Traditionally, writers of “hard” Sf are supposed to work within the framework of the known laws of physics as far as possible, but are allowed to make use of two “impossible” assumptions. One is space travel at speeds faster than that of light, which is forbidden by the equations of relativity theory, and which no scientist believes to be possible. The other is, or was, time travel, which flies in the face of common sense, and is “obviously” impossible. But in recent years, relativists have been forced to the uncomfortable conclusion that, in fact, time travel is not ruled out by Einstein’s equations.
Here is the English language version of an article of mine which first appeared in Italian in the sober pages of the science fact magazine l’Astronomia. The bottom line is that there is nothing in the laws of physics which forbids time travel, with all that that implies. The safety net favoured by relativists in our location is that actually constructing such a machine would involve very advanced technology. But that is a far cry from it being scientifically impossible (like travelling at a speed faster than that of light), and as Arthur C. Clarke once said, any sufficiently advanced technology is indistinguishable from magic.
Scientific understanding of the way the Universe works, in the form of the general theory of relativity, has now progressed to the point where it is possible to provide you with the following simple instructions for building a time machine. This is now a practicable possibility, limited only by the available technology; we can accept no responsibility, however, for any paradoxes caused by the operation of such a machine.
First, catch your black hole. Do not try to find a black hole in the container in which you received these instructions. The black hole is not supplied with the instructions, and is not included in the price.
A black hole is an object which has such a strong gravitational pull that it wraps spacetime around itself, like a soap bubble, cutting off the inside of the hole from the rest of the Universe. To give you some idea of what this involves, imagine turning our Sun into a black hole. The Sun is about a million times bigger, in terms of volume, than the Earth. But in order to turn it into a black hole, it would have to be squeezed into a sphere only a few kilometers across—about the size of Mount Everest, or the Isle of Wight.
Nevertheless, astronomers are sure that black holes like this do exist. They can detect them by their gravitational influence on nearby stars—if you see a star being tugged sideways by something that isn’t there, the chances are that the invisible something is not the infamous cat Macavity, but a black hole.
As you are no doubt aware from your study of Einstein’s equations, every black hole has two ends, and is properly regarded as a “wormhole”, linking two different locations in spacetime by a tunnel through hyperspace. We suggest that in order to avoid problems with spaghettification (see below), the black hole should have a minimum mass of about 100 times the mass of our Sun. This will make it very easy to tow the hole to a convenient location (such as the back yard of the Solar System, between the orbits of Mars and Jupiter) by dangling a moderate sized planet (you may find Jupiter convenient for this task) in front of it and moving the planet. The gravitational attraction between the planet and the black hole will then bring the hole along behind like a donkey following a carrot.
If you do not have a spacecraft capable of towing planets, we refer you to our leaflet “Build Your Own Spaceship”, available from the usual address.
It is now necessary to ensure that both ends of the black hole are in the same place, but at different times. This is achieved by driving your spaceship into the black hole, and out of the other end of the tunnel. After identifying your location from the star maps provided, tow the other end of the hole back to the Solar System.
You can now adjust the time machine to your own specification using the relativistic time dilation procedure. This involves whirling the second end of the black hole round in a circle, at a speed of approximately half the speed of light (that is, 150 million kilometers per second) for an appropriate period. The relativistic time dilation effect will ensure that a time difference builds up between the two ends of the hole. After checking the time difference from the usual geological indicators, to ensure just the amount required, you may then bring the hole to a halt, and your time machine is ready to use.
WARNING: We can take no responsibility for difficulties caused by careless use of the time machine. Before attempting to use the time machine, please read the following historical background and explanation of the granny paradox:
When astronomer Carl Sagan decided to write a science fiction novel, he needed a fictional device that would allow his characters to travel great distances across the Universe. He knew, of course, that it is impossible to travel faster than light; and he also knew that there was a common convention in science fiction that allowed writers to use the gimmick of a shortcut through “hyperspace” as a means around this problem. But, being a scientist, Sagan wanted something that would seem to be more substantial than a conventional gimmick for his story. Was there any way to dress up the mumbo-jumbo of Sf hyperspace in a cloak of respectable sounding science? Sagan didn’t know. He isn’t an expert on general relativity—his background specialty is planetary studies. But he knew just the man to turn to for some advice on how to make the obviously impossible idea of hyperspace connections through spacetime sound a bit more scientifically plausible in his book Contact.
The man Sagan turned to for advice, in the summer of 1985, was Kip Thorne, at CalTech. Thorne was sufficiently intrigued to set two of his PhD students, Michael Morris and Ulvi Yurtsever, the task of working out some details of the physical behaviour of what the relativists call “wormholes”—tunnels through spacetime. At that time, in the mid-1980s, relativists had long been aware that the equations of the general theory provided for the possibility of such hyperspace connections. But before Sagan set the ball rolling again, it had seemed that such hyperspace connections had no physical significance and could never, even in principle, be used as shortcuts to travel from one part of the Universe to another.
Morris and Yurtsever found that this widely held belief was wrong. By starting out from the mathematical end of the problem, they constructed a set of equations that matched Sagan’s requirement of a wormhole that could be physically traversed by human beings. Then they investigated the physics, to see if there was any way in which the known laws of physics could conspire to produce the required geometry. To their own surprise, and the delight of Sagan, they found that there is. To be sure, the physical requirements seem rather contrived and implausible. But that isn’t the point. What matters is that it seems that there is nothing in the laws of physics that forbids travel through wormholes. The science fiction writers were right—hyperspace connections do, at least in theory, provide a means to travel to far distant regions of the Universe without spending thousands of years pottering along through ordinary flat space at less than the speed of light.
The conclusions reached by the CalTech team duly appeared as the scientifically accurate window dressing in Sagan’s novel when it was published in 1986, although few readers can have appreciated that most of the “mumbo-jumbo” was soundly based on the latest discoveries made by mathematical relativists. And then, like a cartoon character smiting himself on the head as the penny dropped, the relativists realised that this isn’t the end of the story.
The point is that these tunnels, or wormholes, go through spacetime, not just space. Einstein taught us that space and time are inextricably linked, in a four-dimensional entity called spacetime. You can’t, in the words of the old song, have one without the other. It follows that a tunnel through space is also a tunnel through time. The kind of hyperspace connections described in Contact, and based on real physics, could indeed also be used for time travel.
The CalTech researchers have shown how two black holes like this could lie at opposite ends of a wormhole through hyperspace. And the two black holes can lie not just in different places, but at different times—or even at the same place but in different times. Jump in one hole, and you would pop out of the other at a different time, either in the past or the future. Jump back in to the hole you popped out of, and you would be sent back to your starting point in space and time.
The time tunnel you haver constructed using the above instructions always has the end that has been whirled around at half the speed of light in the future compared with the “stationary” end. Jump in the mouth that has been moved, and you emerge from the stationary mouth at the time corresponding to the clocks attached to the moving mouth—in the past, compared with where you started. You can set the interval of the time difference to be anything you like, using the time dilation effect, but you can never go back into the past to an earlier time than the moment at which you completed the time machine. In order to do that—for example, to go back in time to watch the 1966 World Cup Final—you need to find a naturally occurring time machine, or one built by an ancient civilization and left in orbit around a convenient star (see our leaflet, Locating Alien Civilizations The Easy Way). One obvious possibility would be to take a naturally occurring microscopic wormhole, and expand it to the required size using cosmic string.
Cosmic string, of course, is the material left over from the Big Bang of creation, which stretches across the Universe but has a width much narrower than that of an atom. Among its other interesting properties, cosmic string experiences negative tension—if you stretch a piece, instead of trying to snap back into its original shape, it stretches more. Any experienced do-it-yourself enthusiast will appreciate that this offers a useful means to hold the throat of a wormhole open.
HAZARDS: Please read the following section before entering the black hole:
The kind of black hole astronomers are familiar with, containing as much mass as our Sun, would have a very strong tidal pull. What this means is that as you fell into it feet first, your feet would get pulled harder than your head, so your body would stretch. At the same time, tidal forces would squeeze you sideways. The relativists have a technical term for the resulting effect; they call it “spaghettification”. In order to avoid spaghettification, the black holes that provide the entrances and exits to hyperspace should ideally contain about a million times as much mass as our Sun, and be about as big across as our entire Solar System. This is impractical at the present state of technology, but the hundred solar mass black holes we recommend can be navigated successfully, avoiding spaghettification, if care is taken to avoid the central singularity. We accept no responsibility for injuries caused by reckless driving.
2. The granny paradox
BE CAREFUL who you bring back from the future with you, and what activities they get up to while visiting your time. Suppose you use the time machine to go forward in time a few decades, and bring back a young man to visit his granny when she was a young girl, before his mother was born. The traveller from the future may, either by accident or design, cause the death of his granny as a young girl. Now, if granny died before his mother was born, obviously he never existed. So you never brought him back in time, and granny was never killed. So you did bring him back in time … and so on. WE DO NOT ACCEPT RESPONSIBILITY for paradoxes caused by careless use of the time machine.
As well as the paradoxes, time travel opens up the possibility of strange loops in which cause and effect get thoroughly mixed up. In his story “All You Zombies”, Robert Heinlein describes how a young orphan girl is seduced by a man who turns out to be a time traveller, and has a baby daughter which is left for adoption. As a result of complications uncovered by the birth, “she” has a sex change operation, and becomes a man. “Her” seducer recruits “her” into the time service, and reveals that he is in fact “her” older self. The baby, which the older version has meanwhile taken back in time to the original orphanage, is a younger version of both of them. The closed loop is delightful, and, we are now told, violates no known laws of physics—although the biology involved is decidedly implausible. WE DO NOT ACCEPT RESPONSIBILITY for travellers stuck in time loops.
And now, you are ready to enjoy decades of harmless amusement with your time machine. In the event of difficulties, please do not hesitate to contact our customer service department, which is located at the usual address, and in the year 4242 AD.
DEEP SCIENCE: Readers interested in the scientific theory underlying time machine construction, rather than just the practical aspects, may be interested to know something of current black hole research. Quite apart from the large black holes you would need to build a working time machine, the equations say that the Universe may be full of absolutely tiny black holes, each much smaller than an atom. These black holes might make up the very structure of “empty space” itself. Because they are so small, nothing material could ever fall in to such a “microscopic” black hole—if your mouth is smaller than an atom, there is very little you can feed on. But if the theory is right, these microscopic wormholes may provide a network of hyperspace connections which links every point in space and time with every other point in space and time.
This could be very useful, because one of the deep mysteries of the Universe is how every bit of the Universe knows what the laws of physics are. Consider an electron. All electrons have exactly the same mass, and exactly the same electric charge. This is true of electrons here on Earth, and studies of the spectrum of light from distant stars show that it is also true of electrons in galaxies millions of light years away, on the other side of the Universe. But how do all these electrons “know” what charge and mass they ought to have? If no signal can travel faster than light (which is certainly true, many experiments have confirmed, in ordinary space), how do electrons here on Earth and those in distant galaxies relate to each other and make sure they all have identical properties?
The answer may lie in all those myriads of microscopic black holes and tiny wormhole connections through hyperspace. Nothing material can travel through a microscopic wormhole—but maybe information (the laws of physics) can leak through the wormholes, spreading instantaneously to every part of the universe and every point in time to ensure that all the electrons, all the atoms and everything that they are made of and that they make up obeys the same physical laws.
And there you have the ultimate paradox. It may be that we only actually have universal laws of physics because time travel is possible. In which case, it is hardly surprising that the laws of physics permit time travel.
For more about black holes in general, cosmic string, and time travel in particular, see:
John Gribbin, In Search of the Edge of Time (US title Unveiling the Edge of Time), Penguin, London and Harmony, New York.
John and Mary Gribbin, Time & Space, Dorling Kindersley, London.
Kip Thorne, Black Holes and Time Warps, Norton, New York, and Picador, London.
And not forgetting my novel Timeswitch (PS publishing).