快猫短视频

IMAGINE a tunnel through the fabric of space-time which you could enter near the Earth and, after travelling for just a few hours, emerge near Alpha Centauri more than 4 light years away. If the ends of the tunnel were moving relative to each other you could even use it to travel backwards or forwards in time.

As yet, no one has come even close to constructing such a 鈥渨ormhole鈥�, but Einstein鈥檚 general theory of relativity clearly shows that such shortcuts could exist. What is more, last year an Italian physicist suggested that one day there might be a way to construct a 鈥渕icrowormhole鈥� in the laboratory. And a group of American physicists believes that if there are wormholes out in space, either surviving from the big bang or constructed by advanced extraterrestrials as part of a pan-Galactic transport system, then we might even be able to detect them.

Space travel

The fact that general relativity allows for the existence of wormholes was discovered very soon after the publication of Einstein鈥檚 theory in 1915. But would it be possible in principle for light or a spaceship to travel through them? This question was not answered until 1988, when Kip Thorne and Michael Morris of the California Institute of Technology in Pasadena were asked to concoct a plausible faster-than-light method of travelling between stars for Carl Sagan鈥檚 science fiction novel Contact.

Thorne and Morris recognised that such a wormhole would have to permit travel both in one end and out the other and therefore cannot have a one-way 鈥渉orizon鈥� (black holes are said to have a one-way horizon because nothing, even light, ever escapes).

Furthermore, travellers must be subjected to only modest accelerations and must not be torn apart by tidal forces 鈥� if you were falling feet-first towards a black hole, the gravitational field would be so huge that the difference between the pull on your feet and your head would rip you apart. When Thorne and Morris imposed these constraints on the equations of general relativity, they discovered a set of general solutions each corresponding to a traversable wormhole.

According to Thorne, anyone trying to create a traversable wormhole could try one of two strategies. The first would be to conjure one literally out of nothing. Quantum theory states that if we could zoom in on a small enough scrap of space we would discover that the amount by which it is 鈥渨arped鈥� 鈥� another way of describing the size of its gravitational field 鈥� fluctuates randomly from place to place like a choppy sea as adjacent regions steal energy from each other in an eternal game of give and take.

On scales smaller than the so-called Planck-Wheeler length 鈥� a mere 1.62 脳 10^-35 metres or roughly 20 orders of magnitude smaller than an atomic nucleus 鈥� these 鈥渜uantum gravitational fluctuations鈥� may become so violent that space actually boils and becomes a 鈥渜uantum foam鈥� riddled with short-lived 鈥渜uantum wormholes鈥� (see page 30).FIG-20223902.jpg

Some physicists have speculated that it might be possible to enlarge these. One possibility, raised three years ago by Thomas Roman of Central Connecticut State University, New Britain, in 1993, is that such an enlargement may even have occurred spontaneously during the first split-second of the Universe when, according to the theory of inflation, space expanded at a truly phenomenal rate.

Another possibility is that a sufficiently advanced civilisation might be able to reach down into the quantum foam and artificially enlarge a wormhole to a usable size. The problem is that, at present, theorists have no quantum theory of gravity to tell them about the properties of the quantum foam, or even whether it exists.

The second strategy for creating wormholes proposed by Thorne involves starting from scratch and warping and twisting macroscopic space. However, this means doing some pretty drastic things to space. To see why, imagine intelligent ants that live on the surface of a sheet of paper and wish to travel between two points. If the paper is gently folded in two so that the points are brought closer together, the ants can either take the long route over the two-dimensional surface or connect the two points by a paper tube which provides a shortcut through the third dimension (see above).FIG-20223901.jpg

Such a tube is analogous to a wormhole driven through higher dimensional space. Just as the intelligent ants will be unable to connect their tube without tearing two holes in the paper, no physical process can make a wormhole without ripping space itself.

A rip in space is a place where space-time comes to an abrupt end, as it does at the enormously dense 鈥渟ingularity鈥� at the heart of a black hole. However, singularities are described by quantum gravity. So, once again, we will not know whether the strategy is possible until theorists have developed a theory of quantum gravity.

But there could be a third way to make a wormhole. Last year, space scientist Claudio Maccone from Turin suggested using a magnetic field to warp space.

It might appear strange that a magnetic field can have a gravitational effect, but general relativity states that anything that contains energy, including a magnetic field, warps space. The proof of this was published within two years of the publication of the general relativity theory by the Italian physicist Tullio Levi-Civita, who had discovered an exact solution of Einstein鈥檚 field equations corresponding to 鈥渕agnetic gravity鈥�.

Massive magnets

Levi-Civita鈥檚 solution revealed that a static uniform magnetic field, created along the axis of a long solenoid, would create a gravitational field inside the solenoid. The only snag was that the artificial gravity would be measurable only if the magnetic field were about a billion billion times greater than was then possible. Not surprisingly, magnetic gravity was set aside as a mere curiosity.

But last year Maccone pointed out that Levi-Civita鈥檚 鈥渕agnetic gravity鈥� solution to Einstein鈥檚 equations bears a remarkable resemblance to the general class of traversable wormholes suggested by Thorne and Morris for Sagan鈥檚 novel. 鈥淲hat Levi-Civita鈥檚 solution in fact describes is a magnetic wormhole,鈥� says Maccone. However, any wormhole that could conceivably be created by a magnetic field in a laboratory would be so large that only a small portion would be inside the laboratory, which is why Maccone refers to this part of it as a 鈥渕icrowormhole鈥�.

According to Maccone, if such a wormhole were created with a laboratory magnetic field of 2.5 tesla, the radius of curvature of the space inside, a measure of the size of the wormhole, would be about seventeen times the distance between the Sun and Sirius, the brightest star in the sky about 8.7 light years away from Earth. It would take an almost unimaginable magnetic field of a billion billion tesla to create a radius of curvature of 1 metre to squeeze the wormhole into a typical laboratory (Journal of the British Interplanetary Society, vol 48, p 453).

Maccone admits that fields large enough to create a detectable wormhole are way beyond our present capabilities 鈥� the largest field obtainable in a laboratory is around 10 tesla. But he points out that the magnetic field on the surface of compact neutron stars 鈥� stars that are the remnants of supernovae and are made entirely out of densely packed neutrons 鈥� can be close to a billion tesla and might spontaneously create a magnetic wormhole.

If it became possible to create a field this large on Earth, he imagines that a superlong solenoid could create a measurable wormhole. 鈥淚鈥檓 thinking of a solenoid as big as the 3 kilometre-long Stanford Linear Accelerator in California,鈥� says Maccone.

Light test

Maccone says that over such a distance the curvature of space caused by the artificial, magnetic gravity would be sufficient to have an effect on a beam of light. This effect could provide a test for the existence of a wormhole. 鈥淟ight is slowed down in a gravitational field,鈥� he says. 鈥淪o if a light beam were sent through the solenoid from end to end, its speed would be less than it would be in a vacuum. Measuring this dip in the speed of light would prove the existence of a wormhole in the laboratory.鈥�

For the moment, Maccone says he has simply demonstrated that with a large enough static magnetic field, a solution to Einstein鈥檚 equations exists that would make a wormhole possible. But critics point out that it is very difficult to see how a magnetic field could create a wormhole in the first place. 鈥淚t鈥檚 hard to see how a magnetic field could change the topology of space,鈥� says Ian Moss of the University of Newcastle.

However, Maccone insists that a magnetic field can do just this. 鈥淣o cutting and pasting of space is necessary,鈥� he says. He admits that he does not yet understand how the magnetic field changes the topology of space. However, he intends to investigate the effect by seeing what happens as his magnetic field grows from zero, relaxing the condition that the field be static and uniform.

鈥淚f what Maccone is saying is possible then it would be wonderful,鈥� says John Cramer of Washington State University in Pullman. 鈥淏ut I have my doubts.鈥�

Oddly enough, a mechanism for creating a wormhole from scratch without ripping space has already been proposed. In 1966, Robert Geroch of Princeton University in New Jersey found a way to smoothly warp and twist space into a wormhole. But, the price turned out to be very high. Time itself would become twisted so strongly that, during the construction, the machinery making the wormhole would briefly act as a time machine, carrying things back from late to early moments in the construction.

Although theorists initially reacted to Geroch鈥檚 discovery with derision, it is now known that general relativity permits the existence of wormhole time machines and the subject has become the focus of intense theoretical interest (鈥淲ormholes, time travel and quantum gravity鈥�, 快猫短视频, 28 April 1990, p 57).

There is, however, yet another snag. It is not enough simply to find a way to make a wormhole, you also need a mechanism to keep it open. The space in a wormhole is warped so unnaturally that without something holding it open it would snap shut in the blink of an eye. In 1988, Thorne and Morris discovered that their general solutions for traversable wormholes all needed to be threaded with strange material called 鈥渆xotic matter鈥�. This maintained the unnatural warpage of space by pushing outwards on the walls of the wormholes with an enormous 鈥渞epulsive gravity鈥�.

Repulsive gravity is not as crazy as it sounds. According to Einstein, two separate properties of matter contribute to its gravity. One is the amount of energy contained in a unit volume of the matter 鈥� its so-called 鈥渆nergy density鈥�, equal to its density times the square of the speed of light 鈥� and is always positive.

Pressure point

The other contribution comes from the pressure exerted by the matter on its surroundings, just as gas exerts a pressure by hammering on the walls of its container, and in principle the pressure can be positive or negative.

Usually, this pressure is very small compared to the vast amount of energy locked up in the matter. But Thorne and Morris envisaged a kind of matter with vast negative pressure. Matter with negative pressure has a tension, rather like a stretched spring. Exotic material possesses this property in spades. In fact, its negative pressure is so enormous that it actually exceeds its energy density. This changes the 鈥渟ign鈥� of the warpage of space, making gravity repulsive rather than attractive.

Exotic matter is weird stuff. Even so, some theorists have willingly entertained its existence in the first split-second of creation. According to the theory of 鈥渋nflation鈥�, the force that drove the enormous expansion of the Universe immediately after its creation was none other than the repulsive gravity of an 鈥渆xotic鈥� vacuum with a huge negative pressure (鈥淣othing like a vacuum鈥�, 快猫短视频, 25 February 1995, p 30).

Inflation might also provide the means of holding open a macroscopic wormhole that started life as a microscopic wormhole in the first moments of the Universe. Richard Gott, a theorist at Princeton University, and other physicists think that inflation may have created loops of 鈥渃osmic string鈥�, one-dimensional faults in space-time in which the 鈥渆xotic鈥� conditions of the inflationary vacuum are permanently preserved.

And Matt Visser of Washington University in St Louis, Missouri, has suggested that stable macroscopic wormholes could have been created by the simultaneous inflation of quantum wormholes and loops of cosmic string. The loops of string could have held the wormhole open as it rapidly expanded. Alternatively, Visser believes that an artificial wormhole, created by an advanced civilisation, could be stabilised with 鈥渟truts鈥� of exotic material, which would behave like a loop of cosmic string.

The problem is that no one knows if exotic matter still exists in today鈥檚 Universe, which puts rather a damper on traversable wormholes of the kind envisaged by Thorne and Morris. Maccone鈥檚 answer is to dispense with exotic matter altogether. After all, he says, his magnetic wormhole is threaded by nothing but a magnetic field, and a magnetic field blatantly violates Thorne and Morris鈥檚 requirement that whatever holds open a wormhole should exert a greater negative pressure than its energy density. The pressure exerted by the magnetic field because of the mutual repulsion of magnetic field lines is always less than its energy density.

But, says Maccone, Levi-Civita鈥檚 solution demonstrates that a magnetic field does not have to satisfy the same conditions as matter. 鈥淚t鈥檚 a surprising result and I don鈥檛 completely understand it yet,鈥� he admits. 鈥淏ut it seems that no exotic material is needed to make a magnetic wormhole.鈥�

Visser agrees with Maccone that the Levi-Civita solution does not require exotic matter. However, he disputes whether it is a wormhole at all. 鈥淚t鈥檚 a closed spherical universe,鈥� he says. 鈥淚t doesn鈥檛 take you anywhere because you鈥檙e actually in it.鈥�

鈥淚 admit that a magnetic wormhole would be a very peculiar beast,鈥� says Maccone. However, he suggests that it might be possible to 鈥渃ut away鈥� small sections of the wormhole鈥檚 profile just around the north and south poles to create two ends, enabling a light beam to travel through.

But Visser is still not satisfied. 鈥淭o create a mouth and join the region inside to the outside Universe, space will have to fold back on itself,鈥� he says. 鈥淎s far as I can see, the only way to do that is with exotic matter.鈥� If Visser is right then Maccone鈥檚 wormhole does, after all, use exotic matter. It鈥檚 just very well hidden.

Meanwhile, if there are any wormholes out in space, whether they are built from exotic matter or magnetic fields, some of them would have a remarkable property that could make them detectable from the Earth. The detection technique was suggested last year by a group of American physicists, including Cramer and Morris, now at Butler University in Indianapolis. It involves monitoring millions upon millions of distant stars for a period of many years. 鈥淚n theory, if a wormhole mouth happens to pass between the Earth and one of the stars, its gravity will cause the star鈥檚 light to fluctuate in an unusual and distinctive manner,鈥� says Morris.

Mass movements

It鈥檚 all to do with the appearance and disappearance of mass. When matter enters a wormhole, the 鈥渆ntrance鈥� obviously gains mass. However, according to the Russian astrophysicist Igor Novikov, at the same time the 鈥渆xit鈥� mouth loses a corresponding amount of mass. According to Novikov鈥檚 theory, even after the matter has left the other side of the wormhole, it will leave behind its imprint: one side of the wormhole will keep its acquired positive mass and the other side will still behave as if it had lost mass. Ultimately, says Novikov, it might even acquire a negative mass as the effect of successive transits built up.

A negative mass object would be a remarkable thing. Not only would it possess a repulsive gravitational force that would drive away any matter in its vicinity, it would also wreak havoc with light. It is the effect of such an object on light that Cramer and his colleagues have calculated (American Journal of Physics, vol 51, p 3117).

Star bright

If a normal object with a 鈥減ositive鈥� mass happens to pass between the Earth and a star, its gravity bends and magnifies the star鈥檚 light rather like a converging lens. This well-established phenomenon is known as 鈥済ravitational lensing鈥� and it causes the star to brighten for a few days before fading again. The repulsive gravity of a negative mass object would also bend the light from a distant star, but in a different way. 鈥淥ur naive expectation was that it would act as a diverging lens, temporarily dimming a distant star鈥檚 light,鈥� says Cramer. 鈥淗owever, this was not what we found when we did the calculations.鈥�

Cramer was surprised to find that in certain circumstances a negative mass object can actually cause a distant star to brighten more than an equivalent positive mass. This counterintuitive result has its root in the peculiar nature of gravitational lensing. 鈥淲hen light passes through a conventional glass lens, the rays which are most severely bent are those which are farthest from the optic axis,鈥� says Morris. 鈥淗owever, the opposite is true for a gravitational lens since gravity, and its ability to bend light, become weaker with increasing distance from a massive body.鈥�

The implications for a negative mass object are that rays close to the axis are repelled more strongly than those far from the axis. The rays therefore 鈥減ile up鈥� on either side of the lens in what physicists call a 鈥渃austic鈥�. In effect, the rays are pushed away from the axis and focused around the edges of the 鈥渓ens鈥� (see below). This concentration of light rays on either side of the object means that when it moves in front of a star an observer should see two sudden and dramatic jumps in brightness when the rays from the caustic on each side reach Earth. 鈥淭he 鈥榯win-peak鈥� signature of an object with a negative mass is very distinctive,鈥� says Morris.FIG-20223903.jpg

There is a possibility that the repulsive gravity of exotic matter might have a similar lensing effect, increasing astronomers鈥� chances of finding a wormhole. From the point of view of someone travelling through a wormhole, exotic matter has a negative energy density. However, the wormhole鈥檚 gravitational field will always have a positive mass density so, overall, the wormhole could appear to have a positive, zero or negative mass to an external observer.

Fortunately, there is no need to launch a special search for the signature of a negative mass object. For several years now three international teams of astronomers have been routinely monitoring the brightness of millions of distant stars in two places: a nearby galaxy called the Large Magellanic Cloud and in the centre of our own Milky Way. Their quarry has not been wormholes but dark objects which make up the mysterious 鈥渄ark matter鈥� that shrouds the Milky Way. So far, the teams have found the signatures of a dozen or so dark objects which have been dubbed massive astrophysical compact halo objects, or MACHOs (快猫短视频, Science, 29 April 1995, p 20).

A little mischievously, Cramer and his colleagues have called their quarry gravitationally negative anomalous compact halo objects, or GNACHOs, an umbrella term for wormhole mouths and any other, as yet unimagined, negative mass objects.

So does our Galaxy contain any GNACHOs? Morris and his colleagues became very excited when they saw a double peak in lensing data recorded by the Polish Optical Gravitational Lensing Experiment team in 1994. 鈥淲e were very encouraged,鈥� says Cramer. 鈥淭he event was surprisingly like what we were expecting for a wormhole.鈥�

However, a close examination of the 60-day 鈥渓ight curve鈥� revealed that the caustics were subtly different from those predicted for a GNACHO. The team concluded that what the Poles had found was not a wormhole mouth but something almost as exotic: two black holes in orbit round each other (Science, vol 268, p 643).

Cramer says he and his colleagues have alerted the MACHO teams to look for the distinctive wormhole signature, but they are only too well aware how difficult it will be to find one. 鈥淚t鈥檚 a very long shot, I admit,鈥� says Morris.

With this flurry of activity, it seems that wormholes are no longer simply the province of science fiction. But unless the GNACHO searchers get very lucky, and unless the many practical and theoretical problems involved in making a wormhole are overcome, it will be some time before we can take a day trip to Alpha Centauri by travelling through one.