarded as a happy accident.”⁶

To substantiate his incendiary statement, Peirce incorporated data from Lalande’s observations to compute a less eccentric orbit of Neptune. He took issue with the distance limits LeVerrier used, claiming that LeVerrier’s planetary equations could not explain the perturbations of Uranus. In sum, Peirce concluded, “Neptune cannot . . . be the planet of M. LeVerrier’s theory.”⁷

Peirce nevertheless held that the “real” planet Neptune could account for the disturbances in Uranus’s orbit if the problem were reconsidered with a more probable mean distance. Peirce said LeVerrier had arrived at a practical solution to “where among the stars astronomers must look in order to see the disturbing body,”⁸ but had not provided orbital elements for that body. Peirce demanded a complete orbit for Neptune. While awaiting additional observations to fortify their theory, Walker and Peirce continued to tweak their calculations and agreed that “nothing but a rigorous calculation of the perturbations of Neptune can throw any further light on the subject at present.”⁹

For 18 months Walker and Peirce corresponded about the brightness, mass, distance, and motion of Neptune. They tinkered with their calculations as Walker compiled more than 500 observations. Peirce admitted the possibility of error but insisted that the orbit deduced from observation had not yet been reconciled with theory. Likely few in Peirce’s audience either comprehended the details involved or shared his concern with perfecting the theory of the new planet. Certainly, many did not share his comfortable self-assurance with the happy-accident hypothesis.

Reactions at home and abroad

Sears Cook Walker, working at the US Naval Observatory, calculated Neptunian orbits that were at odds with those assumed by discoverers Johann Galle and Heinrich Louis d’Arrest. This portrait first appeared in an 1894 issue of Popular Science Monthly.

Peirce’s effort to make an international splash created nervous ripples in US scientific and political circles. Smithsonian Institution secretary Joseph Henry thought his friend had been premature in criticizing LeVerrier. Geologist James Dwight Dana pronounced Peirce’s actions a “national calamity” and was appalled that Peirce had made himself a “critic upon European astronomy.”¹⁰ Successor to Harvard president Quincy and former US minister to Great Britain, Edward Everett, worried about the public condemnation Peirce might bring on Harvard and the US. He entreated the American Academy not to endorse the improbable happy-accident idea. Everett actually requested that Peirce suppress the announcement of his results because they were so improbable. With characteristic bravado, Peirce replied, “It is still more improbable that there can be an error in my calculations.”¹¹

Three days after the happy-accident pronouncement, Harvard fellow Jared Sparks (who eventually succeeded Everett as the university’s president) recommended a press release to modify Peirce’s position since it was “extremely important that the first impression in Europe should be accurate . . . and [Peirce’s] reputation is so much concerned that no pains should be spared to set the matter in a true light.”¹² Peirce did release a statement that praised LeVerrier’s genius, but he retracted neither the happy-accident hypothesis nor his specific criticisms of LeVerrier’s calculations.

On the other hand, outspoken advocates for US science, such as astronomers Ormsby Mitchel and Benjamin Gould and botanist Asa Gray, applauded Peirce’s efforts in defense of American astronomers who “have been passed over in silence, or met with sneers instead of arguments.”¹³ Gray felt that Peirce’s response to LeVerrier did Peirce “the highest credit” and was “just the style of reply calculated to place [him] at the greatest advantage.”¹⁴ For those and other elite scientists, the pride of national science was at stake in the Neptune controversy. Amid hot debate over predicted and observed orbital elements, there was more concern about national scientific reputation than the correctness of painstaking orbit calculations.

The nascent US scientific community was caught in tension between desiring approval and asserting independence. Some, who wanted to avoid upset, attributed the onslaught of Peirce’s publications and rescissions to overhasty calculation or personal overreaction. Others hoped to use the Neptune discussion to steal some limelight for the good of US science. Since Peirce raised the loudest American voice in the Neptune controversy, Sparks was right: The reputation of US science abroad was interlaced with Peirce’s own European reputation.

So, what was the European response to the criticism from Peirce? The popular press maintained an air of self-assured scientific superiority. More serious scientific institutions radiated disapproval. The Royal Astronomical Society, for one, argued that accidental planetary discovery was unlikely and requested that Peirce suppress his paper. LeVerrier, meanwhile, “resented disparagement of his discovery” and wrote a scathing letter to the National Intelligencer in Washington, DC, in which he attacked Peirce and highlighted errors of detail. Peirce’s response only escalated the situation. When George Bond visited France in 1850, he found LeVerrier still irritated about the exchange. Adams expressed the view that Peirce’s objections were “founded on imperfect views of the nature of the planetary perturbations.”¹⁵ Airy wrote to a colleague that the Americans stressed the phenomena of occultations too much in determining distant longitudes.

Shortly after Peirce announced his happy-accident hypothesis, the priority dispute in Europe died down as some astronomers redirected their antagonism toward US scientists. In November 1847 Glasgow astronomer John Pringle Nichol voiced a general feeling that the controversy had ended among European astronomers, but he continued to attack the happy-accident hypothesis. During an 1848 lecture in New York, he pointedly critiqued Peirce’s view. English polymath John Herschel, whose father had discovered Uranus, used an assault on Peirce’s results to press the joint claims of Adams and LeVerrier. German mathematician Carl Jacobi viewed Peirce’s “monstrous assertion” as harmful to the cause of astronomy in general. He declared it a great public disservice for a scientific authority to undermine a discovery that was “achieved through deep thought and years-long labor” by suggesting that “an accident had prevailed or played a part” in a work that would “be envied by our posterity and by our own time.”¹⁶

Not everyone agreed. Airy—with perhaps his own political reasons—acknowledged that Peirce’s work had proven LeVerrier’s orbital elements to be incorrect. George Bond received praise in the UK as an excellent observational astronomer. Mathematician Carl Friedrich Gauss, too, viewed the US work favorably. He respected Peirce’s position in the controversy and was also impressed by Peirce’s subsequent work in analytic mechanics. The very selective journal Astronomische Nachrichten saw fit to republish Peirce and Walker’s orbit calculations.

Peirce and like-minded countrymen hoped that the Neptune affair was only the beginning of a mathematical dialog with researchers abroad—particularly theoretical and observational astronomers. The 1846 report of the Harvard Observatory indicates a move toward increased cooperation. Specifically, the director of the observatory was expected to “establish and maintain a regular correspondence with the astronomer royal of England, and with the Directors of some of the principal observatories upon the continent of Europe.” Peirce also gained approval to employ an agent in London to “send by every royal mail steamer to Boston, the latest astronomical intelligence received in London.”

At a time when perceived arrogance from the European scientific establishment troubled some US scientists, the Neptune controversy enabled them to mount a defense of US science. While some French and British scientists and administra-tors quibbled over priority, Peirce and Walker—considered upstart US scientists—dared to question LeVerrier’s mathematics. Though the mixed response from Europe distressed colleagues who desired only the approving nod of French and British academies, it also proved that US mathematics was entering the international scientific stage, with Peirce playing a leading role.

Although it is difficult—perhaps impossible—to sort out all the inflammatory letters and rapid-fire calculations and precisely to track Peirce and Walker’s orbit calculations, it appears that the two US scientists were the first to determine an accurate, complete orbit for Neptune. Walker’s early discovery that Lalande had spotted Neptune gave the Americans a significant advantage. Not only was Peirce galvanized by the opportunity provided by the planetary controversy, but he and Walker both worked quickly.

It is remarkable that US scientists challenged their European counterparts—and arguably triumphed—on a mid-19th-century question of cutting-edge research. As Airy wrote in 1847, “The history, since the discovery of the planet, is, I think, more curious than that before the discovery.”¹⁷

Category: 0 ShOwS inTeRst

Neutron target station takes the heat

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Designs for the European Spallation Source to be built in Lund, Sweden

Designs on protons

When complete in 2019, the €1.48bn European Spallation Source (ESS) will be the most powerful source of neutrons in the world. With construction expected to start in 2013, and the facility fully open by 2025, the ESS will produce neutrons by accelerating protons in a linac to 2.5 GeV before smashing them into a seven-tonne target. The neutrons will then be cooled by a moderator and sent to 22 experimental stations to be used by researchers to probe the structure and physical properties of a wide range of solids, liquids and gases. The ESS will specialize in long wavelength, or "cold", neutrons that suit experiments on large-scale structures such as polymers and biological molecules.
But one big problem for those designing the ESS is that this process of "spallation" will deliver so much energy – the proton beam will have a power of 5 MW – that the temperature of the target will jump by more than 100 °C in just 2.8 ms. Indeed, as the target becomes radioactive it will produce a decay heat of 35 kW even when there is no proton beam. Researchers at the ESS are therefore designing a proton target that can not only generate copious amounts of neutrons, but also be able to handle these extreme heat conditions.

Planning ahead

Andreas Jansson, head of the linac beam instrumentation group at the ESS, talks about the uses of neutrons

A neutron-rich material makes for a good proton target and ESS bosses are currently investigating two different options – a lead bismuth eutectics (LBE) alloy or tungsten. LBE is solid at room temperature but at the ESS's operating conditions becomes liquid, which is similar to another possible target material – mercury. On the other hand, tungsten is solid up to 3000 °C and has a very high density of 19.25 g cm^–3, giving it a high neutron yield. The material also has the advantage of longevity, with a life-span of three years or more, compared with six months for a lead–bismuth target.
As Physics World went to press, the ESS board was expected to decide which target to use, with tungsten the clear favourite having got the thumbs up from the ESS's science advisory board in July. Indeed, tungsten is also already used at other neutron-scattering facilities including ISIS in Oxfordshire, which has a solid tungsten target about the size of a house brick. "The material is really the best you can pay for," says Ferenc Mezei, head of the ESS's target division. "There are other materials, iridium for example, that have a higher density but they are much more expensive."

More power

There are some challenges to implanting a target given the heat created by the ESS's huge proton-beam power of 5 MW, which will be around 20 times greater than that at ISIS. One proposed solution is to make the target rotate once every three seconds so that only a certain part is hit by the proton beam at any one time.
One design for the ESS's target is to use a disc – 2.5 m in diameter and 13 cm high – made up of a solid inner hole and an outer ring. The beam will hit the disc edge-on, first encountering the outer layer, which is made up of around 10,000 small rods of tungsten each about 12 cm high and 1.5 cm in diameter. The beam then travels through the inner solid tungsten where it will lose energy so fast that it does not actually reach the centre of the disc. The advantage of using rods in the outer ring, rather than solid tungsten, is that in taking most of the proton beam, they distribute and reduce the stress of the whole target during its rapid rise and decrease in temperature.
The disc is made to rotate so that the 5 MW beam will be distributed such that a section of the disc sees – on average – about the same power density as that at ISIS. This allows that part of the target to cool down by 100 °C in around 3 s before it comes in contact with the beam again.
The sheer size of the target, and its activation, means that researchers cannot build a full prototype to test such high beam powers. However, in designing the ESS's target, researchers can take solace from the fact that the technology has been tested before, for example at ISIS's muon facility, which uses a small rotating graphite target to produce muons – heavier cousins of electrons.
"Rotating targets are around," says Mezei. "So we are confident that this kind of technology will work".
• You can download a PDF of the October 2011 Physics World Big-Science Supplement here.

Category: 2 ShOwS inTeRst

Physicist Proposes That Electron May Be Split In Two

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PROVIDENCE, R.I. — In a paper published today (Aug. 1) in the Journal of Low Temperature Physics, Humphrey Maris, professor of physics at Brown University, proposes that under suitable conditions electrons can undergo a form of fission. He has also discovered there is a significant amount of experimental evidence supporting his theory.

Physicists consider that matter in the world is composed of a large number of elementary particles. Some of these particles, such as the electron and the proton, carry an electric charge, while others, including the neutron and neutrino, are electrically neutral. Although some elementary particles can decay into other particles, it has been regarded as a general principle of physics that an elementary particle cannot be broken into two pieces. Thus, for example, although a neutron can decay into a proton plus an electron and a neutrino, it can never be broken into two half neutrons.
According to quantum theory, the state of a particle is described as its wave function. The probability that the particle will be found in any position is proportional to the square of the wave function at that point in space. Maris’ theory considers what happens to electrons when they are immersed in liquid helium at a temperature of one degree above absolute zero. Previous experiments have shown that an electron in helium becomes trapped in a bubble approximately 100-billionths of an inch in diameter. The bubble drifts through the liquid with the wave function of the electron confined inside it.
Maris shows that when the bubble is illuminated with infrared light, the bubble can divide into two smaller bubbles each containing a part of the wave function of the electron. These two bubbles can then move independently through the liquid and become separated from each other.
In the 1970s, researchers at Bell Laboratories and the University of Michigan performed experiments on the effect of light on electrons in liquid helium. These researchers were unable to explain their surprising results. Maris realized that these old experiments, together with more recent measurements made at the University of Lancaster, could be understood in terms of his theory and provided support for his ideas.
Further experiments to test the theory are under way at Brown University in work supported by the National Science Foundation.

Category: current research, quantum 3 ShOwS inTeRst

The dark-energy game

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The 4% Universe: Dark Matter, Dark Energy, and the Race to Discover the Rest of Reality
Richard Panek
2011 One World/Houghton Mifflin Harcourt £12.99pb/$26.00hb 320pp

Schematic of the universe depicted as a jigsaw puzzle

Puzzling behaviour

The universe is not like a clock, where well-understood parts tick in predictable ways, nor like a balloon expanding or contracting. It is in fact pushing itself apart with a strange kind of energy, and 96% of it is made of an unknown kind of matter. How we discovered this is the subject of The 4% Universe, which condenses the complex, messy and startling tale – people, science, instruments, events – into an easily digestible, fast-paced 243 pages. That is a startling achievement in itself. To the connoisseur of popular science, indeed, the way author Richard Panek tells the tale is as interesting as the events: half drama, half detective story.
The prologue begins with a one-page "wow!" moment. On 5 November 2009 scientists at 16 institutions around the world dropped their collective jaws as they seemed to catch a first-ever glimpse of an entirely new structure of the universe. Two pages follow explaining its significance. Referring to the year when Galileo first used the telescope to reveal entire new worlds previously unknown to humankind, Panek writes "It's 1610 all over again."
What follows in Act One is the story of how cosmology went from speculation to science: how astronomers discovered that the furniture of the universe was more than planets and stars, and was on the move to boot. The universe "had a story to tell", Panek writes. "Instead of a still life, it was a movie," he says. We learn how scientists uncovered this movie's plot by peering over the shoulders of Act One's two main characters: theoretical physicist Jim Peebles, author of the classic textbook Physical Cosmology on the physics of the early universe; and astronomer Vera Rubin, whose work on the galaxy-rotation problem pointed the way to the idea that the universe contains some amount of "dark" matter, invisible to present-day instruments.
Act Two introduces more characters and "the game", in which two different teams of scientists vie to unravel the plot by finding distant "Type 1a" supernovae. The game is played with telescopes equipped with charge-coupled devices, which revolutionized astronomical photography, and with the Hubble Space Telescope, which peered into hitherto invisible corners of the universe, among other equipment. The first team, the Supernova Cosmology Project (SCP), was led by Saul Perlmutter and Carl Pennypacker, particle physicists at the Lawrence Berkeley National Laboratory who applied the tools of their trade to astronomy. In doing so, Panek observes, "[T]hey weren't drifting towards a new discipline. The discipline was drifting towards them."
The second team was known as High-Z, where Z is a term for redshift. Highly redshifted objects are among the oldest and most distant in the universe, meaning that they would bear the clearest traces of any expansion or contraction. High-Z's main members were Adam Reiss and Brian Schmidt, who hailed from Harvard University and viewed supernovae as their area of expertise. They saw the Berkeley group as being out to "beat them at their own game". While SCP had a six-year head start, High-Z recruited the "old-boy network" to, in effect, beat the Berkeley group at beating them at their own game.
In 1997 the two teams converged – simultaneously, yet reluctantly – on two wild, toothfairy-like ideas: that the universe contained "dark matter they couldn't see and [a] new force they couldn't imagine". In Act Three, all the main characters introduced so far in the drama gather at a meeting where the SCP's results (picked up by discerning newspaper reporters) suggest that "SCP was beating [High-Z] at beating the SCP at beating [High-Z] at their own game". Then High-Z outdid that by securing full credit in the media. The discovery of this new force – soon dubbed "dark energy" – became Science magazine's "breakthrough of the year" in 1998.
The new idea – that the universe's expansion is accelerating – both simplifies things, by explaining a lot of puzzling data, and makes them more complex, by raising a lot of questions.
In Act Four, SCP and High-Z make plans to hunt for answers to one question – dark matter – while struggling over credit for the other, dark energy. The existing picture of the universe turns "preposterous". But as Perlmutter remarks on the final page of the book, what usually attracts physicists to their field is "not the desire to understand what we already know but the desire to catch the universe in the act of doing really bizarre things". And so, at the book's conclusion, while one chapter in astronomy ends, another begins.
Panek tells the story briskly yet warmly, capturing personalities and not overlooking controversies. He chooses characters carefully. Through Rubin, for instance, we not only learn about dark matter, but also what it is like to be a woman in science, literally balancing child and career: textbook in one hand, pram in the other. Panek also has a knack for summarizing developments concisely and efficiently, such as in the following passage about how astronomy became more specialized over time:
You couldn't just study the heavens anymore; you studied planets, or stars, or galaxies, or the Sun. But you didn't study just stars anymore, either; you studied only the stars that explode. And you didn't study just supernovae; you studied only one type. And you didn't study just Type 1a; you specialized in the mechanism leading to the thermonuclear explosion, or you specialized in what metals the explosion creates, or you specialized in how to use the light from the explosion to measure the deceleration of the expansion of the universe – how to perform the photometry or do the spectroscopy or write the code.
Inevitably, Panek makes some compromises, and the seams of his crisp storytelling occasionally show. Galileo is mentioned once too often, and Panek's apothegmatic style can ring precious, as in this remark about the signal from a radio antenna: "[T]his time the source wasn't a radio broadcast from the West Coast. It was the birth of the universe." The reader sometimes feels manipulated, too. That "wow!" moment that kicks things off so dramatically in the prologue? You don't find out until page 197 that it was phoney – not a discovery after all.
Another author might have explored why it initially seemed to be a discovery, why its announcement was hyped even after problems were uncovered, and what this says about science and scientists. But by this time, you are so absorbed in the story that you do not care that much. And the book does convey a good picture of scientists in the act of catching the universe doing really bizarre things – while also showing that this is why they took the job. Give this book to your non-scientist friends to show them what it is all about – and to fellow scientists as a model of how to write popular science.

Category: astronomy, atom, history, optics 0 ShOwS inTeRst

Cloaking space–time

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Most existing invisibility cloaks are designed to hide objects from view. But as Martin McCall and Paul Kinsler explain, it could also be possible to make "space–time" cloaks that allow selected events to go undetected – perfect for the ultimate bank heist

Photo of man standing by a robbed bank vault

The ultimate bank heist

Our view of the world is determined by what our eyes see, our ears hear and our noses smell, or what the philosopher Bertrand Russell termed "sense data". But we know from simple optical illusions that our eyes can be fooled – things are not necessarily always what they seem. However, the techniques that physicists have recently developed to manipulate the path taken by light and other electromagnetic radiation are not mere tricks of the eye: they are real advances that can result in some fascinating and useful effects.
By making specially engineered "metamaterials", we can now create primitive versions of Harry Potter's invisibility cloak. After diverting light around an object – like water flowing round a tree stump in a river, or cars parting to either side of a traffic island – we can seamlessly reintegrate it afterwards. Our senses are subverted, not by trickery, but because the light reaching our eyes is the same as if the object were not there. By changing the paths of light rays through space to hide an object at a selected location, we are able to make what is called a "spatial cloak".
But imagine if we could make a cloak that operates not only in space but in time as well. To understand how such a "space–time" cloak might work, consider a bank housing a money-filled safe. Initially, all incoming light continuously scatters off the safe and its surroundings, revealing the rather dull scene of an undisturbed safe visible to surveillance cameras. But imagine, near some specified time, splitting all the light approaching the safe into two parts: "before" and "after", with the "before" part sped up, and the "after" part slowed down. This would create a brief period of darkness in the stream of illuminating photons. If the photons were a stream of cars on a motorway, it is as if the leading cars were to speed up and those trailing behind were to decelerate, creating a gap in the traffic edged by bunches of cars (a dark period with bright edges – see t₃ in figure 1).
Now imagine that during the moment of darkness, a safe-cracker enters the scene and steals the money, being careful to close the safe door before he leaves. With the safe-cracker gone, the process of speeding up and slowing down the light is reversed, leading to an apparently untouched, uniform illumination being reconstituted. As far as the light reaching the surveillance cameras is concerned, everything looks the same as it did beforehand, with the safe door firmly shut. The dark interval when the safe was cracked has literally been edited out of visible history.
To complete our motorway analogy, it is as if the cars have acted to first open up and then close a gap in traffic, leaving no disturbance in the flow of vehicles. There is now no evidence of that temporary car-free interlude, during which the proverbial chicken may even have crossed the road without getting squashed. So by manipulating how light travels in time around a region of space, we can, at least in principle, make a space–time cloak that can conceal events – an "event cloak", if you will.

Transform and go

Figure 1: Towards a space–time cloak

Both space and space–time cloaks use a general method called "transformation optics", whereby cloak designers decide what route they want light to take before calculating what sort of material the light should pass through to achieve that aim. The point is that light rays travel along paths that can be mathematically altered – for example from straight lines to curves. However, to create the desired distortions of the ray paths, we need our material to be carefully designed, a process that is usually expressed in terms of coordinate transformations. We can then use Einstein's "principle of covariance", which says that all physical theories are independent of the coordinates used, to calculate the material properties that will produce the desired light trajectories. Whereas regular (i.e. spatial) invisibility cloaks apply this principle only in space (figure 1a), an event cloak applies it in space–time (figure 1b) – after all, time is as much a coordinate as space, with both appearing in Maxwell's equations for the electromagnetic field.
What is remarkable is that the event cloak leaves the light rays undeviated from their path from source to detector – they do not curve in space, instead they curve in space–time. It is their speed, not direction, that changes as a function of both position and time. But because our proposal is based on speeding light up in some places and slowing it down in others, we have to ensure that the average speed of the light in our material is less than it would be in a vacuum. After all, since nothing can travel faster than light in a vacuum, our method, which involves speeding up part of the light, would otherwise not work. Another important detail is ensuring that the cloaking light rays do not point towards the past. The simple circular space–time cloak of figure 1b, although ideal for explanatory purposes, unfortunately does include such rays. Thankfully, the design can be modified to remove such features.

From dream to reality

It is easy to imagine all sorts of things that could be done with an event cloak – from the big and fanciful to the small and potentially more useful. Making one in practice would, of course, be another challenge entirely. What we would need is a set of parallel metamaterial layers, each containing an array of tiny metallic elements, the conduction electrons in which would interact with light in a way that could be easily controlled. Such tiny elements, or "meta-atoms", are the usual way of building up the metamaterials used in ordinary spatial cloaks, but what we need is a more adaptable interaction. In particular, we want to be able to independently adjust the response of each layer in the metamaterial as time passes.
Assuming such a material can be made, illuminating light travelling perpendicular to the layers would not "see" a heterogeneous structure, but a smooth effective medium – if, that is, its wavelength is much bigger than both the meta-atoms and the spacing between the metamaterial sheets. However, because of the presence of addressable metallic elements, the average speed of the light through the material can be dynamically adjusted. The metamaterial properties can thus be controlled so that they produce the characteristic dark-spot intensity null of the space–time cloak at the desired space and time.

Figure 2: Star Trek transporters and beyond

Events occurring in the cloakable space between the central layers (figure 2a) near the chosen time will occur in the dark, and so be hidden from – and unsuspected by – any observer. Although this dark spot can exist over as long a distance as we like, it moves, and lasts only for a relatively short time that depends on the performance and thickness of the metamaterial. For example, a metre-scale cloaking device would only be able to cloak an interval of a nanosecond or so, while current technological limitations would probably reduce this by a factor of 10 or even 100.
Assuming that a future generation is able to produce a high-performance, macroscopic, fully functioning space–time cloak, one party trick that it could perform would be to create the illusion of a Star Trek-type transporter (figure 2b). What we would need to do is take our metamaterial cloak made from meta-atoms much smaller in size than the wavelength of light and carve a central corridor down the middle. As the null in the illuminating light passes over the central region, someone could run in the dark from one end (A) of the corridor to the other (B). But as far as any outside observer is concerned, it would appear as if the person had instantly relocated from A to B in true Star Trek style.
More plausibly, consider an experiment that cloaks a small box containing excited atoms (figure 2c). The atoms will spontaneously decay, emitting photons according to the usual exponential Poisson statistics. However, the light emitted by the atoms as the intensity null passes over the box is affected by the closing of the cloak. What this means is that any light emitted during the cloaked interval is compressed into a much shorter time period, escaping the cloak as a brief but intense flash of light. This phenomenon is more than just of abstract interest because it could be the first ever experimental signature produced by a working space–time cloak.
Finally, a space–time cloak could be used to control the flow signals in an optical routing system (figure 2d), where one node might need to receive and process signals simultaneously from different channels. For example, one channel might be a clock signal that the external circuit demands is never interrupted, while the other channel may contain data that nevertheless must be processed as a priority. This conflict could be resolved by a space–time cloak that briefly opens up a gap in the clock signal. The node could process the priority bits during the gap, and then seamlessly reconstitute the clock signal by closing the cloak. This would enable an "interrupt-without-interrupt" operation that might be useful in quantum computing, which inherently deals with correlated data channels.

Practical questions

Although mathematics can tell us the precise electromagnetic properties required of a space–time cloak, actually making such a device is well beyond current metamaterials technology. For example, the material has to be able to couple the electric and magnetic fields in a specific way. What is surprising is that this exotic coupling has the side effect of making it appear to the light as though the medium is in motion, despite remaining stationary. If, however, we are content with making an imperfect space–time cloak, then such a device does lie within the range of current technology and would involve building the cloak from optical fibre. We estimate that an event cloak in 3 km-long fibre with a 1 km-long opening section, a 1 km long operating section and a 1 km-long closing section, could obscure events lasting up to several nanoseconds.
Optical fibres are potential candidates because their refractive index can be increased simply by raising the intensity of the beam they carry, thereby slowing the light as required. This could be done by suddenly increasing the intensity of a "control" beam, with the resulting intensity step-change travelling down the fibre and inducing a travelling change in light speed. If the fibre also contained a second, constant, "monitor" beam, photons in that beam would travel faster than the control beam before the intensity increase, but more slowly afterwards – exactly what is needed to open the dark interval in our space–time cloak.
We could then transfer this monitor beam into another fibre with a new control beam that this time suddenly decreases in intensity. This reverses the previous speed differential, closing down the dark interval, and recreating the original unvarying monitoring light beam. To return to our motorway analogy, it is as if the intense part of the control beam is a shower of rain moving along with part of the traffic, forcing only those drivers to slow down. The gap in traffic opens when the trailing cars are rained on and slow down, and closes when the rain shower switches to instead drench the leading cars, making them slow down as the trailing cars speed up.

Photo of a motorway with gaps in traffic

Blind spot

In practice, such a cloak would be imperfect because we are only able to modify the electrical properties of the fibres, since they are non-magnetic. This imperfection leads to stray reflections, allowing the cloak to be detected. To remove all reflections we would have to modify both electric and magnetic properties. Fortunately, though, the details of what was going on inside the cloak would still remain hidden.

The road ahead

Although lots of researchers around the world are trying to make spatial cloaks – in some cases with a good deal of success – no-one has yet tried to demonstrate a space–time cloak in the lab. However, there seems to be no obvious reason why such a cloak – and an experimental signature confirming it, such as the atoms-in-the-box test – could not be achieved quite soon, perhaps even within a few years. Once the principle has been shown, we can then start looking into applications along the lines suggested above, particularly the idea of being able to use an event cloak to resolve computational conflicts in optical processing systems.
Ultimately, it may even be possible for the operation of a space–time cloak to be triggered by events preceding those to be hidden by the device. One possible downside, though, is that covert processing and computation could then be instigated by rogue data infiltrating a system, without the system ever being aware that it had been hacked. To return to our analogy of a chicken crossing the road through a gap in the traffic, it is as if a particularly devious and clever chicken actually choreographs the whole routine beforehand by manipulating the speed limits (to open up the gap) and then again after crossing (to close it again). So while we may never know why the chicken crossed the road, at least we can imagine how it did it.

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