Author: Samuel Joseph George
In 1916, Albert Einstein first proposed his general theory of relativity, which remains the standard model of gravity to this day. Twenty years later, he and his longtime colleague Nathan Rosen published a paper showing that the formulation of general relativity contains a curved-space structure that could, in principle, connect two distant points through a tunnel-like shortcut in curved space.
The purpose of Einstein and Rosen's paper was not to promote faster-than-light travel or travel between universes. Rather, they were attempting to explain fundamental particles such as the electron as spatial tunnels characterized by lines of electric force.
The Einstein–Rosen bridge is based on general relativity and on the work of Karl Schwarzschild, who found a solution to Einstein's equations. One of the remarkable predictions arising from these equations was the existence of black holes.
A black hole is a region of space from which nothing, not even light, can escape. Black holes can be regarded as the endpoint of the evolution of massive stars. However, this brief description does little to make them easier to understand or to diminish their mysterious nature.
Black holes are the endpoint of the evolution of stars with masses at least 10 to 15 times that of the Sun. If a star of this mass or greater undergoes a supernova explosion, it may leave behind a relatively massive stellar remnant. Since there is no outward force to oppose gravity, the remnant collapses under its own gravity.
Eventually, the star collapses toward a point of zero volume and infinite density, creating what is known as a singularity.
As the density increases, the paths of light rays emitted by the star become increasingly curved, until eventually the rays become trapped in orbits around the star from which they cannot escape. Photons emitted by the star are trapped by the intense gravitational field and never leave these orbits. Since no light can escape once the star reaches infinite density, it is called a black hole.
The basic idea of wormholes is almost as old as the concept of general relativity itself. A few months after Einstein formulated his equations, Schwarzschild found the first exact solution to Einstein's equations.
One notable prediction of Schwarzschild geometry was that if a mass m were compressed within a critical radius rs, now known as the Schwarzschild radius, its gravity would become so strong that even light could not escape.
The Schwarzschild radius of a mass m is given by:
Interestingly, in 1784, John Michell had found the correct Schwarzschild radius on the basis of an incorrect theory. This English geologist realized that, in principle, gravity could become so strong that nothing, not even light, could escape from an object. To produce such gravity, an object would have to be extremely massive and unimaginably dense.
At the time, the conditions required for the existence of what Michell called “dark stars” seemed physically impossible. His ideas were published by the French mathematician and philosopher Pierre-Simon Laplace in two successive editions of The System of the World, but were removed from the third edition.
In 1795, Laplace proposed the following equation, which showed the relationship between mass and radius required for the formation of a black hole:
The complete Schwarzschild geometry consists of a black hole, a white hole, and two universes connected at their horizons by a wormhole.
The name black hole was coined by John Archibald Wheeler in 1968. Before Wheeler, these objects were often called “dark stars” or “frozen stars.”
It was the Austrian physicist Ludwig Flamm who realized that the Schwarzschild solution to Einstein's equations—known as the Schwarzschild metric—actually describes a wormhole connecting two regions of two different universes, or two distant regions of the same universe.
A white hole can be thought of as a black hole running backward in time. Just as black holes swallow objects irreversibly, white holes “spit” objects back out. However, white holes cannot exist because they violate the second law of thermodynamics.
The prediction of black holes did not pose a problem for Einstein, but he realized that black holes contained singularities at their centers. At the singularity, all known laws of physics begin to break down.
This idea was deeply troubling to Einstein. He disliked these singularities, and the fact that they were hidden from the outside universe by a black hole's event horizon was not sufficient for him. He did not subscribe to the idea that “if you cannot see something, you do not need to worry about it.”
He therefore began working with Rosen. In 1935, the two scientists wrote a paper providing evidence for the existence of a bridge between a black hole and a white hole. They called this structure the Einstein–Rosen bridge.
The purpose of Einstein and Rosen's paper was not to promote faster-than-light travel or travel between universes. Instead, they were attempting to explain fundamental particles such as the electron as spatial tunnels characterized by lines of electric force.
Science-fiction writers, however, adopted the idea of the Einstein–Rosen bridge and applied it to spacecraft traveling through what is now commonly called a wormhole.
Thus, an idea that Einstein had originally developed as a theoretical description of particles was later adopted by science-fiction writers as a way of circumventing a problem imposed by Einstein's general theory of relativity: the impossibility of traveling faster than light.
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| The illustration shows an Einstein–Rosen bridge with a spacecraft entering the wormhole. However, in the original Einstein–Rosen theory, the possibility of objects larger than an electron passing through the wormhole was not even considered. Therefore, the scenario depicted by science-fiction writers is not physically correct. |
The Einstein–Rosen bridge was troubling to many physicists of that era because such a tunnel could, in principle, allow information to be transferred faster than light, thereby violating one of the fundamental principles of special relativity known as Einsteinian causality.
In 1962, John Wheeler discovered that the Einstein–Rosen bridge structure in a field-free space is dynamically unstable. He showed that if such a wormhole were somehow opened, it would close before even a single photon could pass through it, thereby preserving Einsteinian causality.
This led to two different classifications of wormholes:
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| There are at least two types of Lorentzian wormholes. Inter-universe wormholes (top) connect one universe to another, while intra-universe wormholes (bottom) connect two distant regions within the same universe. |
Lorentzian wormholes are essentially shortcuts through space and time, but they close immediately unless some form of negative energy can keep them open. Small amounts of negative energy can be produced in the laboratory through a phenomenon known as the Casimir effect.
One consequence of Lorentzian wormholes is that objects passing through them could move not only through space but also through time—assuming that parallel universes exist.
Euclidean wormholes are even stranger because they exist in imaginary time and are inherently virtual quantum-mechanical phenomena. These wormholes are of particular interest to quantum field theorists.
In 1865, at a time when relativity, quantum mechanics, and modern cosmology did not yet exist, Charles Dodgson wrote Alice's Adventures in Wonderland.
The subject of this children's story was parallel worlds. There is a famous scene in which Alice follows a white rabbit down a hole. Today, this hole could be described as an Einstein–Rosen bridge.
In Wonderland, the laws of physics no longer apply, and therefore strange processes can take place. It is important to remember, however, that Dodgson had no idea what kind of mechanism could make such events possible.
The idea of using a wormhole to travel across vast distances was employed by Carl Sagan in 1985 while writing his novel Contact. He wanted to devise a way for one of the characters in the story to travel faster than light without violating relativity.
Unfortunately, at present, wormholes are more a subject of science fiction than established science.
A wormhole is a theoretical feature of the mathematical solutions of general relativity. If their existence were ever established, they could potentially be used to traverse enormous distances very rapidly.
It has never been established that wormholes actually exist, and there is no experimental evidence confirming their existence. Nevertheless, it is certainly fascinating to think about the possibilities that their existence could create.