Knocking on Heaven's Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World - Lisa Randall (2011)



The methods scientists use today are the latest incarnation of a long history of measurements and observations that have been developed over time to verify and—as importantly—rule out scientific ideas. This need to go beyond our intuitive apprehension of the world to advance our understanding is reflected in our very language. The root used in Romance languages for the verb “to think”—pensum—comes from the Latin verb “to weigh.” English speakers, too, “weigh” ideas.

Many of the formative insights that ushered science into its modern expression were developed in Italy in the seventeenth century, and Galileo was a key player. He was among the first to fully appreciate and advance indirect measurements—measurements made with an intermediate device—as well as to design and use experiments as a means of establishing scientific truth. Moreover, he conceived abstract thought experiments that helped him create and consistently formulate his ideas.

I learned about Galileo’s many insights that fundamentally changed science when I visited Padua in the spring of 2009. One impetus for my visit was a physics conference that the Paduan physics professor Fabio Zwirner had organized. The other was to receive an honorary citizenship of the city. I was delighted to join my fellow physicist attendees as well as the esteemed group of fellow “citizens,” including the physicists Steven Weinberg, Stephen Hawking, and Ed Witten. And—as a bonus—I had a chance to learn some science history.

My trip was auspiciously timed, as 2009 was the 400th anniversary of Galileo’s first celestial observations. The citizens of Padua were particularly attentive, since Galileo had been lecturing at the university there at the time of his most significant research. To commemorate his famous observations, the town of Padua (as well as Pisa, Florence, and Venice—other towns that figured prominently in the scientific life of Galileo) had arranged exhibits and ceremonies in his honor. The physics talks took place in a hall in the Centro Culturale Altinate (or San Gaetano), the same building that housed a fascinating exhibit that celebrated Galileo’s many concrete accomplishments and highlighted his role in changing and defining what science means today.

Most people I met appreciated Galileo’s achievements and conveyed their enthusiasm for modern scientific developments. The interest and knowledge of the Paduan mayor, Flavio Zanonato, impressed even the local physicists. The head of the city not only actively engaged in scientific conversation at a dinner following the public lecture I gave, but during the lecture itself he surprised the audience with an astute question about charge flow at the LHC.

As part of the citizenship ceremony, the mayor gave me the key to the city. The key was fantastic—it lived up to my movie images of what such a thing should be. Large and silver and nicely carved, it prompted one of my colleagues to ask if it was out of a Harry Potter story. It was a ceremonial key—it doesn’t actually open anything. Yet it was a beautiful symbol of entry—to a city of course but also, in my imagination, to a rich and textured portal of knowledge.

In addition to the key, Massimilla Baldo-Ceolin, a professor at the University of Padua, gave me a Venetian commemorative medal known as an osella. It is engraved with a quote from Galileo that is also on display at the physics department of the university: “Io stimo più li trovar un vero, benché di cosa leggiera, che ‘l disputar lungamente delle massime questioni senza conseguir verità nissuna.” This translates as “I deem it of more value to find out a truth about however light a matter than to engage in long disputes about the greatest questions without achieving any truth.”

I shared these words with many colleagues at our conference since this is in fact a guiding principle to this day. Creative advances often originate with tractable problems—a point we will return to later on. Not all the questions we answer have immediately radical implications. Yet advances, even seemingly incremental ones, occasionally lead to major shifts in our understanding.

This chapter describes how the current observations that this book presents are rooted in developments that occurred in the seventeenth century, and how the fundamental advances made at that time helped define the nature of theory and experiment that we employ today. The big questions are in some respects the same ones that scientists have been asking for 400 years, but because of technological and theoretical advances, the little questions we now ask have evolved tremendously.


Scientists knock on heaven’s door in an attempt to cross the threshold separating the known from the unknown. At any moment we start with a set of rules and equations that predict phenomena we can currently measure. But we are always trying to move into regimes that we haven’t yet been able to explore with experiments. With technology and mathematics we systematically approach questions that in the past were the subject of mere speculation or faith. With better and more numerous observations and with improved theoretical frameworks that encompass newer measurements, scientists develop a more comprehensive understanding of the world.

I better understood the key role Galileo played in developing this way of thinking as I explored Padua and its historical landmarks. The Scrovegni Chapel is one of its most famous sites, housing Giotto’s frescoes from the early fourteenth century. These paintings are notable for many reasons, but to scientists the extremely realistic image of the 1301 passing of Halley’s comet (over the Adoration of the Magi) is a marvel. (See Figure 6.) The comet had been clearly visible to the naked eye at the time the painting was made.

But the images weren’t yet scientific. My tour guide pointed to an astral image in the Palazzo della Ragione that she had initially been told was the Milky Way. She remarked that a more expert guide had afterward explained to her the anachronistic nature of the interpretation. At the time the painting was made, people were just illustrating what they saw. It might have been a starry sky, but it was not anything so well defined as our galaxy. Science, as we understand it today, was yet to arrive.


FIGURE 6 ] Giotto painted this scene, which appears in the Scrovegni Chapel, in the early fourteenth century when Halley’s comet was visible to the naked eye.

Before Galileo, science relied on unmediated observations and pure thought. Aristotelian science was the model for the way people had tried to understand the world. Math could be used to make deductions, but the underlying assumptions were taken on faith or in accordance with direct observations.

Galileo explicitly refused to base his research on a “mondo di carta” (a world of paper)—he wanted to read and study the “libro della natura” (the book of nature). In achieving this goal, he changed the methodology of observation and, furthermore, recognized the power of experiments. Galileo understood how to construct and use these artificial situations to make deductions about the nature of physical law. With experiments, Galileo could test hypotheses about the laws of nature that he could prove—and, as importantly, disprove.

Some of his experiments involved inclined planes: the tilted flat surfaces that feature so prominently—and somewhat annoyingly—in every introductory physics text. For Galileo, inclined planes weren’t just some made-up classroom problem, as they sometimes appear to introductory physics students. They were a way to study the velocity of falling bodies by spreading out the descent of objects over a horizontal distance so that he could make careful measurements of how they “fell.” He measured time with a water chronometer, but he also cleverly added bells at specific points so that he could use his gifted musical ear to listen and establish speed as a ball rolled down, as illustrated in Figure 7. Through these and other experiments dealing with motion and gravity, Galileo, along with Johannes Kepler and René Descartes, laid the foundation for the classical mechanical laws that Isaac Newton so famously developed.

Bells Per Unit of Time


FIGURE 7 ] Galileo measured how quickly a ball went down an inclined plane, using bells to register their passage.

Galileo’s science also went beyond what he could observe. He created thought experiments—abstractions based on what he did see—in order to make predictions that would apply to experiments no one at the time could actually perform. Perhaps most famous is his prediction that objects—in the absence of resistance—all fall at the same rate. Even though he couldn’t set up the idealized situation, he predicted what would occur. Galileo understood gravity’s role in objects falling toward the Earth, but he also knew that air resistance slows them down. Good science involves understanding all the factors that might enter into a measurement. Thought experiments and actual physical experiments helped him to better understand the nature of gravity.

In an interesting historical coincidence, Newton, one of the greatest physicists to continue this scientific tradition, was born the year that Galileo died. (At a talk Stephen Hawking gave, he expressed his pleasure that his own birth came precisely three centuries later.) The tradition of designing physical or thought experiments, interpreting them, and understanding their limitations is one that scientists today continue, whatever their year of birth. Current experiments are more subtle and rely on far more advanced technology, but the idea of creating an apparatus to confirm or rule out the predictions from hypotheses continues to define science and its methods in research today.

In addition to experiments—the artificial situations he created to test hypotheses—another of Galileo’s game-changing contributions to science was understanding and believing in technology’s potential for advancing our observations of the universe as it presents itself. With experiments, he moved beyond pure intellect and reason, and with new devices, he moved beyond unfiltered observations.

Much of earlier science relied on direct unmediated observations. People touched or saw objects with their own senses, not through an intervening device that in some way altered the images. Tycho Brahe, who among other things discovered a supernova and accurately measured the orbits of the planets, made the last famous astronomical observations before Galileo entered the scene. Tycho did use precise measuring instruments, such as large quadrants, sextants, and armillary spheres. He in fact designed and paid for the construction of instruments of greater precision than anyone had used before, leading to measurements that were sufficiently accurate to allow Kepler to deduce elliptical orbits. Yet Tycho made all his measurements through careful observations with his naked eye, with no intermediary lens or other device.

Notably, Galileo had an artistically trained eye and an astute musical ear—he was, after all, the son of a music theorist and lutenist—but he nonetheless recognized how observations that employed technology as a mediator to his observations could improve on his already formidable faculties. Galileo trusted that the indirect measurements he could make with observational tools at both large and small scales would go far beyond those made purely with his unassisted faculties.

Galileo’s best-known application of technology was the use of telescopes to explore the stars. His use of this instrument changed the way we do science, the way we think about the universe, and the way we see ourselves. Galileo didn’t invent the telescope. It was invented in 1608 by Hans Lippershey in the Netherlands—but the Dutch used telescopes to spy on others, hence the alternative name of spyglass. Yet Galileo was among the first to realize that the device was a potentially potent tool to make observations of the cosmos not possible with the naked eye. He updated the spyglass invented in the Netherlands by developing a telescope capable of magnifying sizes by a factor of 20. Within a year of being presented with a carnival toy, he turned it into a scientific instrument.

Galileo’s act of observing through intermediate devices was a radical departure from previous ways of measuring and represented a major advance essential to all modern science. People were initially suspicious of such indirect observations. Even today, some are skeptical about the reality of the observations made with big proton colliders or the data that computers on satellites or telescopes record. But the digital data cataloged by these devices are every bit as real as—and in many respects more accurate than—anything we can observe directly. After all, our hearing comes from oscillations of air hitting our eardrums and our vision from electromagnetic waves hitting our retinas and being processed by our brains. This means that we too are a sort of technology—and not a highly reliable one at that, as anyone who has experienced an optical illusion can attest. (See Figure 8 for an example.) The beauty of scientific measurements is that we can unambiguously deduce aspects of physical reality, including the nature of elementary particles and their properties, from experiments such as those physicists perform today with large and precise detectors.


FIGURE 8 ] Our eyes are not always the most reliable means of ascertaining external reality. Here the two checkerboards are the same, but the dots on the one to the right make the squares appear very different.

Although our instinct might be that observations made unaided with our eyes are the most reliable and that we should be suspicious of abstraction, science teaches us to transcend this all too human inclination. The measurements we make with the instruments we design are more trustworthy than our naked eyes, and can be improved and verified through repetition.

In 1611, the church accepted the radical proposition that indirect measurements are valid. As Tom Levenson relates in his book Measure for Measure,7 the scientific establishment of the church had to decide whether observations from a telescope were trustworthy. Cardinal Robert Bellarmine pressed the church scholars to decide this issue, and on March 24, 1611, the four leading church mathematicians concluded that Galileo’s discoveries were all valid: the telescope had indeed produced accurate and reliable observations.

Another commemorative brass medallion that the Paduans shared with me beautifully summed up the pivotal nature of Galileo’s achievement. On one side is a picture of the 1609 presentation of the telescope to the Signoria of the Republic of Venice and to the Doge, Leonardo Dona. The other side has an inscription noting that the act “marks the true birth of the modern astronomical telescope” and begins the “revolution in man’s perception of the world beyond planet Earth,” “a historic moment that crosses the boundaries of Astronomy, making [it] one of the starting points of modern Science.”

Galileo’s observational advantages led to an explosion of further discoveries. Repeatedly, as he stared up into the cosmos, he found new objects that were beyond the range of the naked eye. He found stars in the Pleiades and throughout the sky that no one had seen before, sprinkled among the brighter ones that were already known. He publicized his discoveries in his famous 1610 book, Sidereus Nuncius (Starry Messenger), that he raced to complete in about six weeks. He hastily performed his research while the printer worked on the manuscript, eager to impress and gain the support of Cosimo II de’ Medici, the Grand Duke of Tuscany—and a member of one of Italy’s richest families—before someone else with a telescope might manage to publish first.

Because of Galileo’s insightful observations, an explosion of understanding occurred. He asked a different type of question: how rather than why. The detailed discoveries that were possible only with his telescope naturally led him to the conclusions that were to anger the Vatican. Specific observations convinced Galileo that Copernicus had been correct. For him, the only worldview that could consistently explain all of his observations relied on a cosmology in which the Sun, and not the Earth, was the center of the galaxy around which all planets orbited.

The moons of Jupiter were among the most critical of these observations. Galileo could see the moons as they appeared and disappeared and moved in accordance with their orbit around the giant planet. Before this discovery, a stationary Earth seemed the obvious and only way to explain the Moon’s fixed orbit. The discovery of Jupiter’s moons meant that it too had satellites in tow despite its motion. This lent credence to the possibility that the Earth could also be moving and even orbiting about a separate central body—a phenomenon that was explained only later when Newton developed his theory of gravity and its prediction of the mutual attraction of celestial objects.

Galileo named Jupiter’s moons Medicean stars, in honor of Cosimo II de’ Medici—further demonstrating his understanding of funding—another key aspect of modern science. The Medicis indeed decided to support Galileo’s research. Later on however, after Galileo had been granted funding for life from the city of Florence, the moons were to be renamed Galilean satellites in honor of their discoverer.

Galileo also used his telescope to observe the hills and valleys of the Moon. Before his discoveries, the heavens were thought to be perfectly unchanging, ruled by absolute regularity and constancy. The prevailing Aristotelian view maintained that while everything between the Moon and the Earth was imperfect and inconstant, celestial objects beyond our planet were supposed to be spherical and invariant—of divine essence. Comets and meteors were considered weather phenomena like clouds and winds, and our term meteorology harks back to this classification. Galileo’s detailed observations implied that imperfection extended beyond the human and sublunar domain. The Moon was not a perfectly smooth sphere and was in fact more similar to the Earth than anyone had dared to suppose. With the discovery of the textured topography of the Moon, the dichotomy between terrestrial and celestial objects was called into question. The Earth was no longer unique, but seemed to be a celestial object like any other.

The art historian Joseph Koerner explained to me that Galileo could use light and shadows to identify craters in part because of his artistic background. Galileo’s perspectival training helped him understand the projections he saw. He immediately recognized the implications of these images, even though they weren’t fully three-dimensional. He wasn’t interested in mapping the Moon, but in understanding its texture. And he understood right away what he saw.

The third significant set of observations that validated the Copernican point of view related to the phases of Venus—illustrated in Figure 9. These observations were particularly significant in establishing that celestial bodies orbited around the Sun. The Earth clearly was not unique in any obvious way, and Venus clearly didn’t rotate around it.


FIGURE 9 ] Galileo’s observation of the phases of Venus demonstrated that it too must orbit the Sun, invalidating the Ptolemaic system.

From an astronomical perspective, the Earth was not so special. The other planets behaved like ours, orbiting the Sun with satellites orbiting them. Furthermore, even beyond the Earth—evidently sullied by human beings—not everything was unblemished perfection. Even the Sun was besmirched by sunspots that Galileo had also identified.

Armed with these observations, Galileo famously concluded that we are not the center of the universe and that the Earth revolves around the Sun. The Earth is not the focal point. Galileo wrote up these radical conclusions. In doing so, he defied the church—although he later professed to reject Copernicanism in order to reduce his punishment to house arrest.

As if his observations and theorizing about the large scales of the cosmos were not enough, Galileo also radically altered our ability to perceive small scales. He recognized that intermediate devices could reveal phenomena at small scales, just as they did at large ones, and he advanced scientific knowledge at both frontiers. In addition to his (in)famous astronomical investigations, he turned technology inward—to investigate the microscopic world.

I was a little surprised when a young Italian physicist, Michele Doro, who was my guide to the San Gaetano exhibit in Padua, said without hesitation that Galileo had invented the microscope. I’d say that outside Italy at least the consensus is that it was invented in the Netherlands, but whether it was Hans Lippershey or Zacharias Janssen (or his father) is anyone’s guess. Whether or not Galileo invented the telescope (and he almost certainly didn’t), the fact is that he built a microscope and used it to observe smaller scales. It could be used to observe insects with accuracies never before possible. In his letter to friends and other scientists, Galileo was the first we know of to write about the microscope and its potential. The exhibition displayed the first publication to display the systematic observations that could be made with a Galilean microscope: dating from 1630, it illustrated Francesco Stelluti’s detailed studies of bees.

The exhibit also showed how Galileo had studied bones—exploring how their structural properties would need to change with size. Apparently, in addition to his many other insights, Galileo was acutely aware of the significance of scale.

The exhibit left no doubt that Galileo fully understood the methods and goals of science—the quantitative, predictive, and conceptual framework that tries to describe definite objects, which act according to the dictates of precise rules. Once these rules have provided well-tested predictions about the world, they can be used to anticipate future phenomena. Science searches for the most economical interpretation that can explain and predict all observations.

The story of the Copernican revolution nicely illustrates this point too. In Galileo’s era, Tycho Brahe, the great observational astronomer, came to a different—and wrong—conclusion about the nature of the solar system. He supported an odd hybrid of the Ptolemaic system, with the Earth at the center, and the Copernican system, where planets orbited the Sun. (See Figure 10 for a comparison.) The Tychonic universe agreed with observations, but it wasn’t the most elegant interpretation. It was, however, more satisfactory to the Jesuits than Galileo’s view, since according to Tycho’s premises—as with the Ptolemaic theory that Galileo’s observations contradicted—the Earth didn’t move.8


FIGURE 10 ] Three proposals to describe the cosmos: Ptolemy postulated that the Sun, along with the Moon and other planets, circled the Earth. Copernicus (correctly) suggested that all the planets orbit the Sun. Tycho Brahe postulated that nonterrestrial planets orbited the Sun, which in turn orbited the Earth at the center.

Galileo rightly recognized the jury-rigged nature of the Tychonic interpretation and came to the correct and most economical conclusion. Newton’s rival Robert Hooke later noted that both the Copernican and Tychonic theories agreed with Galileo’s data, but one was more elegant, saying “but from the proportion and harmony of the World, [one] cannot help but embrace the Copernican Arguments.”9 Galileo’s instincts about the truth of the more beautiful theory turned out to be correct, and his interpretation ultimately prevailed when Newton’s theory of gravity explained the consistency of the Copernican setup and predicted planetary orbits. Tycho Brahe’s theory, as was true for Ptolemy’s, was a dead end. It was wrong. It wasn’t absorbed in later theories because it couldn’t be. Unlike the situation with an effective theory, no approximation of the true theory leads to these non-Copernican interpretations.

As the failure of the original Tychonic theory showed, and as Newtonian physics verified, the subjective criterion of the more economical explanation can also play an important role in the initial scientific interpretation. Research involves the search for underlying laws and principles that will encompass the structures and interactions being observed. Once a sufficient number of observations exist, a theory that economically incorporates the results while providing a predictive underlying framework ultimately wins out. At any point in time, logic takes you only so far—something particle physicists are painfully aware of as we await the data that will ultimately determine what we believe about the underlying nature of the universe.

Galileo helped lay the groundwork for how all scientists work today. Understanding the progression that he and others initiated helps us to better understand the nature of science—in particular, how indirect observations and experiments help us ascertain the correct physical description—as well as some of the major questions that physicists ask today. Modern science builds on all his insights—the usefulness of technology, experiment, theory, and mathematical formulation—in its attempts to match observations to theory. Critically, Galileo recognized the interplay of all these elements in formulating physical descriptions of the world.

Today we can be more free in our thinking, allowing the Copernican revolution to continue as we explore the outer reaches of the cosmos, and theorize about possible extra dimensions or alternative universes. New ideas continue to make human beings less and less central, both literally and figuratively. And observations and experiments will either confirm or reject our proposals.

The indirect methods of observation that Galileo employed currently find dramatic expression in the Large Hadron Collider’s elaborate detectors. A final display in the Paduan exhibit showed the evolution of science up to modern times, and even presented pieces of LHC experiments. Our guide confessed he had been confused by this until he recognized that the LHC is the ultimate microscope to date, probing shorter distances than have ever been observed.

As we enter new regimes of precision in measurement and theory, Galileo’s understanding of how to design and interpret experiments continues to reverberate. His legacy lives on as we use devices to create images far from visible to the naked eye and apply his insights into how the scientific method works, using experiments to confirm or refute scientific ideas. The conference participants in Padua were thinking about what might be found soon and what it could mean, in the hope we will soon once again cross new thresholds of knowledge. In the interim, we’ll keep knocking.