Crossable Labyrinths: Wormholes as Bifurcating Spacetime Paths

I confess: when I first encountered Einstein and Rosen’s 1935 bridge—that mathematical wormhole connecting distant regions of spacetime through a geometric throat—I recognized immediately my own Garden of Forking Paths. Not metaphor. Not analogy. The same structure: reality as labyrinth where shortcuts tunnel through the fabric itself, where distance becomes illusion, where every path contains all paths simultaneously.

The Einstein-Rosen Labyrinth

General relativity (1915) revealed what philosophers suspected: spacetime is not container but geometry, curved by mass-energy into shapes that fold back upon themselves. The Einstein-Rosen bridge emerges from certain solutions as tube connecting two black holes—a wormhole in Wheeler’s vivid 1957 coinage, the worm tunneling through the apple’s surface to reach the opposite side without crossing the exterior. Perfect metaphor for what literature does: narrative shortcuts through causality itself.

But there is a problem, and it is the same problem that plagues all labyrinths: traversability. The standard Einstein-Rosen bridge collapses faster than light can cross it. Enter through the black hole mouth, and you are crushed at the singularity before reaching the other side—the throat pinches closed, the path folds into itself, the shortcut becomes trap. This is not failure of imagination but consequence of geometry: spacetime curves in ways that forbid passage, that transform promise into prison.

To traverse requires what physicists call exotic matter—substance with negative energy density that violates classical energy conditions. This matter would create outward pressure, antigravity holding the throat open against its tendency to collapse. Just as my fictional labyrinths require impossible architecture (staircases that ascend while descending, libraries containing all books including the catalog of catalogs), traversable wormholes require impossible physics.

Exotic Matter Holds Open the Throat

The Morris-Thorne wormhole (1988) designed for Carl Sagan’s Contact specifies traversability criteria with precision that would satisfy any librarian cataloging infinite books: throat large enough for human passage, tidal forces survivable (no spaghettification), geometry stable indefinitely, passage permitted both directions. An elegant solution—horizon-free, singularity-free, purely geometric. Light bends around it like lens; some trajectories loop back while others pass through to the distant mouth.

But elegance demands price. The wormhole requires exotic matter lining the throat—matter with negative energy density (ρ < 0) that violates the null energy condition. A photon moving through gains energy, impossible under classical physics. Where to obtain such substance? Three speculative sources present themselves like three paths in forking garden:

First, the Casimir effect: two parallel plates in quantum vacuum create attractive force through restricted fluctuations—negative energy density measured in 1997 laboratories. But the effect is tiny, would require astronomical amounts, perhaps more matter than universe contains. Second, cosmic strings: hypothetical topological defects from early universe with negative tension that stretch rather than curve spacetime. Might stabilize wormhole geometry, though none have been observed. Third, unknown physics entirely—dark energy exhibits negative pressure but probably lacks concentration to hold throat open.

Topological censorship theorem confirms suspicion: general relativity forbids sustained negative energy, ensures wormhole-like structures close before observer can cross. Classical physics protects itself against shortcuts, against violations of distance and duration. The map refuses to replace the territory, even when mathematics permits the replacement.

All Paths Taken Simultaneously

I wrote The Garden of Forking Paths in 1941, sixteen years before Hugh Everett proposed many-worlds interpretation of quantum mechanics. My protagonist’s ancestor composes novel where “all possible outcomes occur; each one is the point of departure for other forkings.” Critics find contradictions: hero dies in chapter three, lives in chapter four. But this is not error—it is the truth about time itself.

“In all fictional works,” I wrote, “each time a man is confronted with several alternatives, he chooses one and eliminates the others; in the fiction of Ts’ui Pên, he chooses—simultaneously—all of them.” This is Everett’s relative state formulation: wave function never collapses, measurement entangles observer with system, creates branches where you measure spin-up in one universe and spin-down in another, both existing, neither privileged.

Ts’ui Pên “believed in an infinite series of times, in a growing, dizzying net of divergent, convergent and parallel times.” Time as labyrinth where every choice generates new passages, where all corridors exist simultaneously in structure vaster than any single consciousness can traverse. David Deutsch, quantum computing pioneer, observed: “Everett’s is a very Borgesian picture of reality.” Physics arrives, eventually, where metaphysics already dwells.

The strange loop—Hofstadter’s self-referential recursion where consciousness emerges from patterns perceiving patterns perceiving patterns—reveals the same structure. Move upward through hierarchy, unexpectedly return to starting point. The “I” that observes is observed by the “I” that observes the observing. Infinite regression, consciousness as labyrinth containing itself.

Even Baudrillard’s simulacra—symbols replacing reality until map overwhelms territory, until reflection becomes more real than reflected—instantiates the principle. Many paths up the mountain, each valid, each true, none complete. The pluralism of spiritual practices mirrors the pluralism of quantum branches: all methods work because reality supports infinite approaches to itself.

Time Machines and Closed Loops

Morris and Thorne showed that traversable wormholes permit time travel. The method: move one mouth at relativistic velocity (twin paradox—moving clock runs slow), then return it. The mouths now have age difference: one aged one year, the other ten. Step through the wormhole in 2025, emerge from the aged mouth in 2016—travel nine years into your own past.

This creates closed timelike curve: worldline looping back to own past, enabling paradoxes. Kill your grandfather before your father’s birth, erase your own existence. Three solutions present themselves like three suspects in detective story:

Novikov self-consistency: only self-consistent histories occur. Try to kill grandfather, gun jams, events conspire to prevent paradox. Universe protects its own logical coherence. Second, many-worlds: killing grandfather creates new branch where you were never born, but you arrived from different branch where you exist. Paradox dissolves into multiplicity. Third, Hawking’s chronology protection: laws of physics prevent closed timelike curves—quantum fluctuations diverge near time machine, destroy it before activation.

I prefer the second solution. “Time forks perpetually toward innumerable futures,” I wrote in 1941. Not metaphor but physics: every choice creates branching universe, every wormhole connects infinite timelines, every observer navigates labyrinth of possibilities where all paths coexist. Wormholes do not create time travel so much as reveal time’s essential nature: not line but garden, not sequence but structure, not flow but eternal coexistence of all moments in geometric whole.

The Library Contains Itself

What physics calls wormhole, literature calls narrative shortcut. In Tlön, Uqbar, Orbis Tertius, parallel world intrudes on ours through objects that shouldn’t exist—artifacts from impossible geometry. In The Aleph, a point contains all spacetime simultaneously: wormhole to everywhere/everywhen, infinite library compressed into single location.

The traversable wormhole remains speculative—theoretically permitted by general relativity equations, practically implausible without exotic matter probably unavailable to our universe. But this does not diminish its significance. Some truths exist in mathematics before they exist in matter, in metaphysics before they manifest in measurement. The labyrinth was always there; physics merely provides new language for ancient architecture.

We accept wormholes easily, perhaps because we intuit that spacetime itself is labyrinthine—curved back upon itself, riddled with shortcuts between distant points, structured by infinities that render linear causality illusory. Every text contains all texts, every moment contains all moments, every observer navigates garden of forking paths where traversability depends not on exotic matter but on recognition: the throat was always open, the bridge always crossable, the library always infinite.

The wormhole, like the story, offers passage to those willing to enter geometry stranger than simple distance permits.