Einstein Versus Bohr is unlike other books on science written by experts for non-experts, because it presents the history of science in terms of problems, conflicts, contradictions, and arguments. Science normally "keeps a tidy workshop." Professor Sachs breaks with convention by taking us into the theoretical workshop, giving us a problem-oriented account of modern physics, an account that concentrates on underlying concepts and debate. The book contains mathematical explanations, but it is so-designed that the whole argument can be followed (...) with the math omitted. Professor Sachs' story begins with classical and nineteenth century physics, describes the early discoveries in particle theory, and introduces the "old" quantum theory, which evolved into the quantum mechanics of the Copenhagen School. Such important ideas as the Einstein Photon Box experiment and the Einstein-Podolsky-Rosen Paradox, and Schrodinger's Cat Paradox are clearly expounded, followed by a completely fresh explanation of relativity in conceptual terms, showing how apparent paradoxes can be removed by Einstein's own interpretation, especially that of his later years. Professor Sachs gives a detailed comparison of the fundamentals of the quantum and relativity theories, suggesting how the contradictions might be resolved. In an epilogue, he makes suggestions, with reference to religious notions, Taoism, and Buber's theory of I-Thou, for generalizing Einstein's approach beyond physics. (shrink)

Einstein algebras have been suggested (Earman 1989) and rejected (Rynasiewicz 1992) as a way to avoid the hole argument against spacetime substantivalism. In this article, I debate their merits and faults. In particular, I suggest that a gauge‐invariant interpretation of Einstein algebras that avoids the hole argument can be associated with one approach to quantizing gravity, and, for this reason, is at least as well motivated as sophisticated substantivalist and relationalist interpretations of the standard tensor formalism.

This volume is the first systematic presentation of the work of Albert Einstein, comprising fourteen essays by leading historians and philosophers of science that introduce readers to his work. Following an introduction that places Einstein's work in the context of his life and times, the book opens with essays on the papers of Einstein's 'miracle year', 1905, covering Brownian motion, light quanta, and special relativity, as well as his contributions to early quantum theory and the opposition to (...) his light quantum hypothesis. Further essays relate Einstein's path to the general theory of relativity (1915) and the beginnings of two fields it spawned, relativistic cosmology and gravitational waves. Essays on Einstein's later years examine his unified field theory program and his critique of quantum mechanics. The closing essays explore the relation between Einstein's work and twentieth-century philosophy, as well as his political writings. (shrink)

The reluctant revolutionary -- The patent slave -- The golden Dane -- The quantum atom -- When Einstein met Bohr -- The prince of duality -- Spin doctors -- The quantum magician -- A late erotic outburst -- Uncertainty in Copenhagen -- Solvay 1927 -- Einstein forgets relativity -- Quantum reality -- For whom Bell's theorem tolls -- The quantum demon.

Much of the history of physics at the beginning of the twentieth century has been written with a sharp focus on a few key figures and a handful of notable events. Einstein’s Generation offers a distinctive new approach to the origins of modern physics by exploring both the material culture that stimulated relativity and the reaction of Einstein’s colleagues to his pioneering work. Richard Staley weaves together the diverse strands of experimental and theoretical physics, commercial instrument making, and (...) the sociology of physics around 1900 to present a complete view of the collective efforts of a group whose work helped set the stage for Einstein’s revolutionary theories and the transition from classical to modern physics that followed. Collecting papers, talks, catalogues, conferences, and correspondence, Staley juxtaposes scientists’ views of relativity at the time to modern understandings of its history. Ultimately, Einstein’s Generation tells the story of a group of individuals whose work engendered some of the most significant advances of the twentieth century—and challenges our celebration of Einstein’s era above all others. (shrink)

Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. We show that representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something real, (...) the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein’s preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein’s attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927. (shrink)

I discuss various formulations of stochastic Einstein locality (SEL), which is a version of the idea of relativistic causality, that is, the idea that influences propagate at most as fast as light. SEL is similar to Reichenbach's Principle of the Common Cause (PCC), and Bell's Local Causality. My main aim is to discuss formulations of SEL for a fixed background spacetime. I previously argued that SEL is violated by the outcome dependence shown by Bell correlations, both in quantum mechanics (...) and in quantum field theory. Here I reassess those verdicts in the light of some recent literature which argues that outcome dependence does not violate the PCC. I argue that the verdicts about SEL still stand. Finally, I briefly discuss how to formulate relativistic causality if there is no fixed background spacetime. (shrink)

This excellent, semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, and more) and coverage of Einstein’s special and general theories of relativity, discussing the concept of simultaneity, kinematics, Einstein’s mechanics and dynamics, and more.

This paper situates Einstein's theory of relativity within broader networks of communication. The speed of light, explained Einstein, was an unsurpassable velocity if , and only if , it was considered in terms of »arbitrary« and »voluntary« signals. Light signals in physics belong within a broader set of signs and symbols that include communication and military signals, understood by reference to Helmholtz, Saussure, media philosophies from WWII to '68 (Lavelle, Ong, McLuhan) and Derrida. Once light signals in physics (...) are considered in relation to semaphore, print, telegraph, radio, computers and tape recorders, Kittler and Habermas provide us with conflicting ways for understanding science and technology, rationality and consensus. We conclude with a study of »flash and bang« in popular accounts of relativity theory to understand the role of theoretical science in the transmission of information and violence. (shrink)

I argue that, contrary to folklore, Einstein never really cared for geometrizing the gravitational or the electromagnetic field; indeed, he thought that the very statement that General Relativity geometrizes gravity "is not saying anything at all". Instead, I shall show that Einstein saw the "unification" of inertia and gravity as one of the major achievements of General Relativity. Interestingly, Einstein did not locate this unification in the field equations but in his interpretation of the geodesic equation, the (...) law of motion of test particles. (shrink)

In this paper, I accomplish a conceptual task and a historical task. The conceptual task is to argue that (1) Einstein’s Principle of Separability (henceforth “separability”) is not a supervenience principle and that (2) separability and entanglement are compatible. I support (1) by showing that the conclusion of Einstein’s incompleteness argument would still follow even if one assumes that the state of a composite system does not supervene on the states of the subsystems, and by showing that what (...) Einstein says in “Quantum Mechanics and Reality” (1948) strongly suggests that separability is not a principle about how subsystem states relate to the state of composite systems. I support (2) by showing that if separability was incompatible with entanglement, then Einstein’s argument would be incoherent in a trivial way. Thus, by arguing for (1) and (2) I directly challenge what has been, and still is, a very common reading of separability. The historical task is to offer the first detailed review of the different ways in which separability has been defined by physicists and philosophers in the last 60 years. Among other things, such a review distinguishes three different definitions of the principle, and shows that since the 1990s and up until the present date, it became standard to take separability (as presented by Einstein) to be a supervenience principle. (shrink)

Einstein regarded as one of the triumphs of his 1915 theory of gravity - the general theory of relativity - that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of (...) inertia and both the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920. (shrink)

Kant's original version of transcendental philosophy took both Euclidean geometry and the Newtonian laws of motion to be synthetic a priori constitutive principles—which, from Kant's point of view, function as necessary presuppositions for applying our fundamental concepts of space, time, matter, and motion to our sensible experience of the natural world. Although Kant had very good reasons to view the principles in question as having such a constitutively a priori role, we now know, in the wake of Einstein's work, (...) that they are not in fact a priori in the stronger sense of being fixed necessary conditions for all human experience in general, eternally valid once and for all. And it is for precisely this reason that Kant's original version of transcendental philosophy must now be either rejected entirely or radically reconceived. Most philosophy of science since Einstein has taken the former route: the dominant view in logical empiricism, for example, was that the Kantian synthetic a priori had to be rejected once and for all in the light of the general theory of relativity. (shrink)

This book brings together papers from a conference that took place in the city of L'Aquila, 4–6 April 2019, to commemorate the 10th anniversary of the earthquake that struck on 6 April 2009. Philosophers and scientists from diverse fields of research debated the problem that, on 6 April 1922, divided Einstein and Bergson: the nature of time. For Einstein, scientific time is the only time that matters and the only time we can rely on. Bergson, however, believes that (...) scientific time is derived by abstraction, even in the sense of extraction, from a more fundamental time. The plurality of times envisaged by the theory of Relativity does not, for him, contradict the philosophical intuition of the existence of a single time. But how do things stand today? What can we say about the relationship between the quantitative and qualitative dimensions of time in the light of contemporary science? What do quantum mechanics, biology and neuroscience teach us about the nature of time? The essays collected here take up the question that pitted Einstein against Bergson, science against philosophy, in an attempt to reverse the outcome of their monologue in two voices, with a multilogue in several voices. (shrink)

Einstein, in his “Zur Elektrodynamik bewegter Körper”, gave a physical (operational) meaning to “time” of a remote event in describing “motion” by introducing the concept of “synchronous stationary clocks located at different places”. But with regard to “place” in describing motion, he assumed without analysis the concept of a system of co-ordinates.In the present paper, we propose a way of giving physical (operational) meaning to the concepts of “place” and “co-ordinate system”, and show how the observer can define both (...) the place and time of a remote event. Following Einstein, we consider another system “in uniform motion of translation relatively to the former”. Without assuming “the properties of homogeneity which we attribute to space and time”, we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, “one-way” and “two-way” velocities of light, symmetry, the “group property” of inertial reference frames, length contraction and time dilatation, and the “twin paradox”. Finally, we point out a flaw in Einstein’s argument in the “Electrodynamical Part” of his paper and show that the Lorentz force formula and Einstein’s formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck’s formula for mass suffices. (Except for the reference to Planck’s formula, we restrict ourselves to Physics of 1905.). (shrink)

Recent studies have shown that Einstein did not write the EPR paper and that he was disappointed with the outcome. He thought, rightly, that his own argument for the incompleteness of quantum theory was badly presented in the paper. We reconstruct the argument of EPR, indicate the reasons Einstein was dissatisfied with it, and discuss Einstein's own argument. We show that many commentators have been misled by the obscurity of EPR into proposing interpretations of its argument that (...) do not accurately represent Einstein's own views. Finally, we evaluate Einstein's own incompleteness argument, concluding that recent experimental findings have likely shown it to be unsound. (shrink)

Einstein considered fallibilist methodology obvious and metaphysics the challenging heuristic of physics. This philosophy is a minority view in academic philosophy. Most commentators on Einstein reject it and either refuse to ascribe it to him or declare it an impediment to his researches, his own opinion to the contrary notwithstanding.

Hans Reichenbach, a philosopher of science who was one of five students in Einstein's first seminar on the general theory of relativity, became Einstein's bulldog, defending the theory against criticism from philosophers, physicists, and popular commentators. This book chronicles the development of Reichenbach's reconstruction of Einstein's theory in a way that clearly sets out all of its philosophical commitments and its physical predictions as well as the battles that Reichenbach fought on its behalf, in both the academic (...) and popular press. The essays include reviews and responses to philosophical colleagues, such as Moritz Schlick and Hugo Dingler; polemical discussions with physicists Max Born and D. C. Miller; as well as popular articles meant to clarify aspects of Einstein's theories and set out their philosophical ramifications for the layperson. At a time when physics and philosophy were both undergoing revolutionary changes in content and method, this book is a window into the development of scientific philosophy and the role of the philosopher. (shrink)

Written by the man considered the "Person of the Century" by Time magazine, this is not a glimpse into Einstein's personal life, but an extension and elaboration into his thinking on science. Two of the great theories of the physical world were created in the early 20th century: the theory of relativity and quantum mechanics. Einstein created the theory of relativity and was also one of the founders of quantum theory. Here, Einstein describes the failure of classical (...) mechanics and the rise of the electromagnetic field, the theory of relativity, and of the quanta. Written in German by Einstein himself, the book is faced, page-by-page, with a translation by the noted Professor of Philosophy Paul Arthur Schilpp. (shrink)

SummaryThe Bohr‐Einstein debate on the interpretation of quantum mechanics may be viewed as a discussion on the epistemological status of knowledge gained by physics. It is shown that in fact the advent of quantum theory has led, in a new context, to an old philosophical controversy between epistemological realism and phenomenalism . An inquiry into this controversy, taking into account the contemporary understanding of quantum mechanics based on the axiomatic study of its foundations, leads to the conclusion that contrary (...) to widespread opinion, it is perfectly possible to formulate quantum mechanics in an entirely realistic manner according to the postulate of Einstein. We demonstrate that Bohr's episteme‐logy, in which the role of experimental arrangements in the physical description is taken as a starting point, does not necessarily imply phenomenlism, but may be justifiably considered as a complementary standpoint to the realistic epistemology of Einstein, which is based on the notion of a mental construction which pictures reality. (shrink)

Albert Einstein deliberately and repeatedly expressed his general religious views. But what were his views of mysticism? His statements on the subject were few, relatively obscure, and often misunderstood. A coherent answer requires setting those statements in historical, cultural, and theological context, as well as examining Einstein's philosophical and religious views. Though the Einstein that emerges clearly rejected supernatural mysticism, his views of “essential” mysticism were—though largely implicit—more nuanced, more subtle, and ultimately more sympathetic than “mere appearance” (...) suggests. (shrink)

Albert Einstein was the most influential physicist of the twentieth century. Less well-known is that fundamental philosophical problems, such as concept formation, the role of epistemology in developing and explaining the character of physical theories, and the debate between positivism and realism, played a central role in his thought as a whole. Thomas Ryckman shows that already at the beginning of his career, at a time when the twin pillars of classical physics, Newtonian mechanics and Maxwell’s electromagnetism, were known (...) to have but limited validity, Einstein sought to advance physical theory by positing certain physical principles as secure footholds. That philosophy produced his greatest triumph, the general theory of relativity, and his greatest failure, an unwillingness to accept quantum mechanics. This book shows that Einstein’s philosophy grew from a lifelong aspiration for a unified theoretical representation encompassing all physical phenomena. It also considers how Einstein’s theories of relativity and criticisms of quantum theory have shaped the course of twentieth-century philosophy of science. Including a chronology, glossary, chapter summaries, and suggestions for further reading, _Einstein_ is an ideal introduction to this iconic figure in twentieth-century science and philosophy. It is essential reading for students of philosophy of science, and also suitable for those working in related areas such as physics, history of science, or intellectual history. (shrink)

In this paper, we examine the relationship between general relativity and the theory of Einstein algebras. We show that according to a formal criterion for theoretical equivalence recently proposed by Halvorson and Weatherall, the two are equivalent theories.

Why did Einstein tirelessly study unified field theory for more than 30 years? In this book, the author argues that Einstein believed he could find a unified theory of all of nature's forces by repeating the methods he used when he formulated general relativity. The book discusses Einstein's route to the general theory of relativity, focusing on the philosophical lessons that he learnt. It then addresses his quest for a unified theory for electromagnetism and gravity, discussing in (...) detail his efforts with Kaluza-Klein and, surprisingly, the theory of spinors. From these perspectives, Einstein's critical stance towards the quantum theory comes to stand in a new light. This book will be of interest to physicists, historians and philosophers of science. (shrink)

In this article we analyse the role of the principle of relativity and the generalisation of Lorentz transformations in Einstein's relativistic physics, whose philosophical ideal was the construction of an image of nature endowed with maximum unity and logical simplicity. In his critical-rationalist realism, Einstein aimed to develop a "conception of the world" that expressed the logical unity of nature. Throughout his scientific career, this philosophical programme led him to produce "great syntheses", seeking compatibility between different physical systems.

The question whether quantum discontinuity can or cannot provide an answer to Zeno's Paradoxes is reopened. It is observed that what is usually understood by the term "discontinuity", namely, Einstein's conception of the photon as described by himself and all others, is unsuitable to the task because, essentially,it reduces to the trivial 'discontinuity' of objects scattered in space. By contrast, quantization of energy levels, which are not in space but can only alternate in time, provide the right sort of (...) discontinuity required. Discrete quantized orbits, corresponding to eigen-frequencies, are irreducible, and nothing is allowed to stand in-between them in satisfaction of the quantum postulate, furnishing the requisite, and so far missing, immediate nextness of a point to a certain other. In this way, Zeno's Runner need not postpone his first step indefinitely, always waiting upon an infinity of preceding steps, before it can be taken. There is now a point that is next to a point and so a step on that point, which is the first step. It follows that, if one kind of discontinuity, Einstein's, is incapable of offerring an answer to Zeno, while another kind can, the two are discrepant. One of them, the former, is not a kind of discontinuity properly so called at all, though evidently the consequence of one. (shrink)

Introduction : Einstein's Jewish science -- Is Einstein a Jew? -- Is relativity pregnant with Jewish concepts? -- Why did a Jew formulate the theory of relativity? -- Is the theory of relativity political science or scientific politics? -- Einstein and the Jewish intelligentsia -- Einstein's liberal science? -- Conclusion : Einstein's cosmopolitan science.

In a recent paper, I have analysed and criticised Leggett and Garg’s argument to the effect that macroscopic realism contradicts quantum mechanics, by contrasting their assumptions to the example of Bell’s stochastic pilot-wave theories, and have applied Dzhafarov and Kujala’s analysis of contextuality in the presence of signalling to the case of the Leggett–Garg inequalities. In this chapter, I discuss more in general the motivations for macroscopic realism, taking a cue from Einstein’s criticism of the Bohm theory, then go (...) on to summarise my previous results, with a few additional comments on other recent work on Leggett and Garg. [To appear in: E. Dzhafarov, Contextuality from Quantum Physics to Psychology.]. (shrink)

In this note, we point attention to and briefly discuss a curious manuscript of Einstein, composed in 1938 and entitled “Unified Field Theory,” the only such writing, published or unpublished, carrying this title without any further specification. Apparently never intended for publication, the manuscript sheds light both on Einstein′s modus operandi as well as on the public role of Einstein′s later work on a unified field theory of gravitation and electromagnetism.

Einstein's gravitational redshift derivation in his famous 1916 paper on general relativity seems to be problematic, being mired in what looks like conceptual difficulties or at least contradictions or gaps in his exposition. Was this derivation a blunder? To answer this question, we will consider Einstein’s redshift derivations from his first one in 1907 to the 1921 derivation made in his Princeton lectures on relativity. This will enable to see the unfolding of an interdependent network of concepts and (...) heuristic derivations in which previous ideas inform and condition later developments. The resulting derivations and views on coordinates and clocks are in fact not without inconsistencies. However, we can see these difficulties as an aspect of an evolving network understood as a “work in progress”. (shrink)

(1987). Einstein's brand of verificationism. International Studies in the Philosophy of Science: Vol. 2, No. 1, pp. 33-54. doi: 10.1080/02698598708573301.

In a notable article entitled “What is the Theory of Relativity?” written at the request of The Times and published in its November 28, 1919 edition, Albert Einstein famously distinguished “theories of principle” from “constructive theories.” Einstein placed relativity theory among the principle theories. His distinction has recently received increased attention, especially as it relates to scientific explanation. In particular, there has been considerable discussion of how to explain why there obtain the Lorentz transformations as well as of (...) how to account for the Lorentz covariance of the dynamical laws. Some .. (shrink)

One of the most important contributions of Einstein to the philosophy of science is the distinction between two types of scientific theories: ‘principle’ and ‘constructive’ theories. More recently, Flores proposed a more general distinction, classifying scientific theories by their functional role into ‘framework’ and ‘interaction’ theories, attempting to solve some inadequacies in Einstein’s proposal. Here, based on an epistemic criterion, we present a generalised distinction which is an improvement over Flores approach. In this work (i) we evaluate the (...) shortcomings related to Flores’s proposal, (ii) we present an epistemological criterion that opens the door for a more general classification of any scientific theory in all of the natural science into two distinct groups, which we call ‘mechanistic theories’ and ‘structural theories’, and (iii) we show that such a criterion is connected to Flores’ proposal while overcoming issues of all previous approaches. (shrink)

The ArgumentIn this paper I present and argue for a model of conceptual development in science and apply it to the transition from classical to modern physics associated with Einstein. The model claims a continuous and rational transition between incompatible subsequent conceptual systems in mathematical science and explains its mechanism. The model was developed in a study of the transition from preclassical to classical mechanics. I argue for a strong structural analogy between the transition from preclassical to classical mechanics (...) on the one hand and from classical to modern physics on the other. The first transition is briefly sketched here by reference to Galileo and his disciples; in the second transition Planck and Lorentz on the one hand and Einstein on the other play the respective roles.A detailed and documented reconstruction of the transition from preclassical to classical mechanics on the basis of this model has already been published and is only briefly referred to in the paper. The transition from classical to modern physics is portrayed here much more extensively—though of course merely in broad brush strokes. Einstein–s role in this transition is reconstructed in the light of a conceptualization of his scientific knowledge as an active structure of thought, shaped by his intellectual experience. In this way, the development of his individual thinking is shown to be part of the overall process of conceptual transformation from classical to modern physics. The reconstruction sketched in this paper is to be considered as a proposal to be substantiated, reformed, and improved by future detailed studies. (shrink)

The purpose of this paper is to highlight the importance of constraints in the theory of relativity and, in particular, what philosophical work they do for Einstein's views on the laws of physics. Einstein presents a view of local ``structure laws'' which he characterizes as the most appropriate form of physical laws. Einstein was committed to a view of science, which presents a synthesis between rational and empirical elements as its hallmark. If scientific constructs are free inventions (...) of the human mind, as Einstein, held, the question arises how such rational constructs, including the symbolic formulation of the laws of physics, can represent physical reality. Representation in turn raises the question of realism. Einstein uses a number of constraints in the theory of relativity to show that by imposing constraints on the rational elements a certain ``fit'' between theory and reality can be achieved. Fit is to be understood as satisfaction of constraint. His emphasis on reference frames in the STR and more general coordinate systems in the GTR, as well as his emphasis on the symmetries of the theory of relativity suggests that Einstein's realism is akin to a certain form of structural realism. His version of structural realism follows from the theory of relativity and is independent of any current philosophical debates about structural realism. (shrink)

Using the special theory of relativity to show that if mental events have a temporal location, then they must have a spatial location.

Einstein Meets Magritte: An Interdisciplinary Reflection presents insights of the renowned key speakers of the interdisciplinary Einstein meets Magritte conference (1995, Brussels Free University). The contributions elaborate on fundamental questions of science, with regard to the contemporary world, and push beyond the borders of traditional approaches. All of the articles in this volume address this fundamental theme, but somewhere along the road the volume expanded to become much more than a mere expression of the conference's dynamics. The articles (...) not only deal with several scientific disciplines, they also confront these fields with the full spectrum of contemporary life, and become new science. As such, this volume presents a state-of-the-art reflection of science in the world today, in all its diversity. The contributions are accessible to a large audience of scientists, students, educators, and everyone who wants to keep up with science today. (shrink)

The Einstein equations can be written as Fierz-Pauli equations with self-interaction, $W\gamma _{ik} = - G_{ik} + \tfrac{1}{2}g_{ik} g^{mn} G_{mn} - k(T_{ik} - \tfrac{1}{2}g_{ik} g^{mn} T_{mn} )$ together with the covariant Hilbert-gauge condition, $(\gamma _i^h - \tfrac{1}{2}\delta _i^k g^{mn} \gamma _{mn} )_{;k} = 0$ where W denotes the covariant wave operator and G ik the Einstein tensor of the metric g ik collecting all nonlinear terms of Einstein's equations. As is known, there do not, however, exist plane-wave (...) solutions γ ik(z)with g ik Z,i Z,k=0of these equations such that what is essential to the introduction of gravitons is not satisfied in general relativity. This nonexistence corresponds with the uncertainty relation,Δp(Δg*)2(Δx)3≥h hG/ c 3 concerning the total nonlinear gravitational field g *ik =g k +γ k. (shrink)