"Questions of Causation"

 

Sarah Jones Nelson

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February 8, 2019 Revised Version

 

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I. Causal Systems

 

The origins and evolution of spacetime raise open questions of causation. How does emergence from an entangled initial state explain a classical universe described by Einstein gravity? How will quantum gravity modify our picture of the early universe? How can string theory as quantum theory with classical origins describe temporal change?

 

Our motivation is coherence in initial-state physics as prolegomena to a new paradigm of phenomena prior to fossil evidence from the cosmic microwave background (CMB). We correlate the philosophy and physics of mechanisms at initial and possible preceding states of confirmed observables such as gravitational waves.

 

Ludwig Wittgenstein's positivist fallacy that physical facts are all the facts contradicts the physics of quantum entanglement and acausal time evolution with dynamical complex information emerging from a classical origin inaccessible to   the senses.   We investigate the limits of sense data in assessing nonphysical facts such as   the EPR paradox in order to formalize intelligible standards of verification that separate physics from the metaphysics of events without observational means to refute theory.

 

We describe initial-state properties of the observable universe derived from the Planck map. The empirical task is to analyze the measured distribution of temperatures and related physical mechanisms of what happened roughly   13.7   billion   years   ago in order to construct a physical foundation of theory. The ontological task is to separate physics from metaphysics and to formalize categories differentiating observable from unobservable phenomena. An empirical foundation of physical theory presupposes tangible evidence of physical reality, the evolving substance perceived through the senses.

 

René Descartes was the first philosopher to analyze the nature of evidence the senses can verify as reliable truth. He was the first mathematician to claim that the mind can deduce all physical laws for any possible world or universe, an idea that inspired Wilhelm Leibniz to formalize physical and metaphysical laws of possible worlds or universes. His contemporary Isaac Newton knew as well as Descartes, however, that the senses can be unreliable in ascertaining any or all the laws of this universe or any possible other. Newton refuted Cartesian metaphysics but believed that God’s untestable providence was the cause of gravity.

 

Foundational physical theory results from observable facts, but all the facts are not yet in on the truths or causes of physical reality. We do not yet understand the causal structure of spacetime; we have not yet invented an observational technology to probe the dynamics of the expanding phase, the dark sector, and black hole interiors. Nor have we evolved as a species to infer from sense data whether physical law can unify quantum and classical physics, explain the causes of nonlocality, or describe an infinite landscape of universes with an open set of nonphysical properties that contravene the evidence of the senses.

 

Strong physical foundations of theory uphold existing theory that works and demonstrate a consistent mathematical logic of numerical causation. Now, observables are indispensable to foundational criteria in verifying or falsifying theory. For example, neutrino oscillations are early enough observables of initial-state evidence for the emergence of gravity at the initial phase. Where observables elude sense data, we infer measures of physical or mathematical probabilities in cases like entanglement in quantum field theory (QFT) as the framework of string theory - or any metaphysic of a possible infinity of worlds.

 

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II. Physics and Metaphysics

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We distinguish physical   from   metaphysical   facts   in    order   to   categorize   data from the CMB, our best empirical evidence on   which   to   build   physical foundations of theory for the observable evolution of spacetime. But the standard cosmological model is incomplete. The existence of a “big bang” is conjectural. We have no verifiable analysis of classical and quantum dynamics of the primordial state or preceding events explaining the mechanisms that caused acceleration of cosmic expansion as an emergent phenomenon.

 

The standard assumption that quantum mechanics should apply at the primordial regime and on all scales is contested, with the possible exception of gravity. The gravitational effects of dark matter and dark energy on structure formation are unknown. The ontology of the wave function is unintelligible, the past history of random states incoherent, acausal nonunitary time evolution a deep mystery. The horizon and interior of black holes are uncertain. The core conjectures of string theory are incomplete because sense data do not yet exist to test it; fundamental unobservables outside the (3 + 1)-dimensional will limit any theoretical framework of testability until equations within the theory can account for temporal dynamics. All of the above suggest the metaphysical character of contemporary physics.

 

Classical and quantum physics present observable data that still elude a complete and coherent cosmological model. Toward empirical coherence, we seek data for quantum or entangled properties of an emerging initial state consistent with Einstein gravity. Are the related causal dynamics of spacetime observable on a boundary shared by quantum and classical systems? Gerard ‘t Hooft suggests the possibility of theories in which quantum and classical systems can co-exist on a boundary allowing dual mappings of both systems describing the same time evolution. Can the underlying forces of quantum gravity as an emerging system in a classical regime be testably formalized toward this end? How can purely physical theory describe the initial boundary conditions of quantum gravity?

 

Observations show empirically discernible patterns in the Planck map that may explain important aspects of these boundary conditions. The key code for the CMB is a spherical harmonic transform. Primordial adiabatic perturbations exist in the power spectrum. Empirically the CMB is consistent with Gaussianity and statistical isotropy (SI). SI assumes there is no obviously special place on the sky; the CMB is consistent with primordial 3D-mass distribution with the power spectrum. Looking at the Gaussian distributions we see properties of a flat universe with a striking distribution of temperatures, adiabatic perturbations, and single field slow-roll (SFSR) inflation in an early universe dominated by displacement of a scalar field. SFSR inflation has the empirical consequence of B-modes, and the quest for B-modes is motivated by SFSR inflation. What set the initial conditions for SFSR?

 

SFSR inflation looks like pre-1925 quantum mechanics (QM) with many experimental values resulting from a century of atomic spectroscopy. The first patterns were recognized by Johann Balmer in 1885 and explained by Niels Bohr in 1913. The Bohr quantization seemed pulled out of nowhere. The Einstein A coefficient then realized an indeterminate nature, which explained a great deal, but ended incoherently. QM (1925-1930) changed everything. Does the history of the idea of inflationary cosmology resemble aspects of this scenario?

 

Since the 1980’s inflationary cosmology has been the dominant paradigm. Many find inflation a compelling story about a phase transition that produced a period of expansion. Is it an empirically true story of a flat, homogeneous and isotropic universe, or is it a metaphysical story of key elements in the data we sense? Can we start inflation from the Planck scale? Physical theory in precision cosmology requires foundational, testable initial conditions. It requires explanation of phenomena such as the future, density, the dark sector, quantum gravity, primordial gravity waves, and the horizon problem. Critics of inflation such as Paul Steinhardt claim that it explains none of these things any more than the nearly scale-invariant density fluctuation spectrum or red tilt, a small deviation from scale-invariance. We do not know how the inflation homogeneity required for inflationary dynamics came about any more than how the flatness of the potential required for inflation arose.

 

Inflation originally assumed a phase transition requiring bubbles – SFSR inflation – at the core of its story with the consequence suggesting the problem of a too-smooth universe. Quantum fluctuations brought into the theory present the problem of the way they evolve in the inflation field. Also, SFSR inflation requires initial conditions that seem improbable.

 

Is this a pragmatic critique? Few theories are thought to have the advantages of inflation. Looking at the distribution in the skies, we see signs of prediction. For many, alternatives to inflation seem incorrect. But the real problem is the second law of thermodynamics, which states that things get more random going forward and less random going backwards. The key here is gravitational degrees of freedom. Inflation does not work in time reversal, nor does it account for the empirical structure of the observable universe.

 

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III. Testability

 

Any version of the standard cosmological model requires testable initial conditions that predict a certain outcome. Steinhardt's critique of the inflationary model shows that exponential inflation can produce any outcome, depending upon how the conditions are defined or thought to separate quantum effects from the classical background. Furthermore, for   any    prediction   of     inflation not confirmed by observation, we get a model that agrees with it because a resulting multiverse can suggest any model in which the initial conditions of energy density grow more slowly than Planck density. Inflation’s theoretical language of fine-tuned initial conditions implies states of existence for which we do not yet have measures. Also, for reasons shown ahead, we need a conformal picture of galaxies inside and outside our particle horizon. Can the inflationary model give us this picture?

 

In observational cosmology we seek millions of numbers from the CMB and large-scale structure. What are our options for solutions that differ from the inflationary paradigm? Look at the rings in the CMB sky. Are they signatures of a bubble collision from early- universe phase transitions? Related open questions of the causal dynamics of dark matter and dark energy in turn raise the question as to whether string theory can resolve these problems. Or shall we turn to the bispectrum and primordial non-Gaussianity?

 

How can string theory formalize the physics of singularities, the mechanisms of expansion, and fluctuations in the cosmic microwave radiation that inflation must explain? Is conformal invariance a fundamental feature of the elementary constituents of physical reality that it suggests?

 

What of the trans-Planckian effects we see in the initial conditions from perturbations? Is there a possible residual from a pre-existing phase? The effects are most pronounced at the largest scales. The mathematics of Mendelian genetics was too sophisticated for most scientists; nontrivial patterns of heredity were thus ignored for 35 years. Has the community ignored residual patterns in the CMB?

 

About trans-Planckian effects, does any amount of inflation exist to account for the early universe before our observable universe? Is any possible residual observable from a pre-expanding phase? Imagine the future of the observable universe by looking back into the initial past. What parameters and conditions can be inferred after the expanding phase? Can we start inflation from the Planck scale? A sharp distinction still obtains from Einstein onward between inflation and theoretical structure. The inflationary model may turn out to be a metaphysical, untestable concept predicting select aspects of physical reality.

 

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IV. Untestability

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Apart from inflationary theory, how do we explain what happened before the initial singularity? What events may have preceded the primordial scenario, and what is its remote future? Sir Roger Penrose has advanced a theory of conformal cyclic cosmology (CCC) to describe the pre-phenomenology of the observable   universe. CCC is a radical proposal that now exceeds the known parameters of conventionally testable cosmology. At present its equations are incomplete; the model is speculative. But it may help explain the   nature of   the    primordial scenario and our   remote future by a conformally smooth evolution - solving the horizon problem as to why the universe is smooth and uniform - by using classical equations.

 

The current aeon in the CCC picture of a Λ-driven exponentially expanding remote future predicts the gradual fade-out of mass via the Higgs mechanism, with a collision between super-massive black holes spiraling into each other in the form of gravitational radiation, and with the crucial presence of the cosmological constant. CCC corresponds to present expectations for the remote future of our own universe; the previous aeon’s exponential expansion eliminates an inflationary phase for a beginning. CCC also explains the remarkable suppression of gravitational degrees of freedom that give rise to the puzzlingly extreme low entropy of the initial singularity.

 

In CCC mathematical equations for a crossover from each aeon to the next follow the requirements of Einstein’s general relativity: a positive cosmological constant Λ and conformal regularity at crossover. Uncertainties remain, however, about fade-out particle masses in the very remote future, and the re-emergence of mass early in the subsequent aeon from which particle masses at the crossover must vanish in order for it to be conformally smooth. Also, CCC requires a key role for dark matter, a natural partner for gravity, but dark matter must decay away for CCC to be consistent. In this sense the equations of CCC relate to issues in particle physics.

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We can argue for alternative explanations in the CMB sky of the presence in M-values of signals in concentric sets, the rings predicted by CCC from black hole mergers in the previous aeon. These rings may produce a slight, distant increase or decrease in temperature at a more uniform and slightly lower variance than the norm. The signals appear present in a highly non-isotropic distribution at variance with the conventional picture of temperature fluctuations resulting from random quantum events in an inflationary phase.

 

Theorists seek more empirically testable explanations for events during or before the initial state. We may need an exact quantum mechanical result around the singularity or some noncollapsing initial condition. The equations point to the fact that if the cosmological constant is right, we see an eternity. Based on the starting point of the initial singularity we may see the Weyl curvature at zero. Conformally can we extend a dense, hot initial state to something before it by means the inflationary model lacks? Conformal physics makes sense of conformal continuation in which something existed before the initial state. Gravitational waves might give us data for looking back before this state.

 

Bouncing cosmology, an alternative to CCC and inflation, is one such possible scenario constrained by CMB data. The bounce scenario describes phenomena of contracting and expanding phases that explain smoothness and flatness by looking at two regions of the CMB sky on opposite sides and extrapolating back, assuming no inflation and no singularity at variance with classical laws. Nonsingular bounce models can allow sufficient time for the two sky regions to make causal contact and smooth before the CMB decoupled and captured the density fluctuations, so that light or any other force can transverse the distance since the initial state. Also, the smoothing or contracting phase contains fluctuations in rare patches that fade out and end, thus averting the multiverse problem in inflationary cosmology.

 

Models of a nonsingular cosmological bounce at variance with standard singularity theorems modify contracting dynamics of collapse to a point for a big bang singularity. In Neil Turok’s bounce model, the effects of quantum mechanics produce instead the rebounding dynamic that precludes such a singularity. Anna Ijjas and Paul Steinhardt by contrast use the equations of classical mechanics to propose a bounce by way of a null energy condition violating, with energy more gravitationally self-repulsive than vacuum energy, sufficient to produce a bounce, and below the Planck scale at finite scale factors that avert collapse to a point and predict and an expansion in a classical scalar field. This predicts a stable, smooth transition from the bounce to expansion confirmed by observations of an isotropic, flat homogeneous universe.

 

Peter Graham, David Kaplan, and Surjeet Rajendran propose the possibility -- during a contracting phase in semi-classical general relativity -- of four compact spatial dimensions at each point within a vector field of vorticity that dynamically violates the NEC in said dimensions and thus averts a singularity in such a way as to solve the cosmological constant. They propose also the theoretical relevance to traversable Lorentzian wormholes.

 

Theoretical physicist Juan Maldacena’s AdS/CFT correspondence, the holographic conjecture of 1997, relates gauge theories in particle and condensed matter physics to gravity at the quantum scale. He describes traversable wormholes as asymptotic objects of a manifold realized in Anti-deSitter space. Wormholes in theory connect discrete points of spacetime and exhibit the properties of teleportation caused by two interacting boundaries in a gravitational regime of entangled double or coupled quantum systems that transfer complex information bits through a wormhole. This is a geometrical theory in Hilbert Space with a smooth classical transfer between the two interacting systems. A wormhole can be caused by two entangled black holes as quantum systems analogous to a collapsing universe.

 

A wormhole interior corresponds to a black hole interior; perturbations caused by the quantum process of interactive coupling can shift back the black hole horizon to make the interior more observable. This step from theory toward the phenomenology of black holes predicted by Stephen Hawking occurs within an entangled Hawking radiation. Theoretically, Maldacena’s conjectures show promise for black hole observables that might confirm the empirical power of string theory and correlative mechanisms of quantum phenomena with classical properties. Fine-tuning remains to be done involving degrees of freedom for the AdS/CFT correspondence to tell us more about gravity and the observable universe we perceive through the senses. For this reason it forms a new metaphysic of rigorous mathematical logic toward observable phenomena: the best of many possible worlds in progress.

 

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V. The Future of Metaphysics

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Visions of wormholes and black holes as objects of physical theory reflect the Gedankenexperiment that led Einstein to discover general relativity. Did classical mechanics exist before his thought experiments? Yes, theoretically, in the possible world of metaphysics. But since the early 20th century, Wittgenstein’s extremely influential dogma that the sensed physical world is “everything that is the case” has trivialized metaphysics as “nonsense.” Our first modern metaphysicians, Descartes, Spinoza, and Leibniz gave us deeply nontrivial analysis and logic in the rationalist tradition that separated the natural philosophy of possible worlds from empirical science. Newton first formalized this separation between the disciplines; Locke, Hume, and Kant followed suit.

 

An analogous, less coherent separation between theoretical and empirical physics now divides the scientific community. As a result, an impasse between the nonphysical, mathematical facts of untestable but provable theory, and the testable facts of physical reality, has shaken the foundations of scientific truth. A new metaphysic of observables within theory will gradually resolve the conflict. Meanwhile, the core conjectures of string theory and string dualities will divide theoretical from the falsifiable science of experimental confirmation.

 

The criterion of falsifiability defining science grew from positivist orthodoxy that the evidence of the senses is necessary and sufficient to verify any scientific truth of factual statements about the cosmos, laws of nature, and the set of all integers. This century-old expression of naïve realism is insufficient to possible-worlds and quantum physics presupposing dimensions, infinities, and causal complex dynamics for which observational and analytical tools in computational physics are under construction.

 

A coherent paradigm of verification must now clarify the limits of the senses in assessing evidence in theoretical and empirical science. Bayesian analysis in itself is insufficient to predict the uses of imagination and Gedankenexperiment unconstrained by probability and standard rules of testability for nonphysical phenomena. Consider the difference between abstract and realistic art with impressionism on the boundary between abstraction and figuration. An analogous difference separates theoretical from empirical physics. Mathematical physics lives on the boundary between these two bodies of evidence as proof or law of nature.

 

Einstein once stated that no answer can be admitted as epistemically sound unless justified by the observable facts of experience. Karl Popper upheld the corresponding positivist orthodoxy that “a theory must be falsifiable to be scientific.” His claim lacks knowledge of 21st-century mathematical physics and theoretical science contradicting the dogma of epistemic physicality.

 

A systematic, coherent, and intelligible reinterpretation of Enlightenment metaphysics within evidentiary categories of scientific investigation must now parametrize the boundary between physical and nonphysical aspects of phenomena clarifying the difference between theoretical and empirical facts. Criteria of verifiability will correspond to the categories of investigation that necessarily refer either to physical or metaphysical properties of the relevant phenomena, with boundary conditions defined for phase-transitional aspects of mathematical physics that bridge the two categories of explanation and prediction.

 

Metaphysics is nontrivial. Every physical theory representing an actual infinity assumes Plato’s metaphysic of an unobservable infinite set of numbers existing in the possible world of ideal forms. As noted above, Leibniz used Descartes’ platonism in his conjecture of possible worlds, ours being the best of all. Voltaire savaged him in Candide as the naïve Dr. Pangloss oblivious to the grotesque world of suffering for which Leibniz coined the concept of theodicy. But Voltaire missed his underlying message: Newton’s laws demonstrate that ours is the best possible world or universe divinely perfected as if by Ockham’s razor. Also, Voltaire made the category mistake of confusing mathematical logic with moral discourse of good and evil.

 

Leibniz’s contemporary Isaac Newton lamented in the 3rd edition of the Principia that although he had explained phenomena “of the Heavens and of our sea by the power of Gravity,” he refrained from assigning cause to gravity. “Certainly this power,” he wrote, “arises from some Cause which penetrates to the center of the Sun and Planets….And which Acts not according to the Quantity of the Surfaces of the Particles upon which it acts (as Mechanical Causes used to do) but according to the Quantity of the solid Matter: And where Action is extended every Way to immense Distances, so as events do decrease in the duplicate Proportion to those Distances….But the Cause of these properties of Gravity I have not yet been able to draw from the Phaenomena: And I do not make Hypotheses.   For   whatsoever is not drawn from the Phaenomena is to be called a Hypothesis. And Hypotheses, whether they be Metaphysical, or Physical, or of Occult Qualities, or Mechanical, have no place in Experimental Philosophy.”

 

Early Enlightenment ideas of causation originated in natural philosophy that contradicted the mechanical theory of Descartes and Galileo, his contemporary co-inventor of unprecedented precision in a mechanical philosophy to give rise to infinitesimal calculus and analytic geometry. Galileo discovered a revolutionary system of mathematical analysis based upon measurable laws of observation contradicting the standard formalisms of Aristotle’s Physics and Metaphysics.

 

In 1633, Descartes self-censored Le Monde, ou Traité du monde et de la lumière, his treatise on light: a new Copernican philosophy consistent with Galileo’s proof of causal laws describing the observable mechanics of matter. Both had hoped to make nature intelligible without referring to natural law philosophy as the mirror of moral law in a dangerous heresy of causal principles for which morality was inconsequential.

 

The 17th-century revolution in particle physics resulted from the first patent of the telescope by the German-Dutch spectacle maker Hans Lippershey, in 1608, soon after the first performance of Shakespeare’s Hamlet in Oxford, where Francis Bacon was busy inventing moral realism at Magdalen College. The telescope ushered in the material culture of a new discipline: mathematical physics. This formally separated physics from natural philosophy at variance with Galileo’s departure from Aristotelian and biblical polemics of causation. Physics now became a function of observations, not moral discourse. The act of testable observation thus became necessary and sufficient to explain the properties of laws known by observational tools, not the innate truths of reason.

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From Aristotle to Aquinas, Newton, and Hume, the tacit metastructure of causation has always signified oneness: a unified, self-consistent system of deeply connected dynamics hidden from sense perception. From Genesis to the inflationary scenario, the founding narratives of causation have always presupposed one arbitrary acausal point at the beginning of spacetime unobservable and inaccessible to the senses. The fact of unobservable initial conditions continues to complicate questions of evolving physical systems of initial-state quantum mechanics that emerge from a   classical system in which, according to Netta Engelhardt, the behavior of null hypersurfaces determines gravitational dynamics.

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The standard cosmological model reflects indeterminate aspects of Enlightenment physics and philosophy of causation. Factual evidence for any initial state remains conjectural and open to conflicting interpretations of quantum and classical phenomena describing an inflationary, conformal, bouncing, or infinite possible worlds preceding the primordial state of evolving observables from the CMB.

 

Because factual evidence for the physical and nonphysical properties of any initial state is indeterminate, observables are necessary but insufficient to foundational criteria for verification or falsification of theory. Popper’s criterion of falsifiability for scientific proof constrains methods of verifying nonphysical initial-state phenomena described, for example, by AdS/CFT and gravity relating black-hole, particle and condensed matter physics prior to the expanding phase.

 

Coherent physical theory of indeterminate or unobservable phenomena predicts unbiased results that confirm experimental observation where theory is incomplete, for example, from very early neutrino oscillations, as Edward Witten once explained to me. Where observables elude the community, we infer probable states in such cases as dynamical emergence from quantum entanglement. Where the acausal phenomena break down known laws, we go back to the cosmic drawing board unimpeded by the rule of falsifiability.

 

The new physics must formalize coherent initial-state classical and quantum theory. We require a new causal paradigm bridging philosophy and the physics of quantum gravity in initial and possible preceding states of confirmed observables. Verifiable theory describing gravitational waves from a prior state, however, must first explain both observable and unobservable causal dynamics for the Book of Nature to be read between the lines.

 

Causal dynamics and causal structures of physical systems are fundamental to underlying forces hidden from sight.   If, in fact, primordial gravitional waves will explain events before the initial state, the scientific community must be prepared with a coherent new paradigm of pre-phenomenology for the coming revolution in computational physics. Popper’s criterion of falsifiability is necessary for sense-data verification, but it makes unrealistic demands upon theory, for example, of unobservable mechanisms now being probed by computational tools.

 

We live in a world of paradox. Newtonian physics cannot explain the causal complexity of quantum and classical systems Newton had no idea exist. If Hawking and Penrose were right that only a theory of initial conditions has predictive power, we must pay attention to computational physics of physical evolution from initial dynamical states at spins and speeds as unobservable as gravitational waves to Newton. Leibniz produced the first coherent unified description of physical and metaphysical causal laws we now know are approximate at best. Will the standard cosmological model be modified by a computational revolution in mathematical physics? In this the best of all possible worlds, anything is possible.

 

Sarah Jones Nelson

Department of Philosophy

Princeton University

Princeton, New Jersey

 

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Acknowledgments

 

In appreciation of participants at CMB@50, Department of Physics, Princeton University, 2015: Neta Bahcall, Wendy Freedman, Juan Maldacena, Lyman Page, James Peebles, Roger Penrose, Martin Rees, Suzanne Staggs, David Spergel, Paul Steinhardt, Christopher Tully, Erik Verlinde, Herman Verlinde, and Edward Witten. I am grateful also to Freeman Dyson and Karen Uhlenbeck.

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