Simply put, the Schrödinger wave equation shows that the evolution of a particle’s quantum state through time is both continuous and thoroughly deterministic.[5]  For physicists, ontological ambiguity in quantum theory arises not in the evolution of a particle’s quantum state, but when they attempt to precisely measure both the position and the momentum of a particle.

            (4) Quantum theory formalises this supposed ontological ambiguity through the Heisenberg uncertainty principle: which attests that, because of a given particle’s dual nature as both wavefunction field and point-particle, there exists an inversely proportionate possibility of measuring with precision either the particle’s position or its momentum:

x is the particle’s position along a spatial dimension.

p stands for the particle’s momentum.

ħ is the reduced Planck’s constant.

∆ (delta) represents a difference operator (e.g. x₂-x₁).

The Heisenberg uncertainty principle can also pertain to the relationship between a given particle’s energy and time.  In effect, it demonstrates the fundamental inability to know with absolute precision a pair of attributes of a given particle, if those attributes have a mutually dependent relationship within the mathematical formalism of the theory.

The probabilistic nature of quantum theory has led to all manner of philosophizing over its ontological implications.  Some extreme interpretations see these probabilistic wavefunctions and the role of the observer in forcing a particle to ‘leap’ from an indeterminate quantum state into a measurable state as an indication that consciousness (or at least a classical detection apparatus) plays a pivotal role in the generation of matter in the universe.[6]  More conservative interpretations see quantum theory as just as deterministic as Newtonian (and Einsteinian) classical mechanics.[7]  Most theorists would agree that the formalism of quantum states evolve in an exceedingly predictable fashion and can and have been used to make astonishingly accurate measurements, for example, Dirac’s equation for the magnetic moment of an electron.[8]

            The uncertainty principle implies another conundrum: according to general relativity, spacetime is smoothly curved.  But were we to examine space on smaller and smaller scales, accepting that even the gravitational spacetime field is subject to the uncertainty principle, as we approach the Planck scale, or 10^-33 centimetres, we would observe violent quantum fluctuations due to the incommensurabilities inherent in the wavefunctions of point-particles on such a tiny scale.  Smooth spacetime geometry breaks down and we are faced with what physicist John Wheeler has coined ‘quantum foam’.  Mathematically, this problem manifests when calculations attempt to synthesize the equations of general relativity and quantum mechanics: such attempts have so far produced physically impossible results.

            (5) Consistent with the ambiguity implied by field/particle duality, quantum theory can describe forces in terms of particles as well; these force particles are sometimes called ‘messenger’ particles, treating the force acting between two ‘matter’ particles as if it were a form of information.  For example, the theory can describe the strong nuclear force felt between protons and neutrons within the nucleus of an atom as the exchange of a messenger particle called a ‘gluon’.

            (6) Quantum entanglement: two or more spatially distinct particles may share the same quantum state (an aggregated wavefunction).  Therefore, it may be possible to make predictions about non-local, but entangled particles that, in certain respects, defy the law that no information can pass between entities faster than the speed of light.[9]

            (7) With the exception of the latest quantum field theories, quantum theory assumes a background of absolute time and space; it does not incorporate the constraints of special nor general relativity.  The most current quantum field theories do incorporate special relativity, thus a relativistic, albeit flat, four-dimensional Minkowski spacetime.  But no widely acknowledged quantum theory accounts for gravity: neither the force itself, hypothesized as a messenger particle called a ‘graviton’, nor the effects of spacetime curvature due to general relativity.

In addition to being an exceedingly effective explanation for the dynamics of the subatomic world, quantum theory has contributed to or given outright birth to many important technologies including: applied chemistry, nuclear fission, the laser, the diode, the electron microscope, and perhaps most significantly, the transistor, integral to all electronics including the computer.  Yet in spite of quantum theory’s demonstrated predictive accuracy, many theorists would agree that quantum theory feels somewhat like a kluge[10], with: its unwieldy proliferation of subatomic particles organized into symmetry groups[11]; the seventeen or so constants that must be inserted into the formalism and that the theory has no way of explaining through its own internal logic[12]; the qualification that only quantum theories that are ‘renormalizable’ yield workable results[13]; and lastly, the unsettling ontological ambiguity, mentioned above, between field and point-particle states.  Such theoretical deficiencies leave most theorists (and a fair share of experimentalists as well) understandably unconvinced that, with quantum theory to explain the subatomic world and general relativity to describe the universe as a whole, we currently have in our possession a plenary cosmology.

As for the key basic-level metaphors of quantum theory, I would argue that they are the particle and the field, which emerge from ħ, the reduced Planck’s constant[14], and ψ, the wavefunction, respectively, in the above formulas.  Of the three essences, substance, form, and patterns of change, energy, as a substance, plays the most prominent role.  (The essence of the quantum universe is also number, and in particular, complex-plane geometry and probability statistics).  Energy manifests in the form of particles, discrete quanta, based on the attributes—such as spin, charge, momentum—that inhere in the informational space that describes the entire system, for instance, the Hamiltonian[15] operator in the Schrödinger wave equation.  Similar to the energy-density tensors of general relativity, the geometry of quantum theory encodes information: the basket of attributes that embody a particle’s quantum state, e.g. its position, momentum, charge, and spin, among others.  Newton theorized light as tiny material corpuscles.  Maxwell’s theory of electromagnetism described light as a harmonically oscillating fluid-like field of electromagnetic energy.  Quantum theory seems to paradoxically offer up both: it defines light as a wavefunction and as a discrete quantum point-particle, the photon.  It even organises the particle groups that comprise the standard model into a spectrum.  The particles emerge at discrete positions along an energy spectrum of multiple fields that correspond to the various attributes that give the particles their distinct form.[16]

Consistent with this dualism, quantum theory can articulate change, then, in two forms: one, as the exchange of messenger particles (force) between matter particles[17]; and two, as the evolution through time of a probabilistic wavefunction.  Accordingly, one could argue that the great innovation (and ontological problematic) in quantum theory, in terms of its conceptual metaphors, is to introduce into its model of physical reality a new essence, a new pattern of change: namely, to formalize change as the event-structure itself.  We saw that Newtonian cosmology has an object-event structure: rigid bodies function as the figure and absolute space and a distinct space-like time serve as the ground.  Change is understood as motion of these rigid bodies through space.  Newtonian causation, therefore, concerns itself with location: causation is the forced movement of a rigid body to a new location.  Special and general relativity, on the other hand, employ a location-event structure: the ground is spacetime, and the figure, subordinate to the ground, is, in special relativity, plastic bodies with eyes, and in general relativity, energy itself.  Change is the motion of turning: rotations through spacetime, including motion along a curved trajectory (signifying the effect of the force of gravity).  In special relativity, we can read causation as the exchange of possessible attributes, such as length and duration, between the monocular plastic bodies.  In general relativity, causation is the forced movement of an energy-density entity to a new location within the informational space.  Each theory, then, privileges one event structure over another, conceptualizing being as well as causation primarily in terms of either figure or ground.  Quantum theory resists this commitment: it incorporates an event structure duality into its overall framework.  And what governs a flip from its location-event structure to one that emphasizes an object-event?  It would seem that such a turnabout occurs precisely through the act of measurement.

To do justice to quantum theory’s event-structure duality, we must describe causation in two antipodal yet complementary ways.  Before measurement, states are locations within fields ‘coupled’ to and ultimately manifesting as point-particles.  Change is motion, then, within this field: in the case of the Schrödinger wave equation, motion through the informational Hamiltonian space.  Change is also turning: the harmonic oscillations in the complex-plane of the probabilistic wavefunction field.  Accordingly, causation within the location-event moiety of the theory is forced movement to a new location.

The fact that wavefunctions embody statistical probabilities would seem to provoke the various non-deterministic interpretations of quantum theory.  Disquieted by the prospect of acknowledging the seeming import of a ‘throw of dice’ to reality, it is understandable that the proponents of such interpretations would make assertions similar to that made by Bachelard: that ‘ambiguity attaches not to our knowledge of reality but to reality itself.’[18]  Yet the probabilities of wavefunctions operate in the complex-plane, the realm of the square root of negative one, a mathematical imaginary used for mimicking precisely the motion of harmonic oscillation.  Wavefunctions, as such, have relevance solely to the informational spaces that allow physicists to make predictions about the physical universe, not directly to the physical universe itself.  Furthermore, one could argue, as Lakoff and Johnson do, that the mathematics of probability rely on yet another metaphor to be meaningful, the metaphor that equates causation with correlation.  Lakoff and Johnson write:

The Causation Is Correlation metaphor is at the heart of the concept of probabilistic causation.  The concept of probabilistic causation is a complex concept.  It is composed of Causation Is Correlation plus another very common metaphor, our principle metaphor for probability, namely, Probability Is Distribution. […] The Distribution Of An Occurrence In The Past For A Population → [maps to] The Probability Of Such An Occurrence In The Future For An Arbitrary Individual In That Population.  This metaphor is so common that it may be perceived as a truth rather than a metaphor.[19]

In this reading, probabilities are not absolutely random: they map from aggregates of past observation, from a body of historical experience.  As such, wavefunction fields are a conceptual means for accommodating a greater degree of information within the quantum theoretical model, rather than actual physical entities.  This, in turn, allows for a greater degree of accuracy in making predictions about the physical universe.  In this sense, determinism is the capacity for a theory to accommodate more information, to have a broader explanatory scope.  Accordingly, one could argue that quantum theory, in spite of its probabilistic component, is more deterministic than Newtonian cosmology.[20]  The old question, inspired by quantum theory, about whether the fundamental objects in the universe are fields or particles traditionally yields the paradoxical answer: both.  Reading the fields and particles of quantum theory not as real physical entities but as conceptual metaphors yields a different answer to the question: neither.

In the object-event moiety, the one corresponding to what quantum theorists call ‘state reduction’ or the act of measurement[21], attributes are possessions: particles possess charge, spin, mass, momentum, and various other attributes.  Change is replacement: particles lose and gain attributes; particles are even created and annihilated within the roil of the quantum foam.  As such, the object-event moiety declares causation to be exchange: matter particles exchange force particles, which manifests as particle interaction.[22]  In the ‘quantum leap’ from wavefunction locations to particle exchange that occurs as a consequence of the act of measurement, we see yet another metaphor for causation emerge from the theory: causation is progeneration.  The informational fields, in a certain sense, give birth to measurable particles.  It is the interanimation between these three contrasting causation metaphors: the location-event causation of the quantum field, the object-event causation of the quantum particle, and the progeneration causation that issues from the event-structure duality hinging on the act of measurement that, taken together, grant quantum theory its robustness in explaining the subtleties of the universe on subatomic scales.  Ironically, it is also this muddle of causation metaphors that makes quantum theory feel, for both physicists and laymen, like a kluge.

The almost universally accepted standard model of quantum theory came to maturity in the seventies.  Since then, the more ambitious theoretical physicists have concerned themselves with scenarios that arise when the theory of the very large, general relativity, and the theory of the very small, quantum theory, come into direct conflict.  These scenarios arise when physical phenomena are very large (e.g. high energy densities) and very small simultaneously.  Two such scenarios that preoccupy contemporary physicists are: black holes, where massive amounts of matter get compressed into a quantum-sized space; and the split-second immediately following the Big Bang, where the entire universe was compacted into a comparably microscopic extent.  In these physical extremes, both theories break down and, as such, provide a strong incentive for physicists, ever the extremophiles, to concoct a new theory, one that reconciles quantum theory with general relativity, and thus would allow them to explore with greater predictive power these exotic physical scenarios, black holes and the very early universe.

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