Those of you who have heard my other talks to the Society, would know of my interest in the ancient civilizations of the past and might expect the possibilities of time travel would excite me. It’s true that the idea of chatting with Plato, observing with Hipparchus or using the great library of Alexandria for reference would be my dream. But how realistic is this dream. What are the chances of practical time travel?

1.1 Time

The actual nature of time is a mystery. Traditional societies often regard time as cyclic, following the seasons, often with the idea that history repeats itself over thousands of years. In science, the classical tradition in physics, typified by Isaac Newton, regarded time as an absolute standard unaffected by the world. In his book the Principia (1687), Newton wrote that time:

(quoted in book 9.11 p.86)

1.2 Spacetime

However, in the early 20th century, this idea of time began to be challenged. In 1908 a mathematician, Hermann Minkowski linked the three dimensions of space with time to form the concept of Spacetime. Minkowski pronounced:

Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

(quoted in book 9.11 p.103)

The concept of spacetime is crucial for time travel since it makes the past and future as real as the present, all exist in spacetime. Sometimes spacetime is illustrated in block like diagrams. Minkowski influenced Einstein to develop his theories of spacetime - Relativity.

1.3 Consciousness

One area I have not had time to investigate is how our consciousness of time might be changed to effect time travel. We all are aware that our perception of the flow of time can change; slow in a traffic jam, fast on holiday. There is evidence that our perception of time quickens as we get older. There are brain diseases which slow the passage of time for some sufferers. We also have the use of hallucinogenic drugs to provide an illusion (?) of time travel. There are also various ‘New Age’ or Shamanistic ideas where we can leave our bodies and visit other times and places. I do not dismiss out of hand these ideas, but intend to concentrate on the physical time travel of matter rather than just our consciousness.

2.1 Relativity

Einstein’s theories of Relativity provide the theoretical framework to time travel. There are two related theories, the Special and the General.

2.1.1 Special Relativity

Special Relativity (SR) was proposed by Albert Einstein in 1905. It concerns light, mass, movement and time and incorporates the famous equation E=MC² , it has the following consequences for time travel: as an object approaches the speed of light, its mass increases, its length shortens and time slows down. As an object approaches the speed of light, its internal clock runs slower. This effect is called ‘time dilation’.

2.1.2 Forward travel in time: ‘twin effect’

Forward time travel is possible. This can be demonstrated by the ‘twin effect’. Let us take two brothers, identical twins, one becomes an astronaut and flies off in a rocket at speeds close to that of light, the other remains on Earth. The twin who stays on Earth waits ten years for his brother to return, but when he does a remarkable effect is demonstrated, the twin who stayed on Earth has aged ten years but the astronaut twin only one year. Due to his high speed travelling the astronaut has only experienced one year, while ten years have passed on Earth. The twin effect is due to time dilation and it presents the possibility of travel to the future at an accelerated rate. However, this would be a one way journey.

2.2 General Relativity

Proposed by Albert Einstein in 1915 General Relativity shows how gravity bends or curves spacetime. In 1975-6 the Chesapeake Bay Experiment proved the effects of gravity on time, two very accurate atomic clocks were synchronised, then one flown in an aircraft over Chesapeake Bay whilst the other stayed on the ground, when brought together it was found that the clock in the aircraft had run faster than the one on the ground. On the face of it this might seem to contradict the ‘twin effect’ described above, but what is proved here is simply the effect of the Earth’s gravity in slowing time, by 3 billionths of a second an hour. Proof of the ‘Twin Effect’ came with evidence that the speed of the aircraft slowed the clock. General Relativity (GR) is the theory applicable to building time machines. I will deal with the construction of time machines further on (s.5). The point to note here is that the gravity of large masses slows clocks and bends space.

2.2.1 Closed Timelike Curves (CTCs)

In 1949 a mathematician working with Einstein proposed an interpretation of GR which would permit time travel. Kurt Gödel suggested that spacetime could contain Closed Timelike Curves (CTCs). A CTC is a kind of loop in spacetime. A spaceship could use these curves to travel into the past or future and return. However, Gödel’s theory requires a rotating universe for which there is no evidence.

2.2.2 Recent developments in General Relativity (GR)

Since Gödel’s work, GR has proved a fertile area for time travel theories, with the work of Newman, Unti and Tamburino in the 1960’s and Frank Tipler in the 1970’s. Tipler provides a plan for a time machine which I will look at later on.

We have seen how time travel to the future is possible under Special Relativity, but is there any way that we can travel back to the past? Travel to the past meets with a number of very serious objections or leads to curious paradoxes.

3.1 Grandfather Paradox

A series of paradoxes deal with the risks to the time travellers own existence. As an example take the Grandfather Paradox. This is where a time traveller to the past prevents his grandfather from meeting his grandmother, thereby denying life to one of the time travellers parents. In this case, what would happen to the time traveller?

3.2 No tourists from the future

A less complicated objection asks: why there are no tourists from the future? If in our future we do build a working time machine, why are we not meeting time travellers today?

An easy answer could just be that time travellers just don’t find year 2000 Milton Keynes interesting! Another answer could be that a time machine cannot send you to times before it was built. So, if I built my time machine in 1995 and it is now 2000, I could visit 1998 but not any time before 1995.

3.3 Information problem (genetic & intellectual)

Another serious objection involves what we might call information or order. This might be either genetic or intellectual. In the case of genetic, say our time traveller is fond of cats, he visits a period in prehistory and finds no cats, disappointed he leaves behind him a few cats which survive and multiply. Where did cats originally come from?

A time traveller is a keen fan of Jane Austen, he has a book of her complete works on him at all times and decides to go back in time to meet her. When he does, he finds her, completely uninterested in writing, so he gives her the book which she copies out and sends to publishers. In this case who wrote the books?

3.4 The Arrow of Time

The above kinds of paradoxes have led many scientists to reject travel backwards in time. They state that there is an ‘Arrow of Time’ that flows only one way from past to future and that this gives the order of causality - from cause to effect. To them any claims for time travel are nonsense. They take support from the Second Law of Thermodynamics.

3.5 The Second Law of Thermodynamics

This law states that heat cannot move from a cooler to a hotter body, but it is widened to include the concept of entropy. Put simply, the universe appears to be move from order to disorder. For example, if you drop a glass it will break into thousands of pieces, you will not see the pieces fall randomly together to form a glass. Another example, you leave a bottle of perfume in a room and the perfume evaporates into the air, you would not see individual perfume molecules condense themselves to refill the bottle. Time can only flow one way according to this view.

3.6 Stephen Hawking and the Chronology Protection Principle

The famous author of ‘A Brief History of Time’, Stephen Hawking has even proposed that the universe has a special ‘Chronology Protection Principle’ to prevent time travel to the past.

So far we have considered time travel largely from the point of view of Relativity theory. But there is another theory in modern physics which might answer some of the time travel paradoxes and offer some encouragement to potential time travellers. This is Quantum Theory. General Relativity explains the actions of large objects like planets, stars and galaxies, Quantum Theory explains the actions of the very small; atoms, electrons, sub-atomic particles.

4.1 The Multiverse, many worlds & parallel universes.

Quantum Theory was developed originally by the German Physicist Max Planck, but it has been developed by many others, including Einstein, Werner Heisenberg, Erwin Schrödinger and Paul Dirac. In one interpretation of Quantum Theory we have the idea of the ‘Multiverse’, this holds that there is not one universe but an infinite number of parallel universes many of which may be nearly identical to our own universe. I will not go into why this idea might be a sensible interpretation of Quantum Theory, but I will go into its implications for time travellers.

4.2 Visiting the pasts of other universes

Parallel universes offer a retort to the paradoxes of time travel. If a time traveller goes back and kills his grandfather, he will not be born in that universe although he will be born in the universe he originally came from. Again, Jane Austen might not have been a writer in one universe, but you can ‘import’ her novels from a universe where she was!

4.3 Tachyons

Other ideas from modern physics may also provide some comfort to potential time travellers: Tachyons are hypothetical particles which travel faster than light. As such they would move backwards in time. But there is no evidence for their existence and no suggestions as to how they might be utilised in time travel.

4.4 Exotic kinds of matter

Other exotic kinds of matter, as yet undiscovered, but with who-knows-what kind of properties could be used in time machines.

Given all this theoretical background how could we actually construct a working time machine? Or do they exist in nature anyway, in the form of black holes, wormholes and other exotic spacetime features?

5.1 Wormholes

Wormholes may exist in nature where a black hole is rotating. This was suggested in 1963 by Roy Kerr (a New Zealand mathematician). The Kerr black hole is rotating and due to centrifugal forces will form a doughnut shaped ring containing a wormhole which can be entered from the poles. A spaceship entering the black hole from one of the poles will not be crushed, but can enter the wormhole. It is thought that the wormhole would act as an Einstein-Rosen Bridge allowing travel to distant times and places.

5.2 Artificial wormholes

Wormholes may exist in nature as black holes, possibly the angle, speed or mass of the spacecraft could be adjusted to allow controlled navigation of these natural wormholes in spacetime. But time travellers would find it easier to open their own artificial wormholes wherever they wanted and simply step in. How could they do this?

5.3 The Kip Thorne time machine

In 1988 Kip Thorne, Michael Morris and Ulvi Yurtsever (book 9.7) made a serious proposal for a time machine using wormholes. The work began with a request from Carl Sagan for a convincing theory of faster than light travel for his science fiction novel "Contact".

5.3.1 Problems with Wormholes

The machine requires the technology of "an arbitrarily advanced civilization" able to counteract some of the problems encountered with wormholes, these can be listed:

• Extreme gravity to crush the traveller
• Unstable - may close itself
• Requires faster than light speeds to travel through
• Intense radiation at opening
• Time slowing/ stopping due to gravity

The Kip Thorne team suggest a ‘transversible wormhole’ where the traveller would face gravity of no more than 1g and journey times of 200 days or less. Two possible methods are suggested.

5.3.2 Fast/Slow Wormholes

In the first machine you have two identical chambers containing large parallel metal plates. Vast amounts of electrical energy is put through the plates opening wormhole entrances. Then one chamber is placed in a spaceship and accelerated close to the speed of light, whilst the other remains on Earth. Using SR the time on the spaceship would be Slow and that on the Earth -Fast. Utilising the Fast/Slow wormholes time travel back and forth would be possible.

5.3.3 The Time Cylinder

In the next machine a cylinder of ‘exotic matter’ would be placed around the time traveller and this would ‘warp’ space and time around them. Unfortunately, both of Kip Thorne’s time machines require not only exotic matter, but also ‘negative energy’ a form of energy which is only just being explored (it has been demonstrated by the ‘Casimir effect’).

5.4 The Frank Tipler time machine

I mentioned earlier that Frank Tipler in his work on GR had proposed a time machine (see book 9.8). Tipler’s time machine requires a huge rotating cylinder, possibly consisting of ten neutron stars, pole to pole, all spinning at a rate of twice a millisecond. This would be an awesome feat of stellar engineering which would be in constant danger of collapse into a black hole. There is a possibility something like this could exist in nature somewhere in the galaxy. The gravitational effect of this cylinder would be to twist spacetime into the past. This can be best explained with the concept of the ‘light-cone’. Light-cones are space-time diagrams which represent the speed of light, spatial dimensions and time. They divide space-time into three areas, the past, the future and a ‘forbidden’ zone which is delineated by the speed of light. Tipler’s machine would ‘tip’ the light-cones around it until, the future section of the cones is tipped into the past. A spaceship could be navigated around the cylinder into whatever period in past or future is desired.

One problem with the Tipler machine is that you could not travel further into the past than the date the machine became operational. Although, this might not be a problem if one was found in nature, or had been constructed billions of years ago by an alien civilization.

5.5 Uses for a time machine

Like any new invention (think of genetically modified organisms) a time machine would offer exciting new possibilities and frightening new threats. The time machine offers the possibility of enormous scientific and historical research, transport across space and time, the possibility of changing history for the better? On the other hand, do we want to interfere with our pasts and risk annihilation? Would the immense resources involved be well spent or environmentally sustainable? Would we have environmental protesters in spaceships trying to halt construction?

Does the power of modern computers have any contribution to time travel studies?

6.1 Illusion

It has been suggested that Virtual Reality (VR) could provide an illusion of time travel. We could plug in our headsets or total immersion body suits and head off on our dinosaur/woolly mammoth hunt!

6.2 Experimentation

More seriously VR could be used in experiments to test time paradoxes. A sufficiently accurate VR simulation of a historical situation, could be used to study the effects of time travel.

Time travel has been extensively covered by Science Fiction writers, it could even be considered the invention of Science Fiction. Certainly scientists have been cautious to publish on time travel for fear of ridicule.

7.1 H.G. Wells

The father of time travel must be H.G. Wells who published a story called "The Time Machine" in 1894 (see book 9.9). In it he has some very interesting remarks on time such as that:

Wells’s time machine is described in his story, it has a saddle for the traveller and is operated by levers, in some ways it was a typical piece of Victorian technology:

In Well’s story the time machine is really only introduced as a method to explore social trends of his own day into the future. The inspiration for the time machine came from the Victorian era, where new machines were constantly being invented to solve every conceivable problem, a time machine was just another wonderful new machine.

7.2 Dr. Who

Another famous fictional time traveller is "Dr. Who". He featured in a BBC television series which started in 1963. The ‘Doctor’ is a human-looking alien who possesses a time machine called the TARDIS. TARDIS is an acronym for Time And Relative Dimensions In Space. From the outside it looks like an obsolete police telephone box, but it is larger within than it appears from outside. How the TARDIS works is a mystery, but it is said to exist outside of our normal spacetime and to travel through The Vortex. In some stories it is said to be powered by a black hole. The TARDIS can transport the Doctor in both time and space, but often seems out of his control, leading him into his many adventures.

How do we conclude this brief survey of time travel? We have seen that modern physics allows the possibility of time travel, certainly into the future, more doubtfully into the past. We have also seen how physicists are beginning to design time machines. These early designs may resemble the time machines of the future in a similar way to how Leonardo da Vinci’s (1452-1519) plans for flying machines resemble a 747 of today. Certainly as our present civilization would struggle to deflect an Earth bound asteroid, the technologies required for building time machines, such as stellar engineering and opening wormholes, seem far off into the future.

9.1 Nigel Calder, ‘Einstein’s Universe’, 1979, Pelican Books ISBN 0140224076

(describes the Chesapeake Bay Experiment pp.72-73)

9.2 Paul Davies ‘God and the New Physics’, 1983, Penguin Books

ISBN 014013462X

9.3 David Deutsch ‘The Fabric of Reality’, 1997, Penguin Books

ISBN 0140146903 (Chapter 12 is devoted to time travel)

9.4 John Gribbin "In search of the edge of time" 1992, Bantam Press, ISBN 0593024095 (chapter 7 is on building time machines, there is a copy at CMK Library 530.11GRI)

9.5 Stephen W. Hawking ‘A Brief History of Time’ 1988, Bantam Press, ISBN 0593015185 (who hasn’t read it, or at least bought a copy?)

9.6 Michio Kaku ‘Hyperspace’, 1994, OUP, ISBN 0192861891 (chapter 11 is on time machines in this very readable book)

9.7 M.S. Morris, K.S. Thorne, and U. Yurtsever, "Wormholes, Time Machines and the Weak Energy Condition," Physical Review Letters 61 (1988):1446 (I have not been able to review this article)

9.8 Frank Tipler "Rotating cylinders and the possibility of global causality violation",

Physical Review D vol.9 pp.2203-6: 1974 (I have not been able to review this article)

9.9 H.G. Wells ‘Selected Short Stories including The Time Machine’, 1958, Penguin Books ISBN 0140013105

9.10 Michael White & John Gribbin ‘Stephen Hawking A Life in Science’, 1992, Penguin Books ISBN 014027168 (Chapter 17 describes the recent scientific interest in time travel)

9.11 G.J. Whitrow ‘The Nature of Time’, 1972, Penguin Books ISBN 0140218793

10.1 http://www-history.mcs.st-andrews.ac.uk/

University of St. Andrews online history of mathematics archive (excellent for biographical details of scientists).