The title of Heinrich P盲s鈥檚 latest paper might not mean much to you. To those who know their theoretical physics, however, 鈥淐losed timelike curves in asymmetrically warped brane universes鈥� contains a revelation. It suggests that time machines might be far more common than we ever thought possible.
Forget trawling the universe in search of rotating black holes or exotic wormhole tunnels that could supposedly let us hop from one instant to another. According to P盲s, a physicist at the University of Hawaii at Manoa, and his colleagues, the door to a time machine could be anywhere and everywhere in our universe. And unlike most other scenarios for time travel, we can test this one here on Earth. 鈥淚 think the ideas presented are wonderful and exciting,鈥� says Bill Louis, a physicist at Los Alamos National Laboratory in New Mexico and co-spokesperson for the MiniBoone neutrino experiment at Fermilab, near Chicago. 鈥淭he question is are they true or not.鈥�
Louis is right to be cautious. Although nothing in the laws of nature appears to rule out time travel, physicists have always been uneasy about it because it makes a mockery of causality, the idea that cause always precedes effect. Violating causality would play havoc with the universe, for instance, allowing you to travel back in time and prevent your own birth.
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Such paradoxes are what led Stephen Hawking to propose his 鈥渃hronology protection conjecture鈥�. This basically says that some principle of physics, perhaps as yet undiscovered, will always come to the rescue and prevent time travel from happening. Yet no one had been able to flesh out the details until three years ago when several groups of researchers claimed that string theory, physicists鈥� best stab at a prospective 鈥渢heory of everything鈥�, was beginning to close the door on time machines (快猫短视频, 20 September 2003, p 28).
All very well, except theoretical physicists are notorious for never taking no for an answer. P盲s and his colleagues Sandip Pakvasa of the University of Hawaii and Thomas Weiler of Vanderbilt University in Nashville, Tennessee, have been re-examining string theory. It views the fundamental building blocks of the universe not as point-like particles but vibrating strings of energy; the faster the vibration the greater the mass of the particle.
Such vibrating strings can account for the myriad interactions of all the known subatomic particles, such as quarks and electrons. But there is a catch 鈥� it only works if the strings vibrate in a space-time with 10 dimensions rather than the four with which we are familiar. Proponents of the idea maintain that the extra dimensions are either so fantastically small that we have not noticed them, or so large and warped in such a way that, again, they have remained hidden from view.
This has led to the suggestion that our universe may be like a four-dimensional membrane or 鈥渂rane鈥� adrift in a higher-dimensional space-time. All of the particles and forces in our universe would be trapped in our brane like flies on fly-paper, so we would have no knowledge of any dimensions other than the four we experience, even though our brane might be floating in a 10-dimensional space-time, or 鈥渂ulk鈥�. 鈥淚f it is, then there is the possibility of short cuts through higher-dimensional space,鈥� says P盲s. 鈥淚t鈥檚 such short cuts that make time travel possible.鈥�
鈥淭ime machines might be far more common than we ever thought possible鈥�
It is not too difficult to visualise such a short cut. Suppose our brane-universe is bent back on itself within a large extra dimension, making it the four-dimensional equivalent of a pancake folded in two. Then you could imagine leaving the brane at one point, travelling a short distance through the bulk and re-entering the brane at a point far away from your starting point.
There is a problem with this picture, however. Although we can visualise a universe where such a short cut is possible, it cannot be our universe. That is because the space-time of such a severely folded brane is not compatible with Einstein鈥檚 special theory of relativity, which posits a 鈥淓uclidean geometry鈥� where space is perfectly flat. Since numerous tests of special relativity have shown that its predictions in our locality are accurate to better than 1 part in a million, it is very unlikely that our universe is shaped like a folded pancake.
Instead P盲s, Pakvasa and Weiler consider a space-time where our universe is a flat brane that is immersed in a bulk whose own dimensions are seriously warped. Because the brane is flat, special relativity still applies there. Yet in the bulk, P盲s, Pakvasa and Weiler have found that the large dimensions can be distorted in such a way that special relativity does not apply within them. This means that anything moving through the fifth dimension can break one of the founding principles of special relativity: it can travel faster than the speed of light as we know it.
This has dramatic consequences for inhabitants stuck on the brane. To them, any entity that takes a short cut through the bulk appears to vanish and then pops up again at some point on the brane far sooner than it could have had it kept to the brane. For some inhabitants of the brane world, the entity appears to have travelled faster than the speed of light. Weirder still, to others it has also travelled backwards in time. That鈥檚 because special relativity says that from certain frames of reference, faster-than-light travel is equivalent to travelling backwards in time. 鈥淪uch off-brane short cuts can appear as 鈥榗losed timelike curves鈥�,鈥� says P盲s 鈥� again, that鈥檚 code for time machines.
Escape from the brane
The trouble with this idea is that it assumes there is some way to escape the confines of the brane and travel out into the bulk. How could we do this? Fortunately string theory provides a way out. In the theory almost all of the building blocks of matter are represented by strings whose ends are forever anchored to the brane. This means they can never escape into the fifth dimension and take a short cut through space-time. But there are two crucial exceptions: the hypothetical carrier of the gravitational force, called the graviton, and a fourth type of neutrino called a sterile neutrino (after the three ordinary kinds of neutrino). In string theory these are represented by closed loops of string. Since they have no ends attached to the brane, they are free to leave and travel into the bulk.
String theorists have pointed to this property of gravitons to explain why gravity is tremendously weaker than nature鈥檚 other fundamental forces, such as electromagnetism. The idea is that gravity is so weak because a large proportion of gravitons leak away into the extra dimensions of the bulk. More intriguingly, however, their ability to take short cuts through the bulk also means gravitons and sterile neutrinos are potential time travellers. 鈥淚f we can manipulate them, we can study time travel experimentally,鈥� says P盲s.
None of this will be easy. No one has ever spotted a graviton or a sterile neutrino, and the odds of detecting them are slim, to say the least (快猫短视频, 18 March, p 32). Trillions of ordinary neutrinos pass through our bodies every second, yet we feel nothing because they so rarely interact with electrons and atoms. Sterile neutrinos are even less communicative because they are thought to interact only via the feeble gravitational force and the exchange of the elusive Higgs boson 鈥� an as yet undetected particle believed to endow all particles with mass.
P盲s and his colleagues point out that a quirk of quantum mechanics could save the day. According to the laws of quantum physics, neutrinos can flip from one kind to another. Experiments in Japan and the US designed to detect neutrinos on the rare occasions they do interact with matter have confirmed that neutrinos spewed out by the sun and those from space do indeed change type. This phenomenon should affect sterile neutrinos too, changing them into ordinary, detectable neutrinos and back again. What鈥檚 more, the odds of this happening increase whenever the density of the material the neutrinos are travelling through changes abruptly.
鈥淎 quirk of quantum mechanics could allow us to test time travel right here on Earth鈥�
This has inspired P盲s and his colleagues to propose an experiment that could test their ideas. They suggest sending a beam of ordinary neutrinos through the Earth, from a research station at the South Pole towards a detector located at the equator. When they enter the ground, some of the neutrinos will flip into sterile neutrinos. Capable of taking a short cut though the extra dimensions of the bulk, these sterile neutrinos will reach the other side of the Earth first, apparently having travelled faster than light. As they pass out of the ground into the air again, they will flip back into ordinary neutrinos, which can be detected. Because the Earth is rotating, these faster-than-light neutrinos can appear to have arrived before they set off.
Such an experiment is beyond our current technological capabilities but, remarkably, P盲s says it is a realistic proposition within the next 50 years. Of course, it requires two things. The first is the existence of sterile neutrinos. While many physicists are keen on the idea of sterile neutrinos, they are barely beyond theoretical flights of fancy. The other is that we live in an asymmetrically warped space-time, as P盲s prescribes. How plausible is this?
When Einstein鈥檚 came up with his general theory of relativity, he showed us how space-time can be warped or flat, but his equations tell us nothing about the actual shape of our universe 鈥� merely that different shapes are possible. For instance, cosmologists have no way of knowing if space stretches out to infinity or curves back on itself. This opens the door to many different types of time machines, some more plausible than others.
One famous solution to Einstein鈥檚 equations, formulated by mathematician Kurt G枚del, describes a universe that rotates rapidly. Instead of travelling in straight lines, light will appear to travel in a spiral. G枚del realised that this allows a traveller to outrun light and return to their starting point before they left. In other words, G枚del鈥檚 rotating universe is a time machine. 鈥淏ut we know we don鈥檛 live in such a universe,鈥� says P盲s.
Another time machine exists inside rotating black holes, where space-time becomes so warped that space and time change places. The trouble is, as P盲s points out, rotating black holes are inaccessible to us. Then there is the space-time surrounding an infinitely long, rapidly rotating cylinder, as proposed by physicist Frank Tipler. P盲s is quick to dismiss it too. 鈥淚t requires huge masses rotating unphysically fast,鈥� he says.
Among the other leading contenders are wormholes, microscopic tubes of space-time that act as tunnels from one point to another. But before you climb into one, there is a problem: wormholes snap shut in an instant unless propped open by a supply of something called exotic matter. Unlike the familiar stuff found on Earth, which always feels the pull of gravity, this exotic matter has repulsive gravity, halting the wormhole鈥檚 collapse. 鈥淲e don鈥檛 know whether such matter exists and if it is stable,鈥� says P盲s.
P盲s confesses that the scenario his team has examined also requires exotic matter to warp the fifth dimension, but he still maintains that it is more plausible than the other scenarios. What sets their space-time apart from wormholes is that the hypothetical exotic matter is hidden away in the higher-dimensional bulk instead of roaming around the brane. If it exists, this might explain why we have never seen it.
Understandably, the idea is not without its critics. Sydney Deser of Brandeis University in Waltham, Massachusetts, is convinced, as was Einstein, that time machines are not possible and does not like 鈥渦nphysical鈥� exotic matter. He believes that concealing it in the bulk, as P盲s鈥檚 team suggests, is little better than a scenario in which it is out in the open. 鈥淚t鈥檚 only a matter of degree,鈥� he says.
P盲s, however, points out that the kind of space-times he and his colleagues have considered can do away with a number of problems that have plagued general relativity. For instance, faster-than-light connections between far-flung parts of the cosmos would have allowed heat to flow back and forth across the early universe. This would have evened out any temperature variations, explaining the uniformity that cosmologists observe. This could provide an alternative to the theory of inflation, in which cosmologists believe space-time was stretched unimaginably fast after the big bang, and which would also account for the evenness in temperature. While the majority of cosmologists believe in inflation, no one has explained the detailed physics behind it.
Warped universe
Others do not find asymmetrically warped space-times so plausible. 鈥淚 certainly think the idea is interesting, but I have some worries,鈥� says Tony Padilla of the University of Barcelona in Spain. 鈥淔or a start, I think it is premature to claim that these space-times are 鈥榥atural鈥�. One needs to examine their stability first, and in this case I would expect the solution to be unstable, although I could be wrong.鈥�
Padilla concedes that it is possible that we may one day find a stable brane universe with the properties described by P盲s鈥檚 team. 鈥淚鈥檓 just not convinced we are there yet,鈥� he says.
John Cramer of the University of Washington in Seattle agrees that the work outlines some interesting ideas. 鈥淭he scheme, however, requires asymmetrically warped brane universes 鈥� and our universe may not be one of these,鈥� he cautions. 鈥淣evertheless, it鈥檚 a fascinating proposal.鈥�
Of course, if time travel is possible in the way P盲s envisages, it may be accessible only to special particles like sterile neutrinos and gravitons, and therefore won鈥檛 cause much havoc in the everyday universe. P盲s takes a pragmatic view of all this. As long as the possibility of time machines remains, he believes it is worth exploring experimentally. 鈥淓ven if time travel is not possible, by manipulating particles like sterile neutrinos we can explore the physics that intervenes to prevent it,鈥� he says.
鈥淎nything travelling through the fifth dimension can move faster than the speed of light as we know it鈥�
The first answers might come soon courtesy of the MiniBoone neutrino experiment at Fermilab. It could confirm the existence of sterile neutrinos and short cuts in extra dimensions as early as this year. Then again, if time travel really is true, maybe the answer has already been published.
