Wormholes

Bridges through Space

Wormholes are, in essence, structures which connect two points in space nontrivially, i.e. in a way that isn't just a straight path between the points. There are many theoretical types of wormholes, but they can all be arranged into two general categories—non-traversable and traversable. Non-traversable wormholes cannot be traveled through, either due to some quirk of their structure or because they suffer gravitational collapse faster than any object could possibly traverse them. A traversable wormhole would require the use of exotic matter to prop it open and prevent it from collapsing. The Ellis wormhole, also known as the Thorne-Morris bridge, is one such wormhole.

Despite being first formulated all the way back in the 20th century, the Ellis wormhole is today the most widely utilized type of wormhole. The structure itself is a four-dimensional spacetime tunnel with two spherical mouths at separate points in three-dimensional space. It does not contain any singularities or one-way horizons, and is therefore fully two-way traversable. It is the easiest to make of the known types of traversable wormholes, and requires the least amount of exotic matter. Furthermore, the Ellis wormhole has no mass, meaning that it is a nongravitating, purely geometric phenomenon.

Any object entering a wormhole through one mouth exits through the other instantaneously, travelling between the two mouths in a manner that is effectively faster than the speed of light. Because of this, they are incredibly useful for rapid interstellar (and sometimes interplanetary) transportation, and they are in wide use across inhabited space.

A Note on Faster-than-Light Travel

It has been known for a long time that "true" faster-than-light travel is impossible. For example, a continuously accelerating starship would never accelerate past the speed of light; it would grow closer and closer to lightspeed, but never quite reach it. A wormhole is able to facilitate apparent faster-than-light travel because any object traversing it does not exceed the speed of light locally at any point in time, but it still travels faster than light globally, in that it travels between the two wormhole mouths faster than light could had it traveled in normal space. Light travelling through the wormhole would still, however, beat the object, so no physical laws are broken.

Bridges through Time

Wormholes connect points not just in space, but in spacetime. It is possible to induce a clock difference in the two mouths of a wormhole through time dilation, either by placing one of the mouths in a strong gravity well or by accelerating it to relativistic speeds. From an outside perspective, the mouths have experienced time differently. However, from the perspective of the wormhole, whose interior is completely stationary relative to itself, the mouths are the same age. Any object traversing the wormhole will still travel through space, just as before. But now, it will also travel through time.

When faced with the prospect of time travel, one might begin to consider the time paradoxes associated with the ability to influence one's past. However, so long as the separation of a wormhole's mouths remains spacelike (i.e. separated more by space than time), such causality violations cannot occur. This is because no object is able to travel between the two wormholes fast enough to be able to transmit information into its own past. It is only when the mouths' separation becomes timelike (i.e. separated by more time than space) that the possibility of a causality violation arises. But even then, one does not occur because of a principle known as the Chronology Protection Principle.

Chronology Protection and the Visser Collapse

Every wormhole has a "paradox radius"—this is the shortest distance that the wormhole's mouths can be from each other while still maintaining spacelike separation. When the mouths enter each others' paradox radii, it is possible for an object to travel between the two mouths in such a way that it can influence its own past. However, before a causal violation can occur, the wormhole undergoes Visser collapse. Light traversing the wormhole spontaneously refocuses, and quantum fluctuations at the wormhole mouths spike to incredibly high levels, causing the wormhole to detonate.

Causality-Respecting Network Architecture

The Visser collapse represents a serious roadblock for anyone wishing to create a wormhole network. Considering that wormholes are typically deployed at relativistic speeds to save time, one small mistake in node placement could result in the collapse of one or even many wormholes along the network, resulting in possibly catastrophic infrastructure damage.

Luckily, there are a few ways to avoid such a disaster. Low-speed deployment (at around 0.2c or less) ensures that the wormhole mouths suffer minimal relative time dilation, but it is by definition relatively slow. Midpoint deployment schemes where both wormhole mouths are taken to the midpoint between their final positions before being delivered to them result in both mouths experiencing roughly the same amount of time dilation and therefore having very little induced clock difference. A more advanced method involves placing a significantly massive gravitational source near one mouth in order to reduce its clock difference.

The method most widely used today is reactionless deployment, where non-time-dilation-inducing reactionless propulsion is used to deploy one wormhole mouth directly to its destination. Although not as fast as trivial deployment, as minimum time to use of the wormhole depends on the dilated time experienced by the mouth in transit rather than the total transit time from the perspective of an observer at rest, it is faster than midpoint deployment since reactionless drives can reach higher speeds than traditional propulsion methods, and it ensures that the wormhole mouths suffer no relative time dilation whatsoever.

Einstein-Rosen Bridges

Also known as Schwarzschild wormholes, these were the first type of wormhole to be theorized. They are intrinsic to the Schwarzschild black hole metric, a theoretical model of a black hole that is eternal and has no charge or angular momentum. This is by no means an accurate description of any real black hole, but it was useful as an early model of non-flat spacetime, and it was ultimately what led to the first real discussions about wormholes.

The Schwarzschild metric requires that spacetime be maximally extended, i.e. have no edges. Thus, the black hole described by the metric must have an interior "white hole" region through which infalling geodesics can be extended. This interior region can be thought of as a separate universe, one where time is reversed and mass-energy spews out of the white hole. The patch of spacetime connecting the two universes is the Einstein-Rosen bridge.

It is unlikely that Einstein-Rosen bridges actually exist, but even if they did, they would not be traversable; the normal Einstein-Rosen bridge connecting black hole to white hole would be both infinitely long and infinitely thin at its midpoint. Worse, Einstein-Rosen bridges connecting points in the same universe would immediately undergo gravitational collapse before even light could make it through. Therefore, they would not be useful for long-distance travel without the use of exotic matter to prop them open.