See You Maybe on the Other Side

Going from one point in space to another without actually traversing the distance. Does that sound mind-bendingly improbable? And stretching our mind even a bit further, the destination of that eccentric journey may well be located in a different universe altogether or lie in the past.

It is Albert Einstein’s theory of general relativity that is responsible for the possibility of such thoughts.

Roughly speaking, general relativity explains how gravity is the consequence of large masses bending spacetime. So, instead of thinking that objects are attracted towards each other by the force of gravity — as per Sir Isaac Newton’s law of universal gravitation — the behaviour of matter in Einstein’s theory follows the curvature of spacetime.

A remarkable accomplishment of general relativity is that many of its predictions have been experimentally confirmed: the concept of black holes; the bending of light (gravitational lensing) as well as light losing energy when moving away from places with strong gravitation (gravitational redshift); the particular motion of the planet Mercury (perihelion shift); time slowing down in the presence of strong gravity (gravitational time dilation); and the existence of gravitational waves.

If so many theoretical projections by general relativity indeed see the light of day in our Universe, what do we make then of the prediction of wormholes?

What Are Wormholes?

A wormhole is a hypothetical tunnel connecting two separate regions in spacetime within the same universe or between different universes, serving essentially as a shortcut. The term spacetime encapsulates the idea that three-dimensional space is no longer independent from time — this space-time relationship is developed in Einstein’s theory of special relativity.

Fig. 1. A schematic view of the travelling paths from point A to B in the same universe: via the normal (longer) route versus via the wormhole, i.e. the shortcut. (Source: adapted from Ignaciobernabeu).

The usual set-up of a wormhole is a black hole as point of entry — an edge of spacetime that only permits information to enter, not leave — whereas its exit is defined by a white hole — an edge of spacetime that only tolerates an outflow, not an inflow of information.

Depending on its type, a common feature of a wormhole is that, even if an object travels through the wormhole at speeds below the speed of light, it can still arrive sooner at point B (see Fig. 1) than a ray of light that would have stayed on the normal path from point A to B cruising at the speed of light.

As a result, we could bridge astronomical distances in a shorter time period — effectively taking a shortcut and making intergalactic space travel more plausible.

Under some assumptions, general relativity endorses the theoretical existence of wormholes — dubbed as Schwarzschild wormholes — but they have up until this moment not been observed either directly or indirectly.

Why Don’t We Detect Them?

Lack of Stability

First off, the typical wormhole — referred to as an Einstein-Rosen bridge, which is an example of a Schwarzschild wormhole — is very unstable.

In fact, John Wheeler and Robert Fuller revealed back in 1962 that this type of wormhole, linking two regions of the same universe, will pinch off due to gravitational pressure long before any ray of light managed to squeeze through (see the middle figure of Fig. 2).

Understandably, Einstein-Rosen bridges are not traversable because of these enormous tidal forces, which would rip any traveller apart.

Solution 1: Exotic Matter

Notwithstanding these daunting prognoses, Kip Thorne and Mike Morris showed in a 1988 paper that a wormhole could be held open with the assistance of exotic matter — labelled as a Morris-Thorne wormhole.

Exotic matter is matter that can exhibit a negative mass-energy density or negative pressure, therefore falling beyond the scope of conventional physics of the Standard Model which requires positive values of these matter characteristics.

Being repulsive in nature — as opposed to gravitation which is attractive — this negative energy density would then deflect hazardous radiation and counter the inwards gravitational pressure. In this way, an object could, in principle, make it through the wormhole unscathed at a sufficiently high speed.

On macroscopic scales, negative mass violates important energy conditions in general relativity and is thus forbidden. This is why exotic matter does most likely not exist in our Universe.

However, on the tiniest of scales — the realm of quantum physics — some situations do allow for such violations. As a matter of fact, and contrary to what we may believe about empty space, a vacuum is not empty. According to quantum mechanics, it is filled with virtual particles with both positive and negative energies popping in and out of existence — this constant change in energy is what is technically termed as vacuum fluctuations of the quantum field.

As a consequence, quantum effects enable certain regions in space to carry a negative energy, which subsequently represents a counterforce to gravitation to prevent the collapse of the wormhole.

Despite this appealing conceptual stability solution, we have no way of knowing whether we could practically make and survive the crossing. In the words of Anthony Carapetis: “Ultimately, the feasibility of traversable wormholes cannot be determined until we either have a validated theory of quantum gravity, or direct empirical evidence.”

Solution 2: Quantum Connections

Doing away with exotic matter altogether, Ping Gao et al. suggest that an external quantum connection, i.e. quantum entanglement, between the two wormhole mouths (see bottom figure of Fig. 2) can alternatively provide the internal, repulsive negative mass-energy density needed to sustain a stable, traversable Morris-Thorne wormhole.

Fig. 2. Einstein-Rosen bridges pinch off immediately under gravitational pressure. Quantum entanglement of the black holes would preserve wormhole stability. (Source: Quantamagazine).

In addition, their quantum entanglement approach to wormholes looks promising in view of another outstanding problem in theoretical physics: the black hole information paradox. That is, physicists are at loss when trying to answer the question: As no information can ever get lost, where did the information that fell into a black hole go once that black hole has vaporized away (Stephen Hawking has demonstrated that black holes evaporate)?

Within the context of quantum entangled black holes coupled via a wormhole, the solution lies in the possibility that the information absorbed by the first black hole is recovered in the Hawking radiation emitted by the second black hole.

If such conjecture finds its way to a concrete experiment (several researchers are currently working on this), it could go a long way towards helping lay down the groundworks for the theory of quantum gravity, i.e. the unification of quantum mechanics with general relativity.

Solution 3: Dark Energy

The ordinary matter that you see around you, including stars and galaxies, merely counts for 4% of the total amount of matter in the Universe. The remaining chunk turns out to be dark matter (29%) and dark energy (67%).

Dark matter is a hitherto unknown form of matter that explains, among other phenomena, why stars towards the outer edges of a spiralling galaxy display similar velocities to the ones closer to the centre (with only ordinary matter present, the stars farther away would have lower velocities).

Dark energy is brought into the equation to account for the observed accelerated rate of expansion of our Universe. While dark energy possesses a positive energy density value (so, its energy attracts matter), it is repulsive in nature due to its dominant feature of negative pressure (which repels matter).

Fig. 3. Data based on extremely luminous galactic nuclei (quasars) indicating the transition from deceleration to acceleration caused by dark energy. (Source: BerkeleyLab).

Against this background, Francisco Lobo has calculated that a particular form of dark energy — called phantom energy — can be applied to achieve wormhole stability, given the usefulness of its repulsive nature in counteracting the wormhole’s gravitational pressure.

Numerous other researchers are working on a plethora of dark energy-driven models of traversable wormholes, including Piyali Bhar et al., Ali Eid, Deng Wang and Xin-He Meng, Mahdi Kord Zangeneh, Alaeddin Sayahian and Hooman Moradpour, Prieslei Goulart, and Ali Övgün.

At this point in time, scientists do not have a full grasp of the nature of dark energy nor its properties, making it an active field of research.

Solution 4: Strings

By adjusting the geometry of a Morris-Thorne wormhole and confining the presence of exotic matter to just a thin layer, Matt Visser managed to construct a wormhole whereby a traveller is able to traverse it while circumventing the region of exotic matter and at the same time being free from experiencing any life-threatening tidal forces.

Visser based his work on string theory, which regards strings as the fundamental entities of our Universe instead of the elementary particles and forces of the Standard Model, such as the electron, quark or W boson. More concretely, he obtained a stable wormhole by incorporating negative string tension into his models.

Another idea by Panagiota Kanti et al. warrants stability of the wormhole structure without invoking any exotic matter nor dark energy, and its solution is rooted in superstring theory — specifically, the dilatonic Einstein-Gauss-Bonnet theory. Then again, some researchers claim that it is critically unstable.

Fig. 4. Introducing some modifications to general relativity can lead to stable wormholes without the use of exotic matter. (Source: adapted from physicsforme).

But as yet, the search by experimental physicists for these basic strings remains elusive. If evidence were to be found, it could invigorate scientists working on string-based wormhole models.

Not the Right Size

Whereas the reality of macroscopic wormholes continues to be purely theoretical, microscopic wormholes, in contrast, might have a greater chance of being physically real and disappear less quickly.

As mentioned previously (see the subsection “Solution 1: Exotic Matter”), the vacuum is riddled with virtual particles. This lively sea of short-lived particles is referred to as quantum foam, whose existence has been experimentally confirmed (see, for instance, the Casimir effect, the Lamb shift, or the determination of the mass of the top quark).

In this context, Remo Garattini, for one, suggests that the vacuum consists of a coherent ensemble of microscopic wormholes. Moreover, Gonzalo Olmo et al. show that, when their modelled fluid gravitationally collapses towards the Planck scale (the smallest known scale), gravitation becomes repulsive, allowing a microscopic wormhole to form. Quite intriguingly, they affirm that “the generation of [microscopic] wormholes under realistic conditions is possible.”

What is more, by the same token that quantum entangled black holes could lead to the geometric manifestation of a macroscopic wormhole structure (see subsection “Solution 2: Quantum Connections”), the entangled virtual particles within the quantum foam might give rise to non-traversable microscopic wormholes, according to Diego Rubiera-Garcia et al.

For obvious reasons, we would not be capable of traveling through microscopic wormholes. And even if we could detect them, we currently do not dispose of the necessary technology to scale them to appropriate sizes for our use.

However, Nematollah Riazi et al. offer a possible way out: microscopic wormholes that were created within the quantum foam at the birth of our Universe (13.8 billion years ago) may have been stable enough to surf the wave of cosmic inflation, converting them into macroscopic two-way traversable wormholes. Alas, these macroscopic structures have not been spotted so far.

From a different angle, Juan Maldacena and Alexey Milekhin also propose a solution for a humanly traversable wormhole. By means of certain mathematical correspondences, they tie quantum theory to spacetime geometry, finding negative Casimir energy in the process which contributes to design a stable wormhole.

How Real Can It Get?

Looking at the work of many physicists, it appears that the theoretical prediction of wormholes remains just that: theoretical.

But Nelson Mandela once said that it always seems impossible until it is done. And that must have been precisely the thoughts of the physics community when detecting gravitational waves on the early morning of September 14, 2015, or when announcing the first image of a black hole’s silhouette on April 10, 2019.

Could wormholes be next in line of natural phenomena waiting to be discovered by science?

Perhaps the researchers who succeeded to mimic the behaviour of a wormhole in a laboratory with the use of magnetic fields are on to something.

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