In string theory lore, this all changed in 1984 when Michael Green at Cambridge University, who had been working with John Schwarz for several years on improving the theory, published what Brian Greene has dubbed a ‘landmark’ paper[9] that claimed to resolve the problems that had marginalized string theory for the past ten years.  In a gesture that perhaps mimics the inflationary auto-promotionalism of the information technology industry, many string theorists refer to the appearance on the physics scene of this revised theory by Green and Schwarz as ‘the first superstring revolution’.  Green and Schwarz accomplished this by incorporating supersymmetry into the theory (hence the ‘super’ in ‘superstring’).  Supersymmetry is a principle that provides for the pairing of fundamental particles, organized in the standard model into the two moieties of bosons and fermions[10], and that offers the promise of integrating bosons and fermions in a mathematically cohesive way such that many of the inconsistencies in quantum field theory—or string theory—may cancel out.  Supersymmetry also suggests the possibility of the unification of all five fundamental forces into what is sometimes called ‘supergravity’.  But as a consequence of the manner in which it organizes the particle groups (known as ‘supergroups’), supersymmetry predicts the existence of a new array of partners for the known quantum particles—what are sometimes referred to as ‘sparticles’.[11]  The incorporation of supersymmetry into Green and Schwarz’s new superstring theory allowed the model to reduce the number of posited spacetime dimensions from twenty-six down to ten.[12]  It also did not predict particles of negative mass, such as tachyons.  Another hallmark of their new superstring theory was that it recalibrated the string tension from the relatively large (and untenable) scale of the original bosonic string theory down to about the Planck scale, or 10^-33 centimetres.  Like bosonic string theory, superstring theory predicts the graviton.  Green and Schwarz’s superstring theory, which has since come to be known as Type I string theory, reinvigorated string theory’s claim to be a theory of quantum gravity.

Shortly after Green and Schwarz’s superstring theory reignited a flurry of interest within the theory community, other theorists proposed alternative and potentially competing versions of superstring theory—whose composition depended largely on how supersymmetry was incorporated into the theory’s overall structure.  These competing versions of superstring theory are known, respectively, as: Type IIA, Type IIB, Heterotic O(32), and Heterotic E₈ x E₈.[13]  Further work in the late 1980s and early 1990s showed that, although they share certain features, the various theories diverge enough to suggest a significantly contrasting picture of physical reality.  Brian Greene describes the mood within the string theory community since then: ‘This has been an embarrassment for string theorists because although it’s impressive to have a serious proposal for the final unified theory, having five proposals takes significant wind from the sails of each.’[14]  For physicists, the criteria by which they judge a theory require that it have a certain inevitability, a clear sense of uniqueness.  That five reasonably plausible versions of string theory have come to coexist suggests that these theories, although they share a strong conceptual continuity, may also have built into their internal logic too many degrees of freedom, too many possible permutations and thus physical consequences, which directly contradicts the principle of inevitability.  The embarrassment for string theorists lies in these versions’ excessive flexibility: they lack the requisite rigidity for generating (or retroactively ‘predicting’) the observed particularities of the physical world.

Work on the five competing versions of string theory continued more or less independently until 1995, when, at the premier annual string theory conference (called, appropriately enough, ‘Strings’, and held that year at the University of Southern California), Edward Witten, from the Institute for Advanced Study, presented a paper[15] that launched what the community has come to call ‘the second string theory revolution’.  Essentially, Witten’s solution to string theory’s embarrassment of riches was to suggest that its five versions were actually different perspectives, symptoms of the perturbative approximation methods employed in the theories’ mathematical formalism, that all point toward one unified framework, which he dubbed ‘M-theory’.[16]  Witten proposed that the ten spacetime dimensions called for in the earlier theories were also an approximation: M-theory requires eleven.[17]  With this and other adjustments, the realization emerges that the five theories (and one more called eleven-dimensional supergravity) can be paired off based on three dualities having to do with coupling constants and the geometry of spacetime itself.  In M-theory, then, a web of duality pairs unifies the disparate earlier theories into one meta-theory: Type IIA can pair off with Type IIB, as well as 11-D supergravity; Heterotic O can pair off with Heterotic E and Type I, and so on.  As one of its entailments, Witten’s revisioning of string theory also implies that strings do not exist solely as one-dimensional point-particle extensions: they can also extend into two or more spatial dimensions, forming what are called ‘membranes’, ‘p-branes’, or simply ‘branes’.  Shortly thereafter, Joseph Polchinski, from the University of California, Santa Barbara, posited[18] as another duality solution the existence of open string membranes that extend into a timelike structure, now known as ‘D-branes’.[19]

It is important to note here, though, that Witten himself, along with the rest of the string theory community, is acutely aware of M-theory’s limitations.  As mentioned earlier, M-theory points toward a quantum theory of gravity, but does not actually articulate it.  Much of the work in the field since 1995 has focused on the search for a more coherent and precise expression of M-theory.  M-theory has since spawned its own revisions.  For example, in 1996 Cumrun Vafa, from HarvardUniversity, published a paper[20] that proposed an ‘F-theory’, which calls for twelve rather than eleven spacetime dimensions, along with other modifications in the geometric structure of its spacetime.  As we shall be seeing later, when we consider the arguments of string theory’s detractors, the efforts of the past ten years, though resulting in a veritable onslaught of papers[21], has yet to provide a third ‘revolution’, one that can claim to offer a formalism that possesses the required inevitability for a universally convincing model of physical reality.

While some string theorists work on refining M-theory, another subdiscipline attempts to reconcile the currently conceived formalism of the theory with known astrophysical phenomena.  A paper authored by Juan Maldacena of the Institute for Advanced Study, epitomizes such efforts. [22]  Simply put, Maldacena argues that if the geometry of a certain ten-dimensional string theory model is reconfigured, it becomes consistent with the holographic principle, which stems from studies of information loss in black holes and posits that a physical model of (n – 1) dimensions can correspond exactly to a physical model of n dimensions, an effect analogous to a holographic projection.  For the purposes of the discussion at hand, what is significant here is that string theorists are actively borrowing concepts from astrophysics in order to make their models more robust, so that they better corroborate more experimentally grounded physics.  Another example of this is a paper[23] published by Cumran Vafa and Andrew Strominger, also of HarvardUniversity, that undertakes a comparable calculation of the information states of a certain type of black hole using a string theory formalism.

These kinds of approaches seek to mould string theory to better conform to astrophysics; other approaches attempt to inject string theory into astrophysical cosmologies in order to radically revise them.  Polchinski’s D-brane contribution has inspired just such an alternative cosmology to the one that serves as the almost unanimously acknowledged standard explanation for the history of our universe: that it originated from a Big Bang and that its spacetime structure is currently expanding.  In a D-brane-based scenario, the four spacetime dimensions of our universe may exist as a ‘braneworld’ within a larger and enveloping eleven-dimension meta-universe.  One version of the braneworld cosmology has replaced the Big Bang with a ‘Big Splat’; two braneworlds intermittently collide to provoke the expansion of our braneworld universe.  Other speculations occupy themselves with concepts such as tears in the ‘fabric’ of spacetime, wormholes, infinitely extended extra dimensions rather than miniscule, curled-up ones, or gravity ‘leakage’.[24]  Traweek reports that the experimenters within the high energy physics community often ‘chastise’ the theorists ‘for being “too mathematical”, or alternatively, for lacking “physical intuition”, or “cooking up schemes out of air”’. [25]  Most astrophysicists, grounded, as they insist, in the demands of a strict empiricism, would undoubtedly take a comparable stance: that the bulk of these speculative scenarios depart so exorbitantly from the state-of-the-science that they ought to be considered merely ‘fanciful’ conceits. Yet physicists often justify these speculative jaunts in light of the relative stagnation of currently reigning theories, the rather unexciting ‘mop up’ work of ‘normal science’.

Yet another subdiscipline of string theory that has emerged after M-theory’s debut aims to more fully integrate the theory with general relativity, beyond predicting the existence of the graviton (the force of gravity) as the consequence of one particular string vibrational mode.  Like special relativity, M-theory’s precursors assume an essentially flat spacetime background.  But general relativity demands that spacetime exhibits curvature: the very topology of spacetime warps and ripples in direct relation to its own gravitational pull, in proportion to its energy density.  General relativity implies a fully relativized universe, where spacetime itself is no longer infinitely divisible and infinitely extensive, but rather, granular and finite.  The underlying gravitational field, composed of a multitude of gravitons linked together in a kind of mesh or fabric, constitutes space and time, and were we able to probe this fabric at a sufficiently tiny scale, we would observe lacunae in space.  Work concentrating on such a finite and granular spacetime fabric has led string theorists to posit yet another type of brane, called a ‘zero-brane’[26], whose behaviour at the Planck scale, the theorists contend, is best described not by the commutations and anticommutations of Riemannian geometry, but by a formalism developed in the early 1990s by the French mathematician Alain Connes called ‘noncommutative’ geometry.[27]  Edward Witten has also attempted to integrate M-theory with another background independent spacetime theory originating from general relativity: Roger Penrose’s ‘twistor’ theory.[28]

Let us now consider complaints made by string theory’s critics.  Almost unanimously, they are quick to point out that string theory seems to concern itself only tangentially with observational data.  This is a direct consequence of the scale of the fundamental string, the Planck scale.  Current accelerator technologies are only capable of probing scales on the order of a thousand times smaller than the atomic nucleus.  The Planck scale is smaller than that by a factor of more than a million billion.  Even the Large Hadron Collider at CERN will not be able to probe such remote scales.  Experimentalists calculate that in order for an accelerator/collider to have the capacity to probe the Planck scale, it would require more energy than all the energy in the entire known universe combined.[29]  String theorists such as Brian Greene hope that the Large Hadron Collider will serve a more modest purpose: to confirm the existence of sparticles, the particle duals predicted by supersymmetry.  But still, although string theory attempts to incorporate supersymmetry, it is not the only theory to do so.  Many high energy theorists would consider the existence of sparticles as merely circumstantial evidence.  String theorists also propose that astrophysics might provide evidence for the existence of strings.  Analogous to the cosmic background microwave radiation that astrophysicists currently study, the explosive expansion of the universe in the split second following the Big Bang may have also left traces of strings stretched out to macroscopic proportions.  String theorists suggest that new astrophysical instruments such as LIGO (Laser Interferometer Gravitational-Wave Observatory) and LISA (Laser Interferometer Space Antenna), designed to detect gravitational waves, may also help to confirm the existence of cosmic-scale strings.[30]  Several physicists have proposed an experiment to probe, albeit indirectly, extra dimensions larger than the Planck scale, yet still microscopic, a scenario that certain versions of string theory predict.[31]

Many prominent physicists have become outspoken critics of string theory, including Roger Penrose, Sheldon Glashow, Lawrence Krauss, Philip Anderson, and Peter Woit.[32] The detractors all seem to rely on the Popperian argument that string theory, since it is so far removed from experimental observation, has the fatal quality of being unfalsifiable.  In its defence, physicists such as Steven Weinberg anticipate that string theory, with its radical reconceptualization of fundamental particles, as well as spacetime itself, may eventually suggest new ways to formulate experiments such that current technological limitations can be overcome.[33]  Critics such as Penrose and Krauss also contest the physical status of string theory’s proposed extra dimensions.[34]  But it would seem that the sheer size of the string theory community—with over a thousand members internationally—and perhaps the opacity of the theory itself—with its highly specialized mathematical argot—insulates it from any decisively ruinous criticism.[35]

Let us now examine string theory’s conceptual metaphors.  The following formula, known as the Nambu-Goto action, comes from bosonic string theory:[36]

This equation describes the ‘string action’ of a relativistic classical string: relativistic, in the sense that the formula incorporates the constraints of special relativity, where the motion of bodies in spacetime may only asymptotically approach the speed of light; and classical, in the sense that—with this particular version—it has yet to be quantized, e.g. made to conform to the conditions of quantum theory.  The formula also does not accommodate the dynamic metric of general relativity.   While the Nambu-Goto action lacks the synthetic scope of comparable formulae in more contemporary versions of string theory, it nevertheless expresses certain core features that later, more sophisticated formulae retain.

S stands for the string action.

T represents string tension.

c is the constant for the speed of light.

∫ is the symbol for the integral function in calculus.

d is a derivative (the differential function in calculus).

τ (tau) is a time unit, where f and i represent initial and final positions.

σ (sigma) is a length unit, from an arbitrary start at 0 to a final position σ₁.

The various Xs represent the Minkowski metrics of extra spatial dimensions.

Essentially, the Nambu-Goto action articulates precisely the motion of a one-dimensional string, extended in σ, through a space-like time dimension τ.  The motion of the string along these two dimensions forms what is known as a ‘world sheet’.  The world sheet, as a whole, exists within a multidimensional spacetime.  This version of the Nambu-Goto action does not specify exactly how many extra dimensions a relativistic spacetime requires.  Another quantized version of the Nambu-Goto action, because of the constraints of special relativity, calls for exactly twenty-six spacetime dimensions.  Barton Zwiebach writes:

 [W]e have seen that the condition of Lorentz invariance of quantum string theory simultaneously fixes the dimensions of spacetime and the constant shift in the masses of the particles.  In superstring theory a similar calculation fixes the dimensionality of spacetime to the value of D = 10.  The fact that string theory cannot be a good Lorentz invariant quantum theory in any arbitrary dimension shows that string theory is very constrained.  Even more, since the dimension of spacetime is uniquely selected by the requirement of consistency, we can say that string theory predicts the dimension of spacetime![37]

Common sense tells us that we live in a physical universe of three spatial dimensions.  Our bodies move in those dimensions: up and down, left and right, back and forth.  Modern physics conceptualizes time in a comparable manner.  Within the formalism of Newtonian cosmology, time transforms into a space-like dimension: an axis, much like the forward and back our bodies locomote along, composed of an array of points.  These points are measured out into a metric in comparison to the motion of an arbitrarily chosen body (for the metric of seconds, etc., the motion of the earth around the sun).  With special relativity, Einstein made the extraordinary claim that space and time, as dimensions, form a contiguous whole, spacetime.  Special relativity makes predictions that subsequent experiments have confirmed with astonishing accuracy. 

Scientific theories would seem to function admirably in this fashion: a theory reconceptualises physical reality in a precise way; physicists then draw inferences and design experiments based on that reconceptualisation—what Kuhn calls the work of ‘normal science’; the experiments, satisfactorily diverse in methodology and independently repeated, then either validate or falsify the theory.  What we could only imagine indirectly and never experience directly then attains the status of ontological essence; theory gets institutionalised.  Accordingly, string theorists, as scientists, can claim that the precise formalism of their theory actually predicts extra dimensions.  The scientific method has demonstrated time and again that this lurching forward, this hectic process of ruptures and shifts, is exactly how it succeeds.  As Bachelard suggests, ‘The belief in reality is essentially the conviction […] that what is real but hidden has more content than what is given and obvious.’[38]  The ongoing effort to extend stable scientific knowledge hinges on a perpetual blending of imaginative space—of conceptual metaphors—with the nonmetaphorical physical space accessible to the body.  Denying the ontological validity of what is ‘given and obvious’, making it mere surface, motivates this epistemological vocation to mine the depths.  Quixotically, scientific positivism succeeds by classifying not substance, but form, as the deeper essence.  Substance, then, carries the burden of positivism’s human ghost.  In Newtonian cosmology, the rigid body’s material essence reaches out and embraces.  With special and general relativity, the substance energy feels most human—as it watches, expands and contracts (almost like breathing), falls in and slides down. The energy of quantum theory busily exchanges messages.  How is the string, then, human?

            I would argue that the key variable in the Nambu-Goto action is T₀, the string tension.  In the formula, T₀ is the most meaningful variable: its value determines what kind of particle the string manifests as.  The string tension, with its continuous range of values, determines the vibrational frequency of the string, which in turn, in the quantized version of the formula, causes the string to leap from one position to another along the particle spectrum.  Imagine that the Nambu-Goto action is a kind of gizmo with cogs and sprockets that represent integration, differentiation, and the precise commutations of the various extra spatial dimensions.  Discrete quantum particles pop out of this gizmo when we press a button, e.g. do a calculation.  But the gizmo only has one dial—with a continuous range of frequencies.  As we turn the dial, the gizmo’s internal mechanisms gyrate in such a way that when we press the button, a known particle from the standard model will pop out.  So far, in their tinkerings with this gizmo—or its variants—string theorists have only been able to generate ‘semi-realistic particle physics’.[39]  They have been unsuccessful in getting the formalism to reproduce exactly the entire spectrum of particles in the standard model.  In this sense, as of yet, string theory cannot be considered backwards compatible.  Furthermore, although attempts have been made, no current string theory successfully incorporates general relativity.  It is very much a work in progress.

            Embedded within the Nambu-Goto action, we see the basic-level metaphor of the string emerge: taught along the dimension σ and vibrating, like a violin string, in accordance with its string tension.[40]  Like quantum theory, the primary essence in string theory is energy—tension as a kind of energy—which manifests in the form of a string whose pattern of change is the string action.  According to string theory, the essence of the universe is also number, in particular, calculus, Riemannian geometry, and in some of the latest versions, noncommutative geometry.  To be consistent with its theoretical predecessors, the concept of change, in string theory, maps both to the motion of spacetime rotations and to the exchange of messenger particles (as force).  Strings possess attributes, most notably, tension and open or closed ends.  The source-path-goal schema of string theory follows the world sheet.  String states are locations on the world sheet; motion along the world sheet represents changes of state.  Therefore, having a location-event structure, string theory principally employs a location causation—where causation is the forced movement of a string to a new location.  String theory also expresses a progeneration causation: strings generate quantum point-particles.  This innovation allows string theory to promise a certain conceptual simplification of the microcosm: the menagerie of exotic particles in the standard model all disclose their essential uniformity.  Form in quantum theory becomes a pattern of change in string theory—the holomorphic frequencies of string tension.

Clearly, the other striking novelty in string theory is its insistence on extra spatial dimensions.  As mentioned above, the mathematics of extra dimensions itself is not such a novelty: mathematical operators such as Hamiltonians frequently make use of them to bind extra-spatial physical attributes such as spin and charge to spatial dimensions.  In this sense, one could consider Hamiltonians as informational spaces.  Metaphorically, this strategy is a kind of extrapolation where extra spatial dimensions are simply spatial dimensions.  Physicists multiply and project the up/down, left/right, forward/back of our embodied experience to form a physical imaginary.  Yet it would seem that the string theorists’ insistence on the physical reality of these extra dimensions belies a certain positivist epistemology.  The privileging of formalism, of essence as form, above all other ontologies, forces physicists into making the awkward argument that conceptual metaphors such as rigid bodies, point-particles, probabilistic fields, and multidimensional strings are real entities.  Even if some battery of future experiments—such as the search for sparticles or macroscopic extra dimensions—were to confirm string theory’s prediction that the universe has ten (or eleven, twelve, or twenty-six) spacetime dimensions, that would not necessarily validate the assertion that those dimensions were physically real.  Our bodies move in three spatial dimensions.  Instruments such as accelerators and colliders are situated and operate in three spatial dimensions.  Positive results from such instruments would only confirm that spacetime, as an informational space, behaves in ways consistent with the formalism’s structure.  Ultimately, I would argue that the multidimensional spacetime of string theory is a conceptual metaphor that blends an imaginative space with the physical space of our embodied experience.  It is an informational space, not a physical space.  As such, we could only know the universe of string theory haptically, like a blind man tapping out his way through the world.  Our walking stick: conceptual metaphor.

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