I propose as a hypothesis, based on this single thought experiment, that single gravitons may be unobservable by any conceivable apparatus. If this hypothesis is true, it would imply that theories of quantum gravity are untestable and therefore scientifically meaningless. The classical universe and the quantum universe could then live together in peaceful coexistence. No incompatibility between the two pictures could ever be demonstrated. Both pictures of the universe could be true, and the hope of a unified theory could turn out to be an illusion.
IMPOSSIBLE INEXACTNESS
SATYAJIT DAS
Derivatives expert, risk-management consultant; author, Extreme Money: The Masters of the Universe and the Cult of Risk
Inexactness is an end often seen as the beginning. Its profound beauty transects science, mathematics, method, philosophy, linguistics, and faith.
In 1927, Werner Heisenberg showed that uncertainty is inherent in quantum mechanics. It is impossible to simultaneously measure certain properties of a particle—position and momentum. In the quantum world, matter can take the form of either particles or waves. Fundamental elements are neither particles nor waves but can behave as either and are merely different theoretical ways of picturing the quantum world.
Inexactness marks an end to certainty. As we seek to measure one property more precisely, the ability to measure the other property is undermined. The act of measurement negates elements of our knowledge of the system.
Inexactness undermines scientific determinism, implying that human knowledge about the world is always incomplete, uncertain, and highly contingent.
Inexactness challenges causality. As Heisenberg observed: “Causality law has it that if we know the present, then we can predict the future. Be aware: In this formulation, it is not the consequence but the premise that is false. As a matter of principle, we cannot know all determining elements of the present.”
Inexactness questions methodology. Experiments can prove only what they are designed to prove. Inexactness is a theory based on the practical constraints of measurement.
Inexactness and quantum mechanics challenge faith as well as concepts of truth and order. They imply a probabilistic world of matter, where we cannot know anything with certainty but only as a possibility. It removes the Newtonian elements of space and time from any underlying reality. In the quantum world, mechanics are understood as a probability without any causal explanation.
Albert Einstein refused to accept that positions in spacetime could never be completely known and quantum probabilities did not reflect any underlying causes. He did not reject the theory but the lack of reason for an event. Writing to Max Born, he famously stated, “I, at any rate, am convinced that He [God] does not throw dice.” But as Stephen Hawking later remarked, in terms that Heisenberg would have recognized, “Not only does God play dice, but . . . he sometimes throws them where they cannot be seen.”
Allusive and subtle, the power of inexactness draws on its metaphorical property, which has allowed it to penetrate diverse fields, such as art theory, financial economics, and even popular culture.At one level, Heisenberg’s uncertainty principle is taken to mean that the act of measuring something changes what is observed. But at another level, intentionally or unintentionally, Heisenberg is saying something about the nature of the entire system—the absence of absolute truths and the limits to our knowledge.
Inexactness is linked with various philosophical constructs. Søren Kierkegaard differentiated between objective truths and subjective truths. Objective truths are filtered and altered by our subjective truths, recalling the interaction between observer and event central to Heisenberg’s theorem.
Inexactness is related to linguistic philosophies. In the Tractatus Logico-Philosophicus, Ludwig Wittgenstein anticipates inexactness, arguing that the structure of language provides the limits of thought and what can be said meaningfully.
The deep ambiguity of inexactness manifests itself in other ways: the controversy over Heisenberg’s personal history. In 1941, during the Second World War, Heisenberg and Niels Bohr, his former teacher, met in occupied Denmark. In Michael Frayn’s 1998 play Copenhagen, Margrethe, Bohr’s wife, poses the essential question, which is debated in the play: “Why did he [Heisenberg] come to Copenhagen?” The play repeats their meeting three times, each with different outcomes. As Heisenberg, the character, states: “No one understands my trip to Copenhagen. Time and time again I’ve explained it. To Bohr himself, and Margrethe. To interrogators and intelligence officers, to journalists and historians. The more I’ve explained, the deeper the uncertainty has become.”
In his 1930 text The Principles of Quantum Mechanics, Paul Dirac contrasted the Newtonian world and the quantum one: “It has become increasingly evident . . . that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies.”
There was a world before Heisenberg and his uncertainty principle. There is a world after Heisenberg. They are the same world, but they are different.
THE NEXT LEVEL OF FUNDAMENTAL MATTER?
HAIM HARARI
Theoretical physicist; former president, Weizmann Institute of Science; author, A View from the Eye of the Storm
A scientific idea may be elegant. It may also be correct. If you must choose, choose correct. But it’s always better to have both.
“Elegant” is in the eye of the beholder. “Correct” is decided by the ultimate judge of science, Mother Nature, speaking through the results of experiments. Unlike the standard TV talent contests, neither “elegant” nor “correct” can be determined by a vote of the public or by a panel of sneering judges. But the feeling that an idea is elegant often depends on the question being asked.
All matter consists of six types of quarks and six types of leptons, with seemingly random unexplained mass values, spanning more than ten orders of magnitude. No one knows why, within these twelve building blocks, the same pattern repeats itself three times. Some of these objects may also convert into each other, under certain circumstances, by unexplained rates called “mixing angles.” The twenty-odd values of these rates and masses seem to have been arbitrarily chosen by someone (Nature or God). This is what the Standard Model of Particle Physics tells us. Is this elegant? It does not seem so.
But the fact that mountains and snakes, oceans and garbage, people and computers, hamburgers and stars, diamonds and elephants, and everything else in the universe are all made of only a dozen types of fundamental objects is truly mind boggling. That is exactly what that same Standard Model says. So is it elegant? Very much so.
My great hope is that nature is actually even more elegant. The twelve fundamental quarks and leptons and their antiparticles all have electric charges 0, 1⁄3, 2⁄3, and 1 or the negative values of the same numbers. Each value repeats exactly three times.
There is no satisfactory explanation for many questions: Why are all charges multiples of 1⁄3 of the electron charge? Why does each value between 0 and 1 appear on the list, and do so the same number of times? Why do they never acquire more than three doses of that quantity? Why does the same entire pattern repeat itself three times? Why do the leptons always have integer charges and the quarks non-integers? Why are quark charges and lepton charges at all related to each other by simple ratios?
The fact that mosquitoes, chairs, and tomato juice are all electrically neutral results from the unexplained equality of the magnitudes of the electric charges of protons and electrons, causing atoms to be neutral. This follows from the quark charges having precise simple ratios to the lepton charges. But why doesn’t the electron have a charge of, say, 0.8342 of that of the proton? Why do they have exactly the same charge value?
An elegant explanation for these puzzles would appear if all quarks and leptons (and therefore all matter in the universe) consisted of only two building blocks, one with electr
ic charge of 1⁄3 that of the electron and one without electric charge. Then all combinations of such three objects might exactly create the known pattern of quarks and leptons and neatly answer the above questions. The bizarre list of masses and conversion rates of the quarks and leptons would still remain unexplained but would be relegated to a level of discussion of understanding the dynamical forces binding the two more fundamental basic objects into a variety of compounds, rather than as a God-given or nature-given list of more than twenty free fundamental parameters.
An elegant explanation? Certainly. Correct? Not necessarily, as far as we know now. But you can never prove that particles are not made of more fundamental objects. This may well be discovered in the future without contradicting any current data, especially if the new structure is revealed only at smaller distances and higher energies than anything we have seen so far, or if it obeys a strange new set of basic physics rules. Needless to say, such a simple hypothesis needs to tackle many additional issues, some of which it does beautifully, while in others it fails badly. That may be the partly justified reason for the general negative attitude of most particle physicists to this simple explanation.
I find the idea of creating the entire universe from just two types of building blocks (which I call Rishons, or primaries) an elegant and enticing explanation of many observed facts. The book of Genesis starts with a universe that is “formless and void,” or, in the original Hebrew, “Tohu Vavohu.” What better notations for the two fundamental objects than T (Tohu, “formless”) and V (Vohu, “void”), and then each quark or lepton would consist of a different combination of three such Rishons, like TTV or TTT. This may remain forever as an elegant but incorrect idea, or it may be revealed one day as the next level of the structure of matter, following the atom, the nucleus, the proton, and the quark. Ask Mother Nature. She understands both “elegant” and “correct,” but she is not yet telling.
OBSERVERS OBSERVING
ROBERT PROVINE
Neuroscientist and psychologist, University of Maryland; author, Curious Behavior: Yawning, Laughing, Hiccupping, and Beyond
The request for a favorite deep, elegant, and beautiful explanation left me a bit cold. “Deep,” “elegant,” and “beautiful” are aesthetic qualities I associate more with experience and process than explanation, especially that of the observer observing. Observation is the link between all empirical sciences and the reason physicists were among the founders of experimental psychology. The difference between psychology and physics is one of emphasis; both involve the process of observers observing. Physics stresses the observed, psychology the observer. As horrifying as this may be to hyperempiricists, who neglect the observer, physics is necessarily the study of the behavior of physicists, biology the study of biologists, and so on.
Decades ago, I discussed this issue with John Wheeler, who found it obvious, noting that a major limit on cosmology is the cosmologist. When students in my course on Sensation and Perception hear me say that we’re engaging in the study of everything, I’m absolutely serious. In many ways, the study of sensation and perception is the most basic and universal of sciences.
My passion for observation is aesthetic as well as scientific. My most memorable observations are of the night sky. Others may name the discovery of a T. rex fossil or the sound of birdsong on a perfect spring day. To see better and deeper, I build telescopes, large and small. I like my photons fresh, not collected by CCD or analyzed by computer. I want to encounter the cosmos head on, letting it wash over my retina. My profession of neuroscience provides its own observational adventures, including the unique opportunity to close the circle by investigating the neurological mechanism through which the observer observes and comes to know the cosmos.
GENES, CLAUSTRUM, AND CONSCIOUSNESS
V. S. RAMACHANDRAN
Neuroscientist; professor & director, Center for Brain and Cognition, University of California–San Diego; author, The Tell-Tale Brain
What’s my favorite elegant idea? The elucidation of DNA’s structure is surely the most obvious, but it bears repeating. I’ll argue that the same strategy used to crack the genetic code might prove successful in cracking the “neural code” of consciousness and self. It’s a long shot, but worth considering.
The ability to grasp analogies, and to see the difference between deep and superficial ones, is a hallmark of many great scientists. Francis Crick and James Watson were no exception. Crick himself cautioned against the pursuit of elegance in biology, given that evolution proceeds happenstantially. “God is a hacker,” he said, adding (according to my colleague Don Hoffman), “Many a young biologist has slit his own throat with Occam’s razor.” Yet his own solution to the riddle of heredity ranks with natural selection as biology’s most elegant discovery. Will a solution of similar elegance emerge for the problem of consciousness?
It is well known that Crick and Watson unraveled the double-helical structure of the DNA molecule: two twisting complementary strands of nucleotides. Less well known is the chain of events culminating in this discovery.
First, Mendel’s laws dictated that genes are particulate (a first approximation, still held to be accurate). Then Thomas Morgan showed that fruit flies zapped with X-rays became mutants with punctate changes in their chromosomes, yielding the clear conclusion that the chromosomes are where the action is. Chromosomes are composed of histones and DNA; as early as 1928, the British bacteriologist Fred Griffith showed that a harmless species of bacterium, upon incubation with a heat-killed virulent species, changes into the virulent species. This was almost as startling as a pig walking into a room with a sheep and two sheep emerging. Later, Oswald Avery showed that DNA was the transformative principle here. In biology, knowledge of structure often leads to knowledge of function—one need look no further than the whole of medical history. Inspired by Griffith and Avery, Crick and Watson realized that the answer to the problem of heredity lay in the structure of DNA. Localization was critical, as, indeed, it may prove to be for brain function.
Crick and Watson didn’t just describe DNA’s structure, they explained its significance. They saw the analogy between the complementarity of molecular strands and the complementarity of parent and offspring—why pigs beget pigs and not sheep. At that moment, modern biology was born. There are similar correlations between brain structure and mind function, between neurons and consciousness. (I’m stating the obvious here only because there are some philosophers, called “new mysterians,” who believe the opposite.)
After his triumph with heredity, Crick turned to what he called the “second great riddle” in biology—consciousness. There were many skeptics. I remember a seminar Crick gave on consciousness at the Salk Institute here in La Jolla. He’d barely started when a gentleman in attendance raised a hand and said, “But Dr. Crick, you haven’t even bothered to define the word ‘consciousness’ before embarking on this.” Crick’s response was memorable: “I’d remind you that there was never a time in the history of biology when a bunch of us sat around the table and said, ‘Let’s first define what we mean by life.’ We just went out there and discovered what it was—a double helix. We leave matters of semantic hygiene to you philosophers.”
Crick did not, in my opinion, succeed in solving consciousness (whatever it might mean). Nonetheless, he was headed in the right direction. He had been richly rewarded earlier in his career for grasping the analogy between biological complementarities, the notion that the structural logic of the molecule dictates the functional logic of heredity. Given his phenomenal success using the strategy of structure-function analogy, it is hardly surprising that he imported the same style of thinking to study consciousness. He and his colleague Christof Koch did so by focusing on a relatively obscure structure called the claustrum.
The claustrum is a thin sheet of cells underlying the insular cortex of the brain, one on each hemisphere. It is histologically more homogeneous than most brain structures, and unlike most brain structures (which send and recei
ve signals to and from a small subset of other structures), the claustrum is reciprocally connected with almost every cortical region. The structural and functional streamlining might ensure that when waves of information come through the claustrum, its neurons will be exquisitely sensitive to the timing of the inputs.
What does this have to do with consciousness? Instead of focusing on pedantic philosophical issues, Crick and Koch began with their naive intuitions. “Consciousness” has many attributes—continuity in time; a sense of agency or free will; recursiveness, or “self-awareness,” etc. But one attribute that stands out is subjective unity: You experience all your diverse sense impressions, thoughts, willed actions, and memories as a unity—not as jittery or fragmented. This attribute of consciousness, with the accompanying sense of the immediate present, or the “here and now,” is so obvious that we don’t usually think about it; we regard it as axiomatic.
So a central feature of consciousness is its unity—and here is a brain structure that sends and receives signals to and from practically all other brain structures, including the right parietal (involved in polysensory convergence and embodiment) and the anterior cingulate (involved in the experience of “free will”). Thus the claustrum seems to unify everything anatomically, and consciousness does so mentally. Crick and Koch recognized that this might not be a coincidence: The claustrum may be central to consciousness—indeed, it may embody the idea of the Cartesian theater, taboo among philosophers—or at least be the conductor of the orchestra. It is this kind of childlike reasoning that often leads to great discoveries. Obviously, such analogies don’t replace rigorous science, but they’re a good place to start. Crick and Koch’s idea may be right or wrong, but it’s elegant. If it’s right, they have paved the way to solving one of the great mysteries of biology. Even if it’s wrong, students entering the field would do well to emulate their style. Crick was right too often to ignore.
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