Tag: Highlight

Deconstructing the intuitions underlying physicalism and illusionism

Reading | Metaphysics

Arthur Haswell, BA | 2025-02-07

The idealist metaphysical and economic implications of von Neumann’s mathematics of quantum theory

Reading | Metaphysics

Matthew Cocks, PhD | 2025-01-24

John von Neumann was one of the most extraordinary figures of the twentieth century. In a 1999 biography, Norman Macrae wrote that von Neumann “was a prodigious child and a prodigious student, and through his brief fifty-three years grew steadily more prodigious. In each century there are a handful of people who … write a few equations on a few blackboards, and the world changes” [1]. In a more recent review of von Neumann’s life entitled The Man from the Future, former editor at Nature, Ananyo Bhattacharya, relates how

At the Institute of Advanced Study in Princeton, where he was based from 1933 to his death in 1957, von Neumann enjoyed annoying distinguished neighbors such as Albert Einstein and Kurt Gödel by playing German marching tunes at top volume on his office gramophone. Einstein revolutionized our understanding of time, space and gravity. Gödel … was equally revolutionary in the field of formal logic. But those who knew all three concluded that von Neumann had by far the sharpest intellect. [2]

Von Neumann’s intellectual contributions were many and varied. He applied his mathematical gifts to a wide range of disciplines and was revolutionary in many of them. He is probably best known for his contributions to mathematics and computer science, as well as central involvement with the Manhattan Project. His work in all these areas helped shape the modern world.

But whilst his legacy is, as Bhattacharya observes, “omnipresent in our lives today” [3], it may be through innovations in areas other than computing and military technology that von Neumann has the potential to have an even greater societal impact over the coming decades. In particular, in the perhaps seemingly unrelated fields of theoretical physics and economics.

At different stages in his career, von Neumann was heavily involved in the development of economic theory and to this day is credited with making substantial contributions to the discipline. Indeed, his daughter Marina von Neumann Whitman became a noted economist and was the first woman to serve on the United States President’s Council of Economic Advisors [4].

Von Neumann’s 1928 paper, ‘On the Theory of Parlour Games,’ is today recognized as the founding work of game theory and, although the paper only briefly considers economic issues, it laid the groundwork for the extensive application of game theory to economic matters. Von Neumann later returned more explicitly to the connection in 1944 with the publication of the highly influential co-authored, Theory of Games and Economic Behavior.

Addressing a separate area of economics, von Neumann’s 1937 paper, ‘A Model of General Economic Equilibrium,’ was revolutionary in shaping present day economic methodology. Bhattichari notes that because of the paper “Mathematicians, inspired by von Neumann’s achievement, poured into economics and began applying fresh methods to the dismal science. By the 1950s the subject was transformed” [5].

Around the time of his 1928 paper on game theory, von Neumann was concurrently turning his mathematical attention towards the problems in physics resulting from the 1925 discovery of quantum mechanics. His 1932 Mathematical Foundations of Quantum Mechanics presented the first rigorous mathematical framework for quantum theory. Bhattacharya notes that, to this day, the formulation “remains definitive … [von Neumann] presented the theory as coherently and lucidly as anyone could” [6]. Physicists Bruce Rosenblum and Fred Kuttner have called quantum theory the most successful in the history of science, writing:

Quantum theory works perfectly … [It] has been subject to challenging tests for eight decades. No prediction by the theory has ever been shown wrong. It is the most battle-tested theory in all of science. It has no competitors … [7]

However, in formulating the theory, von Neumann seriously put to question prevailing assumptions about the nature of reality, arriving at the extraordinary conclusion that the mind plays a direct role in the physical world. In the contemporary context, the relationship between physics and consciousness has been receiving renewed attention, but the specific rationale behind von Neumann’s original perspective on this issue often seems to go overlooked. Either his formulation is not mentioned at all, or his conclusion is simply noted without an explanation, before the discussion then moves on.

But von Neumann’s theoretical thought process is remarkably straightforward for the lay person to grasp. He discusses the issue in the final chapter of the book, which focuses on the now famous ‘measurement process.’ In this chapter, von Neumann describes how the prediction of the flow of events in the physical world cannot proceed without including a ‘measurement,’ or more fundamentally, an ‘observation.’ To use an analogy, without incorporating the observation it would be like trying to mathematically model the flow of water out of a hose pipe without acknowledging the existence of the hose pipe.

Physicist Nick Herbert has noted that we see in the chapter a “severe test for his professionalism” [8], as von Neumann follows the mathematical logic to arrive at his conclusion. Henry Stapp, who collaborated with some of the founders of quantum mechanics, has stated that he considers von Neumann’s logic in the chapter to be “impeccable” [9]. The final conclusion comes not from a vague extrapolation or speculation (as sometimes characterized) but, as Herbert summarizes, “from one of the world’s most practical mathematicians deducing the logical consequences of a highly successful and purely materialistic model of the world” [10].

Starting on page 419, von Neumann considers the situation of measuring a temperature using a standard thermometer. He then proceeds to effectively pursue a search for the ‘observer.’ He begins with the measuring device itself (the thermometer) and, having incorporated all the physical processes taking place in the thermometer fully into the mathematical model (in principle at least), notes that it remains necessary for the theorist to say that the thermometer “is seen by the observer” [11].

He then follows mathematically the sequence of physical events from the thermometer to the person’s eye, through the eyeball to the image formed on the retina, incorporating all these processes into the model. Having done so, he notes that it continues to be necessary to say “this image is registered by the retina of the observer” [12]. He then persists, following this logic right through to the chemical reactions in the individual’s brain. But, as he notes, “no matter how far we calculate— … to the scale of the thermometer, to the retina, or into the brain, at some time we must say: and this is perceived by the observer” [13]. That is, he continues, “we must always divide the world into two parts, the one being the observed system, and the other the observer” [14].

Having pushed the boundary between the two as far as he can, he finally concludes that “it is inherently entirely correct that the measurement or the related process of the subjective perception is a new entity relative to the physical environment and is not reducible to the latter. Indeed, subjective perception leads us into the intellectual inner life of the individual …” [15].

Despite his statement that “we must always divide the world into two parts,” the analysis implies metaphysical idealism, not dualism. Reflecting upon the application of the theory, von Neumann states that “experience only makes statements of this type: an observer has made a certain (subjective) observation; and never any like this: a physical quantity has a certain value” [16].

Discussing the use of the word ‘observation’ in quantum theory, astronomical physicist Richard Conn Henry has said that “unfortunately the word ‘observation’ carries an implication that they must be observations of something. But the observations are not of anything. They are just observations. Period” [17]. In a short 2005 essay in Nature, Conn Henry bluntly laid out the metaphysical implications, writing that “The only reality is mind and observations … The Universe is entirely mental” [18].

It is well known that many early quantum physicists concurred with von Neumann on the fundamental role of the mind in quantum mechanics. Famously, Max Plank admitted publicly to regarding “consciousness as fundamental” [19]. Sir Author Eddington similarly wrote that the “substratum of everything is of mental character” [20]. And von Neumann’s friend Eugene Wigner reflected that “it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness” [21].

But over the course of the twentieth century these metaphysical implications became ignored and obscured within the physics community, and therefore with the public at large. It is well documented that a culture of what physicist David Mermin called “shut up and calculate” [22] became prevalent amongst physicists, and to this day even the mention of consciousness can be taboo in many physics departments. David Chalmers and Kelvin McQueen have identified that consciousness has also been sidelined by physicists due to the difficulties of being mathematically precise and potentially the association with Eastern religious traditions [23]. A range of other more materialist ‘interpretations’ [24] have therefore been developed over the decades and received greater attention.

But a wider acknowledgement of the implications of von Neumann’s formulation of quantum theory, in combination with other emerging evidence pointing in a similar metaphysical direction [25], would likely lead to a profound cultural shift in worldview [26]. It therefore becomes a pertinent question as to how such a fundamental societal shift could influence another of von Neumann’s areas of interest: economics.

Most commentators agree that the development of modern economics has been largely underpinned by a materialist metaphysic. From the start, economic thought was heavily influenced by the method of the natural sciences and the Newtonian mechanistic worldview. Carol Leutner Anderson has written that “the historical development of both capitalism and socialism shows them to be metaphysically linked to the concept of a reality as revealed through scientific discovery” [27].

The founder of modern economics, Adam Smith, was strongly predicated in this direction, reducing the study of society down to its smallest parts—in his case, that of the self-seeking individual. Smith once wrote:

Human society, when we contemplate it in a certain abstract and philosophical light, appears like a great, an immense machine, whose regular and harmonious movements produce a thousand agreeable effects. [28]

Economist Lewis Hill has observed how David Ricardo’s “secularized rationalism,” Karl Marx’s “dialectical materialism,” and the influence of the positivist philosophical tradition in economics carried forward a materialist approach [29]. Donald Oswald has discussed the “creed of classical science” that influenced John Stewart Mill’s view of reality and that, in Mill’s view, “the basic intelligibility of nature is guaranteed by its conformity to mechanical principles” [30]. Nicholas Georgescu-Roegen has observed how the Marginalist Revolution of the late 19^th century depicted “the economic process as a mechanical analogue” [31] and Barry Smith has written about how Carl Menger and the influential Austrian School of economics subscribed to a “commonsense realism” [32] and scientific realism.

However, as mentioned, there were notable exceptions. In parallel with his Newtonian approach, and like Newton [33], Adam Smith held a broader metaphysical worldview. Smith was, after all, primarily a moral philosopher. Jerry Evensky writes about how “Smith sees the world as the Design of the Deity, a perfectly harmonious system reflecting the perfection of its designer” [34]. Lewis Hill suggests that, taken within the larger context of his writings, both Smith’s “obvious and simple system of natural liberty” and famous “invisible hand” analogy can be understood to reflect the metaphysical assumptions more explicit in his other writings. Hill concludes that Smith’s “metaphysical preconceptions gave his economics direction and purpose” [35] and suggests that the discipline later lost sight of these metaphysical roots.

More recently, Bernardo Kastrup has argued that the dominant materialist metaphysics in the West is “highly symbiotic with our economic system,” underpinning society’s love affair with material goods and motivating the drive towards material success. He writes that “The materialist worldview has caused many of us to project numinous value and meaning onto things” [36].

How economics would be conceived differently under idealist assumptions, therefore, is an open question and would depend upon the consensus form of idealism reached. But a few clues may perhaps be found in the philosophical literature. For instance, in the writings of the British Idealists of the late 19^th and early 20^th century. Significantly influenced by German Idealism, they were particularly noted for the way in which their metaphysics directly influenced their writings on social, political, and economic issues.

In some respects, the British Idealists took economics back to its Smithian roots by giving central concern to issues of morality and ethics. The Idealist Edward Caird wrote that “Economic science is of equal extent with moral science” [37]. The Idealists saw moral development as inextricably bound with an individual’s progress towards ‘self-realization,’ broadened to take in, as W. J. Mander writes, “our wider potential for full human personhood” [38]. David Boucher and Andrew Vincent have summarized:

Idealism was often an intensely moralistic philosophy … It emphasized both the responsibilities of individuals to seize the opportunities to make themselves more virtuous, and of the owners of capital to transform their workshops into schools of virtue. [39]

Daily work therefore was seen as a means towards self-realization. Whilst not considered one of the British Idealists, the connection between daily work and character growth was also brought out by the famous Cambridge University economist Alfred Marshall, who was influenced by idealism. Simon Cook observes that “Marshall’s specifically economic ideas were developed against the background of an idealist philosophy” [40]. Whilst Marshall’s metaphysical leanings are not explicit in his writings, they are potentially detectable, as can be seen in the definition given on the first page of his famous 1890 textbook:

Economics is the study of mankind in the ordinary business of life … It is on the one side a study of wealth; and on the other, and more important side, a part of the study of man. For man’s character has been moulded by his every-day work … more than by any other influence unless it be that of his religious ideals … [41]

This immediate focus on the role of economic participation in the development of an individual’s character stands in contrast to the more technical definitions provided in contemporary economics textbooks.

Whilst the British idealists were deeply concerned with the alleviation of poverty and other social ills, they did not eschew private property, and indeed even saw property ownership as a means towards self-realization. For instance, the influential idealist T.H. Green supported private property as “a way of manifesting and developing ourselves as persons” [42].

A cultural shift towards idealism could, therefore, potentially see the overarching purpose of the economy called into question more explicitly than at present, with the relationship between economics, morality, and personal growth given more central attention [43].

Idealism could also lead to a revised relationship with material possessions, which would have significant implications for consumption patterns. In his 2016 book, Quantum Economics, theoretical physicist Amit Goswami takes von Neumann’s conclusions at face value and discusses an ‘Economics of Consciousness.’ He suggests that a post-materialist economy would see a reduction in material consumption as the population focuses more on its “higher needs” [44], and people would also seek greater meaning from their daily work [45]. This, he writes, would lead to a more sustainable economic model and general rise in overall well-being.

Philosopher Robert Koons has also considered how a post-materialist political economy could evolve [46]. He argues that materialism is at the root of both Marxism and modern liberalism and that both the right (libertarianism) and left (egalitarian) wings of liberalism have their origins in the materialism of the early modern period. This, he suggests, has led to a dominance of economic models in political theory.

Koons argues that materialist assumptions have led to a conception of political theory as fundamentally a theory of conflict. If human beings are conceptualized as fundamentally material systems, then there is no reason to assume a natural harmony between them. This, he says, is distinct from the Aristotelian view, which sees a human essence; the meaning or significance of being human, which leads to a natural formation of friendships and cooperation in society.  Once the confidence in natural harmony is given up, then society is forced to the opposite extreme of seeing conflict as natural. The constant possibility of conflict then leads to a range of actions to prepare for this possibility—such as the accumulation of power, reputation, and resources.

Koons discusses how the early non-materialist philosophy of the feudal world revolved around ideas of harmony, multiple centers of authority, and local custom. Consequently, under an alternative to materialism (Koons favors an Aristotelian model, but is open to idealism as a possibility), he expects that this could lead to more localism or variation from place to place, more traditional customary ideas, a more complex web of political and social institutions, production that’s both less market driven and less bureaucratic—more local and familial in nature—and an emphasis on small-scale sustainable technologies.

And so, however a post-materialist economy would ultimately pan out, it seems clear that it could look quite different to the one we see today. Whilst undoubtably revolutionary, John von Neumann’s contributions to economics were primarily aligned with the materialist tradition of the discipline, extending and advancing the mathematical and mechanistic approach. But it is perhaps through his work in theoretical physics that he could indirectly have his most significant and long-lasting impact. The cultural transformation that would likely result from a wider acknowledgement of the metaphysical implications of his 1932 Foundations could fundamentally transform how the economy is conceived, structured, and lived.

 

References

[1] Norman Macrae (1999) John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More, American Mathematical Society, pp. 3-4.

[2] Ananyo Bhattachrya (2021) The Man from the Future: The Visionary Ideas of John von Neumann, Allen Lane, p. xi.

[3] Bhattachrya (2021), p. xiv.

[4] The 2012 book launch talk at the Columbia School of International Public Affairs for her memoir The Martian’s Daughter: A Memoir can be viewed at: https://www.youtube.com/watch?v=Dfg_vsnTRBA

[5] Bhattachrya (2021), p. 151

[6] Bhattachrya (2021), p. 60-61

[7] Bruce Rosenblum and Fred Kuttner (2011) Quantum Enigma: Physics Encounters Consciousness, Oxford University Press, p. 269 and p. 54

[8] Nick Herbert (1987) Quantum Reality: Beyond the New Physics, an Excursion into Metaphysics, Knopf Doubleday Publishing Group, p. 156

[9] Conversation with Henry Stapp, Beyond Science and Religion podcast.  Available at: https://webtalkradio.net/internet-talk-radio/2012/10/07/conversations-beyond-science-and-religion-henry-stapp-and-the-mindlike-reality/

[10] Nick Herbert (1993), p. 157

[11] John von Neumann (1955) The Mathematical Foundations of Quantum Mechanics, Princeton University Press. [Originally published in German in 1932], p. 419

[12] John von Neumann (1955), p. 419

[13] John von Neumann (1955), p. 419

[14] John von Neumann (1955), p. 420

[15] John von Neumann (1955), p. 418

[16] John von Neumann (1955), p. 420

[17] Conversation with Richard Conn Henry, 25 August 2014, Beyond Science and Religion podcast. Available at: https://www.spreaker.com/episode/conversations-beyond-science-and-religion-the-mental-universe–14298531

[18] Richard Conn Henry (2005) ‘The mental Universe’, Nature, Vol. 436, Issue 29, p. 29. Perhaps remarkably, in a 2014 interview, nine years after its publication (see [16]), Conn Henry noted that he was not aware of having received any public criticism for the article.

[19] Plank, M., interview in The Observer, 25 January 1931, 17 (column 3)

[20] Eddington, A. (1928) The Nature of the Physical World, Macmillan, p. 281

[21] Wigner, E. (1961) ‘Remarks on the mind-body question’, reprinted in Wheeler, J.A. and Zurek, W.H. (eds) (1983) Quantum Theory and Measurement, Princeton University Press, p. 172

[22] David N. Mermin (2004) ‘Could Feynman have said this?, Physics Today, Vol. 57, Issue 5, pp. 10-12.

[23] David Chalmers and Kelvin McQueen (2021) ‘Consciousness and the collapse of the wave function’, in S. Gao (ed), Consciousness and Quantum Mechanics, Oxford University Press, p. 4.

[24] For a discussion see: Christopher A. Fuchs and Asher Peres (2000) ‘Quantum theory needs no “interpretation”’, Physics Today, Vol. 53, Issue 3, pp. 5-6.

[25] For example, see: Edward Kelly, Adam Crabtree and Paul Marshall (eds) (2015) Beyond Physicalism: Towards Reconciliation of Science and Spirituality, Rowman and Littlefield; Etzel Cardena (2018) ‘The experimental evidence for parapsychological phenomena: A review’, American Psychologist, Vol. 73, No. 5, 663-677; Bernardo Kastrup (2019) The Idea of the World: A Multidisciplinary Argument for the Mental Nature of Reality, John Hunt Publishing; Marco Masi (2023) ‘An evidence-based critical review of the mind-brain identity theory’, Frontiers in Psychology, Vol. 14; Carlos Eire (2023) They Flew: A History of the Impossible, Yale University Press

[26] For a classic discussion on the relationship between science and culture see: Margaret Jacob (1988) The Cultural Meaning of the Scientific Revolution, McGraw-Hill

[27] Carol Leutner Anderson (1982) ‘Economics and metaphysics: Framework for the future’, Review of Social Economy, Vol. 40, Issue 2, p. 216

[28] Cited in Kim, K. (1997) ‘Adam Smith: Natural theology and its implications for his method of social inquiry’, Review of Social Economy, Vol. 55, No. 3, p. 329

[29] Hill, L. (1979) ‘The metaphysical preconceptions of the economic science’, Review of Social Economy, Vol. 37, No. 2, p. 191

[30] Donald J. Oswald (1987) ‘Metaphysical beliefs and the foundations of modern economics’, Review of Social Economy, Vol. 45, No. 3, p. 285

[31] Georgescu-Roegen, N. (1971) The Entropy Law and The Economic Process, Harvard University Press, cited in Martin, D. (1990) ‘Economics as ideology: On making “the invisible hand” invisible’, Review of Social Economy, Vol. 48, No. 3, p. 282.

[32] Smith, B. (1990) ‘Aristotle, Menger, and Mises: an essay in the metaphysics of economics’, History of Political Economy, Annual supplement to vol. 22, p. 268

[33] For a discussion see Part 1 of: Meyer, C. (2020) Return of the God Hypothesis: Three Scientific Discoveries that Reveal the Mind Behind the Universe, HarperCollins

[34] Evensky, J. (1987) ‘The two voices of Adam Smith: moral philosopher and social critic’, History of Political Economy, 19, pp. 447-448

[35] Hill, L. (1979), p. 191

[36] Bernardo Kastrup (2014) Why Materialism is Baloney: How True Skeptics Know There is No Death and Fathom Answers to Life, The Universe, and Everything, Iff Books, p. 8

[37] Colin Tyler (2017) Common Good Politics: British Idealism and Social justice in the Contemporary World, p. 39

[38] W.J. Mander (2016) Idealist Ethics, Oxford University Press, p. 155

[39] David Boucher and Andrew Vincent (2000) British Idealism and Political Theory, Edinburgh University Press, p. 22

[40] Cook, S. (2009) The intellectual foundations of Alfred Marshall’s economic science : a rounded globe of knowledge, New York : Cambridge University Press, p. 3

[41] Alfred Marshall (1997) Principles of Economics, Prometheus Books, p. 1

[42] W.J. Mander (2011) British Idealism: A History, Oxford University Press, p. 237

[43] For discussions on economics and morality see: Amartya Sen (1991) On Ethics and Economics, Wiley and Samuel Bowles (2016) The Moral Economy: Why Good Incentives are No Substitute for Good Citizens, Yale University Press

[44] Goswami, A (2015) Quantum Economics: Unleashing the Power of an Economics of Consciousness, Virginia: Rainbow Ridge Books, p. 171

[45] For a recent overview of the literature on meaningful work see: Blustein, D, Lysova, E. and Duffy, R. (2023) ‘Understanding decent work and meaningful work’, Annual Review of Organizational Psychology and Organizational Behavior, 10, pp. 289–314

[46] Robert C. Koons talk at Texas Tech University, 22 January 2014, ‘The Waning of Materialism and the Future of Western Civilization’. Available at: https://www.youtube.com/watch?v=GZLHKlwue20

Spacetime may be a mere perspectival model within a universal mind

Reading | Physics

Ben Werner, M.Sc. | 2025-01-10

Introduction

This essay discusses several paradoxes within physical theory that can be resolved with the concept of macroscopic “quantum spacetime”—specifically, complex projective space, which is the geometric space of quantum wave functions. Whereas this argument does not contradict general relativity as a theoretical model of spacetime, if the actual geometry of spacetime is in fact complex projective space, the implication is that non-dual consciousness must be the substratum of the universe, within which a macroscopic quantum wavefunction forms the universal noumena behind individual subjective experiences.

The most familiar of the paradoxes discussed in this essay is quantum “spooky action at a distance.” Each of these paradoxes can be conceptually resolved by adopting a view that Euclidean spacetime—in which we construct our classical concept of the universe from a human perspective—is a model within a macroscopic complex projective space. The statement that Euclidean geometry may be constructed as a model within a more fundamental projective geometry is matter-of-factually true from a geometric-theoretical standpoint [1]. And the statement that the geometric basis of quantum wavefunctions is complex projective space is also matter-of-factually true [2]. However, the core idea proposed here—that complex projective space is the actual spacetime within which the universe exists at all scales, including the human scale—is not an accepted fact. Whereas this idea does not conflict with presently accepted physical theory (because Euclidean spacetime may be constructed as a model within complex projective space) it does contradict the implicit assumption behind the development of physical theory: that a physical reality exists independently of the subjective observer. This contradiction derives from the fact that, if we suppose complex projective space as the actual geometry of spacetime, then Euclidean spacetime can only appear from a point of perspective i.e., as the experience of a subjective observer.

For readers unfamiliar with projective space, a recommended foundational resource is [1], wherein projective, Euclidean, spherical, and hyperbolic geometries are developed alongside each other. Whereas the dimensions of real projective space are orthogonal real number lines, the dimensions of complex projective space are complex numbers, wherein the orthogonality of dimensions is due to the orthogonality between the real and imaginary components of complex numbers. An understanding of (complex) projective space may be developed through several different approaches. Within the context of this essay, the following concepts are particularly meaningful:

• Projective space is the geometrical formalization of a space ‘seen from all perspectives at once.’ Accordingly, Euclidean space can be constructed as a model within projective space, equivalent to taking a single point of perspective within the projective space. Projective space is the more elementary geometry, with fewer axioms than Euclidean space.
• There is no meaning to distance (and hence separation) within projective space. This fact aligns with complex projective space being the geometric basis of quantum wavefunctions (and “spooky action at a distance” due to entanglement). There is no meaningful way to define or visualize separate objects within projective space.
• Complex projective space can be understood as a geometry intrinsic to complex numbers, rather than an amalgamation of number and geometry as with the construction of “orthogonal number lines” in Euclidean geometry. This aligns with a metaphysics where consciousness is fundamental, wherein seemingly ‘unconscious’ ideas can form the basis of structure and physical laws that govern an objective world.

The following sections describe several paradoxes within physical theory—and experiments—that can be conceptually resolved by assuming that the observed universe appears within (macroscopic) complex projective spacetime. These paradoxes have only appeared in physical theory within the last few decades, as a result of the effort to ‘fill in the gaps’ of a grand unified theory, unifying quantum and classical models. The resistance of physical theory to grand unification may be because we have left out something essential, namely, the structure of the conscious space within which the universe appears.

The paradoxes discussed in this essay are:

• The paradox of entanglement of photons over vast distances.
• The paradox of static virtual fields (the fact that electrostatic and magnetostatic fields have an imaginary wave number).
• The paradox of the missing negative mass/energy (the fact that we do not observe negative mass/energy yet are surrounded by it according to physical theory).
• The paradox of instantaneous virtual field propagation (the experimental observation that changes in virtual electromagnetic field components propagate instantaneously).

 

The paradox of entangled photons over vast distances

This paradox (mentioned in the introduction) is often framed by the extreme example of light emitted from a distant galaxy—perhaps billions of lightyears away—which, according to quantum mechanics, might represent entanglement (non-separability) between a system in the distant galaxy and a system on Earth. Within a conceptual model of a universe set within Euclidean space, quantum entanglement seems to imply some kind of instantaneous field propagation connecting the two systems—a possibility excluded by special relativity and the limiting speed of light. Special relativity seems to explain this paradox away with the assertion that, from the frame of the light wave, the universe is flat and hence there is no separation between the two systems. However, the paradox remains as long as we believe that the resting frames of the two systems (modeled as three Euclidean dimensions of space plus a fourth dimension of time) are fundamentally as real as the frame of reference of the light wave.

Conceptual resolution of the paradox: A 2D projective plane may be constructed from a 2D Euclidean plane by co-identifying each pair of antipodal points along the edge of the 2D Euclidean plane. Similarly, we can transform the model of a light wave traveling through 4D Euclidean spacetime into the same light wave within complex projective space by co-identifying the point in time when the light wave is emitted with the point in time when the light wave is absorbed. This aligns with a principle of quantum mechanics which states that the emission and absorption of a light wave is a single event. Accordingly, the paradox of entanglement of photons over vast distances can be conceptually resolved by assuming that the fundamental spacetime of the universe is (macroscopic) complex projective space. In this view, the universe exists as an entangled whole, even while we experience a perceptual model of a universe of separate objects set within Euclidean spacetime. This idea aligns with an instinctual feeling that a ‘universal-now’ exists in a meaningful sense, in spite of our being taught—per special relativity—that such universal-now is not an actual reality. However, there is no conflict between an actual universal-now and special relativity, provided that we clarify that the universal-now applies to an entangled universe of non-separate wavefunctions. If we want an objective experience of a distant galaxy, we must still transmit that experience via light waves and/or travel through space at less than the speed of light to said galaxy. How a person might experience an entangled universe in the universal-now, and whether there is any way to communicate or visualize such an experience, is a separate matter. The implication of the concepts proposed in this essay is that such an experience would be more fundamental to our capacity as conscious entities than reflecting on a mental model of a universe set within 4D Euclidean spacetime.

 

The paradox of static virtual fields

For internal consistency within quantum-electrodynamics, the photons associated with electrostatic and magnetostatic fields are defined as virtual photons, in contrast with the real photons associated with electromagnetic waves [3]. While the wave number of a real photon is always a real number, the wave number of a virtual photon is an imaginary number, implying that, while real photons have real energy, virtual photons (in a certain sense) have imaginary energy. An interpretation that the energy of electrostatic and magnetostatic fields is imaginary presents a paradox, because an observed (real world) quantity can only be imaginary with respect to some other quantity with which it is in relative harmonic motion. For example, a simple pendulum has a kinetic energy and a potential energy, each of which can be measured as a real quantity, just as the energy of electrostatic and magnetostatic fields can be measured as a real quantity. However, if the pendulum is swinging back and forth, its potential and kinetic energy are imaginary with respect to each other. Similar examples can be given for the quantities that describe anything that is rotating, oscillating, or vibrating. Therefore, it is a paradox that electrostatic and magnetostatic fields are static and imaginary. The implication of this paradox is that, if we are measuring a quantity that is static and imaginary, then we as observers, or something about the act of observing, must be characterized by a motion that is rotating, oscillating, or vibrating (in spite of the fact that we are not conscious of such a motion in our normal sensory observation of the world). The notion of a hidden harmonic motion is reinforced by the fact that we are ‘bounded’ by harmonic motion: at the quantum scale, everything is characterized by vibration; at the speed of light, only light waves exist; and at the cosmological scale, there is a beginning and an end to the flat spacetime within which our objective experience happens, perhaps in a repeating fashion, where the end of one universe may be the beginning of another universe [6].

Conceptual resolution of the paradox: The paradox of static virtual fields can be resolved with the concept that the fundamental space in which electrostatic and magnetostatic fields exist is complex projective space, which is itself the space of quantum wavefunctions. An analogy of surfing ocean waves might be helpful to develop this concept. It is easy to see that, if we are riding an ocean wave, the wave will appear static to us, even though it is moving from the perspective of someone standing on the shore. Visualizing static virtual fields within a quantum wavefunction is more difficult, because a wavefunction is not an observable object like an ocean wave. Electromagnetic waves are themselves quantum wavefunctions, and even though we are accustomed to visualizing them as waves moving through space, the invariance of light speed with respect to one’s frame of reference means that we can never observe a light wave as an object. The same fact holds true for quantum wavefunctions describing stationary particles: the wavefunction itself is never observable. However, just as we can register the effect of an electromagnetic wave in the oscillating electric and magnetic fields of an antenna, static electric and magnetic fields can be thought of as registering a macroscopic quantum wavefunction. Whereas the non-observability of a light wave can be attributed to the invariance of light speed, the non-observability of a macroscopic quantum wavefunction could be attributed to the asymmetry in how we experience space versus time: within our Euclidean view of spacetime, we perceive a macroscopic extent of space at any moment, but we only perceive a microscopic extent of time at any moment.

Since a quantum wavefunction encompasses equivalent scales of space and time within complex projective space, we can only measure or perceive the components of such wavefunctions that fit within our Euclidean view of spacetime, which, again, consists of a macroscopic extent of space but a microscopic extent of time. An experience of a ‘complete’ macroscopic quantum wavefunction could only happen in complex projective space, which would be an experience ‘outside’ the passing microscopic moment in Euclidean time. Projective space is defined as space “seen from all perspectives at once,” which would be to say that all points of perspective are entangled (non-separable) within a macroscopic quantum wavefunction. Therefore, such an experience would be coincident with a dissolution of the subject-object division; that is to say, with a shifting of identity away from a single point of perspective. Such a ‘movement’ would not be the movement of something observable like a physical pendulum, but rather a hidden (normally ‘unconscious’) movement intrinsic to the co-existence of Euclidean spacetime (supporting a subject-object division) and complex projective space (in which a subject-object division is impossible). This may be the hidden movement implied by the paradox of static virtual fields.

 

The paradox of missing negative mass/energy

Negative mass/energy is sometimes referred to as “exotic” because it is never directly observed, even though its existence is necessitated by our physical models. At the cosmic scale, the most current measurements of the expansion rate of the universe tell us that the universe is essentially flat [7], meaning that the positive spacetime curvature correlated with observable positive mass/energy must be balanced by a negative spacetime curvature of an unobserved negative mass/energy. The overall shape of the universe, as the whole of spacetime, seems to be a balance of positive and negative curvature. Furthermore, since photons and anti-photons are the same thing, anything moving at lightspeed is balanced positive and negative energy. And at the smallest scale—the Planck scale—quantum theory predicts that the vast majority of energy present in quantum vacuum fluctuations are virtual particles, which are intermediaries between positive and negative solutions to the energy-momentum relation. The paradox, therefore, is that the universe appears to be fundamentally a balance of positive and negative mass/energy, and yet we only observe positive mass/energy at the human scale. We seem to be literally ‘bounded’ by a balance of positive and negative mass/energy at the micro and macro limits of the universe, and at the limit of light speed.

Conceptual resolution of the paradox: The non-observability of quantum wavefunctions can account for why we do not observe negative mass/energy directly at the human scale, in spite of the ubiquity of negative mass/energy in counterbalance to positive mass/energy at the boundaries of our objective experience. In order to frame the meaning of negative mass/energy within physical theory, we can turn to the recent synthesis of information theory and physical theory, which indicates the equivalence of mass/energy and information/entropy [8, 9]. From this frame, we can see that negative information/entropy, and hence negative mass/energy, does not describe particles and objects; instead, it describes the entanglement of particles and objects within a larger whole—i.e., within a quantum wavefunction [10]. From this perspective, it makes sense that we cannot objectively observe negative mass/energy. An experience of negative mass/energy implies a direct experience of the entanglement (the non-differentiability) of all things within our field of experience. Such a non-dual experience, equivalent to a dissolution of the subject-object division, is not an objective experience of discrete objects framed within a Euclidean spacetime governed by a chain of cause-and-effect, but rather, an integration of subject and object within a macroscopic complex projective space pointed to by this paradox in present physical theory.

 

The paradox of instantaneous virtual field propagation

It is well known that nothing with real mass/energy can travel faster than the speed of light. If anything with real mass/energy were to travel faster than the speed of light, it would violate causality—i.e., a coherent order of cause and effect. However, it may not be well known that changes in virtual fields do propagate instantaneously. This has been demonstrated in frustrated internal reflection experiments [4, 5]. Such changes in virtual fields do not constitute radiated light—they are fields associated locally with a physical object. Within the framework of quantum-electrodynamics, such fields are equivalent to the electrostatic and magnetostatic fields. We are familiar with instantaneous quantum phenomena over distance, such as quantum tunneling and quantum coupling. These instantaneous quantum phenomena are understood not to violate causality because the states on either side of the phenomenon (such as the states of two quantum-coupled particles) are mutually causal—i.e., they cannot be known independently. The paradox of instantaneous virtual field propagation is the implication of a mutually-causal relationship between macroscopic objects that are charged or magnetic (objects that possess electrostatic or magnetostatic fields) and something else, in spite of the fact that observable objects always appear to obey classical laws of cause and effect in relation to their environment.

Conceptual resolution of the paradox: If we were to identify a moment in which the substance of the particles and the objects they now compose were in mutually-causal relationship, it would be at the point of the Big Bang (and perhaps equivalently within black holes), where the curvature of time equals the curvature of space, such that space and time are non-differentiable. After this moment—or rather, as time appears to the observer as a Euclidean dimension orthogonal to space—the objects populating space appear disentangled from each other, acting on each other through a chain of cause-and-effect. ‘Re-entangling’ these objects would imply running time in reverse (in violation of the Law of Entropy) through an impossibly complex and intricately-coordinated series of events, or alternatively, by forcing them together into a black hole. This essay presents an argument that, in a certain sense, the objects we observe are already entangled within a macroscopic complex projective space that is within our capacity to experience at any moment as conscious entities. The implication of instantaneous virtual field propagation is that an objectively observable component of a macroscopic quantum wavefunction is present within Euclidean spacetime in the form of electrostatic and magnetostatic fields.

 

Bibliographical references

[1] Stillwell, John (2005). The Four Pillars of Geometry, Springer Press, ISBN 978-1-4419-2063-8

[2]  Ashtekar, Abhay and Schilling, Troy A. (1997). “Geometrical Formulation of Quantum Mechanics” arXiv:gr-qc/9706069v1

[3] Peskin, M.E., Schroeder, D.V. (1995). An Introduction to Quantum Field Theory, Westview Press, ISBN 0-201-50397-2

[4] Nimtz, G. (2011). “Tunneling Violates Special Relativity”.  Foundations of Science, 41: 1193-1199. arXiv:1003.3944  Note by B. Werner: The interpretation in this citation that tunneling violates special relativity is not correct, given the interpretation that the energy in the instantaneous field changes are purely imaginary. However, the data is nonetheless relevant to the argument presented in this essay.

[5] Eckle, P. et al.  (2008).  “Attosecond Ionization and Tunneling Delay Time Measurements in Helium”.  Science, 322: 1525.

[6] Gabriel Unger, Nikodem Poplawski. (2019) “Big bounce and closed universe from spin and torsion.” Astrophys. J. 870, 78. arXiv:1808.08327

[7] Planck Collaboration, (2015) “Planck 2015 results. XIII. Cosmological Parameters.” Astronomy and Astrophysics. arxiv.org/abs/1502.01589

[8]  Bekenstein, Jacob D. (1981). “Universal upper bound on the entropy-to-energy ratio for bounded systems”. Physical Review D (Particles and Fields), Volume 23, Issue 2, 15 January 1981, pp.287-298. 10.1103/PhysRevD.23.287

[9]  Shoichi Toyabe et al. (2010). “Information heat engine: converting information to energy by feedback control”. Nature Physics 6, 988-992. arXiv:1009.5287

[10]  N.J. Cerf and C. Adami. (1997). “Negative entropy and information in quantum mechanics”  arxiv.org/abs/quant-ph/9512022v3

The sky is in here, not just out there: How outdated language insulates us from reality

Reading | Astronomy

Harriet Witt, BA | 2024-12-06

Once the dashboard of our everyday perception is fully compatible with the Copernican Revolutionary perspective, we’ll look back and laugh at the many millennia when we thought the sun rises in the east, passes overhead and sets in the west. Today we know that the sun’s daily path across our sky is apparent motion. What actually happens over the course of the day is that we see the sun from a progression of perspectives, as we’re being rotated from west to east around our planet’s axis. When we face the sun on the western horizon, watching it appear to go down, we’re actually being back-rolled away from the sun by our Earth’s rotation. The action is with us, not with the sun. Sadly, our everyday language does not yet convey this Copernican perspective.

For many millennia, we believed that night falls—that the sky grows dark—at day’s end. Now we know that this darkening is apparent. What actually happens is that our planet rotates us away from the sun and into her shadow—into the darkness that people call “night.” The action is with us, not with the night. Sadly, our everyday language does not yet convey this Copernican perspective.

For many millennia, we believed that years come and go. Now we know that the so-called passing of years is apparent motion. What’s actually happening over the course of a year is that our planet is orbiting us around the sun in a 595-million-mile journey. Sadly, our everyday language does not yet convey the facts that a ‘year’ is a pre-Copernican word for an orbit, and that we wouldn’t experience years if our planet weren’t orbiting us through them.

With our language lagging behind our science, we have yet to embody the Copernican Revolution.

Words are the containers into which we pour our thoughts. So long as we continue pouring our thoughts into pre-Copernican language containers—i.e. speaking in terms of sunrise, sunset, nightfall and years passing—we perpetuate the notion that we live on a motionless Earth, with the universe revolving us. This static, hubristic mindset compromises our ability to solve the dynamic problems of climate change.

Nobody in our society is tasked with ‘languaging’ the Copernican perspective for living on a planet with climate change. This task is what I’ve come to think of as “Copernicus 2.0.” I borrowed this term from one of my astronomy students at Maui Community College. He used it to describe the experiential brand of astronomy that I teach. Over the decades that I’ve been developing this material with input from my students, “Copernicus 2.0” has evolved into a curriculum with thought experiments and somatic exercises. My goal is to better align our thinking with our moving, living planet.

The context for this is the following: In 1980 I started teaching astronomy under the starry sky at an environmental education center serving the Atlanta area schools. By day I taught a class called “Hello Gaia!” It was inspired and informed by NASA’s work with Dr. James Lovelock in the 1970s. The methods that Lovelock developed for addressing NASA’s questions about life on Mars catalyzed him to write his 1979 book, Gaia: A New Look at Life on Earth. Since I taught “Hello Gaia!” in a forest, I was able to share and explore with my students a dynamic, holistic perspective that was too controversial for many university academics at the time.

“Hello Gaia!” was equally inspired and informed by Buckminster Fuller’s 1969 book, Operating Manual for Spaceship Earth. Thanks to Fuller, I became aware of the language lag between the Copernican Revolution and the speech patterns of our everyday lives. By continuing to use pre-Copernican terms like ‘sunrise,’ ‘sunset,’ ‘nightfall’ and ‘years passing,’ we numb ourselves to the dynamism of the only planet in the known universe that supports human life. Fuller addressed this problem with an in-depth exploration of the “Spaceship Earth” metaphor. He also advised us to replace the obsolete words ‘sunrise’ and ‘sunset’ with scientifically accurate words. Instead of saying ‘sunrise,’ say ‘sun-sight,’ because the sun isn’t coming up; our rotating planet is bringing it into view. Instead of saying ‘sunset,’ say ‘sun-eclipse,’ because the sun isn’t going down; our rotating planet is eclipsing it. Because Fuller inspired and informed “Hello Gaia!,” I’ve been building on his language foundation ever since.

Very unexpectedly, in 1988, my husband’s work brought us to a small Pacific island that’s closer to Samoa than it is to California. This place, Maui, has been home ever since. Because I was born and raised in metropolitan New York City, our move impacted me much in the way that an asteroid impact reshapes the course of a river. Here in the jungle, the value of my Rutgers University Phi Beta Kappa key plummeted to zero. I was ashamed of my ignorance about the Polynesians, whose skill at “way-finding” enabled them—over the course of centuries—to become native Hawaiians. For longer than anyone knows, way-finders have been successfully navigating thousands of miles of open ocean with no need of the maps or technology that Western science mistakenly claims are necessary.

What’s at the root of this mistaken claim? Finding the answer meant digging deep—questioning Western science in a way that I’d never done. It also meant looking at Homo sapiens through a lens that I—a descendant of northern Europeans—had never done. This was painful in the short run, but powerful in the long run.

I learned that, throughout the initial 99% of Homo sapiens’ existence, we were hunter-gatherers, relying on the sky as our calendar, clock and compass. Recently we invented the time-keeping devices that we depend on today. Our dependence on these clever conveniences has had consequences: It has disconnected us from the daily and seasonal cycles of sunlight by which our master body clocks regulate our health and well-being. It has also weakened the pattern-recognition skills that kept us in sync with nature’s daily and seasonal cycles throughout the 99% of our existence when our nighttime calendar-clock was the predictable arcing of constellations across our sky.

Fortunately, some indigenous people—including some native Hawaiians—retain these pattern-recognition skills, so they still know how to live by the calendar-clock of the sky. Several years ago, a group of them, in Honolulu, created an online curriculum—using state-of-the-art graphics—to share their knowledge. With the help of these online classes, I’m now aware that during the 99% of our human existence when the sky was our calendar-clock astronomy was about correlating the natural cycles we saw in the sky with the natural cycles we experienced on the ground. This meant that our astronomy was experiential. It also meant that we enjoyed an intimate relationship with the cosmos. Today, our earth-and-sky pattern-recognition skills are so atrophied that we’ve lost this intimacy. Now we conceptualize our universe as remote and impersonal, with no place or purpose for people—unless you qualify as an astronaut.

During one of our online Hawaiian classes, the teacher asked: “Have you ever seen any dates or times written on the sky?” As I suddenly realized that I’d never questioned the reality of dates and times, my face turned red. Eventually, as I did the work of questioning, I learned that the dates and times we rely on today are artifacts of the ingenuity that gave us indoor clocks and calendars. Even though these dates and times are artificial, they’ve become hardwired into the perceptual apparatus of industrialized humans. Since our perceptual apparatus shapes our thinking, it shapes the way we deal with climate change.

As we struggle with climate change, we’re recognizing the limitations of commodifying nature for the personal profit of a select few. We’re also learning to stop asking, “How can we arrive at understanding by breaking matter down into smaller and smaller pieces?” Instead, we’re learning to start asking, “What keeps life-on-Earth functioning as a whole, dynamic system?”

I can think of no way to adequately address this latter question without facing the following fact: Even though dates and times are artificial constructs, they’ve become hardwired into our perceptual apparatus because they’re integral to our system of 24 time zones. This system was fabricated by railroad corporations in the 1800s to facilitate train scheduling and increase profits.

According to this system, today’s date is the same in both the northern and southern hemispheres—despite the fact that these hemispheres are always experiencing opposite life conditions, because they’re always experiencing opposite seasons. For example, on June 21^st at the north pole it’s daytime 24/7. Simultaneously, at the south pole, it’s nighttime 24/7. Life at the north pole is frenetically reproducing, while life at the south pole is dead or dormant. On September 21^st at the north pole, darkness is starting to dominate. Simultaneously, at the south pole, daylight is starting to dominate. Because this system of calendar dates is how we’re scheduling our lives, we’re disconnecting from nature—and from our own nature.

Nature’s annual cyclical change in the amount and angle of sunlight is what we commonly call ‘seasons.’ Seasons are critical to life on Earth because our Sun’s light is transformed into our Earth’s life by photosynthesizing plants. With this transformation of light into life, astronomy becomes biology.

This astronomy-biology interface is the realm of Copernicus 2.0. It demonstrates that, when we regulate our lives—and therefore our thinking—by a railroad system, we disrupt the natural synchrony between our planet and her living systems. This disruption of our biological rhythms has psychological and physical consequences, which American Scientist magazine has called “social jet lag” in a cover story about the problem. This disruption is also presenting us with a question that’s being addressed by the science of chronobiology: What becomes possible when we do pay attention to nature’s cyclical time and align our actions with it? This is the context in which my students and I have been developing Copernicus 2.0. As an example of this material, I share with you a thought experiment which addresses the issue of calendar dates. It is as follows.

By this time tomorrow, we will be 1.63 million miles from where we are now, thanks to our Earth orbiting us around the sun. By this time a year from now, we will have completed a 595-million-mile journey and we’ll be back at the point in our annual orbit where we are now. The fact that we can measure a year in miles has significant implications for our understanding of time and space. Equally significant is the fact that, by this time a year from now, we’ll be completing a 595-million-mile orbital annual journey and will be back at the point in our orbital relationship with the sun where we are now. This point in our orbit where we are now is indicated by today’s date on our calendar. Even though this is a point in our orbital space, our schools are teaching that a calendar date represents a point in time.

How did a point in space come to be labeled as a point in time? Could this labeling be the result of the pre-Copernican belief that years somehow “come and go?” Can we address this confusion regarding space and time without considering the fact that dates, times, and time zones are merely artifacts of industry?

Like Bernardo Kastrup, I look forward to the day when the term “Copernican Revolution” is no longer just about accurate celestial mechanics, but also about you and me as actively involved passengers-participants in our planet’s 3.5-billion-year experiment with life.