Notes
Introduction
2005 marked the centenary of one of the most remarkable publications in the history of science, Albert Einstein’s ‘‘On the Electrodynamics of Moving Bodies,’’ in which he presented a theory that later came to be known as the Special Theory of Relativity (STR).
This 1905 paper is widely regarded as having destroyed the classical conceptions of absolute time and space, along with absolute simultaneity and absolute length, which had reigned in physics from the times of Galileo and Newton to the dawn of the twentieth century.
As we embark upon a new century, the Special Theory is now 100 years old, and a great deal has transpired in both philosophy and physics since its first publication. It therefore seems appropriate at this time to seek a fresh appraisal of the theory’s central claims, especially concerning the elimination of absolute time and absolute simultaneity.
Part I
The classical concepts of time and space were codified by Isaac Newton in his epochal Philosophiae Naturalis Principia Mathematica (1687). In the Scholium to his definitions in the Principia Newton, in order to overcome certain prejudices of ‘‘the common people,’’ who conceive of quantities such as time, space, place, and motion only in terms of ‘‘the relation they bear to sensible objects,’’ drew a distinction with respect to these quantities between ‘‘absolute and relative, true and apparent, mathematical and common’’. The most striking feature of this distinction is the independence of absolute time and space from the relative measures thereof. Absolute time or simple duration exists regardless of the sensible and external measurements which we try, more or less successfully, to make of it. Similarly, Newtonian space is absolute in the sense that it is distinct from the relatively moving spaces associated with inertial frames and, hence, also independent of the physical measures we apply to it. But Newtonian time and space are also absolute in an important and relevant second sense. Newtonian time is absolute in the sense that the simultaneity of two events e1 and e2 requires only a two-place relation of simultaneous with between e1 and e2, rather than a three-place relation among e1, e2, and a reference frame (or a three-dimensional hyper-surface of space-time), namely, e1’s being simultaneous with e2 relative to a reference frame F. Newtonian space is similarly absolute in the sense that length is a monadic property of physical objects, rather than a relational property of physical objects that includes a relation to a reference frame or hypersurface.
Relativity already governed Newtonian mechanics, that is to say, it was impossible for a hypothetical observer associated with an inertial frame to perform mechanical experiments which would disclose to him whether he was in motion or at rest. Newton’s three laws of motion and his universal law of gravity applied strictly only to the frame of absolute space or to inertial frames which are at rest with respect to absolute space, but they could be transformed and expressed in any sensible and apparent inertial frame. This principle of relativity had already been enunciated by Galileo and comes to expression in the Galilean transformation equations relating the coordinates of an event in one reference frame to the coordinates assigned to that event relative to some other reference frame. Newton’s mechanics assumed that the Galilean transformation equations were the appropriate means of transforming Newton’s physics from one frame to another.
There was a loophole, however, in Galilean relativity that became apparent during the nineteenth century. Although mechanics had been relativised, electrodynamics had not. Maxwell’s electromagnetic theory (1865) implied that electromagnetic waves propagate through a medium, an ‘‘aether’’ or field, at a constant velocity c, which is independent of the motion of the source of the waves. Consequently, by measuring the speed at which light waves in the luminiferous aether pass through one’s measuring apparatus, one could determine what mechanics alone could not discover, namely, whether the inertial system in which the experiment was performed was at rest or in motion with respect to the aether. Since the aether was conceived to be at rest with respect to absolute space, any motion through it would be absolute, rather than merely relative. Detection of such motion on the part of any hypothetical observer would therefore provide him with what Newtonian mechanics alone could not, namely, knowledge of his situation with respect to absolute space and time.
The failure of nineteenth century attempts to detect the earth’s motion through the aether prompted a crisis in physics which compelled men like FitzGerald, Lorentz, Larmor, and Poincaré to reject the Newtonian assumption that the Galilean transformation equations were sufficient to obtain invariant laws about observed phenomena in electrodynamics and mechanics and to adopt instead the relativistic Lorentz transformations. In so doing, they had already sounded the death knell of Newtonian physics, for they had relativised the sensible measures of absolute time and space in a way undreamt of by Newton. Measures of simultaneity and of length will vary from frame to frame and so become relative to reference frames. But since absolute time and space are independent of their sensible measures, the relativity of these measures did not lead these theorists to abandon the notion that there really exists absolute simultaneity and absolute length, even if these quantities remain undetectable to us.
Einstein inaugurated a ‘‘scientific revolution’’ in his 1905 paper by interrupting the research program of Lorentz and others with a radically different approach. Foundational to this approach was the denial of absolute space and the consequent redefinition of time and simultaneity so as to deny their absolute status as well. What Einstein did, in effect, was to eliminate Newton’s absolute time and space on the grounds that they were unobservable in principle, and along with them the aether, thus leaving behind only their sensible measures, so that sensible time became the only time there is and sensible space the only space there is. Since these had by now been relativised to inertial frames, one ends up with the relativity of simultaneity and of length.
Part II
How could Einstein ‘‘know’’ that absolute time and space do not exist? Most historians of science now recognize that Einstein’s rejection of Newtonian absolute time and space was predicated upon a positivist philosophy of science. It is now widely acknowledged that at the philosophical roots of Einstein’s theory lay an epistemological positivism of Machian provenance which issued in a verificationist analysis of the concepts of time and space. The introductory sections of Einstein’s 1905 paper are predicated squarely upon verificationist assumptions. Einstein takes it for granted that all our judgments in which time plays a role must have a ‘‘physical meaning,’’ where physical meaning is given by operational definitions. Operationalism is already a strong form of verificationism, but there is more. Einstein goes on to say that ‘‘a mathematical description of this kind has no physical meaning unless we are quite clear as to what we will understand by ‘time’.’’ The meaning of ‘‘time’’ is made to depend upon the meaning of ‘‘simultaneity,’’ which is defined locally in terms of occurrence at the same local clock reading. When it comes to judgments concerning the simultaneity of distant events, the concern is to find a ‘‘practical arrangement’’ to compare clock times. In order to ‘‘define’’ a common time for spatially separated clocks, we adopt the convention that the time which light takes to travel between two relatively stationary observers A and B is the same from A to B as from B to A in a round trip journey – a definition which presupposes that absolute space does not exist. For that definition presupposes that A and B are not at relative rest but both moving in tandem absolutely, or in other words that neither absolute space nor a privileged rest frame exists. The only justification for that assumption is that it is observationally or sensibly impossible to distinguish uniform motion from rest relative to such a frame, and if absolute space and absolute motion or rest cannot be sensibly observed, they therefore do not exist (and may even be said to be meaningless). Such an inference is clearly verificationist and amounts to a variation on Berkeley: ‘‘To be is to be perceivable.’’ This sort of inference unjustifiably draws an ontological conclusion from a mere epistemological assumption.
Thus, in Einstein’s formulation time and space are reduced to sensible measures based on periodic motions (such as natural or constructed clock pointer movements) and rigid measuring rods, measures that are relative to local inertial frames. Simultaneity is defined in terms of clock synchronization via light signals. All of this is done by mere stipulation. Newton’s absolute time and space, which transcend operational definitions, are assumed to be mere figments of our imagination. Through Einstein’s operational definitions of time and space, Mach’s positivism triumphs in the STR. Reality is reduced to what our physical instruments say.
Unfortunately for Einstein’s Special Theory, however, its epistemological and ontological assumptions are now seen to be questionable, unjustified, false, perhaps even illogical. In a recent review, Tyler Burge remarked that ‘‘the central event’’ in philosophy during the second half of the twentieth century has been ‘‘the downfall of positivism and the re-opening of discussion of virtually all the traditional problems in philosophy’’. In light of the collapse of positivism and in light of its essential role in the epistemological foundations of the STR, a reappraisal of the time concept in Relativity Theory is long overdue. For apart from a verificationist critique of some sort, it is no longer obvious why the received view is to be preferred to the views of Lorentz and Poincaré, which are consistent with the Newtonian ideas of absolute time and absolute simultaneity.
Certain contemporary theorists have attempted to free STR of its verificationist assumptions, but it is questionable whether such efforts have been successful. For example, the philosopher of physics Graham Nerlich has been most critical of Einstein’s original verificationism and develops a non-reductionistic ‘‘realist’’ theory of relativistic space-time. Such relativistic substantivalism remains verificationist, however, to the extent that it assumes that time and space, although not identical with observable clock movements and rigid rods, must possess only those properties that are measurable by observable clocks and rigid rods. This assumption underlies the views of all those who hold that the ‘‘essence’’ of Special Relativity is Lorentz invariance, since Lorentz invariance ultimately requires that law-like behavior is the behavior that would be measurable by light-clocks and rigid rods if such clocks and rods were present. Similarly, Eli Zahar, who attempts to provide a non-verificationist foundation for Special Relativity, in fact ends up relying on an implicit verificationism after all.
Part III
It is remarkable that the Special Theory has thus far managed to survive largely unscathed the collapse of its essential epistemological underpinnings. One wonders how this can be so. Undoubtedly a major part of the answer is the understandable one that physicists are not epistemologists; physicists typically know no more about epistemology, the philosophy of language (e.g. problems with the verificationist criterion of semantic meaning), and ontology than philosophers typically know about physics. The precise philosophical arguments for the illogicality, falsity, or unjustifiably of the epistemological, semantic, and ontological presuppositions of the Special Theory remain, with a few exceptions, unknown among physicists.
The price paid for the growth of knowledge is increased specialization, which, paradoxically, also prevents or reverses the growth of knowledge, since specialists in one field often base their work on premises that (unbeknownst to them) have been refuted or disconfirmed in another field. The only solution we can see for this problem is that the training or schooling of physicists ought to include schooling in philosophy (and, as we shall see, the converse should hold for philosophers). Perhaps this is most practicable in the form of there being thinkers who take as their specialization the intersection of physics and philosophy and the works of these thinkers, at least in ‘‘introductory formats’’, being a part of the education of both physicists and philosophers. If this proves unfeasible and the situation remains as it presently stands, the unpalatable situation may result that neither physicists nor philosophers are in a position to have adequately justified beliefs about space and time but only philosophers of physics (or the few thinkers who are both philosophers and physicists, such as David Albert and Bas Van Fraassen, and, from the side of physics, Niels Bohr and David Bohm, who developed philosophical theories in addition to physically interpreted equations).
Apart from leaving unaddressed the epistemological and semantic presuppositions of STR, there is an even stronger factor behind physicists’ unwillingness to abandon the Special Theory. The Special Theory is a part of orthodox quantum field theory (QFT) (quantum electrodynamics and quantum chromodynamics), which aims to unify the Special Theory with quantum mechanics. Physicists would be at a loss as to how to proceed if they rejected the Special Theory as unjustified, since they (for the most part) believe that this would require them to reject QFT.
In the light of this dependence on Special Relativity, physicists are not likely to abandon it unless it is observationally disconfirmed and there is an observationally adequate theory available to replace it. In fact, there is a theory that is not merely observationally equivalent to the Special Theory, but also observationally superior to it, namely Lorentzian or neo-Lorentzian theory. Lorentz’s theory is regarded by many physicists who have studied Lorentzian theory, such as J.S. Bell, to be observationally equivalent to the Special Theory. However a Lorentzian or neo-Lorentzian theory is, in fact, observationally superior to the Special Theory (a fact that Bell, surprisingly, did not point out), since a Lorentzian theory, in contrast to the Special Theory, is consistent with the relations of absolute, instantaneous simultaneity implied by the EPR correlations that were observed in Aspect’s confirmations of Bell’s theorems. Special Relativistic QFT is no less disconfirmed by Aspect, et al. than is Special Relativity. Physicists do not appreciate the fact that a (non-orthodox) QFT can be formulated in terms of a Lorentzian theory, in which case it would avoid both disconfirmation by the Bell-Aspect observational data and the criticism of the untenability of the epistemological basis of the Special Theory.
One reason the Bell-Aspect experiments do not cause worry among most relativistic quantum field theorists is that the discussion of the Bell-Aspect experiments is isolated from the discussions of relativistic theories and is confined (for the most part) to discussions of non-relativistic quantum mechanics. There may be good reasons for this. But it may also reflect the worry that physicists do not know how to solve the problem of reconciling the Bell-Aspect experiments with relativistic QFT.
An even more ‘‘glaring’’ problem that a Lorentzian theory of absolute time can solve is that orthodox (special relativistic) QFT has not been fully or successfully ‘‘relativised’’. The absolute simultaneity implied by either collapse or non-collapse interpretations of QM, shows up in orthodox QFT as instantaneous relations (e.g. causal relations or correlations) among space-like separated regions associated with commuting or anti-commuting operators. Since the ‘‘special relativistic’’ ingredients in orthodox QFT are the same as those implied by a space-time formulation of Lorentzian theory, one can formulate a Lorentzian QFT that both explains and predicts the apparent Lorentz invariance and other ‘‘relativistic effects’’ that are observed, and yet is also theoretically and observationally consistent with instantaneous causal relations and correlations (see Chapter 3 for a discussion of the required Lorentzian formulation of QFT).
Physicists who work in the area of General Relativity know that the Special Theory has been surplanted by the General Theory of Relativity (GTR) and that simultaneity does not have the relativity attributed to it by the Special Theory but instead is absolute in the ‘‘cosmic time’’ which emerges through a cosmological application of GTR. However, QFT does not involve GTR and specialists in QFT do not address or take into account the absolute simultaneity relation that belongs to GTR-based cosmogenies (which we discuss in the next section).
It may be concluded that the main reasons many physicists still hold to Special Relativity are (1) an insufficient awareness of the epistemological and other philosophical problems with Special Relativity; (2) the isolation of the discussion of the Bell-Aspect observations from relativistic QFT; (3) the neglect of GTR by specialists in QFT, since GTR is not a part of QFT; and (4) the lack of familiarity with Lorentzian theories and consequent unawareness of how a Lorentzian QFT would not be faced with the manifest problems of orthodox, relativistic QFT. We hope that the discussions in this volume of the epistemological problems with Special Relativity, the discussions of the disconfirmation of the Special Theory by Aspect’s confirmation of Bell’s theorems, the discussion of the absolute simultaneity relation in GTR, and the discussion of Lorentzian theories, will help physicists who still adhere to the Special Theory to become more aware of these issues and to enable them to formulate more theoretically and observationally adequate theories.
Part IV
An explanation of why many philosophers of time remain wedded to the relativity of simultaneity could in part be that there has developed in twentieth century philosophy of time a habitual or even ‘‘orthodox’’ belief that absolute simultaneity and a tensed or (to borrow McTaggart’s convenient nomenclature) A-Theory of time go hand in hand, and that relative simultaneity and the B-Theory go hand in hand. But this ‘‘habit of belief’’ originated with the lay-physicist’s belief that the basic contrast in the theory of time is between ‘‘the flowing Newtonian time that contains relations of absolute simultaneity’’ and ‘‘the tenseless four-dimensional spacetime of Minkowski’’ and that physics presented one with a choice between one or the other. But while A-Theorists are arguably committed to a rejection of Einsteinian or Minkowskian relativity, the B-Theory does not in fact require relativity, since a space-time formulation of Lorentzian theory and even of Newtonian absolutism can be given, and there is nothing in positing a preferred foliation of space-time that commits one to objective tenses or temporal becoming. A-Theorists’ commitment to tense and temporal becoming may make them more open to absolute simultaneity, but the B-Theory is consistent with either relative or absolute simultaneity. If this ‘‘habit of belief’’ remains operative among B-Theorists who reject absolute simultaneity, then the problem is the lack of a sufficient knowledge of contemporary physics.
The problem here is, in a sense, the reverse of the first problem we mentioned above, namely, physicists’ lack of awareness of the many arguments that philosophers have provided against the epistemology, philosophy of language, and ontology presupposed by the Special Theory. The most widespread belief among philosophers is that contemporary physics has proven that simultaneity is relative either in Einstein’s sense that there exists no preferred reference frame or in Minkowski’s sense that there is no preferred foliation of space-time.
In fact, by the early 1920s this claim had been undermined due to the cosmological application of Einstein’s 1915 General Theory. Einstein’s cosmological model of 1917, based on his GTR, and Alexander Friedman’s cosmological model of 1922 (which is now recognized to be the sort of general relativistic cosmological model that is pertinent to our universe) imply a privileged or preferred foliation of space-time. Although the general relativistic space-time manifold can in theory be sliced up arbitrarily, there obtain de facto boundary conditions which determine a preferred foliation. The hypersurface of homogeneity and isotropy is the preferred hypersurface for the formulation of the laws of physics and the measurement of space and time. For example, the statement that the Big Bang occurred 13.7 billion years ago is not based on a measurement relative to any arbitrary reference frame, but to the privileged reference frame, the frame of homogeneity and isotropy, and is therefore absolute. It is regularly noted that a special relativistic or Minkowski metric can be defined infinitesimally close to any point in a universe with a Freidman metric, even though only a Friedman metric applies to the universe itself. The metric that describes the universe determines its spatio-temporal structure, and Friedman’s spatio-temporal structure includes an absolute reference frame, the frame of homogeneity and isotropy. It has often been commented by physicists that Einstein’s GTR thus reintroduced the relations of absolute simultaneity that his STR had denied. In fact, the idea that the hypersurface of homogeneity is the privileged frame, which determines absolute temporal and spatial measurements, has been a part of graduate textbooks on General Relativity or cosmology going back to the 1920s.
Thus, philosophers who embrace relativity because they are under the impression that the evidence of physics implies it are quite mistaken; in fact the opposite is true. Similarly, philosophers who hold to a tenseless or B-Theory of time for the reason that it is implied by Einstein’s 1905 theory or Minkowski’s 1908 theory are unjustified in so doing because the evidence of physics does not in fact imply that those theories are true. Einstein’s 1905 theory and Minkowski’s 1908 theory are ‘‘vacuum solutions’’ to Einstein’s GTR, that is, solutions that hold only if there is no matter in the universe.
The notion that a Friedman universe has an absolute hypersurface of simultaneity remains debatable only in the sense that our universe is not perfectly homogeneous, so that the concept of the hypersurface of simultaneity is the concept of an abstract hypersurface that results from averaging out the variations in the homogeneity of matter on very large scales. Whether or how one can derive a surface of absolute simultaneity in the strict (rather than ‘‘averaged out’’) sense is a matter that is up to debate. Some physicists adopt a ‘‘York slicing,’’ but it is not evident that this resolves the problem of the surface of absolute simultaneity being a concept that relies on the ‘‘averaging out’’ of inhomogeneities.
General Relativity is not the only physical theory developed after 1905 or 1908 that falsifies or casts doubt on the relativistic concepts of simultaneity. Louis De Broglie in 1928 and David Bohm in 1952 developed an interpretation of quantum mechanics that implies that there is a strict plane of absolute simultaneity, in the same sense as Lorentz’s and Newton’s in respect of it being a unique, universal, instantaneous plane of simultaneity that is non-local and space-like. De Broglie’s and Bohm’s theories of absolute simultaneity were largely ignored until J. S. Bell wrote a series of essays about them in the 1960s, which were collected into his 1987 book Speakable and Unspeakable in Quantum Mechanics. Since 1987, the number of adherents to a de Broglie-Bohm interpretation of quantum mechanics has been increasing steadily, as one finds the number of articles about the de Broglie-Bohm theory in physics journals growing from year to year. Several contributors to this volume, Valentini, Maudlin, Smith, and Callender are adherents to the de Broglie-Bohm interpretation of quantum mechanics. Even some competing interpretations of quantum mechanics, namely, those that involve a collapse of the wave function, imply absolute simultaneity, since the collapse of the wave function is instantaneous. The experimental confirmation of Bell’s theorem by Aspect and others implies that there is an instantaneous, non-local, space-like relation of simultaneity that coincides with EPR causal correlations (where ‘‘cause’’ is defined in a counterfactual sense, along lines such as suggested, e.g. by David Lewis). In this volume Maudlin’s essay discusses the most recent experimental findings to date, which give us some idea of the price that must be paid by those who insist upon the relativity of simultaneity in quantum mechanics.
Accordingly, philosophers who believe that simultaneity has the relativistic nature described in Einstein’s 1905 paper or Minkowski’s 1908 paper make manifest the fact that more education is needed about contemporary physics. If physicists need more education in philosophy, philosophers, especially philosophers of time, need more education in contemporary physics.
Part V
The fact that many philosophers need to become more acquainted with the theories of current physics, theories that assert or imply that simultaneity is not relative in the sense of Einstein’s 1905 paper or Minkowski’s 1908 paper, makes a volume of essays such as this one useful for philosophers of time and philosophers in general. The same holds for physicists, even if for different reasons. It is appropriate (if coincidental) that the publication of a work that subjects the thesis of the relativity of simultaneity to a critical analysis should fall on the centennial anniversary of Einstein’s 1905 essay.
This is the first collection of essays (of which we are aware) that is devoted, for the most part, to arguing that simultaneity is absolute. It is also a collection of essays that include writings in both philosophy and physics, perhaps erasing the distinction between them, at least in some cases. All of the chapters are original creations for this volume, some reflecting the cutting edge of research and reflection on the question of absolute simultaneity. Almost all are convinced that the received view that simultaneity is not an absolute relation is not only unwarranted but false. It is our hope, therefore, that this collection will lead to a better understanding among both philosophers and physicists of the problems inherent in making certain assertions about Einstein’s theory of the relativity of simultaneity.
William Lane Craig
Quentin Smith
Notes
Isaac Newton (1966) Sir Isaac Newton’s ‘‘Mathematical Principles of Natural Philosophy’’ and his ‘‘System of the World,’’ trans. Andrew Motte, rev. with an Appendix by Florian Cajori, 2 vols., Los Angeles: University of California Press, 1, p. 6.
A. Einstein (1981) ‘On the Electrodynamics of Moving Bodies’, trans. Arthur I. Miller, Appendix to Arthur I. Miller, Albert Einstein’s Special Theory of Relativity, Reading, Mass.: Addison-Wesley, p. 393.
Tyler Burge (1992) ‘Philosophy of Language and Mind’, Philosophical Review 101, 49.
See Quentin Smith (1998) ‘Absolute Simultaneity and the Infinity of the Past’, in Robin Le Poidevin (ed.), Questions of Time and Tense, Oxford: Oxford University Press.
See William Lane Craig’s chapter in this volume. Also see Quentin Smith (2000) ‘The Inconsistency of STR and the Tensed Theory of Time’, in L. Nathan Oak-lander (ed.), The Importance of Time, Dordrecht, The Netherlands: Kluwer Academic Publishers, and Quentin Smith (1993) Language and Time, Oxford: Oxford University Press.