The Non-Local Universe: The New Physics and Matters of the Mindby Robert Nadeau, Menas Kafatos
Classical physics states that physical reality is local, or that a measurement at one point in space cannot cannot influence what occurs at another beyond a fairly short distance. Until recently this seemed like an immutable truth in nature. However, in 1997 experiments were conducted in which light particles (photons) originated under certain conditions and… See more details below
Classical physics states that physical reality is local, or that a measurement at one point in space cannot cannot influence what occurs at another beyond a fairly short distance. Until recently this seemed like an immutable truth in nature. However, in 1997 experiments were conducted in which light particles (photons) originated under certain conditions and traveled in opposite directions to detectors located about seven miles apart. The amazing results indicated that the photons "interacted" or "communicated" with one another instantly or "in no time," leading to the revelation that physical reality is non-locala discovery that Robert Nadeau and Menas Kafatos view as "the most momentous in the history of science."
In pursuing this groundbreaking argument, the authors provide a fascinating history of developments that led to the discovery of non-locality and the sometimes heated debate between the great scientists responsible for these discoveries. What this new knowledge reveals, the authors conclude, is that the connection between mind and nature is far more intimate than we previously dared to imagine. What they offer is a revolutionary look at the implications of non-locality, implications that reach deep into that most intimate aspect of humanityconsciousness.
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Quantum Nonlocality: An Amazing New Fact of Nature
Man's perceptions are not bounded by organs of perception. He perceives more than sense (tho' ever so acute) can discover.
Reason or the ratio of all we have already known is not the same as it shall be when we know more.
In the strange new world of quantum physics we have consistently uncovered aspects of physical reality at odds with our everyday sense of this reality. But no previous discovery has posed more challenges to our usual understanding of the "way things are" than the amazing new fact of nature known as nonlocality. This new fact of nature was revealed in a series of experiments testing predictions made in a theorem developed by theoretical physicist John Bell in response to a number of questions raised by Albert Einstein and two younger colleagues in 1936. Although Bell's now famous theorem led to the discovery that physical reality is non-local, this was not his primary motive for developing the theorem, and he was quite disappointed by the results of experiments testing the theorem.
Like Einstein before him, Bell was discomforted by the threats that quantum physics posed to a fundamental assumption in classical physicsthere must be a one-to-one correspondence between every element of a physical theory and the physical reality described by that theory. This view of the relationship between physical theory and physical reality assumes that all events in thecosmos are wholly predetermined by physical laws and that the future of any physical system can in theory be predicted with utter precision and certainty. Bell's hope was that the results of the experiments testing his theorem would obviate challenges posed by quantum physics to this understanding of the relationship between physical theory and physical reality.
The results of these experiments would also serve to resolve other large questions. Is quantum physics a self-consistent theory whose predictions would hold in this new class of experiments? Or would the results reveal that quantum theory is incomplete and that its apparent challenges to the classical understanding of the correspondence between physical theory and physical reality were illusory? But the answer to this question in the experiments made possible by Bell's theorem would not merely serve as commentary on the character of the knowledge we call physics. It would also determine which of two fundamentally different assumptions about the character of physical reality is correct. Is physical reality, as classical physics assumes, local, or is physical reality, as quantum theory predicts, non-local? While the question may seem esoteric and the terms innocuous, the issues at stake and the implications involved are, as we shall see, enormous.
Bell was personally convinced that the totality of all of our previous knowledge of physical reality, not to mention the laws of physics, would favor the assumption of locality. The assumption states that a measurement at one point in space cannot influence what occurs at another point in space if the distance between the points is large enough so that no signal can travel between them at light speed in the time allowed for measurement. In the jargon of physics, the two points exist in space-like separated regions, and a measurement in one region cannot influence what occurs in the other. Quantum physics, however, allows for what Einstein disparagingly termed "spooky actions at a distance." When particles originate under certain conditions, quantum theory predicts that a measurement of one particle will correlate with the state of another particle even if the distance between the particles is millions of light-years. And the theory also indicates that even though no signal can travel faster than light, the correlations will occur instantaneously, or in "no time." If this prediction held in experiments testing Bell's theorem, we would be forced to conclude that physical reality is non-local.
After Bell published his theorem in 1964, a series of increasingly refined tests by many physicists of the predictions made in the theorem culminated in experiments by Alain Aspect and his team at the University of Paris-South. When the results of the Aspect experiments were published in 1982, the answers to Bell's questions were quite clearquantum physics is a self-consistent theory and the character of physical reality as disclosed by quantum physics is non-local. In 1997, these same answers were provided by the results of twin-photon experiments carried out by Nicolus Gisin and his team at the University of Geneva. While the distance between detectors in space-like separated regions in the Aspect experiments was thirteen meters, the distance between detectors in the Gisin experiments was extended to eleven kilometers, or roughly seven miles. Since a distance of seven miles is quite vast in comparison with those involved in quantum mechanical processes, the results of the Gisin experiments were startling. They clearly indicate that similar correlations would exist even if experiments could be performed where the distance between the points was halfway across the known universe.
Although the discovery that physical reality is non-local made the science section of the New York Times, it was not front-page news and received no mention in national news broadcasts. On the few occasions where nonlocality has been discussed in public forums, it is generally described as a piece of esoteric knowledge that has meaning and value only in the community of physicists. The obvious question is, Why has a discovery that many regard as the most momentous in the history of science received such scant attention and stirred so little debate? One possible explanation is that some level of scientific literacy is required to understand what nonlocality has revealed about the character of physical reality. Another is that the implications of this discovery have shocked and amazed scientists, and a consensus view of what those implications are has only recently begun to emerge.
The implication that has most troubled physicists is that classical epistemology, which is also known as Einsteinian epistemology, can no longer be viewed as valid. And much of this discussion will seek to demonstrate this is, in fact, the case. This discovery has also revealed, however, the existence of a profound new relationship between parts (quanta) and whole (universe) that carries large implications in terms of our understanding of the character of physical reality in both physics and biology. For reasons that will become clear later, what is most perplexing about nonlocality from a scientific point of view is that it cannot be viewed in principle as an observed phenomenon. The "observed" phenomena in the Aspect and Gisin experiments reveal correlations between properties of quanta, light or photons, emanating from a single source based on measurements made in space-like separated regions. What cannot be measured or observed in this experimental situation, however, is the total reality that exists between the two points whose existence is inferred by the presence of the correlations.
When we consider that all quanta have interacted at some point in the history of the cosmos in the manner that quanta interact at the source of origins in these experiments and that there is no limit on the number of correlations that can exist between these quanta, this leads to another dramatic conclusionnonlocality is a fundamental property of the entire universe. The daunting realization here is that the reality whose existence is inferred between the two points in the Aspect and Gisin experiments is the reality that underlies and informs all physical events in the universe. Yet all that we can say about this reality is that it manifests as an indivisible or undivided whole whose existence is "inferred" where there is an interaction with an observer, or with instruments of observation.
If we also concede that an indivisible whole contains, by definition, no separate parts and that a phenomenon can be assumed to be "real" only when it is an "observed" phenomenon, we are led to more interesting conclusions. The indivisible whole whose existence is inferred in the results of the Aspect and Gisin experiments cannot in principle be itself the subject of scientific investigation. There is a simple reason why this is the case. Science can claim knowledge of physical reality only when the predictions of a physical theory are validated by experiment. Since the indivisible whole in the Aspect and Gisin experiments cannot be measured or observed, we confront here an "event horizon" of knowledge where science can say nothing about the actual character of this reality. Why this is the case will be discussed in detail later.
If nonlocality is a property of the entire universe, then we must also conclude that an undivided wholeness exists on the most primary and basic level in all aspects of physical reality. What we are actually dealing with in science per se, however, are manifestations of this reality, which are invoked or "actualized" in making acts of observation or measurement. Since the reality that exists between the space-like separated regions is a whole whose existence can only be inferred in experiments, as opposed to proven, the correlations between the particles, or the sum of these parts, do not constitute the "indivisible" whole. Physical theory allows us to understand why the correlations occur. But it cannot in principle disclose or describe the actual character of the indivisible whole.
The scientific implications of this extraordinary relationship between parts (quanta) and indivisible whole (universe) are quite staggering. Our primary concern here, however, is a new view of the relationship between mind and world that carries even larger implications in human terms. As we hope to demonstrate, the stark division between mind and world sanctioned by classical physics is not in accord with our scientific worldview. When nonlocality is factored into our understanding of the relationship between parts and wholes in physics and biology, then mind, or human consciousness, must be viewed as an emergent phenomenon in a seamlessly interconnected whole called the cosmos.
All that is required to embrace the alternate view of the relationship between mind and world that is consistent with our most advanced scientific knowledge is a commitment to metaphysical and epistemological realism and a willingness to follow arguments to their logical conclusions. Metaphysical realism assumes that physical reality is real or has an actual existence independent of human observers or any act of observation. Epistemological realism assumes that progress in science requires strict adherence to scientific methodology, or to the rules and procedures for doing science.
If one can accept these assumptions, most of the conclusions drawn here should appear fairly self-evident in logical and philosophical terms. And it is also not necessary to attribute any extra-scientific properties to the whole to understand and embrace the new relationship between part and whole and the alternate view of human consciousness that is consistent with this relationship. We will, however, take care in this discussion to distinguish between what can be "proven" in scientific terms and what can be reasonably "inferred" in philosophical terms based on the scientific evidence.
MIND-MATTER AND THE GHOST OF DESCARTES
As we saw in the Introduction, the view of the relationship between mind and world sanctioned by classical physics and formalized by Descartes became a central preoccupation in Western intellectual life. And the tragedy of the Western mind is that we have lived since the seventeenth century with the prospect that the inner world of human consciousness and the outer world of physical reality are separated by an abyss or a void that cannot be bridged or reconciled.
In classical physics, external reality consisted of inert and inanimate matter moving in accordance with wholly deterministic natural laws, and collections of discrete atomized parts constituted wholes. Classical physics was also premised, however, on a dualistic conception of reality as consisting of abstract disembodied ideas existing in a domain separate from and superior to sensible objects and movements. The notion that the material world experienced by the senses was inferior to the immaterial world experienced by mind or spirit has been blamed for frustrating the progress of physics up to at least the time of Galileo. But in one very important respect it also made the first scientific revolution possible. Copernicus, Galileo, Kepler, and Newton firmly believed that the immaterial geometrical and mathematical ideas that inform physical reality had a prior existence in the mind of God and that doing physics was a form of communion with these ideas.
In the new mathematical language of classical physics, the more amorphous oppositions and contrasts associated with the symbolic map space of ordinary language became oppositions between points associated with number and mathematical relations. Visualizable aspects of physical reality were translated into the map space of newly invented mathematical and geometrical relationshipsthe calculus and analytical geometry. And the remarkable result was that the correspondence between points in the new map space of physical theory and the actual behavior of matter in physical reality seemed to confirm a one-to-one correspondence between every element in the physical theory and the physical reality.
The enormous success of classical physics soon convinced more secular Enlightenment thinkers, however, that metaphysics had nothing to do with the conduct of physics, and that any appeal to God in efforts to understand the essences of physical reality in physical theory was ad hoc and unnecessary. The divorce between subjective constructions of reality in ordinary language and constructions of physical reality in mathematical theory was allegedly made final by the positivists in the nineteenth century. This small group of physicists and mathematicians decreed that the full and certain truth about physical reality resides only in the mathematical description, that concepts exist in this description only as quantities, and that any concerns about the nature or source of physical phenomena in ordinary language do not lie within the domain of science.
The result was, as Alexander Koyré wrote, that we came to believe that the real "is, in its essence, geometrical and, consequently, subject to rigorous determination and measurement." Although the reification of the mathematical idea served the progress of science quite well, it has also, said Koyré, done considerable violence to our larger sense of meaning and purpose:
Yet there is something for which Newtonor better to say not Newton alone, but modern science in generalcan still be made responsible: it is the splitting of our world in two. I have been saying that modern science broke down the barriers that separated the heavens from the earth, and that it united and unified the universe. And that is true. But, as I have said too, it did this by substituting the world of quality and sense perception, the world in which we live, and love, and die, another worldthe world of quantity, or reified geometry, a world in which, though there is a place for everything, there is no place for man. Thus the world of sciencethe real worldbecame estranged and utterly divorced from the world of life, which science has been unable to explainnot even to explain away by calling it "subjective."
True, these worlds are everydayand even more and moreconnected by praxis. Yet they are divided by an abyss.
Two worlds: this means two truths. Or no truth at all.
This is the tragedy of the modern mind which "solved the riddle of the universe," but only to replace it by another riddle: the riddle of itself.
The tragedy of the Western mind, beautifully described by Koyré, is a direct consequence of the stark Cartesian division between mind and world. We discover the "certain principles of physical reality," said Descartes, "not by the prejudices of the senses, but by the light of reason, and which thus possess so great evidence that we cannot doubt of their truth." Since the real, or that which actually exists external to ourselves, was in his view only that which could be represented in the quantitative terms of mathematics, Descartes concluded that all qualitative aspects of reality could be traced to the deceitfulness of the senses.
It was this logical sequence that led Descartes to posit the existence of two categorically different domains of existence for immaterial ideasthe res extensa and the res cognitans, or the "extended substance" and the "thinking substance." Descartes defined the extended substance as the realm of physical reality within which primary mathematical and geometrical forms reside and the thinking substance as the realm of human subjective reality. Given that Descartes distrusted the information from the senses to the point of doubting the perceived results of repeatable scientific experiments, how did he conclude that our knowledge of the mathematical ideas residing only in mind or in human subjectivity was accurate, much less the absolute truth? He did so by making a leap of faithGod constructed the world, said Descartes, in accordance with the mathematical ideas that our minds are capable of uncovering in their pristine essence. The truths of classical physics as Descartes viewed them were quite literally "revealed" truths, and it was this seventeenth-century metaphysical presupposition that became in the history of science what we term the "hidden ontology of classical epistemology."
While classical epistemology would serve the progress of science very well, it also presented us with a terrible dilemma about the relationship between mind and world. If there is no real or necessary correspondence between nonmathematical ideas in subjective reality and external physical reality, how do we know that the world in which "we live, and love, and die" actually exists? Descartes's resolution of this dilemma took the form of an exercise. He asked us to direct our attention inward and to divest our consciousness of all awareness of external physical reality. If we do so, he concluded, the real existence of human subjective reality could be confirmed.
As it turned out, this resolution was considerably more problematic and oppressive than Descartes could have imagined. "I think, therefore, I am" may be a marginally persuasive way of confirming the real existence of the thinking self. But the understanding of physical reality that obliged Descartes and others to doubt the existence of this self clearly implied that the separation between the subjective world, or the world of life, and the real world of physical reality was "absolute."
As we also saw in the Introduction, much of Western religious and philosophical thought since the seventeenth century has sought to obviate this prospect with an appeal to ontology or to some conception of God or Being. Yet we continue to struggle, as philosophical postmodernism attests, with the terrible prospect first articulated by Nietzschewe are locked in the prison house of our individual subjective realities in a universe that is as alien to our thoughts as it is to our desires. This universe may seem comprehensible and knowable in scientific terms, and science does seek in some sense, as Koyré puts it, to "find a place for everything." But the ghost of Descartes lingers in the widespread conviction that science does not provide a "place for man" or for all that we know as distinctly human in subjective reality.
THE NEW PHYSICS AND THE MIND-MATTER PROBLEM
In 1905, not long after Nietzsche declared that we are locked in the "prison house of language" an obscure patent office clerk in Geneva, Albert Einstein, published three papers that signaled the beginning of the second scientific revolution. The first paper was on special relativity, the second on Brownian motion, and the third on the photoelectric effect. The mathematical description of physical reality that Einstein and others developed over the next thirty years undermined or displaced virtually every major assumption about physical reality in classical physics. And the vision of reality in what came to be called the new physics immediately challenged the efficacy of the Cartesian division between mind and world.
Most of the creators of the new physics were acutely aware that the potential impacts of this new scientific worldview on our conceptions of the relationship between mind and world were nothing short of revolutionary. And much of what these now famous scientists said about this new relationship was beautifully conceived and written and replete with ideas that carried large human implications. Although there were a few artists and intellectuals without formal training in higher mathematics and physics who vaguely understood these implications, they were largely ignored, until quite recently, by the vast majority of artists and intellectuals.
The reasons why nonphysicists should be intimidated by the prospect of attempting to understand the implications of the description of nature in relativistic quantum field theory are easily appreciated. The mathematics in the new physical theories was far more complex and difficult to understand than that in classical theories, and the reality described was largely unvisualizable. Hence the general consensus was that the new physics could only be understood by physicists and the rest of us could safely ignore the bizarre and strange reality described in this physics.
During the past two decades, however, those with a background in physics or with more than a passing acquaintance with physics have attempted to describe this reality in laymen's terms. Science fiction writers and filmmakers have exploited some of the bizarre or strange aspects of quantum physics for their own purposes, and many serious scholars have wrestled with the implications of the new physics in their own disciplines. But what we have only recently begun to fully recognize and properly understand is that the description of physical reality in the new physics effectively resolves or eliminates the two-world Cartesian dilemma.
Understanding why this is the case, however, has been frustrated by something more than the mathematical complexity of the new physical theories. As we shall see, virtually all of the major figures initially involved in creating these theories reflected on their implications in human terms. They also took care, however, to distinguish between these personal and private reflections and the actual content or meaning of physical theories. Why these physicists were reluctant to ascribe any human meaning to physical theories, and why most physicists who came after them typically assume that physical theories have no meaning in nonscientific terms, is not difficult to explain.
The explanation is that most physicists, past and present, have been firmly committed to the efficacy of classical or Einsteinian epistemology and to an associated view of the special character of scientific knowledgethe doctrine of positivism. Since the doctrine assumes that the meaning of physical theories resides only in the mathematical description, as opposed to any nonmathematical constructs associated with this description, it essentially disallows the prospect that the physical reality described by physical theory can have any other meaning. This explains why even the most careful attempts to explore the implications of physical theories in human terms are often labeled by physical scientists as anthropocentric at best and New Age at worst.
The doctrine of positivism is premised on classical or Einsteinian epistemology. As we noted earlier, the fundamental precept in this epistemology is that there must be a one-to-one correspondence between every element in a physical theory and every aspect of the physical reality described by that theory. Quantum physics began to pose threats to the efficacy of this epistemology beginning in the 1920s. But it was possible to believe, until quite recently, that these threats could be eliminated by advances in physical theory and associated experiments.
The thought experiment that eventually became the basis for the actual experiments testing predictions made in Bell's theory was originally conceived by Einstein and two younger colleagues. Before the results of the Aspect and Gisin experiments were known, most physicists were apparently quite convinced that they would completely restore our faith in classical or Einsteinian epistemology and in the doctrine of positivism. Einstein's thought experiment grew out of a twenty-three-year debate with Niels Bohr about the relationship between physical theory and physical reality and the special character of the knowledge we call physics. We will later examine the fundamental issues in the famous Einstein-Bohr debate and demonstrate that they have now all been resolved in Bohr's favor.
While the fact that Bohr posthumously won a debate with Einstein may not seem terribly important, this is anything but the case. The court of last resort in science is empirical evidence from repeatable experiments under controlled conditions, and a recent ruling from this court carries very large implications. This ruling not only forces us to abandon classical or Einsteinian epistemology and the assumption in the doctrine of positivism that the full and certain truth about physical reality is disclosed in the mathematical description of this reality. It also reveals that this epistemology and its associated doctrine did not, as many have presumed, purge scientific knowledge of extra-scientific constructs. They merely served to disguise the fact that physicists were unwittingly appealing to the seventeenth-century assumption of metaphysical dualism and the idea that the physical laws that are foundational to physical theories exist "prior to" or "outside of" physical reality. Since most physical scientists continue to believe in classical or Einsteinian epistemology and the doctrine of positivism, much of this discussion will demonstrate why this belief is no longer in accord with our understanding of the actual character of physical reality.
MAPPING THE JOURNEY
If the experiments testing Bell's theorem have, in fact, demonstrated that classical or Einsteinian epistemology is no longer valid, this will require some radical revisions in our understanding of the foundations of scientific knowledge. But what we will term here the "new epistemology of science" does not, for reasons we will make clear throughout, compromise the privileged character of scientific knowledge or its ability to coordinate understanding of the processes of nature. The new epistemology does, however, oblige us to accept the prospects that the sum of the parts in physical reality does not constitute the whole and that the whole in both physics and biology cannot in principle be fully disclosed in physical theory.
In the so-called new biology, a new view of the relationship between parts and wholes has emerged that is remarkably analogous to that disclosed in the new physics. We have long known that emergent behavior associated with wholes in organic matter cannot be explained in terms of the collections of parts in organic matter. A single cell organism, for example, is a whole that displays emergent behavior associated with life that is greater than the sum of its parts or that does not exist in the mere collection of parts. Hence reductionism, which assumes that the whole can be reduced to and fully explained in terms of constituent parts, cannot account for these behaviors.
The list of emergent behaviors in biological reality that cannot be explained in terms of an assemblage of constituent parts has now become quite long. And it has also been demonstrated that the whole of biological life appears to evince emergent behavior that regulates global conditions, such as average Earth temperature and the relative abundance of atmospheric gases. Our current understanding of the relationship between parts and wholes in the biological sciences not only obliges us to abandon purely reductionist explanations of complex biological processes. It also suggests that some aspects of the dynamics of Darwinian evolution are in need of revision.
Recent studies on the manner in which the brains of our ancestors evolved the capacity to acquire and use complex language systems also present us with a new view of the relationship between parts and wholes in the evolution of human consciousness. These studies suggest that the actual experience of consciousness cannot be fully explained in terms of the physical substrates of consciousness, or that the whole that corresponds with any moment of conscious awareness is an emergent phenomenon that cannot be fully explained in terms of the sum of its constituent parts. This research also indicates that the preadaptive changes in the hominid brain that enhanced the capacity to use symbolic communication over a period of 2.5 million years cannot be fully explained in terms of the usual dynamics of Darwinian evolution.
The logical framework that best describes the new relationship between parts and wholes in both physics and biology was originally developed by Niels Bohr in an effort to explain wave-particle dualism in quantum physics. Since physical reality in quantum physics is described on the most fundamental level in terms of exchange of quanta, Bohr realized that the fact that a quantum exists as both wave and particle was enormously significant. As we will demonstrate in more detail later, the wave aspect of a quantum is continuous and spread out over space and time, and the particle aspect is a point-like something localized in space and time. In quantum physics, the wave aspect of a quantum is completely deterministic, and the future of this system can be predicted with complete certainty unless or until it is measured or observed. But when a measurement or observation occurs, the wave becomes a particle and some aspects of the wave function that appear actual or real in the absence of observation disappear as others are realized. It was this strange situation that led Bohr to develop his logical principle of complementarity.
Drawing extensively on Bohr's definition of this framework and applying it to areas of knowledge that did not exist during his time, we will attempt to show that he was correct in assuming that complementarity is the "logic of nature." We will not only appeal to this logic in an effort to explain profound new relationships between parts and wholes in physics and biology; we will also argue that the complementary character of these relationships is remarkably analogous to that between parts (quanta) and whole (universe) revealed in the experiments testing Bell's theorem. This new understanding provides a more consistent view of the manner in which more complex physical systems evolved through the process of emergence from the simplest atom to the most complex structure in the known universethe human brain.
DISPARATE WAYS OF KNOWING
Another of our large ambitions here is to demonstrate that our new understanding of the relationship between parts and wholes in physical reality can serve as the basis for a renewed dialogue between the two cultures of humanists-social scientists and scientists-engineers. When C. P. Snow recognized the growing gap between these two cultures in his now famous Rede Lecture in 1959, his primary concern was that the culture of humanists-social scientists might become so scientifically illiterate that it would not be able to meaningfully evaluate the uses of new technologies. What he did not anticipate was that the two-culture gap would become a two-culture chasm and that the culture of scientists-engineers would become just as responsible for the failure to unify human knowledge as the culture of humanists-social scientists.
Meanwhile, advances in scientific knowledge rapidly became the basis for the creation of a host of new technologies. Yet those responsible for evaluating the benefits and risks associated with the use of these technologies, much less their potential impact on human needs and values, normally have expertise on only one side of the two-culture divide. It is estimated, for example, that roughly half the legislation considered by the U.S. Congress features scientific and technological components that cannot be properly understood in the absence of a fairly high level of scientific literacy. Yet there are few members of Congress who possess this level of scientific literacy, and none to our knowledge holds a Ph.D. in the sciences. More important, many of the potential threats to the human futuresuch as environmental pollution, arms development, overpopulation, the spread of infectious disease, poverty, and starvationcan be effectively solved only by integrating scientific knowledge with knowledge from the social sciences and humanities.
Since we hope to define the terms for peace in the two-culture war in order that members of these cultures can work together to resolve some very real human problems, we will not play fast and loose with knowledge on either side of the two-culture divide. For example, most physics for nonphysicists books say very little about the manner in which classical physics evolved into the new physics, and they also tend to gloss over the finer points in physical theories. We have not done so for a simple reasonthe implications of the amazing new fact of nature called nonlocality cannot be properly understood without some familiarity with the actual history of scientific thought.
In the next three chapters on the history of physical theories and the discovery of nonlocality, a minimal amount of mathematical formalism has been used for illustrative purposes. The mathematical formalism and some of the more difficult scientific material have, however, been placed in sidebars. The intent is to suggest that what is most important about this background can be understood in its absence. Those who do not wish to struggle with the small amount of background discussion in the sidebars should feel free to ignore it. But this material will be no more challenging for the members of the culture of humanists-social scientists than much of the nonscientific material will be for many members of the culture of scientists-engineers. Our hope is that readers from the two cultures will find a common ground for understanding in a book written for both cultures, and that they will meet again on this common ground in an effort to close the gap between these disparate ways of knowing.
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