The Schrodinger's Cat and Wigner's Friend thought experiments, which logically follow from the universality of quantum mechanics at all scales, have been repeatedly characterized as possible in principle, if perhaps difficult or impossible for all practical purposes. I show in this paper why these experiments, and interesting macroscopic superpositions in general, are actually impossible in principle. First, no macroscopic superposition can be created via the slow process of natural quantum packet dispersion because all macroscopic objects are inundated with decohering (...) interactions that constantly localize them. Second, the SC/WF thought experiments depend on von Neumann-style amplification to achieve quickly what quantum dispersion achieves slowly. Finally, I show why such amplification cannot produce a macroscopic quantum superposition of an object relative to an external observer, no matter how well isolated the object from the observer, because: the object and observer are already well correlated to each other; and reducing their correlations to allow the object to achieve a macroscopic superposition relative to the observer is equally impossible, in principle, as creating a macroscopic superposition via the process of natural quantum dispersion. (shrink)

There is no paradox with Schrödinger’s cat in a realist interpretation. In particular, a closer look at the temporal aspect shows that the two macroscopic wave functions (alive and dead) of Schrödinger’s cat are not to be compared with two superposed parts of a microscopic quantum wave function.

I present results of recent work in the field of quantum optics and relate this work to discussions about the theory of quantum mechanics and God's divine action in the world. Experiments involving atomic decay, relevant to event uncertainty in quantum mechanics, as well as experiments aimed at elucidating the so–called Schrödinger’s–cat paradox, help clarify apparent ambiguities or paradoxes that I believe are at the heart of renewed attempts to locate God within our constructed physical theories and tend to narrow (...) the gaps proposed as an opening for divine action. Some problems arise because of imprecise use of nonmathematical language to force quantum mechanics into an intuitive “classical” framework. (shrink)

Schrödinger's Cat & The Golden Bough addresses the relationship between science and mythology from the starting points of Frazer's The Golden Bough and Erwin Schrödinger's famous cat. From the Greek origins of modern scientific thought, Bancroft traces the intertwining and separation of mythology, magic, and science through the ages. Drawing on psychology, mythology, literature, and history of science, the author, a physicist who works with electromagnetic Field Theory, presents a fascinating and provocative cross-disciplinary study.

In 'How Many Lives Has Schrödinger's Cat?' David Lewis argues that the Everettian no-collapse interpretation of quantum mechanics is in a tangle when it comes to probabilities. This paper aims to show that the difficulties that Lewis raises are insubstantial. The Everettian metaphysics contains a coherent account of probability. Indeed it accounts for probability rather better than orthodox metaphysics does.

Erwin Schrödinger and Werner Heisenberg were the originators of two approaches, known respectively as “wave mechanics” and “matrix mechanics”, to what is now called “quantum mechanics” or “quantum theory”. The two approaches appear to be extremely different, both in their technical forms, and in their philosophical underpinnings. Heisenberg arrived at his theory by effectively renouncing the idea of trying to represent a physical system, such as a hydrogen Bohr's atom model for example, as a structure in space—time, but instead, following (...) the lead of Einstein's 1905 theory of relativity, representing only empirically observable properties, such as the transition amplitudes between the stationary states of the atom. These amplitudes can be arranged in square arrays of numbers. In Heisenberg's scheme these arrays, and other like them, are combined according to certain rules that were later recognized by Max Born to be the rules of matrix multiplication. The whole scheme is abstract and mathematical, and avoids using any space—time picture of what is going on at the atomic level. Schrödinger, on the other hand, represented the electron in an atom by a cloudlike wave surrounding the nucleus. This is a space—time structure that, superficially at least, is more in line with the classical physical theories of the eighteenth and nineteenth centuries. -/- Niels Bohr invited Schrödinger to come to Copenhagen to present his ideas, and to discuss this subject with himself, Heisenberg, and others. Schrödinger arrived in Copenhagen on October 1st, 1926, and was immediately intensively engaged by Bohr and the others in a “debate” that lasted for days. Eventually, Schrödinger become ill, and was confined in Bohr's home to a bed, upon which Bohr sat, continuing the discussion. Schrödinger finally exclaimed “If all the quantum jumping is here to stay, then I am sorry that I ever became involved in quantum mechanics”. Bohr replied, “But we are glad that you did!”. (shrink)

Alexander Wendt’s Quantum Mind and Social Science reopens the question of the relevance of quantum mechanics to the social sciences. In response, I argue that due to “quantum decoherence,” the macroscopic world filters out quantum effects. Moreover, quantum decoherence makes it unlikely that the theory of quantum brains, on which Wendt relies, is true. Finally, while quantum decision theory is a potentially revolutionary field, it has not clearly accounted for alleged anomalies in classical understandings of decision making. However, the logic (...) of quantum decoherence can motivate a new approach to the structure-agent problem. (shrink)

Volume 20, Issue 6, June 2020, Page 40-42.

Using formal techniques, Schrodinger's 1935 cat argument is reproduced. Assumptions of the argument are made explicit as axioms and rules of inference; from these a contradiction is derived. The formal statement is then used to elucidate several crucial distinctions, to reject several commonly proposed resolutions, and to sketch an Einsteinian perspective for the argument.

We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this (...) theory, or introduce unusual and controversial interpretative rules and/or ontologies). To that effect, we recall a remarkable phenomenon in the theory of Schrödinger operators (discovered in 1981 by Jona-Lasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric double-well Hamiltonian (which is paradigmatically of Schrödinger’s Cat type) becomes exponentially sensitive to tiny perturbations of the potential as ħ→0. We show that this instability emerges also from the textbook wkb approximation, extend it to time-dependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which the cat is typically either dead or alive, depending on the details of the perturbation). Numerical simulations show that adiabatically arising perturbations may (quite literally) cause the collapse of the wave-function in the classical limit. Thus, at least in the context of a simple mathematical model, we combine the technical and conceptual virtues of decoherence (which fails to solve the measurement problem but launches the key idea that perturbations may come from the environment) with those of dynamical collapse models à la grw (which do solve the measurement problem but are ad hoc), without sharing their drawbacks: single measurement outcomes are obtained (instead of merely diagonal reduced density matrices), and no modification of quantum mechanics is needed. (shrink)

We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this (...) theory, or introduce unusual and controversial interpretative rules and/or ontologies).To that effect, we recall a remarkable phenomenon in the theory of Schrödinger operators (discovered in 1981 by Jona-Lasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric double-well Hamiltonian (which is paradigmatically of Schrödinger’s Cat type) becomes exponentially sensitive to tiny perturbations of the potential as ħ→0. We show that this instability emerges also from the textbook wkb approximation, extend it to time-dependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which the cat is typically either dead or alive, depending on the details of the perturbation).Numerical simulations show that adiabatically arising perturbations may (quite literally) cause the collapse of the wave-function in the classical limit. Thus, at least in the context of a simple mathematical model, we combine the technical and conceptual virtues of decoherence (which fails to solve the measurement problem but launches the key idea that perturbations may come from the environment) with those of dynamical collapse models à la grw (which do solve the measurement problem but are ad hoc), without sharing their drawbacks: single measurement outcomes are obtained (instead of merely diagonal reduced density matrices), and no modification of quantum mechanics is needed. (shrink)

The Schrödinger’s cat paradox has troubled physicists for many years and many ways to solve it has been provided so far. In this paper I will try to provide a different method of solving the Paradox with the help of logical machine and it will look like a hybrid of Wigner’s no-go theorem and the machine of Gödel in his Incompleteness Theorems. And due to the machine the paradox will not require any human intervention to measure the state of the (...) cat, whether it is alive or dead, while the measurement will be made by humans with regard to the statement given out by the machine. (shrink)

By way of an example, Lewis imagines your being invited to join Schrödinger’s cat in its box for an hour. This box will either fill up with deadly poison fumes or not, depending on whether or not some radioactive atom decays, the probability of decay within an hour being 50%. The invitation is accompanied with some further incentive to comply (Lewis sets it up so there is a significant chance of some pretty bad but not life-threatening punishment if you don’t (...) get in the box). Lewis argues that the many minds theory implies that you should get in the box with the cat, despite this making it 50% likely you will die. (shrink)

Recently, Frauchiger and Renner proposed a Gedankenexperiment, which was claimed to be able to prove that quantum theory cannot consistently describe the use of itself. Here we show that the conclusions of Frauchiger and Renner actually came from their incorrect description of some quantum states. With the correct description there will be no inconsistent results, no matter which quantum interpretation theory is used. Especially, the Copenhagen interpretation can satisfy all the three assumptions,, and of Frauchiger and Renner simultaneously, thus it (...) has no problem consistently describing the use of itself. (shrink)

In collapse theories of quantum mechanics such as the GRW theory, the measurement result is represented by the post-measurement state which is still a superposition of different result branches, although the modulus squared of the amplitude of one result branch is close to one. This leads to the tails problem. In this paper, I present a new analysis of the tails problem of collapse theories, and suggest a more complete solution to the problem. First, I argue that the tails problem (...) exists not only in collapse theories, but also in Everett's theory and even in Bohm's theory. Moreover, I point out that the tails problem has two levels: the physical and mental levels, which may be called the objective and subjective tails problems, respectively. One needs to analyze not only the connection between high modulus-squared values and macro-existence, but also the connection between these values and our experience of macro-existence. Second, I briefly review the existing solutions to the objective and subjective tails problems. I argue that although the objective tails problem may be solved more directly, one needs to further investigate the psychophysical connection in order to solve the subjective tails problem. Third, I analyze how the mental state of an observer is determined by her wave function in collapse theories. It is argued that the mental content of an observer is related to the amplitude of each result branch of the superposition she is physically in, and it may be composed of all possible results. Moreover, it is conjectured that the modulus squared of the amplitude of each result branch may determine the vividness of the part of the mental content containing the result. Finally, I argue that this vividness conjecture may help solve the subjective tails problem of collapse theories. (shrink)

The purpose of this paper is to review and clarify the quantum “measurement problem.” The latter originates in the ambivalent nature of the “observer”: Although the observer is not described by the Schrödinger equation, it should nevertheless be possible to “quantize” him and include him in the wave function if quantum theory is universally valid. The problem is to prove that no contradiction may arise in these two conflicting descriptions. The proof invokes the notion of irreversibility. The validity of the (...) latter is questionable, because the standard rationale for classical irreversibility, namely mixing and coarse graining, does not apply to quantum theory. There is no chaos in a closed, finite quantum system. However, when a system is large enough, it cannot be perfectly isolated from its “environment,” namely from external (or even internal) degrees of freedom which are not fully accounted for in the Hamiltonian of that system. As a consequence, the long-range evolution of such a quantum system is essentially unpredictable. It follows that the notion of irreversibility is a valid one in quantum theory and the “measurement problem” can be brought to a satisfactory solution. (shrink)

Complementarity tells us we cannot know precisely the values of all the properties of a quantum object at the same time: the precise determination of one property implies that the value of some other (complementary) property is undefined. E.g. the precise knowledge of the position of a particle implies that its momentum is undefined. Here we show that a Schrödinger cat has a well defined value of a property that is complementary to its “being dead or alive” property. Then, thanks (...) to complementarity, it has an undefined value of the property “being dead or alive”. In other words, the cat paradox is explained through quantum complementarity: of its many complementary properties, any quantum system, such as a cat, can have a well defined value only of one at a time. Schrödinger’s cat has a definite value of a property which is complementary to “being dead or alive”, so it is neither dead nor alive. Figuratively one can say it is both dead and alive. While this interpretation only uses textbook concepts (the Copenhagen interpretation), apparently it has never explicitly appeared in the literature. We detail how to build an Arduino based simulation of Schrödinger’s experiment based on these concepts for science outreach events. (shrink)

We discuss two recent attempts two solve Schrodinger's cat paradox. One is the modal interpretation developed by Kochen, Healey, Dieks, and van Fraassen. It allows for an observable which pertains to a system to possess a value even when the system is not in an eigenstate of that observable. The other is a recent theory of the collapse of the wave function due to Ghirardi, Rimini, and Weber. It posits a dynamics which has the effect of collapsing the state (...) of macroscopic systems. We argue that the modal interpretation cannot account for non-accurate measurements and that both accounts have the consequence that in ordinary measurement situations the observables that ends up well defined are not quite the ones that we want to be well defined. (shrink)

When the fuzzy indeterminacy of quantum mechanics overthrew the orderly world of Isaac Newton, Albert Einstein and Erwin Schrödinger were at the forefront of the revolution. Neither man was ever satisfied with the standard interpretation of quantum mechanics, however, and both rebelled against what they considered the most preposterous aspect of quantum mechanics: its randomness. Einstein famously quipped that God does not play dice with the universe, and Schrödinger constructed his famous fable of a cat that was neither alive nor (...) dead not to explain quantum mechanics but to highlight the apparent absurdity of a theory gone wrong. But these two giants did more than just criticize: they fought back, seeking a Theory of Everything that would make the universe seem sensible again. In Einstein’s Dice and Schrödinger’s Cat, physicist Paul Halpern tells the little-known story of how Einstein and Schrödinger searched, first as collaborators and then as competitors, for a theory that transcended quantum weirdness. This story of their quest—which ultimately failed—provides readers with new insights into the history of physics and the lives and work of two scientists whose obsessions drove its progress. Today, much of modern physics remains focused on the search for a Theory of Everything. As Halpern explains, the recent discovery of the Higgs Boson makes the Standard Model—the closest thing we have to a unified theory— nearly complete. And while Einstein and Schrödinger failed in their attempt to explain everything in the cosmos through pure geometry, the development of string theory has, in its own quantum way, brought this idea back into vogue. As in so many things, even when they were wrong, Einstein and Schrödinger couldn’t help but get a great deal right. (shrink)

In a recent paper, Zukowski and Markiewicz showed that Wigner’s Friend (and, by extension, Schrodinger’s Cat) can be eliminated as physical possibilities on purely logical grounds. I validate this result and demonstrate the source of the contradiction in a simple experiment in which a scientist S attempts to measure the position of object |O⟩ = |A⟩S +|B⟩S by using measuring device M chosen so that |A⟩M ≈ |A⟩S and |B⟩M ≈ |B⟩S. I assume that the measurement occurs by quantum amplification (...) without collapse, in which M can entangle with O in a way that remains reversible by S for some nonzero time period. This assumption implies that during this “reversible” time period, |A⟩M ̸= |A⟩S and |B⟩M ̸= |B⟩S – i.e., the macroscopic pointer state to which M evolves is uncorrelated to the position of O relative to S. When the scientist finally observes the measuring device, its macroscopic pointer state is uncorrelated to the object in position |A⟩S or |B⟩S, rendering the notion of “reversible measurement” a logical contradiction. (shrink)

In a discussion of Schroedinger’s views on quantum theory John Bell says that Schroedinger did not see how “to account for particle tracks in track chambers…and more generally for the definiteness, the particularity, of experience, as compared with the indefiniteness, the waviness, of the wave function. It is the problem he had had with his cat. He thought it could not be both dead and alive. But the wave function showed no such commitment, superposing the possibilities. Either the wave function (...) as given by the Schroedinger equation is not everything or it is not right” (Bell 1987). At a recent conference Bell sermonized against the employment of “for all practical purpose” reasoning- he called it FAP reasoning-to solve this problem (Bell 1989). He argued that we should not be satisfied with any alleged solution which works “for all practical purposes” only while leaving conceptual puzzles unresolved. (shrink)

Animals populate our artistic and philosophical discourses in critical ways. From Jacques Derrida's or Karen Barad's cat, to Donna Haraway's dog, to the fish in Lucien Castaing-Taylor and Véréna Paravel's Leviathan, these animals feature heavily in discussions regarding limits – the limits of the human and thus its relation with non-humans, but also the limits of knowledge itself. Cute or dangerous, real or fantasised, dead or alive: in this article, I juxtapose the various ways that such animals confront us with (...) what Jacques Derrida describes as “the point of view of the absolute other”. Similarly, recent texts stage encounters with animals – thus distributing agency towards a larger variety of beings, carving out space for a previously excluded non-human other. Yet these encounters are mediated in profoundly different ways. In researching how encounters with the animal are differentially inflected and “defracted” respective to the medium in which they are staged, this article invokes questions of form and style within the critical dialogue that attempts to centre non-human animals. Highlighting how formal decisions are not accidental, but rather integral, to the praxis of the philosophy of animality, this article aims to draw attention to how specific forms and styles allow for a moment of contact with a non-human other. To this end, this article examines three oft-cited encounters: Derrida's encounter with his cat, an intense stare with a fish in Leviathan, and Barad's inflection of Schrödinger's cat. This juxtaposition gives insight into the limits of certain styles of producing thought and critically reflects on these works in their discussion of non-human life and agency. (shrink)

I show in this paper why the universality of quantum mechanics at all scales, which implies the possibility of Schrodinger's Cat and Wigner's Friend thought experiments, cannot be experimentally confirmed, and why macroscopic superpositions in general cannot be observed or measured, even in principle. Through the relativity of quantum superposition and the transitivity of correlation, it is shown that from the perspective of an object that is in quantum superposition relative to a macroscopic measuring device and observer, the observer (...) is already sufficiently well correlated to the measuring device that once the object correlates to the measuring device, there is no time period in which the observer can perform an appropriate interference experiment to show that the measuring device is in a superposition. (shrink)

Parmenides’ Poem on Nature contains a proof that the world could not have come into being in time, because no explanation could be given for why it would do so at a given time. This same proof reappears in the Leibniz-Clarke Correspondence, where it is directed against Newtonian absolute time. Newtonians, Leibniz explains, believe that time is homogeneous and absolute, but this makes it inexplicable how God could have chosen to create the world on a given day. Similarly, in his (...) correspondence with Schrödinger in the 1930s, Einstein suggests that certain quantum mechanical occurrences, such as the spontaneous decay of a radioactive atom, are absurd, because they cannot be assigned a definite location in time. In Schrödinger’s version of Einstein’s argument, we must say that the cat dies twice: first, inside the box; yet, second, when we open the box. But both accounts cannot be true. Since each of the authors discussed was aware of the approach of his predecessors, they share a structure. In this article, I develop a unified account of all three. (shrink)

This essay equates Penrose's (1989) Emperor with the scientist engaging in mental (Schrödinger's cat) or real experiments.The simultaneous presence of apparently contradictory phase-spatial symmetry conditions on the various hierarchical levels of biological systems are seen as the result of genetic and neurophysiological information that interferes with the physico-chemical vectors between the structural components of the system, the experimenter being an integral part of this informational causality. Equations pertaining to the lowest structural levels of matter, therefore, may not be extendable over (...) higher levels of biological organization, including human science and technology, which are seen as part and parcel of biology. This situation calls for a formal theoretical biophysics which concentrates on macroscopic processes where life and, above all,Homo sapiens, is involved. (shrink)

Von Neumann's theory of measurement in quantum mechanics is reinterpreted so that the experimental arrangement specifies the location of the “cut” by calling for the separate observation of the object and the measuring apparatus after the initial measurement interaction. The measurement ascertains which element of the mixture describing the final state of the apparatus is actually present. The relevance and feasibility of observing the final coherent state of the object plus apparatus is criticized and the paradoxes of “Schrödinger's cat” and (...) “Wigner's friend” are discussed. (shrink)

Newton's bucket, Einstein's elevator, Schrödinger's cat – these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking? In this revised and updated new edition of his classic text _The Laboratory of the Mind_, James Robert Brown continues to defend (...) apriorism in the physical world. This edition features two new chapters, one on “counter thought experiments” and another on the development of inertial motion. With plenty of illustrations and updated coverage of the debate between Platonic rationalism and classic empiricism, this is a lively and engaging contribution to the field of philosophy of science. (shrink)

This paper contains four new dialogues among Simplicio, Salviati, and Sagredo, on the fate of Schrödinger's cat, the existence of physical quantities, the paradigm of Einstein, Podolsky, and Rosen, and why a watched kettle may boil, after all.

A drastic resolution of the quantum paradoxes is proposed, combining (I) von Neumann's postulate that collapse of the state vector is due to the act of observation, and (II) my reinterpretation of von Neumann's quantal irreversibility as an equivalence between wave retardation and entropy increase, both being “factlike” rather than “lawlike” (Mehlberg). This entails a coupling of the two de jure symmetries between (I) retarded and (II) advanced waves, and between Aristotle's information as (I) learning and (II) willing awareness. Symmetric (...) acceptance of cognizance as a source of retarted waves, and of will as a sink of advanced waves, is submitted as a central “paradox” of the Copernican or Einsteinian sort, out of which new light is shed upon previously known paradoxes, such as the EPR paradox, Schrödinger's cat, and Wigner's friend. Parapsychology is thus found to creep into the picture. (shrink)

David Lewis's untimely death on 14 October 2001 deprived the philosophical community of one of the outstanding philosophers of the 20th century. As many obituaries remarked, Lewis has an undeniable place in the history of analytical philosophy. His work defines much of the current agenda in metaphysics, philosophical logic, and the philosophy of mind and language. This volume, an expanded edition of a special issue of the Australasian Journal of Philosophy, covers many of the topics for which Lewis was well (...) known, including possible worlds, counterpart theory, vagueness, knowledge, probability, essence, fiction, laws, conditionals, desire and belief, and truth. Many of the papers are by very established philosophers; others are by younger scholars including many he taught. The volume also includes Lewis's Jack Smart Lecture at the Australian National University, "How Many Lives has Schrodinger's Cat?," published here for the first time. Lewisian Themes will be an invaluable resource for anyone studying Lewis's work and a major contribution to the many topics that he mastered. (shrink)

We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of superposition such as the one comprised in the famous Schrödinger’s cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exist.We analyze that (...) claim by employing the traditional square of opposition.We suggest that it is difficult to make sense of the idea of contradiction in the case of quantum superpositions. From a metaphysical point of view the suggestion also faces obstacles, and we present some of them. (shrink)

David Lewis's untimely death on 14 October 2001 deprived the philosophical community of one of the outstanding philosophers of the 20th century. As many obituaries remarked, Lewis has an undeniable place in the history of analytical philosophy. His work defines much of the current agenda in metaphysics, philosophical logic, and the philosophy of mind and language. This volume, an expanded edition of a special issue of the Australasian Journal of Philosophy, covers many of the topics for which Lewis was well (...) known, including possible worlds, counterpart theory, vagueness, knowledge, probability, essence, fiction, laws, conditionals, desire and belief, and truth. Many of the papers are by very established philosophers; others are by younger scholars including many he taught. The volume also includes Lewis's Jack Smart Lecture at the Australian National University, 'How Many Lives has Schrödinger's Cat?', published here for the first time. Lewisian Themes will be an invaluable resource for anyone studying Lewis's work and a major contribution to the many topics that he mastered. (shrink)

The Frauchiger–Renner Paradox is an extension of paradoxes based on the “Problem of Measurement,” such as Schrödinger’s Cat and Wigner’s Friend. All these paradoxes stem from assuming that quantum theory has only unitary physical dynamics, and the attendant ambiguity about what counts as a ‘measurement’—i.e., the inability to account for the observation of determinate measurement outcomes from within the theory itself. This paper discusses a basic inconsistency arising in the FR scenario at a much earlier point than the derived contradiction: (...) namely, the inconsistency inherent in treating an improper mixture as a proper, epistemic mixture. This is an illegitimate procedure that is nevertheless endemic if quantum theory is assumed to be always unitary. In contrast, under a non-unitary account of quantum state reduction yielding determinate outcomes, the use of a proper mixture for measurement results becomes legitimate, and this entire class of paradoxes cannot be mounted. The conclusion is that the real lesson of the FR paradox is that it is the unitary-only assumption that needs to be critically reassessed. (shrink)