Physical realizability of macroscopic traversable wormholes: exotic matter, stability, formation, safety, and chronology protection (the Morris-Thorne open questions)

Morris and Thorne (American Journal of Physics 56, 395 (1988)) showed that general relativity admits static, spherically symmetric traversable wormhole geometries - horizon-free, two-way tunnels with survivable tidal forces - but that the material sourcing them must be exotic: at the throat its radial tension must exceed its mass-energy density, $\tau > \rho c^2$, violating the weak, null, dominant, and strong energy conditions, at magnitudes comparable to neutron-star core pressures for kilometer-scale throats. They explicitly left open whether quantum field theory can supply such stress-energy on macroscopic scales, whether the static solutions are dynamically stable, how spacetime topology could be changed to form such objects, whether traversal by human-scale travelers could be safe given the unknown microscopic coupling of the exotic sector to ordinary matter, and whether wormhole-based time machines are forbidden by a chronology-protection mechanism. These five facets remain open: the current literature contains no general no-go theorem and no construction within established physics, and chronology protection remains unproven. The task is to decide the physical status of the macroscopic traversable wormhole across these five linked facets.

Background

In general relativity, a wormhole is a handle connecting two otherwise distant regions of spacetime. The archetypal example, the Schwarzschild solution's Einstein-Rosen bridge, cannot be used for travel: it is hidden behind an event horizon (a one-way causal membrane) and pinches off before anything can cross it. Morris and Thorne (1988) asked what constraints general relativity itself imposes on a traversable wormhole: a static, spherically symmetric tunnel with no horizon at its narrowest point (the throat), crossable in both directions, with tidal accelerations small enough for a human traveler and short proper traversal times. Parametrizing the geometry by a shape function $b(r)$, which fixes how the tunnel's radius narrows, and a redshift function $\Phi(r)$, which fixes the gravitational time dilation along it,

$$ds^{2}=-e^{2\Phi(r)}c^{2}dt^{2}+\frac{dr^{2}}{1-b(r)/r}+r^{2}(d\theta^{2}+\sin^{2}\theta\,d\phi^{2}),$$

they showed that traversability is not forbidden by Einstein's equations, but that the geometry dictates its material source: at a throat of radius $b_0$ the radial tension must be $\tau_0=c^4/(8\pi G b_0^2)$ - comparable to the pressure at the center of the most massive neutron stars for throat circumferences of order tens of kilometers - and, crucially, must exceed the mass-energy density it threads, $\tau_0 > \rho_0 c^2$. Matter with this property is called exotic: for a radially moving observer the measured energy density becomes negative, so the material violates the weak, null, dominant, and strong energy conditions - the positivity assumptions on the stress-energy tensor (the object encoding energy density, pressures, and tensions) that underlie deeply cherished classical results such as the singularity theorems. No known form of matter has the $\tau_0 > \rho_0 c^2$ property, but in 1988 no fundamental principle was known to forbid it either. Quantum field theory does allow locally negative energy densities - the Casimir effect (the attractive stress between conducting boundaries due to modified vacuum fluctuations) and squeezed vacuum states (quantum states with fluctuations redistributed between conjugate observables) are the canonical examples - which is why the problem is not closed within semiclassical gravity (classical geometry sourced by the expectation value of a quantized stress-energy tensor). However, later work established quantum inequalities: lower bounds on the time-averaged (or weighted-averaged) energy density along an observer's worldline, forcing a trade-off between the magnitude and duration of negative energy of rough form $\int \langle T_{\mu\nu}u^\mu u^\nu\rangle f\,d\lambda \gtrsim -C/t_0^4$, where $\lambda$ is the observer's proper time and $t_0$ the characteristic averaging time. These bounds constrain, but do not obviously forbid, wormhole-scale negative energy. The source paper closed by acknowledging a cluster of unresolved issues that jointly decide whether traversable wormholes are physically realizable: (1) whether quantum field effects (squeezed vacua, Casimir-type configurations) or some new field can provide $\tau > \rho c^2$ over macroscopic throat volumes, or whether microphysics ultimately forbids such macroscopic energy-condition violations; (2) the linear and nonlinear dynamical stability of the static solutions against perturbations from traversing objects, ambient matter, and quantum fluctuations; (3) the formation problem - classical general relativity resists changes of spacetime topology, which under fairly general conditions require singularities or acausality (Geroch's 1967 theorem), so producing a macroscopic wormhole, perhaps by enlarging a Planck-scale fluctuation of the hypothesized spacetime foam (the name for the presumed quantum-gravitational fluctuation of geometry at the Planck scale, $\sim 10^{-35}$ m), appears to require quantum gravity; (4) the unknown microscopic coupling between any exotic sector and ordinary matter, which could make traversal lethal even when tidal bounds are satisfied; and (5) causality - a traversable wormhole can be turned into a time machine by relative motion of its two mouths or by placing them at different gravitational potentials, producing closed timelike curves (worldlines returning to their own past); Morris, Thorne, and Yurtsever (1988) argued that quantum vacuum fluctuations diverge at the resulting chronology horizon (the surface beyond which closed timelike curves first appear), and Hawking (1992) elevated this to the chronology protection conjecture, which remains unproven.

Problem Statement

Decide the physical status of the macroscopic traversable wormhole: whether the fundamental laws of physics - general relativity coupled to quantum field theory on curved spacetime, together with any exotic field or quantum state of known fields that a construction invokes, required to form part of a self-consistent physical theory - forbid or permit such objects; either exhibit a self-consistent construction, or establish a fundamental no-go. A macroscopic traversable wormhole is a two-way, horizon-free tunnel whose throat is large enough that tidal accelerations on a human-scale traveler are survivable. A complete construction must jointly satisfy five linked facets inherited from the source: (i) it must supply energy-condition-violating stress-energy with $\tau > \rho c^2$ at the throat on macroscopic scales, in a way compatible with the quantum inequalities that constrain negative energy in quantum field theory; (ii) it must be dynamically stable, at least against perturbations induced by traversal, ambient matter, and quantum fluctuations; (iii) it must admit a physically realizable formation mechanism, consistent with the classical obstructions to spacetime topology change, by which such a wormhole could come to exist; (iv) the microscopic coupling between the exotic sector and ordinary matter must leave traversal survivable, with both tidal and non-tidal hazards bounded; and (v) it must either resist conversion into a time machine or be shown to admit closed timelike curves consistently, without paradox. A complete no-go establishes a fundamental microphysical obstruction to at least one of these facets at the general level - for example, a proof that quantum field theory cannot sustain the required macroscopic negative energy, that such configurations are necessarily unstable, or that the backward time travel such wormholes permit, through the associated quantum backreaction, prevents their construction.

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