How to Build a Time Machine

by Paul Davies

  3 How to build the time machine

  * * *

  Wormholes and time machines today are regarded as out-regeous by most physicists. Kip Thorne

  Some scientists think wormholes may have formed naturally in the big bang, so that an advanced spacefaring civilization might expect to discover one in the galaxy and commandeer it for the purpose of making a time machine. However, it would obviously be more convenient to manufacture one artificially. But how do you go about constructing a traversable wormhole and turning it into a time machine? Here is a possible scheme for a production factory. The construction is a four-stage process, represented by four workshops, containing, respectively, a collider, an imploder, an inflator and a differentiator. Let me explain the purpose of each in turn.

  (see A time machine factory on pages 78–9)

  Caption

  A time machine factory

  The collider

  An obvious and rather fundamental problem stands in the way of any attempt to make a wormhole in a normal region of spacetime. Think how you would go about producing one using a sheet of paper. Although the sheet may be folded over until it touches itself, there is no way you can join the two surfaces to form the wormhole without cutting the paper and pasting it together again. No matter how much you twist and turn, pull and push, at some stage an incision has to be made. The problem is the same as that of taking a ball of putty and turning it into a doughnut shape. You can't avoid tearing at the putty to make a hole. This difficulty is independent of the precise geometry involved; it is a property of the topology of the system.

  In the case of a wormhole in space, the ‘sheet’ is space itself. It is important to realize that the wormhole isn't a hole through anything - it is actually made of space.

  So how do you carry out surgery on space? Nobody knows how to do this on a large scale. Think what it would mean to cut into the space near Earth. Before you pasted it together again, you would have exposed a raw edge. As we saw in chapter 2, edges to space are possible – they are called ‘singularities’ – and are seriously bad news. That was the way the Schwarzschild wormhole was created – at a singularity with infinite density – but it was buried inside a black hole. An

  exposed edge of the sort needed to make a traversable worm-hole would be a naked singularity; such a thing might play havoc with nature. In any case, building a wormhole by making spacetime singularities is too violent; we want to do the job in a more controlled manner.

  A better method is to employ the quantum vacuum. Quantum mechanics is based on Heisenberg's uncertainty principle, which predicts that all physical quantities fluctuate randomly. On an atomic scale, properties like the speed or energy of a particle can be highly uncertain. As a general rule, the smaller the scale, the bigger the fluctuations. At some tiny size, quantum uncertainty will become so big it will produce significant gravitational effects. We can see that by considering energy. According to Heisenberg's uncertainty principle, energy will be uncertain for brief durations, which means its value can change unpredictably. One way to think of this is in terms of borrowing. An electron, say, can borrow energy from nature, so long as it pays it back in a short while. The essence of the uncertainty principle is that the bigger the loan, the quicker the payback time.

  Putting in the numbers, you find that for a duration as brief as a ten million-trillion-trillion-trillionth of a second, known as the Planck time (after Max Planck), so much energy can be borrowed that its mass will seriously warp spacetime, sculpting it into elaborate structures. It's not clear exactly what the upshot is, but John Wheeler has painted a vivid picture of a labyrinth of tubes and tunnels, which he evocatively calls spacetime foam. The size of these structures is about a billion trillion trillionth of a centimetre (known as the Planck length), which is exceedingly small – twenty powers of ten smaller than an atomic nucleus, in fact.

  Now the quantum wormholes I'm talking about aren't permanently embedded in space because they live on borrowed time. The energy needed to bend space into a complex foam is on loan via the Heisenberg uncertainty principle. So quantum wormholes don't last; they come and go at a frenetic pace.

  But what about the cutting-and-pasting problems mentioned above? In the quantum domain, the difficulty of singularities is circumvented. Changes in topology become submerged in the overall quantum fuzziness of everything. Trying to pin down where space might be ripped open is as pointless as attempting to locate where an electron is in an atomic orbit. Such things are intrinsically indeterminate in quantum physics.

  To distinguish the temporary, ghostly, quantum wormholes from big, permanent, real ones, physicists refer to the former as virtual. A virtual wormhole is one that exists fleetingly, care of the Heisenberg uncertainty principle. Thorne has suggested that an advanced civilization might develop the technology to reach into the spacetime foam, pluck out a virtual wormhole, and expand it into a big, permanent one. This means gaining control over nature on a scale of size about 15 powers of ten smaller than our current capabilities.

  A direct approach looks hopeless. However, there may be a way to do it indirectly. One problem about harvesting virtual wormholes from the spacetime foam is that they typically last for only a Planck time before vanishing. To create a permanent wormhole, we must artificially inject enough energy into the spacetime foam to ‘clear’ the loan on the virtual wormhole's behalf, and thereby promote it to a real one. It sounds fanciful, but we do a similar thing all the time in radio transmitters. An electric field can be envisaged as a cloud of virtual photons scurrying around a charged particle such as an electron. If energy is fed into the system – say, by accelerating the electron in a wire – then some of the virtual photons are turned into real photons and flow away from the wire in the form of radio waves.

  Incidentally, the Heisenberg (energy-time) uncertainty principle also has important implications for the nature of empty space: it means there is no such thing as a perfect vacuum. Even when you have removed all particles of matter and all photons, there will still be virtual photons (and virtual versions of all other types of particle) popping into temporary existence Virtual photons permeate all of space, filling it with a seething ferment of quantum activity. What may appear at first to be total emptiness is, in fact, a beehive of fluctuating ghosts, appearing and disappearing in an unpredictable frolic. And this isn't just theory. Virtual photons manifest themselves physically in a number of ways. For example, they jostle electrons in atomic orbits, producing small but measurable changes in the energy levels. They also produce the so-called Casimir effect, which I shall discuss on pp. 89–92.

  The collider is the first step to delivering the required energy to the spacetime foam. It involves a heavy-ion accelerator of the type employed at the Brookhaven National Laboratory on Long Island, New York. This machine is designed to boost the nuclei of atoms such as gold and uranium to colossal energies, and then collide them head on. The nuclei are confined by magnetic fields to a ring-shaped vacuum tube, in which they are accelerated using electric pulses, and arranged so that counter-rotating beams of nuclei are brought into high-speed contact. The collisions are designed to be so violent that they briefly re-create the conditions that prevailed in the universe about a microsecond after the big bang, when the temperature was a searing 10 trillion degrees.

  When the nuclei smash into each other, their constituent protons and neutrons are pulverized, creating a bubble of energized fragments known as a quark–gluon plasma. (Sometimes the dramatic phrase ‘melting the quantum vacuum’ is used.) In effect, the components of the nuclear particles – quarks and gluons – part company and mill around inside an amorphous blob.

  Having created the quark-gluon plasma bubble, the next step is to pass it on to the imploder.

  The imploder

  Although by human standards a quark-gluon plasma is highly energized, it is a long way from our present requirements. The enormous temperature of 10 trillion degrees inside the bubble is still about 19 powers of ten too low t
o affect the spacetime foam. To boost the temperature up to Planck values we need to compress the bubble by a factor of a billion billion. Surprisingly, the total energy involved to achieve this is very modest - about 10 billion joules, equivalent to the total output of a typical power station for only a few seconds. So energy is not a limiting factor at this step. The challenge is to concentrate that much energy into such a small object.

  It's not clear how this might be done, but explosive magnetic pinching could offer a way. Magnetic fields are used to confine conventional low-energy plasmas, such as ionized gases. If the field is intensified, the plasma gets squeezed. Scientists began experimenting with this technique, known as the Z-pinch, in the early 1950s, as part of the programme to develop controlled nuclear fusion. An intense electric current is passed through deuterium gas in a chamber, rapidly ionizing it. The magnetic field of the current then violently pinches the resulting plasma and heats it to millions of degrees. The most refined Z-pinch system in current use is at the Sandia National Laboratories in New Mexico, where electrical pulses of 50 trillion watts from a bank of charged capacitors are concentrated onto ultra-thin tungsten wires.

  The sort of compression needed to reach Planck temperatures demands far more punch than the Sandia system. A collection of thermonuclear bombs arranged in a spherical pattern centred on the target might be able to concentrate a magnetic field enough to implode the quark-gluon bubble. To repeat, the total energy required is not great; it merely needs to be directed at the target bubble rather than spewing into the surroundings. Assuming the concentration problem can be solved, the net effect will be to create a tiny ball with a density of about 10 trillion trillion trillion trillion trillion trillion trillion trillion kilograms per cubic metre, or some 80 powers of ten greater than the density of nuclear matter. This is enough to rival the vast energy fluctuations permitted at the Planck length: a billion-trillion-trillionth of a centimetre – the distance light will travel in a Planck time. Hopefully, the result would be to form either a minute black hole or a wormhole that would become the seed for growing the time machine.

  To implement the compression, some serious problems of basic physics need to be addressed alongside the engineering challenges. Quantum field theory suggests that if a magnetic field gets too strong it may start to create subatomic particles and thereby dissipate itself. Also, magnetic pinching is notoriously unstable. These difficulties could possibly be circumvented by using another type of field altogether, such as the so-called Higgs field that is being sought eagerly by particle physicists.

  Alternatively, an accelerator might be employed in place of an imploder. With conventional electromagnetic technology, Planck energies could be attained only by building an accelerator as big as the solar system, but radical new accelerator techniques might achieve very high energies with much more compact equipment. Also, some theories suggest that major changes to space and time might manifest themselves at energies much less than the Planck energy, and may even lie within the reach of foreseeable technology. If gravity can be manipulated at modest energies, wormholes may form without the need for such enormous compression or acceleration.

  Once a real, albeit miniscule, wormhole is produced, the next step is to inflate it to manageable dimensions.

  The inflator

  Since a Planck-sized wormhole is practically useless, some method has to be used to drastically enlarge it. As we have seen, the crucial ingredient in stabilizing a traversable worm-hole is some sort of exotic matter with antigravitational properties. So the next step in the production process is to feed the nascent microscopic wormhole with exotic matter. Its antigravity would then push the throat of the wormhole outwards, enlarging the size. The scheme I am proposing uses a bank of high-powered lasers with an ultra-fast rotating mirror system.

  Before writing any more about the inflator, I need to explain a bit more about antigravity. In chapter 2 I discussed how it can be produced by negative energy (see p. 71). So how do you create negative energy? A simple method was discovered by the Dutch physicist Hendrik Casimir in 1948. This is what you do. Take two sheets of metal and place them close to each other, face to face. Secure them so they don't move. Now enclose the entire system in a large, thick metal box from which all other material (including gases, electrically charged and neutral particles) have been removed, and cool to absolute zero (-273 degrees centigrade). The slab of empty space between the plates now contains negative energy.

  (see Hendrik Casimir on page 90)

  The explanation

  The Casimir effect is a phenomenon of the quantum vacuum. Strictly, I should not cite it as an example of exotic matter, because it refers to a state of empty space. But this is a terminological quibble: the distinctions between field excitations, matter, and emptiness is very blurred in quantum physics.

  This is why the negative Casimir energy arises. The apparently empty space between the plates is not a complete

  Caption

  Hendrik Casimir

  vacuum, but populated by a seething mass of virtual photons. Like their real counterparts, virtual photons rebound from the metal plates. Being sandwiched between the plates, they are not free to move in any direction, so this restriction affects the variety of virtual photons that can inhabit the interplate region compared with the space outside the plates. In effect, the possibility for some sorts of virtual photons to exist is eliminated by the presence of the plates. As a result, the total energy being ‘borrowed’ (via Heisenberg's uncertainty principle) in the interplate region is a bit less than it would have been without the plates. If we agree that apparently empty space without any plates has exactly zero energy, then the region between the plates must have negative energy. The negative energy manifests itself by producing a tiny force of attraction between the plates.

  Can it be done?

  Yes! It has been done. The Casimir force was first measured in the laboratory in 1958, and has been studied many times since. In these experiments no attempt is made to remove all the (much larger and positive) other sources of energy pervading the system, since the purpose of the experiments is to test Casimir's prediction, not actually to create a region of negative energy. The experiments confirm the theory. The force of attraction between two perfectly reflecting plates one metre square held 0.01 millimetre apart is equivalent to the weight of just a millionth of a gram. But the force grows larger as the plates get closer. With real metal sheets, which are never perfectly flat, the effect is complicated by other factors long before the Casimir force becomes large. However, this hasn't stopped some imaginative theorists toying with ideas of using the Casimir, and other quantum vacuum effects, as the basis of a spacecraft propulsion system.

  Other ways of making negative energy

  The Casimir effect is the most famous, and easiest, method of producing negative energy by disturbing the quantum vacuum. But there are other ways, too. Negative quantum vacuum energy can be created by a single reflecting surface (i.e. a mirror) if it is moved vigorously. In the mid 1970s I studied this ‘moving mirror’ effect in great detail with my collaborator Stephen Fulling. We restricted our work to a simple one-dimensional model, but similar results are likely to apply in real three-dimensional space, too. We found that if a mirror moves with increasing acceleration, a flux of negative energy emanates from its surface and flows out into the space ahead of the mirror. Unfortunately the effect is exceedingly small; it would not be a practical way to generate large amounts of negative energy.

  Probably the most promising negative energy generator is

  the laser – a high-energy source of very pure, or coherent, light. In a typical set-up, a laser beam is passed through a crystal of lithium niobate, shaped like a cylinder with rounded silvered ends to reflect light, so forming a type of optical cavity resonator. The crystal has the effect of producing a secondary beam at a lower frequency in which the pattern of photons is rearranged into pairs. This is technically known as ‘squeezing’ the light. Viewed in terms of energ
y, the squeezed light that emerges contains pulses of negative energy interspersed with pulses of positive energy.

  Crystals are not the only way to squeeze light. If you could manufacture very reliable light pulses containing specifically one, two, three… photons apiece, they could be combined together in such a way as to create squeezed states to order. By superimposing many such states, bursts of intense negative energy could, in theory, be produced.

  The main snag about using lasers is the short duration of the negative energy pulses. Typically, one might last for 10–15 seconds, after which it is followed by a positive energy pulse of similar duration. Some method has to be found to separate the positive from the negative energy parts of the laser beam. The inflator facility I am proposing uses a set of rapidly rotating mirrors with the light striking each mirror surface at a very shallow angle. The rotation would ensure that the negative energy portions of the beam were reflected at slightly different angles from the positive energy parts. Far away from the mirror there would be a small separation of the positive and negative components of the beam, and a further system of reflectors would allow only the negative part to be directed into the wormhole.

  With current laser technology, the numbers look disappointing. Even if negative energy can be directed at a wormhole in a sustained manner, and somehow trapped within the throat, it would require a vast length of time to accumulate enough of it to make a macroscopic wormhole. The theoretical physicist Matt Visser has estimated that a one-metre diameter worm-hole would need a negative energy equivalent to the mass of Jupiter. With perfect separation of positive and negative energy from a million terawatt lasers running flat out and continuously, it would still take far longer than the age of the universe to build up that much negative energy.

  Other inflator devices