“If philosophy is interpreted as a quest for the most general and comprehensive knowledge, it obviously becomes the mother of all scientific inquiry”.1
Assessing influence merely in terms of impact upon the number of other lives, undoubtedly the most influential person of the 20th century is to be found among the terrible trio of dictators, Adolf Hitler, Joseph Stalin, and Mao Tse Tung. Intellectual or (to use an unfashionable term) spiritual influence is not a quantifiable effect of this kind; it can be gauged only more or less imprecisely and impressionistically. Nonetheless, it can be fairly said that in the initial decades of the 21st century the outlook of nearly everyone has been shaped, even if only in reaction to it, by the work and influence of Albert Einstein. Naturally, the claim is most directly confirmable by the present state of physical theory, where consequences of Einstein’s achievements extend to literally every aspect of the current understanding of nature’s most basic entities and processes. Nearly the same might be said for his purported failures, ranging from the critique of quantum mechanical completeness to the introduction of the cosmological constant. More broadly considered, spillovers from both achievements and failures have been developed into technologies, those ubiquitous today (lasers, GPS) and those promised for the future (quantum information transmission and processing).
Still, over and above any impact on science or technology, in his lifetime and continuing today, Einstein, like Freud, is one of few thinkers associated with a fateful alteration of human awareness. Whereas Freud pried open the Pandora’s box of the unconscious, Einstein transformed the concepts of space and time, among the basic constituents of thought. To many, then, and still today, this most fundamental revolution is an unwanted dislocation, an unfathomable, even rude, intrusion into a complacent trust that experience of the everyday world has been, and will continue to be, a reliable template for cognition of nature. As a later, and second chapter, quantum mechanics further reinforced the estrangement from the world as it appears introduced by relativity theory. The consequences of these two epistemological ruptures still play out in remarkable ways in the arenas of contemporary physical theory. But Einstein’s transformation of the concepts of space and time has ramifications extending to human culture as a whole, as Picasso and Braque seem to have recognized with cubism.2
Taking the sage advice to focus on deeds, rather than words, on which achievement should emphasis be placed? An earlier era turned to the special theory of relativity. Positivists pointed to Einstein’s identification of Hume and Mach as anti-metaphysical precursors for dismantling absolute time into the relativity of simultaneity. No doubt they also expected that his critique of quantum mechanics would surely fade away with the passage of time. But ever since John S. Bell reconsidered the EPR argument in the mid-1960s, this expectation has proven faulty. Downstream consequences of Einstein’s ideas and opinions regarding the incompleteness of quantum mechanics have overturned the once-hegemonic reign of complementarity, prompting a number of novel interpretations of quantum mechanics.
Realist tendencies in the foundations of quantum mechanics take inspiration from Einstein’s storied confrontation with Bohr. Such tendencies uphold the existence of an external world independent of the observer, regard physical theory as the description of this mind-independent world, and even adopt a conception of physical state in which quantities have definite values at all times independent of any act of measurement. Quantum entanglement, brought to attention by EPR as an intended criticism of quantum mechanical completeness, is now a primary focus of investigation in the burgeoning field of quantum technology and information theory, not to mention foundational pursuits such as quantum decoherence. Beyond the theories of relativity and quantum mechanics, a case might be made that attention should be paid to accomplishments that Einstein would dismiss as Gelegenheitsarbeit, that is, works performed as the occasion arose. Among these must be counted the 1905 hypothesis of the existence of light quanta, the 1917 derivation of Planck’s law that introduced the concept of stimulated emission, and the first recognition of quantum statistics in 1924. The expanse of Einstein’s influence and legacy is simply too vast for an accurate overview. In lieu of any more comprehensive summation, consideration here is given to just three areas, both physical and philosophical, where his impact is, or should be, readily recognized: 1) the further developments in what he termed his “lifework”, general relativity; 2) the pursuit of theoretical unification in fundamental physics; and 3) the innovative understanding of the scope and limits of physical theories that can, with certain provisos, be recognized as a “realism”.
For much of its first half-century, the general theory of relativity stood well outside the mainstream of theoretical physics. Due to its limited contact with the empirical world (until the 1960s there were few observational tests of the theory), to its unusual mathematical demands, and to the fact that theoretical attention shifted to quantum mechanics and its applications in the mid-1920s, many theorists regarded it as a mainly mathematical theory of little physical relevance beyond its small corrections to the much simpler Newtonian theory of gravity. Astronomers proved an exception, particularly after 1929 when Hubble provided convincing evidence that the universe is expanding; his famous graph related distance of galaxies linearly to their speed of recession. Neglect from physicists was only reinforced for several more decades as the center of theoretical gravity turned in the 1930s to the newly discovered complexities of the atomic nucleus, and in the 1950s to the high-energy physics of particle accelerators and the failing theoretical attempts to comprehend an ever-expanding catalogue of particles. As a result, curious graduate students encountered general relativity either on their own or in mathematics departments where it was considered a formal science largely divorced from observations and the rest of physics. Even at Princeton University, next door to the Institute of Advanced Study, the physics department did not offer a full year course on general relativity until John Wheeler did so in the academic year 1952–1953.3 During this period so few physicists worked on general relativity that one of them (Peter Bergmann) reportedly quipped, “You only had to know what your six best friends were doing and you would know what was happening in general relativity”.4
It is not as if there was no theoretical work to be done. On account of general covariance alone, core concepts of general relativity required critical scrutiny: Is there a meaningful (i.e., generally covariant) notion of the gravitational field’s local energy density? What are “observables” in general relativity? Does general covariance have any physical significance, and if so, what is it? How can general relativity be formulated without violating general covariance in a way that reconciles it with quantum theory? These and similar foundational pursuits, to one or another extent, continue to be explored. On the experimental side, there were other questions to be answered: Would new terrestrial experiments demonstrate the predicted yet still unobserved (until 1960) gravitational redshift? Does gravitational radiation really exist? What possible astrophysical sources might produce detectable gravitational waves?
Fittingly, two surprising observations moved general relativity again to the forefront of theoretical physics. The first was the discovery of enormously energetic quasi-stellar radio sources (quasars) in the early 1960s. The discovery prompted an initial theorem by English mathematician Roger Penrose showing that a sufficiently massive spherically symmetric star, having radiated away enough thermal energy, will gravitationally contract to a physical singularity at Schwarzschild radius r = 0.5 Analyzing the properties of space-time with new mathematical methods, Penrose in collaboration with Stephen Hawking subsequently proved that physical singularities occurred generically in general relativity and are not, as many had earlier believed and as Einstein surely would have preferred, mere coordinate artifacts of the high degree of symmetry required by the Schwarzschild solution. A second telling observation was the accidental discovery in 1964 of the cosmic microwave background (CMB), a remarkably uniform 2.7 K across the entire sky. The CMB is fossil radiation produced as the universe cooled, permitting radiation to decouple from matter some 300,000 years after an initial violent event. The discovery amply confirmed the hypothesis of a Big Bang universe and ruled out rival static or steady state cosmological models. Cosmologists in 1992 identified tiny fluctuations in this primordial radiation as the seeds of formation of galactic structure in the universe. The study of anisotropies in the CMB continues today to be at the forefront of observational cosmology, a data-driven established branch of physics, assisted by satellites (COBE, WMAP, Planck, Webb) advanced technologies and general relativistic models of an expanding universe.
One hundred years after its birth, there has been a tremendous growth in the understanding of general relativity and of its relation to experiment. The theory continues to pass the most exquisite tests; in May 2011 NASA announced the results of satellite (Gravity Probe B) measurements precisely confirming the frame-dragging precession effects near a rotating mass first pointed out by Einstein in 1913.6 General relativity is a lively field of experimental and theoretical research in astrophysics, cosmology, and the dynamics of the early universe. It is used in studying stellar structure and the formation of neutron stars, pulsars, and black holes. It is also at the center of three disciplines that were largely speculative or didn’t exist fifty years ago: black hole physics, gravitational wave research, and inflationary cosmology. These will be briefly reviewed here.
Near the end of Chapter 6, it was noted that Einstein returned to the Schwarzschild solution in April 1939 with a paper in Annals of Mathematics arguing that the so-called Schwarzschild singularities do not exist; in particular, he argued that the total gravitational mass within a given radius of a contracting spherical star cluster would always remain below a certain bound for any realistic system of solar masses. The existence of such a bound would mean that gravitational collapse would cease and the Schwarzschild radius would never be reached. Ironically, within a few months of Einstein’s paper, Robert Oppenheimer and his student Hartland Snyder published a paper (appearing on September 1, the day WW II began in Europe) claiming that, according to general relativity (and excluding various possible interrupting processes), a sufficiently massive spherical star, having exhausted its thermonuclear resources, would gravitationally contract indefinitely to its Schwarzschild radius. In doing so, it would “cut itself off from the rest of the universe”,7 producing what is known today as a “black hole” – the term coined only in 1967.8 As Oppenheimer and Snyder indicated, a black hole is a body created by the gravitational implosion of a massive star with gravity so strong that it is surrounded by an event horizon, a region across which things can enter but from which nothing, not even light, can escape. Today, from the observed motions of gas and stars, it is generally assumed that supermassive black holes (millions or even billions of times more massive than the Sun) lie at the center of most galaxies.
Einstein never directly responded to the Oppenheimer-Snyder paper. But his aversion to singularities was well-known, often expressed, and well-summarized by the relativist Peter Bergmann, one of his assistants in Princeton in the late 1930s:
It seems Einstein was always of the opinion that singularities in classical field theory are intolerable … because a singular region represents a breakdown of the postulated laws of nature…. (O)ne can turn this argument around and say that a theory that involves singularities, and involves them unavoidably, moreover, carries within itself the seeds of its own destruction.9
The seeds of destruction sprouted within general relativity in the 1960s as Roger Penrose proved that a singularity exists within every black hole, and then Penrose, Hawking, and Robert Geroch proved theorems demonstrating the existence of singularities in a wide class of solutions to the Einstein field equations of gravitation.10 It is not entirely certain that Einstein would have been dismayed. His last opinion on the matter seems to suggest that he thought singularities in general relativity might be avoided by either denying the validity of the gravitational field equations in the case of “very high density of field and matter” or, reminding that general relativity presumes an unaesthetic separation of “gravitational field” and “matter”, by holding out the hope that in a unified theory eliminating this dualism, no singularities would arise.11 Today it is widely accepted that general relativity does not coherently extend to the smallest scales and highest energies of the Planck regime, the theoretical meeting place of gravity, quantum mechanics, space and time (10−33 cm; 10−43 sec.; 1019 GeV). One commonly encountered goal of the program of quantum gravity is to demonstrate that at these scales, singularities are theoretically removed by the disappearance of the space-time continuum, replaced perhaps by a discrete structure or a structure from which space and time emerge. In any case, Einstein’s antipathy to singularities is well represented by Penrose’s cosmic censorship conjecture (1969), affirming that a singularity cannot be “naked” but must be “clothed” behind a horizon so that it remains invisible to observation.12
A black hole described by the Schwarzschild solution is static, but a more realistic scenario of gravitational collapse to a black hole will be rotational, creating a spinning object. Roy Kerr in 1963 found another exact solution to the Einstein field equations describing the space-time geometry surrounding an electrically neutral spinning black hole; Kerr’s solution was generalized to a charged configuration by Ted Newman in 1964.13 Remarkably, the Kerr-Newman description of the space-time surrounding a spinning black hole can be specified by only three numbers: the object’s mass, its angular momentum, and its charge. In the early 1970s, Jacob Bekenstein showed that black holes have an entropy proportional to the surface area of their horizon, and though very cold, radiate and so have a temperature; the temperature of a small black hole of only three solar masses was estimated to be less that a millionth of a degree above absolute zero. Hawking and others subsequently developed the “laws of black hole mechanics” in terms of an analogy to thermodynamics.14 In general relativity, the mass of a black hole is the same quantity as its total energy, so its mass plays the role of thermodynamic energy, while a black hole’s surface gravity is analogous to temperature, and the area of its event horizon is analogous to thermodynamic entropy. On the assumption of black hole entropy, Bekenstein in 1972 and Hawking in 1974 formulated an analogue of the second law of thermodynamics showing that black hole entropy will not decrease as matter falls across the event horizon.15
Hawking then was able to theoretically characterize the process by which black holes radiate by pointing to a well-known aspect of quantum theory: particle pair production due to quantum energy fluctuations in empty space. According to quantum field theory, pairs of particles and their corresponding antiparticles are constantly created by energy fluctuations; they promptly annihilate each other due to their opposite charges, hence these particles are called virtual. According to Hawking, when this process occurs at the horizon of a black hole, it can lead to the radiation of a real particle, and the eventual complete evaporation of the black hole. Consider a pair of low mass virtual particles (say, a neutrino and its hypothetical antiparticle, an antineutrino) created at the horizon. In the Hawking process, one will have energy –E, the other energy E. Supposing the one of energy –E falls inwards to the black hole, the other may escape to become a real particle (since its annihilating partner has disappeared); this particle would be observed as Hawking radiation. As the black hole will have to pay the energy debt brought in by the negative energy member of the pair, the outgoing radiation will carry off energy from the black hole. While the process occurs at a stunningly negligible rate, over eons of time (many times longer than the age of the universe), the mass and horizon of a black hole will shrink, leading ultimately to the black hole’s evaporation. Of greater theoretical consequence is that Hawking radiation suggests also that all information regarding the quantum state of the particle falling into the black hole is irretrievably lost. That is a problem for quantum mechanics, since despite its probabilistic character, in principle quantum information is never lost: from complete information about how a process ends – its final state – one can always reconstruct how it began – its initial state (this assumes, as quantum mechanics does, that probabilities of all possible processes must always sum to 1).
In sum, if information is truly lost, quantum mechanics is strictly inconsistent with black hole thermodynamics and its basis in general relativity. The so-called black hole information paradox, once thought resolved in the 1990s, has been revived most recently as one of the central problems of theoretical physics.16
After the completion of general relativity in 1915, Einstein sought on Machian grounds to find global (cosmological) solutions to the gravitational field equations. As was common at the time, he assumed the universe to be unchanging and eternal at the largest scales. Seeking a static global solution in 1917, Einstein added a “cosmological term” to his field equations to counter the gravitational tendency of matter to clump together. The attempted “fix” was contrived, and couldn’t possibly work. Russian mathematician Friedmann would show a few years later that the most natural global solutions of the field equations, without the new term, correspond to a non-static universe either expanding or contracting. After Hubble provided convincing evidence of an expanding universe, Einstein retracted the new term in 1931.17 Curiously, his final pronouncement was not to condemn it on empirical grounds. Writing in 1945, he deemed it “possible from the point of view of relativity” but “to be rejected from the point of view of logical economy”.18
Recall that originally Einstein added the term to the left-hand side of the field equations,
Modern practice, however, places the term on the right-hand side,
where it represents the possible stress-energy of empty space (the quantum vacuum) thus contributing to the stress-energy tensor. If empty space is (as quantum theory requires) filled with vacuum energy, it will exert a repulsive “negative pressure”, a force indistinguishable from Einstein’s cosmological term.19 In short, if quantum theory is correct, the cosmological term is naturally included on the right-hand side of the field equations; moreover, the term represents an energy density of empty space with a constant value. It is a remarkable property of the vacuum that its energy density is not diluted with the expansion of space.
In its re-emergence, the cosmological constant has become a central thorn in the side of fundamental physical theory; Susskind recently termed it “the greatest enigma of theoretical physics”.20 According to quantum theory, vacuum energy arises from energy fluctuations rooted in the Heisenberg uncertainty relations. But if all theoretically possible contributions to vacuum energy stored in all known fields and particles are summed up (admittedly, these contributions are not theoretically well understood), an impossibly large value of vacuum energy density results. Beginning in the 1970s, the idea of supersymmetry was invoked to skirt this result. According to supersymmetry, every boson has a fermionic partner and vice versa; supposing fermionic and bosonic contributions to the vacuum energy to be of different signs, their respective contributions would exactly cancel. A significant difficulty with this putative solution is that supersymmetry has yet to be observed. Nonetheless for some decades many theoretical physicists believed that the value of the cosmological term, corresponding to the energy density of the vacuum, had to be zero; somehow the different contributions from all particles and fields would effectively sum to 0.
Then in 1998, two rival teams of astronomers revealed that observations of redshifts of light from the most distant supernovae pointed to an accelerating expansion of the universe; a completely unexpected finding, the two teams shared the Nobel Prize in Physics in 2011.21 Their finding suggests some kind of energy is fueling the increasing rate of expansion of the universe; this so-called “dark energy” is consistent with a very small, but positive, value of the cosmological constant.22 Moreover, taking the CMB to be a measure of the total energy in the universe after subtracting the total amount of matter (both familiar and “dark”) contained in galaxies and galaxy clusters (about 27 percent of the former), the remaining 73 percent of all that is believed to exist in the universe resides in the constant energy density of empty space, energy of the vacuum. Depending on how the various theoretical contributions to the vacuum are assessed, the observed value of the cosmological constant is outrageously smaller than the theoretically predicted value, anywhere from approximately 10−120–10−60 times less. With good reason, this mismatch has been called “the largest failure in physics, ever”.23 From a completely different direction, attempts to argue that the observed value of the cosmological constant must lie within anthropic bounds remain ill-defined and highly speculative (see §2 below).
Since the 1930s most cosmological models of an expanding universe have employed a particular class of general relativistic models, so-called Friedmann-Lemaître-Robertson-Walker (FLRW) metrics. FLRW metrics are standardly taken as the background model for the universe at the largest scales; such universes are exactly spatially homogeneous (with no center, and no distinguishing features) and isotropic (at any point all directions are equivalent). More realistic refinements are introduced by considering small perturbations of FLRW universes (see below). However the large-scale isotropy of the CMB, together with the cosmological principle (if isotropic for us, then isotropic for any observer), gave rise to the following questions: How can parts of the universe separated by great distances be so observationally similar? How might such an extraordinary degree of spatial homogeneity have been produced? In standard Big Bang models, the distances between regions observed similar today are so large that the regions could not have been in causal contact in the past. Any similarities observed between distantly separated regions would appear to be due to very special initial conditions in the early universe, a highly unsatisfactory situation for physical theory.
Furthermore, the universe is observed to be nearly flat at the largest scales; this means that the mean matter-energy density of the universe is incredibly close to the “critical” value at which the spatial geometry of the universe is Euclidean. But in general relativity, curved space is generic and flatness is a largely unstable exception away from which the universe will almost certainly evolve. As with Einstein’s cosmological constant, a fine balance is required to maintain flatness. As the mean density is related to the rate of expansion, if too large, it would have overwhelmed expansion resulting in a closed space with finite volume and no edge wherein parallel lines would be observed to converge. If the mean density is too little, expansion would have overwhelmed it and the universe would be infinite and open: parallel lines would be observed to diverge. The third possibility, that the large-scale geometry of the universe is Euclidean, corresponds to observation but appears to require another special initial condition, a highly fine-tuned flatness in the very early universe.
In 1980, particle physicist Alan Guth, working on another problem, posited a hypothetical vacuum energy in the very early universe driving a cosmic spatial expansion that would be both enormous and extremely rapid (an exponential function of time).24 Any mechanism of this kind itself requires a bit of fine-tuning (it must not end too soon; it must end when the universe is almost flat) but by rapidly stretching everything out and diluting space, inflation can in principle address the above two fine-tuning quandaries, widely called the “horizon” and “flatness” problems. While inflation is not a theory (there are literally hundreds of possible models of the mechanism producing inflation), it is widely accepted today that an era of inflation did occur in the very early universe. And it is widely believed that the observed value of the cosmological constant, accounting for the accelerating rate of expansion of the universe discovered in 1998, is a weakened relic of the much larger vacuum energy-producing inflation in the very early universe and then effectively switched off.
Traces of an inflationary epoch should show up in the CMB as slight density perturbations consistent with those observed (about 1 part in 100,000). These perturbations are theoretically produced by quantum fluctuations in an inflating sea of vacuum energy, with a distinct spectrum of nonuniformities produced by the different hypothetical mechanisms. The perturbations can be decomposed into scalar and tensor fluctuations; the former are energy density fluctuations that are scale-invariant (hence independent of the space-time metric). The latter arise from perturbations of the FLRW metric and its coupled energy-momentum tensor and are thought to give rise to gravitational radiation that cause a particular polarization pattern in the CMB. In March 2014 it was widely and dramatically reported that such patterns were observed in the CMB by the BICEP2 team, comprising the first direct observational evidence of inflation.25 If confirmed, the finding would have been an extraordinary achievement on two fronts: strong evidence of cosmological inflation, together with confirmation of the existence of gravitational waves. However, further analysis showed that the observed patterns were most likely produced by CMB interactions with intervening cosmic dust, and both claims were withdrawn within a year.
The hypothetical existence of gravity waves goes back to 1916. Exploiting an analogy to the way that a system of moving charges emits electromagnetic waves, Einstein predicted the existence of gravitational radiation.26 To be sure, Einstein had second and even third thoughts about the reality of gravitational waves, famously denying their existence in a 1937 paper with Nathan Rosen that, however, contained an error negating its conclusion.27 The reality of gravitational waves as a legitimate implication of general relativity was not fully accepted by the (very small) community of general relativists until the 1960s after systematic analysis of full nonlinear general relativity by Hermann Bondi and Roger Penrose. They found that changing gravitational fields created by moving masses create waves that propagate at the speed of light, slightly stretching or shrinking the distance between objects lying in their path. Unlike electromagnetic waves, gravitational waves are not vibrations in space-time but of space-time geometry. On account of its extreme weakness, gravitational radiation has been for one hundred years the last significant prediction of the general theory of relativity yet to be observed.
It has long been thought that a characteristic place to look for gravitation waves is a binary star system, two stars orbiting around a common center of mass like a spinning dumbbell, the paradigm of a quadrupole system. Indirect evidence for the existence of gravitational waves appeared in the discovery of the first binary pulsar system (PSR B1913 + 16) by radio astronomers Russell Hulse and Joseph Taylor in 1974; this is a pair of compact neutron stars orbiting a common center very rapidly (period of 59 milliseconds) and losing orbital energy. For their discovery, Hulse and Taylor were awarded the Nobel Prize in 1993. Theoretically, the diminishing orbital energy is radiated away as gravitational waves and observations over three decades have precisely confirmed the rate predicted by general relativity at which the system’s orbit is shrinking. However, this did not comprise a direct observation of gravitational waves.
On September 14, 2015, gravitational waves were detected by the advanced LIGO (Laser Interferometer Gravitational-Wave Observatory) scientific collaboration operated by Caltech and MIT. The signal, detected nearly simultaneously at LIGO observatories in Hanford, Washington, and in Livingston, Louisiana, had the expected sharp “chirp” signature of a violent event, identified as consistent with a computational model of the inspiraling and coalescence of two “surprisingly massive” black holes approximately 1.3 billion light years from Earth.28 Gravitational wave detection is not just another confirmed prediction of general relativity, for it opens an entirely new observational window into the early universe. Prior to 2015, all astronomical and cosmological observations were based on the electromagnetic spectrum from infrared to ultraviolet. It may well be that further observations of the CMB will not be sensitive enough to identify unmistakable evidence of inflation produced by primordial gravitational waves. But since these are slight ripples of space-time produced during inflation, it may be possible to “look behind” the CMB. Their direct detection would furnish an entirely new band of observation, theoretically extending back in time earlier than the formation of the CMB, produced when the universe first became transparent to light. It is widely hoped that gravitational waves will provide direct observational confirmation of an inflationary epoch in the very early universe, and possibly a means of choosing between the current plethora of inflationary models.
By contemporary lights, the unified field theory program occupying Einstein for three decades was a hugely premature, bound-to-fail search for the cosmic world order. It produced no new physics but only a trail of equations too unwieldy or complex to be solved. While Einstein worked in Berlin in the 1920s, before quantum mechanics had monopolized the attention of theorists, the unification enterprise could be viewed as a longshot pursuit of limited inherent interest. But with the discovery of the physics of the nucleus in the early 1930s, tolerance quickly ebbed for a program content to grapple purely formally with a unification of general relativity and classical electromagnetism. Several generations of physicists, schooled in the results-oriented pragmatism of particle physics, dismissed the later Einstein as a stubborn old man incapable of coming to terms with quantum mechanics while choosing to remain willfully ignorant of the exciting new physics of the atomic nucleus. By 1935, Robert Oppenheimer could aptly sum up the view of a large segment of the theoretical community in referring to Einstein (and his dogged pursuit of the unified theory program) as “cuckoo”.29 Freeman Dyson at the Institute of Advanced Study since 1948 relates a story with a similarly harsh assessment.30 On first arriving in Princeton, the young English mathematician and quantum field theorist was most eager to meet Einstein. He thought to prepare beforehand by reading Einstein’s most recent papers on unified field theory. Finding them to be “junk”, Dyson in embarrassment skipped his appointed meeting with Einstein, then carefully avoided making contact for the next seven years until Einstein’s death in 1955. Much later Dyson admitted to being under the influence of a certain arrogance inflicting the theorists who had just developed quantum electrodynamics, at the time the cutting edge of physical theory. Yet as late as the 1990s, particle physicist Abraham Pais – Einstein’s scientific biographer – could remark in a TV documentary:
If Einstein had stopped doing physics in the year 1925 and had gone fishing, he would be just as beloved, just as great. It would not have made a damn bit of difference.31
That Pais’s verdict represents the prejudice of his generation will be confirmed by even the slightest glance at the contemporary literature on foundations of quantum mechanics. But postwar theorists took an understandably dim view of seeking to unify fundamental laws through a speculative method relying on such a vague criterion as mathematical simplicity while ignoring the new frontier of high-energy experiments. The furthest reach of quantum theory through most of the 1960s produced a largely instrumentalist or descriptivist conception of physical theory, as the attempt to provide an adequate taxonomy for the proliferating data of elementary particles emerging in particle colliders. It was easy then to say of Einstein’s speculative method that physical theory is not like that – an ironic judgment since, by 1980 or so, much of fundamental physical theory had become like that. So rapid and prevalent was the new trend that already at the end of the 1980s, Harvard particle physicist Howard Georgi would satirize theorists engaged in pursuit of elegant geometrical unifications of all fundamental interactions, including gravity. According to Georgi, such theorists, led by the sirens of philosophical principles and mathematical elegance while ignoring the real physics of quantum mechanical interactions, suffered from an “Einstein Complex”, that is,
a desire to work on difficult and irrelevant questions just because Einstein did.30
The most prominent example of the contemporary unification program, in 1989 and today, is string theory, the favored candidate for a unified understanding of the basic laws of the universe. String theory (really superstring theory since it requires supersymmetry) is not so much a theory but a so-far-incomplete mathematical framework that makes no testable predictions. It poses questions of considerable philosophical interest about the scientific standing of theorizing that may only allow evaluation through methods of so-called non-empirical confirmation.31 When string theory is coupled with inflationary cosmology (and in particular, with so-called eternal inflation), quite another set of philosophical questions arises.32 Unless some principled reason is found to severely constrain the enormous number of string theories believed possible (admittedly a vague notion, but the range between 10100–10500 is widely bruited about33), each string theory may correspond to a bubble universe produced in the unending (“eternal”) process of inflation. An overabundance of different and distinct universes, each with its own particular values of the fundamental constants of physics, is said to “populate” the landscape of solutions of possible string theories. The result is the so-called “inflationary multiverse”.
How does any of this bear on Einstein’s legacy of unification? Recall Einstein’s seeming declaration of rationalist faith when characterizing the task of the physical theorist:
We wish not only to know how Nature is (and how her processes transpire), but also to attain as far as possible the perhaps utopian and seemingly arrogant goal, to know why Nature is thus and not otherwise.34
No less than an avowal of the principle of sufficient reason, it asserts the theorist is ultimately satisfied only when attaining the very apex of cognitive understanding. Admittedly, immediately following the quoted passage, Einstein quickly refers to this aspiration as “the Promethean element of scientific experience”, implying perhaps a rather unpleasant penalty for hubris. And as seen in Chapter 10, on various occasions Einstein took the opportunity to distance himself from any straightforward endorsement of this kind. As a “tamed metaphysicist” this rationalist aim is deemed a largely motivational and regulative injunction. Nevertheless, it might be argued that Einstein only articulated the most ambitious goal of physical theory since the rise of modern science, whether held consciously or unconsciously, realistically or only as a matter of aspirational faith. On the other hand with the inflationary multiverse, the hope to rationally understand the universe on the basis of a unified theory constrained only by fundamental principles and mathematical simplicity is radically changed, if not surrendered entirely. Consider the attempt to explain the values of physical constants and parameters that today must be put in “by hand” (i.e., with their measured values) in the standard model and in other areas of fundamental physics (such as the observed value of the cosmological constant). Under the mantra of “anything that can happen will happen an infinite number of times”,35 proponents of the inflationary multiverse seek to account for the particular values of constants and parameters we observe as a selection effect: e.g., the fact that the cosmological constant has the tiny value it is observed to have is simply a reflection of our existence: if it were otherwise, we would not be here to measure it. The implications of a sea change of this magnitude upon the very notion of what constitutes an adequate explanation in fundamental physics are currently under debate. It is certainly a “historic fork in the road” and, if taken, a “radical change” from the style of theoretical physics that Einstein exemplified.36
Readers of Arthur Fine’s The Shaky Game: Einstein, Realism and the Quantum Theory (second edition, 1996) will know that the view of science Fine recommends to philosophers as the Natural Ontological Attitude (NOA) is closely fashioned along the lines of a sympathetic portrayal of Einstein’s realism. NOA is a minimalist stance towards science. Both scientific realism and antirealism are distinguished from NOA by what they respectively add to the “core position” that characterizes NOA, namely
(to) accept the results of scientific investigations as “true”, on a par with more homely truths,37
i.e., statements of purported fact in ordinary discourse. The scare quotes around the term “true” receive comment below; the phrase “on a par” is elliptical for something like on a par with respect to the normally assumed trust that a statement is made in good faith, and on the basis of the kind of evidence that warrants its utterance. In placing statements of science on a par with those based on the evidence of the senses, NOA invokes the spirit of Einstein’s remark that “the whole of science is nothing more than a refinement of everyday thinking”.38 Neither scientific realism nor antirealism, what then is NOA? To Fine it is a “nonrealism”, others claim to find that “NOA is a thoroughly realist view”.39 Considering its pedigree, it seems more appropriate to view NOA as a realism, though not a thoroughly realist one. NOA’s realism is metaphysically deflated, taking its lead from a close analysis of Einstein’s responses to quantum mechanics. That analysis convincingly argued that Einstein’s metaphysically realist remarks are “not to be taken at face value”.40
Following Fine’s reconstruction, the core of Einstein’s realism is found not in any particular thesis or doctrine but in two critical moments operating in conjunction; together they enable “Einstein to use the vocabulary of metaphysical realism” but also “to pull its metaphysical sting”.41
The first moment is one of entheorizing. To “entheorize” is to specify a “family of constraints” governing what can be considered a properly realist theory. This is just the “programmatic” aspect of realism set in opposition to the perceived positivist irrealism and instrumentalism of quantum mechanics. In this book, these constraints are termed principles; they include observer-independence and property definiteness (the properties of physical objects have definite values, whether or not they are observed), causality in the sense that the laws of physics should permit univocal prediction of the state of a physical system from exact knowledge of the system at a given time, and a principle of separation, that physical systems are individuated by spatial separation so that an intervention made on one system has no influence on another spatially separate from it.
The list can be lengthened to include representation in space-time (the theory must describe physical phenomena in space and time), general covariance (in the sense that no fixed background space or space-time may appear in a theory), a monist principle that fields are primary (particles and their laws of motion are derivable from the laws of the field), and a principle of unification (that it is conceptually possible to comprehend all physical phenomena and interactions in a single but logically simple mathematical scheme). By suggesting a second-order set of requirements a theory should satisfy in order to be considered a viable representation of physical reality, the pivotal step of entheorizing has more to do with favored contours of understanding and intelligibility, what Toulmin once called “ideals of natural order”,42 rather than attributes of nature itself. It supports a characterization of quantum mechanics as an incomplete theory, and the attempt to portray its empirically confirmed predictions as those of a statistical averaging over the solutions of some underlying deterministic field theory. Characteristically, having laid out such a vision, Einstein will observe there is absolutely no compelling reason, conceptual or metaphysical, why such a world picture must be correct. This underscores the programmatic aspects. No a priori reason can be given that the posed list of constraints is correct or unique, or that any such list can determine a unique resultant theory; certainly more than one theory may satisfy all of a given list, and perhaps do so at the same time.
Nonetheless, there is a strong motivational reason to adhere to this program for realism. It lies in a complex conviction that the independently existing physical world is a highly complex riddle to be solved, that a solution exists, that without such a system of constraints, the number of possible theories is simply too vast to ever allow progress towards it, and finally that general relativity suggests a particular set of such constraints. Analogous to Planck’s striving for permanent features of the physical Weltbild, Einstein’s programmatic realism entertains theories subordinated to ideal regulative criteria based largely on the success of general relativity, in the hope of articulating a more unified image of nature consistent with that success.
The second dialectical moment, operating in tandem with the first, is one of meaning avoidance or deflection. Deflection signals Einstein’s refusal to engage on the traditional philosophical ground of realism, turning attention instead to whether a theory meets the necessary criterion of empirical success that alone merits appellation of the theory as “true”, with the appropriate scare quotes for emphasis. The deflecting move is found above all in Einstein’s rejection of the realist label, and of -isms more generally. The refusal is above all a rejection of realism’s account of a physical theory’s truth or approximate truth as the theory’s correspondence to, or isomorphism with, an external world structure that underlies and produces the phenomena of observation. Hand in hand with rejection of correspondence truth is a dismissal of the realist semantics of reference, that theoretical terms in true physical theories pick out precise structures in the world that are strongly similar to, if not exactly characterized by, the mathematical structure of the referring terms. In place of the usual realist semantics for truth and reference, deflection retains the use of the term “true” but when applying it to physical theories always appends scare quotes (as in the “core position”) to signal that its sole meaning can only be an aim of complete agreement of theory with the totality of observation, in short, empirical adequacy. Justification for this conception of the adequacy of physical theory is always qualified, but appears to be based on Einstein’s experience (above all, with general relativity) of the ability of such theories to obtain coordination with experience (confirmation) “with advantage” (mit Vorteil).43 The latter phrase is significant; “advantage” signals the programmatic entheorizing agenda, an oblique indication that a theory be
a conceptual model (Konstruction) for the comprehension of the interpersonal whose authority lies solely in its confirmation (Bewährung). This conceptual model refers precisely to the “real” (by definition), and every further question concerning the “nature of the real” appears empty.44
This passage, minus the deflecting bit about sole authority, well illustrates the sense in which Einstein is indeed the “paradigm realist”. With it, it is a prototypical manifestation of Einstein’s realism: not a metaphysical doctrine but a motivational impulse necessary to engage in science at all, accompanied by a fervent belief akin to a religious faith in the ability of thought to comprehend what is:
I have found no better expression than “religious” for confidence in the rational nature of reality insofar as it is accessible to human reason. Wherever this feeling is absent, science degenerates into uninspired empiricism.45
Although Einstein’s realism is a godparent of NOA, it is also clear that there are aspects of NOA lacking analogues or precursors there. The entheorizing and deflecting moves are projected by NOA into a broad and encompassing picture of science and its multifarious practices. It is a view of science broadly pragmatic, in the sense of Dewey. Indeed, like Dewey, NOA highlights “the social in science”; once that is taken into account “no further special framework is required for understanding scientific practice … nothing beyond the common framework of everyday pragmatism”.46 Diametrically opposed to everyday pragmatism, however, is the Einstein who called attention to “the Promethean element of scientific experience” and the one who could declare “our experience hitherto justifies us in believing that nature is the realization of the simplest mathematical ideas”, a proclamation as far from refined everyday thinking, and as metaphysical, as can be. Of course the term “our experience hitherto” refers here not to everyday sensory experience but to the retrospective assessment that the mathematical strategy of general covariance produced the winning ticket for his biggest success, the general theory of relativity (see Chapter 10).47
It is Einstein, the “tamed metaphysicist” or “enlightened rationalist”48 lurking behind the purple prose of the 1933 Herbert Spencer Lecture. Even as “enlightened”, it is a rationalism that cannot be deconstructed in quite the same way as his realism, i.e., as stemming from “the pre-rational springs of human behavior”.49 The philosophical passion for theoretical unity is an attitude integral to nearly all of Einstein’s many achievements. From his later failures, one can, as did several generations of physicists, dismiss this passion as simply tilting at windmills. On the other side of the coin, if their utterances are taken at face value, many in the current group of theorists seeking unity of the laws of nature lack Einstein’s intellectual humility in conceding that a methodology of mathematical speculation may simply be rationalist illusion. In something of the spirit of NOA’s “letting science speak for itself”, Einstein’s life and science exhibit a profound role for philosophy in understanding the practice of science. Whether or not this leads to an anti-naturalist picture of science, it reveals, as much as anything, that science is also a practice of faith (and hope) that the world is ultimately comprehensible in human terms. Getting the full picture matters. Einstein remains “the paradigm realist” from whom contemporary philosophy of science may still learn.
1Einstein, “Physics, Philosophy, and Scientific Progress”, 1950 speech delivered in English to the International Congress of Surgeons, Cleveland, Ohio. Text reprinted in Physics Today (June 2005), pp. 46–8; p. 46.
2See Miller, Arthur I., Einstein, Picasso: Space, Time and the Beauty That Causes Havoc. New York: Basic Books, 2001.
3Wheeler, John A., “Mentor and Sounding Board”, in John Brockman (ed.), My Einstein. New York: Vintage Books (Random House), 2007, pp. 27–37; p. 33.
4Reported in Pais, Abraham, “Subtle Is the Lord …” The Science and the Life of Albert Einstein. New York: Oxford University Press, 1982, p. 268.
5Roger Penrose, “Gravitational Collapse and Space-Time Singularities”, Physical Review Letters, v. 14 (no. 3), January 18, 1965, pp. 57–9.
6Gravity Probe B, in an orbit of 640 km, confirmed that the rotating Earth drags a tiny amount of space-time around with it. This is the so-called Lense-Thirring effect, after the two Austrian physicists who in 1918, with Einstein’s assistance, carried out the general relativistic calculation. See C.W.F. Everitt et al, “Gravity Probe B: Final Results of a Space Experiment to Test General Relativity”, Physical Review Letters, v. 106, 221101 (2011), 3 June 2011.
7Oppenheimer’s characterization in 1958, cited by Werner Israel, “Dark Stars: The Evolution of an Idea”, in Stephen Hawking and Werner Israel (eds.), 300 Years of Gravitation. Cambridge and New York: Cambridge University Press, 1987, pp. 199–276; p. 230.
8By John A. Wheeler in the Sigma Xi-Phi Beta Kappa Annual Lecture, American Association for the Advancement of Science, New York, December 29, 1967; see “Our Universe: The Known and the Unknown”, American Scientist v. 56, no. 1 (1968), pp. 1–20; p. 8.
9Bergmann, Peter, “Open Discussion, following papers of S. Hawking and W.G. Unruh”, in H. Woolf (ed.), Some Strangeness in the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert Einstein. Reading, MA: Addison-Wesley Publishing Co., 1980, p. 156.
10More specifically, they showed that space-time is not singularity-free if the following conditions all obtain: 1) the Einstein field equations; 2) a positive energy condition (gravity must act on everything as an attractive force, a condition violated by the cosmological constant); 3) strong causality (time travel is impossible); and 4) there must be a certain amount of matter in the universe. For details, see Earman, John, Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes. New York: Oxford University Press, 1995, Chapter 2.
11“On the ‘Cosmologic Problem’ ”, Appendix added to the second (1945) edition of The Meaning of Relativity, Princeton, NJ: Princeton University Press, Fifth edition, 1956, pp. 109–32; p. 129 and note, p. 124.
12See Clarke, Christopher J.S., “The Cosmic Censorship Hypothesis”, in George Ellis, Antonio Lanza, and John Miller (eds.), The Renaissance of General Relativity and Cosmology. Cambridge, UK: Cambridge University Press, 1993, pp. 86–99.
13See Melia, Fulvio, Cracking Einstein’s Code: Relativity and the Birth of Black Hole Physics. Chicago and London: University of Chicago Press, 2009.
14Bekenstein, Jacob D., “Black-hole Thermodynamics”, Physics Today (January 1980), pp. 24-31; Bardeen, John M., Brandon Carter, and Stephen Hawking, “The Four Laws of Black Hole Mechanics”, Communications in Mathematical Physics v. 31 (1973), pp. 161–70.
15Ibid., Jacob Bekenstein (1980).
16For a readable account, see Matt Strassler, “Black Hole Information Paradox: An Introduction”, https://profmattstrassler.com/articles-and-posts/relativity-space-astronomy-and-cosmology/black-holes/black-hole-information-paradox-an-introduction/. A recent speculative idea of Leonard Susskind and Juan Maldecena proposes to resolve the paradox while preserving consistency between general relativity and quantum mechanics has the moniker “ER = EPR”, wherein EPR correlations between two “entangled” black holes are established via an Einstein-Rosen bridge mechanism. See Tom Siegfried, “A new ‘Einstein’ equation suggests wormholes hold key to quantum gravity”, Science News, August 17, 2016: https://www.sciencenews.org/blog/context/new-einstein-equation-wormholes-quantum-gravity
17The original (1922, 1924) papers of Alexander Friedmann, together with Einstein’s appended notes, have been translated from the original German in Jeremy Bernstein and Gerald Feinberg (eds.), Cosmological Constants: Papers in Modern Cosmology. New York: Columbia University Press, 1986, pp. 49–67. This volume also contains a reprint of Hubble’s 1929 paper, “A Relation Between Distance and Radial Velocity Among Extra-galactic Nebulae”, Proceedings of the National Academy of Sciences v. 15, no. 3 (March 15, 1929), pp. 168–73. Einstein’s 1931 retraction appears in “Zum kosmologischen Problem der allgemeinen Relativitätstheorie”, Sitzungsberichte der Preußischen Akademie der Wissenschaften, Phys-Math. Klasse (1931), pp. 235–7.
18“On the ‘Cosmologic Problem’ ”, Appendix added to the second (1945) edition of The Meaning of Relativity, Princeton, NJ: Princeton University Press, 1956, p. 127.
19Recall (Chapter 6, note 56) that .
Space-time curvature not determined solely by mass-energy densities ρ but also by pressure, so Tμν can have the form ρ + 3P where P is the pressure. Cosmological (FRWL) models assume however a simple form of matter as a cosmological fluid with three non-interacting components radiation, vacuum energy however and pressure-less dust – since in ordinary astrophysical objects, pressure is negligible (P ≪ ρ). However, in empty space (the vacuum), consistency with the energy conservation requires pressure to be of the same magnitude as the negative density (PV = −ρV), and here the stress-energy tensor takes the form ρV + 3PV = −2ρV.
20Susskind, Leonard, The Cosmic Landscape: String Theory and the Illusion of Cosmic Design. New York and Boston: Little, Brown and Co., 2005, p. 11.
21See “The Nobel Prize in Physics 2011, Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess” at www.nobelprize.org/nobel_prizes/physics/laureates/2011/
22Λ = 8πGρΛ, where ρΛ is the energy density of the dark energy.
23Ohanian, Hans C., Einstein’s Mistakes: The Human Failings of Genius. New York: W.W. Norton and Co., 2008, p. 254.
24Guth, Alan, The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Reading, MA and New York: Addison-Wesley Pub. Co., 1997.
25See “Space Ripples Reveal Big Bang’s Smoking Gun”, The New York Times, March 18, 2014; BICEPS 2 abbreviates “Background Imaging of Cosmic Extragalactic Polarization”, second experiment, at the South Pole.
26Solving the weak field gravitational equations in linearized approximation in 1916, Einstein discovered the solutions to have the property of being transverse waves of spatial strain traveling at the speed of light. The paper contains several mistakes.
27See Kennefick, Daniel, Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves. Princeton, NJ: Princeton University Press, 2007.
28As the orbiting distance decreases, the orbital speeds increase, causing the frequency of the gravitational waves to increase until the moment of coalescence. See “Laser Interferometer Gravitational-Wave Observatory (LIGO) Scientific Collaboration” at www.ligo.org.
29Dongen, Jeroen Van, Einstein’s Unification. Cambridge, UK and New York: Cambridge University Press, 2010, p. 186.
30As related in Smolin, Lee, “In Search of Einstein”, in John Brockman (ed.), My Einstein: Essays by Twenty-Four of the World’s Leading Thinkers on the Man, His Work, and His Legacy. New York: Vintage/Random House, 2006, pp. 109–20; pp. 110–11.
31Cited by Landsman, Nicholas Pieter (Klass), “When Champions Meet: Rethinking the Bohr-Einstein Debate”, Studies in History and Philosophy of Modern Physics v. 37 (2006), pp. 212–42; p. 213.
32Georgi, Howard, “Effective Quantum Field Theories”, in Paul Davies (ed.), The New Physics. New York: Cambridge University Press, 1989, pp. 446–57; p. 456.
33See Dawid, Richard, String Theory and the Scientific Method. New York: Cambridge University Press, 2013.
34See Susskind, Leonard, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design. New York: Little, Brown and Co., 2006.
35Weinberg, Steven, “Living in the Multiverse”, in Bernard Carr (ed.), Universe or Multiverse? New York: Cambridge University Press, 2007, pp. 29–42; p. 31.
36“Über den gegenwärtigen Stand der Feld-Theorie”, in Festschrift Prof. Dr. A. Stodola zum 70. Geburtstag. Zurich und Leipzig, Germany: Orell Füssli Verlag, 1929, pp. 126–32, p. 126.
37Guth, Alan, “Quantum Fluctuations in Cosmology and How They Lead to a Multiverse”, arXiv:1312.7340v1 [hep-th] December 27, 2013.
38“We now find ourselves at a historic fork in the road we travel to understand the laws of nature. If the multiuniverse idea is correct, the style of fundamental physics will be radically changed”. Steven Weinberg, in an interview with Alan Lightman on July 28, 2011; quoted in Lightman, The Accidental Universe: The World You Thought You Knew. New York: Vintage/Random House, 2013, p. 5.
39Fine, Arthur, The Shaky Game: Einstein, Realism and the Quantum Theory. Second edition. Chicago: University of Chicago Press, 1996, p. 128.
40Ibid., p. 176: “NOA also is trusting in so far as it regards the sciences themselves as a refinement of common human practices; as Einstein remarked, ‘The whole of science is nothing more than a refinement of everyday thinking’ ”. That quote is taken from the Sonia Bargmann translation of “Physics and Reality”, 1936, in Albert Einstein, Ideas and Opinions. New York: Crown Publishers, 1954, p. 290.
41Musgrave, Alan, “NOA’s Ark: Fine for Realism”, Philosophical Quarterly v. 39 (1989), pp. 383–98; p. 383.
42Fine, The Shaky Game, p. 111.
43Ibid., p. 106.
44Toulmin, Steven, Human Understanding: The Collective Use and Evolution of Concepts, vol. 1. Princeton, NJ: Princeton University Press, 1972.
45“Elementare Überlegungen zur Interpretation der Grundlagen der Quanten-Mechanik”, in Scientific Papers Presented to Max Born. Edinburgh: Oliver & Boyd, 1953, pp. 33–40; p. 34.
46“Reply to Criticisms”, in Paul A. Schilpp (ed.) Albert Einstein: Philosopher-Scientist. Evanston, IL: Northwestern University Press, 1949, p. 680.
47Einstein, letter to M. Solovine, January 1, 1951, in Albert Einstein: Letters to Solovine. New York: Philosophical Library, 1987, p. 119.
48Fine, The Shaky Game, p. 188.
49cf. Barker, Peter, “Einstein’s Later Philosophy of Science”, in P. Barker and C. Shugart (eds.), After Einstein: Proceedings of the Einstein Centennial Celebration of Memphis State University. Memphis, TN: Memphis State University Press, 1981, pp. 133–45; p. 144, n. 13.
50Bachelard, Gaston, “The Philosophic Dialectic of the Concepts of Relativity”, in Paul A. Schilpp (ed.), Albert Einstein: Philosopher-Scientist. Evanston, IL: Northwestern University Press, 1949, pp. 565–80; p. 580.
51Fine, The Shaky Game, p. 110.