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| A visual representation of a wormhole: a shortcut through the fabric of spacetime allowed by the laws of general relativity. |
Picture the universe as a sheet of paper. You are standing at one corner. Your destination is the opposite corner — a journey, let us say, of four billion light-years. The fastest you can travel is the speed of light, so the journey will take four billion years. But someone hands you a pin. You fold the paper so that the two corners touch, and you push the pin straight through. The distance is now, for practical purposes, zero. You step through the hole and arrive instantly. You have not broken the speed limit. You have simply changed the geometry of the road.
This is the basic idea of a wormhole — a tunnel punched through the fabric of spacetime, connecting two distant regions by a path far shorter than any route through ordinary space. The concept sounds like science fiction, and for most of the twentieth century it was treated as such. But in 1988, two physicists at the California Institute of Technology sat down and did the calculation seriously. What they found was extraordinary: general relativity does not forbid wormholes. It permits them. The trouble, as always with the most beautiful ideas in physics, is the price you have to pay to make them work.
The Time Traveler's Paradox · Episode 4
Wormholes and Cosmic Strings:
The Physics of Shortcuts
General relativity allows tunnels through spacetime. Keeping them open requires matter with negative energy — stranger than anything in science fiction. Building a time machine from one is stranger still.
General Relativity
Exotic Matter
Cosmic Strings
~14 min read
Series Guide
The Time Traveler's Paradox
A five-part series investigating time — not as a backdrop to events, but as one of the strangest, most contested objects in all of science.
4
Wormholes and Cosmic Strings: The Physics of Shortcuts (You are here)
The Einstein-Rosen Bridge: A Wormhole That Cannot Be Used
The story begins, as so many stories in modern physics do, with a side effect that nobody was looking for. In 1935, Albert Einstein and his collaborator Nathan Rosen were studying the Schwarzschild solution — the simplest solution to Einstein's field equations, describing a perfectly spherical, non-rotating mass. What they found, when they examined the geometry carefully, was troubling. At the centre of a Schwarzschild black hole, the mathematics produced what appeared to be a bridge — a connection between two separate regions of spacetime, or even two separate universes — joined at a single point.
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| The Einstein-Rosen bridge, discovered in 1935, describes a connection between two regions that pinches shut too quickly for light to pass. |
Einstein and Rosen published this result, and the structure became known as the Einstein-Rosen bridge. For decades, physicists were not sure what to make of it. Was it a genuine feature of spacetime, or a mathematical artefact with no physical meaning? The answer, worked out gradually over the following decades, was both illuminating and deflating: the Einstein-Rosen bridge is real, in the sense that the mathematics is consistent — but it is not traversable. It forms and closes again so rapidly, pinching shut at the speed of light, that no traveller, no signal, not even a single photon, could pass through it from one side to the other. The bridge exists, but it is not a bridge you can cross.
John Wheeler Names the Concept
It was the physicist John Archibald Wheeler who, in 1957, coined the term "wormhole" — a deliberate borrowing from the image of a worm eating through an apple. The worm can travel across the surface of the apple, following the curve of the skin, or it can eat straight through the interior and emerge on the other side having covered far less distance. Wheeler's wormhole was the apple's shortcut, rendered in the language of four-dimensional spacetime. Wheeler imagined a spacetime foam — a roiling, fluctuating structure at the Planck scale (10−35 metres) where tiny virtual wormholes pop in and out of existence constantly, like bubbles forming and collapsing on the surface of boiling water. Whether any of these quantum-scale wormholes could be enlarged and stabilised was, at the time, entirely unclear. It would take another thirty years before anyone worked out the engineering in detail.
Morris and Thorne: Building a Wormhole You Can Actually Walk Through
In 1985, the astronomer Carl Sagan was writing a novel called Contact. He needed a mechanism for his protagonist to travel across interstellar distances faster than light would permit, but he wanted the physics to be at least defensible. He called his friend and colleague Kip Thorne at Caltech and asked, with the cheerful directness of a man who knows he is imposing: is there any way this could actually work? Thorne, rather than dismissing the question, assigned it to his graduate student Michael Morris.
What Morris and Thorne published in the American Journal of Physics in 1988 was not a chapter of a novel. It was a rigorous paper asking: what would a traversable wormhole actually require, given the constraints of general relativity? They worked backwards from the desired result — a stable tunnel through which a traveller could walk in either direction without being crushed, spaghettified, or killed by tidal forces — and asked what distribution of matter and energy would produce such a geometry. Their answer was precise, elegant, and deeply alarming.
The Morris-Thorne Wormhole: Specifications
Year: 1988 — Morris, Thorne, and Yurtsever, Caltech.
Structure: Two mouths connected by a throat. The throat must not pinch shut — it must flare outward, not inward, at the narrowest point.
Throat radius: In the minimum-exotic-matter solution studied by Thorne, the characteristic size of the wormhole mouths is enormous — roughly 600 times the size of the Solar System — in order to keep tidal accelerations tolerable for a human traveller.
Requirement: The throat must be threaded with matter that violates the Null Energy Condition — that is, matter with negative energy density. No known classical matter does this.
Key constraint: A wormhole cannot be used to travel back to a time before it was created and stabilised. It is a machine for time travel into its own past only — limited by the moment of its own construction.
The geometry of a traversable wormhole is, mathematically, a throat — a narrow tube connecting two regions, like the waist of an hourglass. The throat must satisfy what is called the flare-out condition: the cross-sectional area of the throat must increase as you move away from its centre, not decrease. This sounds innocent. In fact, it is devastating. For the flare-out condition to hold, the curvature of spacetime at the throat must be oriented in a way that ordinary matter — matter with positive energy density — cannot produce. The field equations of general relativity are unambiguous on this point: holding a traversable wormhole open requires matter with negative energy density at the throat. This is what Morris and Thorne called exotic matter, and its existence is not simply unknown — it appears to violate the most basic energy conditions that physicists have historically considered sacrosanct.
Exotic Matter: The Ingredient That Should Not Exist
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| The Casimir effect provides experimental proof that negative energy density exists—the "exotic matter" required to stabilize a wormhole. |
Stand in a room and push against the wall. The wall pushes back. Matter, under ordinary circumstances, has positive energy density — it attracts other matter gravitationally, it has positive mass, it presses outward when squeezed. Exotic matter, in the sense required by Morris and Thorne, does the opposite: it has negative energy density, which means it gravitates repulsively. It would push the throat of the wormhole open rather than letting gravity collapse it shut. And to be clear about what "negative energy density" means: this is not antimatter, which has positive energy and falls downward in a gravitational field just like ordinary matter. Exotic matter with negative energy density would fall upward. It would have, in the classical sense, negative mass.
No particle of classical matter observed in any experiment has negative energy density. But — and this is the crucial qualification — quantum field theory does not absolutely prohibit it. In 1948, the Dutch physicist Hendrik Casimir predicted that two uncharged metal plates, placed extremely close together in a vacuum, would experience a small attractive force caused by a suppression of the quantum vacuum fluctuations between them. The energy density of the quantum field between the plates is lower than the energy density of the vacuum itself — which means it is negative relative to the vacuum baseline. This is the Casimir effect, and it has been measured experimentally to extraordinary precision since its first direct confirmation by Steve Lamoreaux in 1997. Negative energy density exists. It is real. It is just extremely small and extraordinarily difficult to produce in useful quantities.
How Much Exotic Matter Would You Actually Need?
The quantities involved are not encouraging. Matt Visser, in his 1989 analysis, showed that you could in principle reduce the amount of exotic matter required by constructing wormholes with polyhedral or "thin-shell" geometries — concentrating the exotic matter at specific edges and faces rather than distributing it throughout the throat. This minimises the exotic matter without eliminating it. The Null Energy Condition must still be violated somewhere at the throat; there is no known way around this in standard general relativity.
"The Casimir effect proves that negative energy density can exist. It also shows just how small it is. Scaling it up to hold a wormhole open is a civilisational engineering challenge — if it is possible at all."
More recently, in 2024, researchers studying modified gravity theories — specifically f(Q,T) gravity with viscosity — have shown mathematically that wormhole solutions can exist without violating energy conditions in extended theories of gravity that go beyond standard Einstein relativity. This does not mean wormholes are easy to build. It means the physics is more nuanced than the 1988 analysis suggested, and that if the universe does operate according to an extended theory of gravity, the exotic matter requirement might be modified or even eliminated — though we do not yet know whether any such extended theory actually describes our universe. Separately, Garattini's 2021 analysis in the European Physical Journal C, using Casimir energy as the stabilising source, found that even under the most optimistic assumptions, the required wormhole throat size remains on the order of 1017 metres — roughly ten light-years across.
How to Turn a Wormhole Into a Time Machine
Here is where the story makes its most startling turn. Suppose, just for the sake of the argument, that you have managed to construct a stable traversable wormhole. Two mouths — call them A and B — connected by a throat. A traveller entering mouth A emerges from mouth B, and vice versa. You have a cosmic shortcut. But you do not yet have a time machine. To get a time machine, you need one more ingredient: you need the two mouths of the wormhole to experience different amounts of time.
Morris, Thorne, and Yurtsever worked this out in their 1988 paper. The mechanism is elegant and relies on exactly the time dilation physics we explored in Episode 2. Take mouth B and accelerate it to a velocity close to the speed of light, fly it out into space for what feels to it like one year, and bring it back. Because of velocity-based time dilation, mouth B has aged one year. But mouth A, which stayed home, has aged — let us say — ten years. The two mouths are now desynchronised in time by nine years: entering mouth A and emerging from mouth B takes you ten years into the past of mouth A's reference frame. You have a time machine. And crucially, it only goes back to the moment when the time discrepancy was created — not to any earlier moment. You cannot use a wormhole to visit ancient Rome. You can only visit the recent past, defined by when the wormhole's two mouths began accumulating their time difference.
The Grandfather Paradox Walks Back In
At this point, Episode 3 comes knocking. If a wormhole can be converted into a time machine, the same closed timelike curves we examined in the previous episode become available. And with them come all three responses we studied: Novikov self-consistency, Many-Worlds branching, and Hawking's chronology protection. The wormhole does not resolve the paradox — it merely provides a specific physical mechanism by which the paradox could, in principle, be realised. Whether the universe allows that mechanism to operate is precisely the question that remains open. The wormhole is the instrument. The paradox is the song it plays.
The Wormhole Time Machine: Three Key Constraints
1. No earlier than construction: A wormhole time machine cannot be used to visit any moment before the wormhole was first built and the two mouths separated in time. History before its creation remains inaccessible.
2. Exotic matter required: Every traversable wormhole solution in standard general relativity requires negative energy density at the throat, violating the Null Energy Condition. No classical matter does this.
3. Quantum instability: Hawking's chronology protection argument applies directly — once the wormhole becomes a time machine, quantum vacuum fluctuations near the mouths are predicted to grow without limit, potentially destroying the wormhole before the time loop closes.
Gott's Cosmic Strings: A Second Road to the Past
In March 1991 — just three years after Morris and Thorne published their wormhole paper — a Princeton astrophysicist named J. Richard Gott published a paper in Physical Review Letters that described a completely different mechanism for generating closed timelike curves. His ingredients required no exotic matter. His time machine was built from cosmic strings.
Cosmic strings are hypothetical one-dimensional defects in spacetime — impossibly thin filaments, potentially stretching across the entire observable universe — that some theories of the early universe predict should have formed during phase transitions in the first fractions of a second after the Big Bang. If they exist, they are genuinely extraordinary objects. Thinner than a proton, they would carry a mass-energy density of roughly 1021 kilograms per metre — meaning a single centimetre of cosmic string would outweigh Mount Everest by a factor of about ten million. They have never been directly observed, but they have not been ruled out either, and they remain part of the active theoretical landscape of cosmology.
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| J. Richard Gott proposed that two cosmic strings moving past each other could warp space enough to allow a journey into the past. |
The Geometry of a Cosmic String: A Cone, Not a Sphere
The key to Gott's time machine is the peculiar geometry that a cosmic string imposes on the spacetime around it. Unlike a planet or a star, which creates a spacetime curvature analogous to a curved bowl, a cosmic string produces something different: it cuts a wedge out of the flat space around it, like removing a slice from a pie and joining the two cut edges. The space around a cosmic string is locally flat — it has no tidal forces, no gravitational field in the ordinary sense — but it is globally conical. A circle drawn around a cosmic string has a circumference less than 2π times its radius. This deficit angle, denoted δ = 8πGμ (where μ is the string's mass per unit length and G is Newton's constant), is what makes the geometry useful. Light and matter passing around the string take slightly different path lengths on either side, creating a natural "shortcut."
Gott showed that two infinite parallel cosmic strings, moving past each other in opposite directions at sufficiently high speeds, would create a spacetime containing closed timelike curves threading around them. A spacecraft flying a precise figure-eight path around the two strings — first around one, then the other, timed to the strings' separation — could complete the loop and arrive back at its starting point in both space and time: a journey into its own past. In May 1991, Time magazine ran a story on Gott's proposal. A conference on time travel was held at the Aspen Center for Physics in 1992, bringing together dozens of physicists to work through the implications. Gott's was the second time machine published in a major physics journal within three years, after Thorne's wormhole. The subject had become, unmistakably, serious physics.
The Problem: An Infinite Machine in a Finite Universe
Gott's solution has a crippling constraint, one that he acknowledged directly: it requires infinitely long strings. Stephen Hawking proved, using a theorem from general relativity, that closed timelike curves cannot be created in a finite region of space from finite-length cosmic strings unless exotic matter is present — and cosmic strings, unlike wormhole throats, are not expected to be composed of exotic matter. Finite loops of cosmic string, analysed by physicists including Hawking and others, tend to collapse into black holes before the closed timelike curves can form, or the energy conditions required turn out to be incompatible with a finite, open universe.
Moreover, 't Hooft, Deser, and others showed that in an open universe — one with finite total energy and momentum — the energy required to accelerate two cosmic strings to the velocities needed for Gott's time machine exceeds the total mass-energy available in the universe. In a three-dimensional spacetime model, the Gott machine simply cannot be assembled from within any open universe that satisfies conservation of energy. Our universe appears to be open. If that is right, Gott's time machine is physically impossible even though it is mathematically consistent.
The Reality Check: What Physics Actually Allows
Step back from the mathematics for a moment and take stock. We have two serious, peer-reviewed proposals for time machines — one from Thorne and colleagues, one from Gott — both published in major physics journals, both mathematically consistent with general relativity. Neither has been dismissed as crackpottery. Neither has been experimentally realised. And each carries a specific, serious physical obstacle that has not been overcome.
Thorne's wormhole requires exotic matter with negative energy density in quantities that current technology — and possibly any conceivable future technology — cannot produce. The Casimir effect proves that quantum mechanics permits negative energy, but the scale is fourteen to twenty orders of magnitude smaller than what is needed, and the energy is bound to specific geometries that cannot simply be scaled up. Gott's cosmic strings require either infinitely long strings (which cannot exist in a finite universe) or a supply of energy exceeding everything our observable universe contains.
Both proposals also face Hawking's chronology protection problem — the quantum vacuum instability that appears to destroy any time machine at the moment it becomes functional. And neither can reach back before its own construction, which means that neither could, in principle, be used to visit any historical period earlier than the day the machine is built.
What these proposals really represent is a proof of concept at the level of mathematics, combined with a set of engineering obstacles that are currently insuperable and may be permanently so. They tell us that the laws of physics, as presently understood, do not flatly rule out time travel — but they impose conditions so severe that nature may be effectively protecting itself from the paradoxes that would follow. Whether that protection is fundamental or merely practical is, at present, unknown.
"The laws of physics do not forbid a time machine. They merely require it to be built from matter that may not exist, using energy the universe may not contain, and they destroy it the moment it becomes operational. Other than that, entirely feasible."
There is something intellectually important, however, in the fact that physicists have taken these proposals seriously. The project of working out the conditions under which time travel would be possible has illuminated deep features of general relativity, quantum field theory, energy conditions, and the relationship between geometry and causality. Even if wormholes and cosmic strings never carry a single traveller, the physics developed in studying them has been extraordinarily productive. Sometimes the value of a thought experiment is not the answer but the landscape of questions it forces you to map.
Up Next · Episode 5 — Series Finale
Is the Present an Illusion? How Your Brain Constructs Time
Physics says the present moment has no special status. Neuroscience says your brain constructs it with a 500-millisecond delay. Both cannot be entirely right — and the tension between them is where the strangest questions live.
References & Further Reading
- Morris, M. S., & Thorne, K. S. (1988). Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity. American Journal of Physics, 56(5), 395–412. — doi.org
- Morris, M. S., Thorne, K. S., & Yurtsever, U. (1988). Wormholes, time machines, and the weak energy condition. Physical Review Letters, 61(13), 1446–1449. — doi.org
- Einstein, A., & Rosen, N. (1935). The particle problem in the general theory of relativity. Physical Review, 48(1), 73–77. — doi.org
- Gott, J. R. (1991). Closed timelike curves produced by pairs of moving cosmic strings: Exact solutions. Physical Review Letters, 66(9), 1126–1129. — doi.org
- Visser, M. (1989). Traversable wormholes: Some simple examples. Physical Review D, 39(10), 3182–3184. — doi.org
- Casimir, H. B. G. (1948). On the attraction between two perfectly conducting plates. Proceedings of the Royal Netherlands Academy of Arts and Sciences, 51, 793–795. — knaw.nl
- Lamoreaux, S. K. (1997). Demonstration of the Casimir force in the 0.6 to 6 μm range. Physical Review Letters, 78(1), 5–8. — doi.org
- Garattini, R. (2021). Generalized absurdly benign traversable wormholes powered by Casimir energy. European Physical Journal C, 81, 9. — doi.org
- Thorne, K. S. (1994). Black Holes and Time Warps: Einstein's Outrageous Legacy. W. W. Norton. — wwnorton.com
Disclaimer
This article is written for general educational purposes. Traversable wormholes and cosmic string time machines are theoretical constructs; neither has been observed experimentally, and the physical obstacles described — exotic matter requirements, energy conditions, quantum instability — represent the current consensus in the peer-reviewed literature as of 2024. The discussion of modified gravity theories and their potential to reduce exotic matter requirements reflects ongoing research and should not be interpreted as a settled scientific conclusion. All external links point to publicly accessible, legally available resources including peer-reviewed journal articles via DOI, publisher pages, and open-access repositories.
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